* [PATCH v1 01/27] x86/fpu: Create helper file for common data macros
@ 2022-12-07 8:52 Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 02/27] x86/fpu: Add file for common data used across svml_s_*_avx2.S files Noah Goldstein via Libc-alpha
` (26 more replies)
0 siblings, 27 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
The macros are useful for creating .rodata definitions and checking
that the offset is correct.
---
.../x86_64/fpu/svml_common_data_macros.h.S | 50 +++++++++++++++++++
1 file changed, 50 insertions(+)
create mode 100644 sysdeps/x86_64/fpu/svml_common_data_macros.h.S
diff --git a/sysdeps/x86_64/fpu/svml_common_data_macros.h.S b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
new file mode 100644
index 0000000000..31bd66835d
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
@@ -0,0 +1,50 @@
+/* Helper macros for creating rodata
+ Copyright (C) 2022 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ https://www.gnu.org/licenses/. */
+
+#ifndef _SVML_COMMON_DATA_MACROS_H_S
+#define _SVML_COMMON_DATA_MACROS_H_S 1
+
+
+.macro check_offset data_section offset
+ .if .-\data_section != \offset
+ .err
+ .endif
+.endm
+
+
+/* Only used in floating point functions at the moment. */
+.macro float_vectorN data_section N offset value
+ check_offset \data_section \offset
+ .rept \N
+ .long \value
+ .endr
+.endm
+
+#define float_block(data_section, offset, ...) \
+ check_offset data_section offset; \
+ .long __VA_ARGS__
+
+
+#define float_vector16(data_section, offset, value) \
+ float_vectorN data_section 4 offset value
+#define float_vector32(data_section, offset, value) \
+ float_vectorN data_section 8 offset value
+#define float_vector64(data_section, offset, value) \
+ float_vectorN data_section 16 offset value
+
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 02/27] x86/fpu: Add file for common data used across svml_s_*_avx2.S files
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 03/27] x86/fpu: Add file for common data used across svml_s_*_avx512.S files Noah Goldstein via Libc-alpha
` (25 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
All rodata that is used by more than one implementation can be defined
here to save .rodata size.
At the moment definitions are only for the following implementations:
atanf
atanhf
log
log10f
log2
tanf
have been added.
---
.../x86_64/fpu/svml_s_common_avx2_rodata.S | 28 +++++++++++++++++++
.../fpu/svml_s_common_avx2_rodata_offsets.h | 26 +++++++++++++++++
2 files changed, 54 insertions(+)
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_avx2_rodata.S
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_avx2_rodata_offsets.h
diff --git a/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata.S b/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata.S
new file mode 100644
index 0000000000..986e8ca685
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata.S
@@ -0,0 +1,28 @@
+#include "svml_s_common_avx2_rodata_offsets.h"
+
+ .section .rodata.avx2, "a"
+ .align 32
+ .globl COMMON_DATA_NAME
+
+COMMON_DATA_NAME:
+ /* Used By: atanf, atanhf, log, log10f, log2, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _OneF, 0x3f800000)
+ /* Used By: atanhf, log, log10f, log2. */
+ DATA_VEC(COMMON_DATA_NAME, _NotiOffExpoMask, 0xff800000)
+ /* Used By: atanhf, log, log10f, log2. */
+ DATA_VEC(COMMON_DATA_NAME, _IBrkValue, 0x3f2aaaab)
+ /* Used By: atanf, atanhf, tanf, tanhf. */
+ DATA_VEC(COMMON_DATA_NAME, _AbsMask, 0x7fffffff)
+ /* Used By: log, log10f, log2. */
+ DATA_VEC(COMMON_DATA_NAME, _ILoRange, 0x01000000)
+ /* Used By: atanhf, log. */
+ DATA_VEC(COMMON_DATA_NAME, _Neg5F, 0xbf000000)
+ /* Used By: atanhf, log. */
+ DATA_VEC(COMMON_DATA_NAME, _Ln2, 0x3f317218)
+ /* Used By: atanhf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _Neg4096, 0xfffff000)
+ /* Used By: atanf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _TanSPI1_FMA, 0x3fc90fdb)
+
+ .type COMMON_DATA_NAME, @object
+ .size COMMON_DATA_NAME, .-COMMON_DATA_NAME
diff --git a/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata_offsets.h b/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata_offsets.h
new file mode 100644
index 0000000000..6b18b721b1
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_avx2_rodata_offsets.h
@@ -0,0 +1,26 @@
+#ifndef _SVML_S_COMMON_AVX2_RODATA_OFFSETS_H
+#define _SVML_S_COMMON_AVX2_RODATA_OFFSETS_H 1
+
+#include "svml_common_data_macros.h.S"
+
+#define COMMON_DATA_NAME __svml_s_common_avx2_data
+
+#define _OneF 0
+#define _NotiOffExpoMask 32
+#define _IBrkValue 64
+#define _AbsMask 96
+#define _ILoRange 128
+#define _Neg5F 160
+#define _Ln2 192
+#define _Neg4096 224
+#define _TanSPI1_FMA 256
+
+#define COMMON_DATA(offset) ((offset) + (COMMON_DATA_NAME))
+#define DATA_VEC(data_name, offset, value) \
+ float_vector32(data_name, offset, value)
+
+#ifdef LOCAL_DATA_NAME
+# define LOCAL_DATA(offset) ((offset) + (LOCAL_DATA_NAME))
+#endif
+
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 03/27] x86/fpu: Add file for common data used across svml_s_*_avx512.S files
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 02/27] x86/fpu: Add file for common data used across svml_s_*_avx2.S files Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 04/27] x86/fpu: Add file for common data used across svml_s_*_sse4.S files Noah Goldstein via Libc-alpha
` (24 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
All rodata that is used by more than one implementation can be defined
here to save .rodata size.
At the moment definitions are only for the following implementations:
atanf
atanhf
log
log10f
log2
tanf
have been added.
---
.../x86_64/fpu/svml_s_common_evex512_rodata.S | 19 +++++++++++++
.../svml_s_common_evex512_rodata_offsets.h | 27 +++++++++++++++++++
2 files changed, 46 insertions(+)
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_evex512_rodata.S
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_evex512_rodata_offsets.h
diff --git a/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata.S b/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata.S
new file mode 100644
index 0000000000..4652b7be41
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata.S
@@ -0,0 +1,19 @@
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+ .section .rodata.evex512, "a"
+ .align 64
+ .globl COMMON_DATA_NAME
+COMMON_DATA_NAME:
+ /* Used By: atanf, atanhf, log10f, log2f, logf, tanf. */
+ DATA_VEC (COMMON_DATA_NAME, _OneF, 0x3f800000)
+ /* Used By: logf, tanf. */
+ DATA_VEC (COMMON_DATA_NAME, _NotiOffExpoMask, 0xff800000)
+ /* Used By: atanhf, logf. */
+ DATA_VEC (COMMON_DATA_NAME, _Neg5F, 0xbf000000)
+ /* Used By: tanf, atanhf. */
+ DATA_VEC (COMMON_DATA_NAME, _AbsMask, 0x7fffffff)
+ /* Used By: atanf, tanhf. */
+ DATA_VEC (COMMON_DATA_NAME, _SignMask, 0x80000000)
+
+ .type COMMON_DATA_NAME, @object
+ .size COMMON_DATA_NAME, .-COMMON_DATA_NAME
diff --git a/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata_offsets.h b/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata_offsets.h
new file mode 100644
index 0000000000..f41020f760
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_evex512_rodata_offsets.h
@@ -0,0 +1,27 @@
+#ifndef _SVML_S_COMMON_EVEX512_RODATA_OFFSETS_H
+#define _SVML_S_COMMON_EVEX512_RODATA_OFFSETS_H 1
+
+#include "svml_common_data_macros.h.S"
+
+#define COMMON_DATA_NAME __svml_s_common_evex512_data
+
+#define _OneF 0
+#define _NotiOffExpoMask 64
+#define _Neg5F 128
+#define _AbsMask 192
+#define _SignMask 256
+
+
+#define COMMON_DATA(offset) ((offset) + (COMMON_DATA_NAME))
+#define DATA_VEC(data_name, offset, value) \
+ float_vector64(data_name, offset, value)
+
+#ifdef LOCAL_DATA_NAME
+# define LOCAL_DATA(offset) ((offset) + (LOCAL_DATA_NAME))
+#endif
+
+#ifdef LOCAL_DATA_NAME_UNALIGNED
+# define LOCAL_DATA_UNALIGNED(offset) ((offset) + (LOCAL_DATA_NAME_UNALIGNED))
+#endif
+
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 04/27] x86/fpu: Add file for common data used across svml_s_*_sse4.S files
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 02/27] x86/fpu: Add file for common data used across svml_s_*_avx2.S files Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 03/27] x86/fpu: Add file for common data used across svml_s_*_avx512.S files Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 05/27] x86/fpu: Build common data files for svml_s_*_{avx512, avx2, sse4}.S Noah Goldstein via Libc-alpha
` (23 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
All rodata that is used by more than one implementation can be defined
here to save .rodata size.
At the moment definitions are only for the following implementations:
atanf
atanhf
log
log10f
log2
tanf
have been added.
---
.../x86_64/fpu/svml_s_common_sse4_rodata.S | 27 +++++++++++++++++++
.../fpu/svml_s_common_sse4_rodata_offsets.h | 25 +++++++++++++++++
2 files changed, 52 insertions(+)
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_sse4_rodata.S
create mode 100644 sysdeps/x86_64/fpu/svml_s_common_sse4_rodata_offsets.h
diff --git a/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata.S b/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata.S
new file mode 100644
index 0000000000..58337635fd
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata.S
@@ -0,0 +1,27 @@
+#include "svml_s_common_sse4_rodata_offsets.h"
+
+ .section .rodata.sse4, "a"
+ .align 16
+ .globl COMMON_DATA_NAME
+
+COMMON_DATA_NAME:
+ /* Used By: atanf, atanhf, log10f, log2f, logf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _OneF, 0x3f800000)
+ /* Used By: atanhf, log10f, log2f, logf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _NotiOffExpoMask, 0xff800000)
+ /* Used By: atanhf, log10f, log2f, logf. */
+ DATA_VEC(COMMON_DATA_NAME, _IBrkValue, 0x3f2aaaab)
+ /* Used By: log10f, log2f, logf. */
+ DATA_VEC(COMMON_DATA_NAME, _ILoRange, 0x01000000)
+ /* Used By: atanhf, logf. */
+ DATA_VEC(COMMON_DATA_NAME, _Neg5F, 0xbf000000)
+ /* Used By: atanhf, logf. */
+ DATA_VEC(COMMON_DATA_NAME, _Ln2, 0x3f317218)
+ /* Used By: atanhf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _AbsMask, 0x7fffffff)
+ /* Used By: atanhf, tanf. */
+ DATA_VEC(COMMON_DATA_NAME, _Neg4096, 0xfffff000)
+
+
+ .type COMMON_DATA_NAME, @object
+ .size COMMON_DATA_NAME, .-COMMON_DATA_NAME
diff --git a/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata_offsets.h b/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata_offsets.h
new file mode 100644
index 0000000000..8f985565d1
--- /dev/null
+++ b/sysdeps/x86_64/fpu/svml_s_common_sse4_rodata_offsets.h
@@ -0,0 +1,25 @@
+#ifndef _SVML_S_COMMON_SSE4_RODATA_OFFSETS_H
+#define _SVML_S_COMMON_SSE4_RODATA_OFFSETS_H 1
+
+#include "svml_common_data_macros.h.S"
+
+#define COMMON_DATA_NAME __svml_s_common_sse4_data
+
+#define _OneF 0
+#define _NotiOffExpoMask 16
+#define _IBrkValue 32
+#define _ILoRange 48
+#define _Neg5F 64
+#define _Ln2 80
+#define _AbsMask 96
+#define _Neg4096 112
+
+#define COMMON_DATA(offset) ((offset) + (COMMON_DATA_NAME))
+#define DATA_VEC(data_name, offset, value) \
+ float_vector16(data_name, offset, value)
+
+#ifdef LOCAL_DATA_NAME
+# define LOCAL_DATA(offset) ((offset) + (LOCAL_DATA_NAME))
+#endif
+
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 05/27] x86/fpu: Build common data files for svml_s_*_{avx512, avx2, sse4}.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (2 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 04/27] x86/fpu: Add file for common data used across svml_s_*_sse4.S files Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 06/27] x86/fpu: Update rodata usage in svml_s_tanhf_*_{avx2, sse4} Noah Goldstein via Libc-alpha
` (22 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
Build them so they can start to be used in the implementations.
---
sysdeps/x86_64/fpu/Makefile | 3 +++
1 file changed, 3 insertions(+)
diff --git a/sysdeps/x86_64/fpu/Makefile b/sysdeps/x86_64/fpu/Makefile
index 7233174ede..e7e747e920 100644
--- a/sysdeps/x86_64/fpu/Makefile
+++ b/sysdeps/x86_64/fpu/Makefile
@@ -14,6 +14,9 @@ libmvec-support += \
svml_d_log_data \
svml_d_pow_data \
svml_d_trig_data \
+ svml_s_common_avx2_rodata \
+ svml_s_common_evex512_rodata \
+ svml_s_common_sse4_rodata \
svml_s_expf_data \
svml_s_logf_data \
svml_s_powf_data \
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 06/27] x86/fpu: Update rodata usage in svml_s_tanhf_*_{avx2, sse4}
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (3 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 05/27] x86/fpu: Build common data files for svml_s_*_{avx512, avx2, sse4}.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S Noah Goldstein via Libc-alpha
` (21 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
No changes to the logic, just change how rodata is handled.
1. Define the rodatas using the new macros so they check that the
offset is correct.
2. Use common data where applicable.
---
.../fpu/multiarch/svml_s_tanhf4_core_sse4.S | 72 +-
.../fpu/multiarch/svml_s_tanhf8_core_avx2.S | 105 +--
.../fpu/multiarch/svml_s_tanhf_rodata.S | 621 ------------------
.../fpu/multiarch/svml_s_tanhf_rodata.h.S | 591 +++++++++++++++++
4 files changed, 680 insertions(+), 709 deletions(-)
delete mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.S
create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.h.S
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf4_core_sse4.S
index bf7687d8ba..824862eb7f 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf4_core_sse4.S
@@ -70,21 +70,22 @@
*
*/
+#include "svml_s_common_sse4_rodata_offsets.h"
-#include <sysdep.h>
+/* tanhf data tables for avx2 and sse4 implementatins
+ defined here. */
+#define AVX2_SHARED_OFFSETS
+#include "svml_s_tanhf_rodata.h.S"
-/* tanhf data tables for avx2 and sse4 implementatins defined here.
- */
-#define ONLY_DECL_OFFSET
-#include "svml_s_tanhf_rodata.S"
+#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_tanhf_sse4)
/* Save copy of input in xmm12. */
movaps %xmm0, %xmm12
- /* Here huge arguments, INF and NaNs are filtered out to callout. */
- movdqu TANHF_DATA(_iExpMantMask)(%rip), %xmm3
+ /* Here huge arguments, INF and NaNs are filtered out to callout. */
+ movdqu AVX2_SHARED_DATA(_iExpMantMask)(%rip), %xmm3
pand %xmm0, %xmm3
@@ -92,9 +93,9 @@ ENTRY(_ZGVbN4v_tanhf_sse4)
pxor %xmm7, %xmm7
/* Save xmm3 for special values check at end. */
movdqa %xmm3, %xmm8
- psubd TANHF_DATA(_iMinIdxOfsMask)(%rip), %xmm3
+ psubd AVX2_SHARED_DATA(_iMinIdxOfsMask)(%rip), %xmm3
pmaxsd %xmm7, %xmm3
- pminsd TANHF_DATA(_iMaxIdxMask)(%rip), %xmm3
+ pminsd AVX2_SHARED_DATA(_iMaxIdxMask)(%rip), %xmm3
psrld $14, %xmm3
movq %xmm3, %rcx
@@ -106,17 +107,14 @@ ENTRY(_ZGVbN4v_tanhf_sse4)
movl %edi, %esi
shrq $32, %rdi
- movaps TANHF_DATA(_sAbsMask)(%rip), %xmm1
+ movaps COMMON_DATA(_AbsMask)(%rip), %xmm1
andps %xmm1, %xmm0
- leaq TANHF_DATA(_lookupTable)(%rip), %rax
+ /* small table specific variables Constant loading. */
+ leaq AVX2_SHARED_DATA(_lookupTable)(%rip), %rax
movups (%rdx, %rax), %xmm2
movups (%rcx, %rax), %xmm6
- /*
- * small table specific variables *
- * Constant loading
- */
movaps %xmm2, %xmm4
movlhps %xmm6, %xmm4
unpckhpd %xmm6, %xmm2
@@ -175,45 +173,45 @@ ENTRY(_ZGVbN4v_tanhf_sse4)
orps %xmm1, %xmm0
/* xmm8 contains mask of special values. */
- pcmpgtd TANHF_DATA(_iExpMask)(%rip), %xmm8
+ pcmpgtd AVX2_SHARED_DATA(_iExpMask)(%rip), %xmm8
movmskps %xmm8, %edx
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 xmm0
+
/* No stack restoration on the fastpath. */
ret
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a tanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx rbp r12 r13 r14 r15 xmm0 xmm12
+
/* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
- call entry will be 16-byte aligned. */
+ call entry will be 16-byte aligned. */
subq $56, %rsp
- cfi_def_cfa_offset(64)
+ cfi_def_cfa_offset (64)
movups %xmm0, 24(%rsp)
movups %xmm12, 40(%rsp)
/* Use rbx/rbp for callee save registers as they get short
- encoding for many instructions (as compared with r12/r13). */
+ encoding for many instructions (as compared with r12/r13). */
movq %rbx, (%rsp)
- cfi_offset(rbx, -64)
+ cfi_offset (rbx, -64)
movq %rbp, 8(%rsp)
- cfi_offset(rbp, -56)
- /* edx has 1s where there was a special value that needs to be handled
- by a tanhf call. */
+ cfi_offset (rbp, -56)
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- tanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 12] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. */
+
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
xorl %ebp, %ebp
bsfl %ebx, %ebp
@@ -228,14 +226,14 @@ L(SPECIAL_VALUES_LOOP):
leal -1(%rbx), %eax
andl %eax, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
+
/* All results have been written to 24(%rsp). */
movups 24(%rsp), %xmm0
movq (%rsp), %rbx
- cfi_restore(rbx)
+ cfi_restore (rbx)
movq 8(%rsp), %rbp
- cfi_restore(rbp)
+ cfi_restore (rbp)
addq $56, %rsp
- cfi_def_cfa_offset(8)
+ cfi_def_cfa_offset (8)
ret
END(_ZGVbN4v_tanhf_sse4)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
index ea3e9f4210..9c524f5df4 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
@@ -70,42 +70,44 @@
*
*/
-#include <sysdep.h>
+#include "svml_s_common_avx2_rodata_offsets.h"
-/* tanhf data tables for avx2 and sse4 implementatins defined here.
- */
-#include "svml_s_tanhf_rodata.S"
+/* tanhf data tables for avx2 and sse4 implementatins
+ defined here. */
+#define AVX2_SHARED_TABLE
+#include "svml_s_tanhf_rodata.h.S"
+
+#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_tanhf_avx2)
- /* Here huge arguments, INF and NaNs are filtered out to callout. */
- vpand TANHF_DATA(_iExpMantMask)(%rip), %ymm0, %ymm4
- vpsubd TANHF_DATA(_iMinIdxOfsMask)(%rip), %ymm4, %ymm2
+ /* Here huge arguments, INF and NaNs are filtered out to callout. */
+ vpand AVX2_SHARED_DATA(_iExpMantMask)(%rip), %ymm0, %ymm4
+ vpsubd AVX2_SHARED_DATA(_iMinIdxOfsMask)(%rip), %ymm4, %ymm2
/* Selection of arguments between [0, 0x04280000] into ymm2. */
vpxor %ymm3, %ymm3, %ymm3
vpmaxsd %ymm3, %ymm2, %ymm2
- vpminsd TANHF_DATA(_iMaxIdxMask)(%rip), %ymm2, %ymm2
+ vpminsd AVX2_SHARED_DATA(_iMaxIdxMask)(%rip), %ymm2, %ymm2
- /*
- * small table specific variables *
- * Constant loading
- */
+ /* small table specific variables *
+ Constant loading. */
vpsrld $14, %ymm2, %ymm1
/* We are splitting xmm1 into 8 GPRs. This may be faster to do with
store/load as we can take advantage of store-forwarding. */
vmovq %xmm1, %r8
- /* We have eliminated all negative values for ymm1 so no need to sign
- extend. */
+ /* We have eliminated all negative values for ymm1 so no need to
+ sign extend. */
movl %r8d, %r9d
shrq $32, %r8
/* Store base of lookup table in rax. */
- leaq TANHF_DATA(_lookupTable)(%rip), %rax
+ leaq AVX2_SHARED_DATA(_lookupTable)(%rip), %rax
- /* Instead of using cross-lane permutes on ymm vectors, use vpinsertf128
- with memory operand. This helps alleviate bottleneck on p5. */
+ /* Instead of using cross-lane permutes on ymm vectors, use
+ vpinsertf128 with memory operand. This helps alleviate
+ bottleneck on p5. */
vmovupd 16(%r9, %rax), %xmm5
vpextrq $1, %xmm1, %rsi
@@ -138,9 +140,9 @@ ENTRY(_ZGVdN8v_tanhf_avx2)
vunpcklpd %ymm1, %ymm5, %ymm3
vunpckhpd %ymm1, %ymm5, %ymm1
- vmovaps TANHF_DATA(_sAbsMask)(%rip), %ymm11
+ vmovaps COMMON_DATA(_AbsMask)(%rip), %ymm11
/* Store special cases in ymm15. */
- vpcmpgtd TANHF_DATA(_iExpMask)(%rip), %ymm4, %ymm15
+ vpcmpgtd AVX2_SHARED_DATA(_iExpMask)(%rip), %ymm4, %ymm15
vandps %ymm11, %ymm0, %ymm4
@@ -184,9 +186,9 @@ ENTRY(_ZGVdN8v_tanhf_avx2)
vmovmskps %ymm15, %edx
vandnps %ymm0, %ymm11, %ymm2
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 ymm0 ymm1 ymm2
+
/* Wait until after branch of write over ymm0. */
vorps %ymm2, %ymm1, %ymm0
/* No stack restoration on the fastpath. */
@@ -195,24 +197,24 @@ ENTRY(_ZGVdN8v_tanhf_avx2)
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a tanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx r12 r13 r14 r15 ymm0 ymm1 ymm2
- /* Use r13 to save/restore the stack. This allows us to use rbp as
- callee save register saving code size. */
+
+ /* Use r13 to save/restore the stack. This allows us to use rbp as
+ callee save register saving code size. */
pushq %r13
- cfi_adjust_cfa_offset(8)
- cfi_offset(r13, -16)
- /* Need to callee save registers to preserve state across tanhf calls.
- */
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
pushq %rbx
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbx, -24)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
pushq %rbp
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbp, -32)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
movq %rsp, %r13
- cfi_def_cfa_register(r13)
+ cfi_def_cfa_register (r13)
/* Align stack and make room for 2x ymm vectors. */
andq $-32, %rsp
@@ -226,16 +228,17 @@ L(SPECIAL_VALUES_BRANCH):
vzeroupper
- /* edx has 1s where there was a special value that needs to be handled
- by a tanhf call. */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- tanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 28] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. Realigning also costs more code size. */
+
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
xorl %ebp, %ebp
tzcntl %ebx, %ebp
@@ -248,25 +251,25 @@ L(SPECIAL_VALUES_LOOP):
serialized stack/callee save restoration. */
vmovss %xmm0, (%rsp, %rbp, 4)
- blsrl %ebx, %ebx
+ blsrl %ebx, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
+
/* All results have been written to (%rsp). */
vmovups (%rsp), %ymm0
/* Restore rsp. */
movq %r13, %rsp
- cfi_def_cfa_register(rsp)
+ cfi_def_cfa_register (rsp)
/* Restore callee save registers. */
popq %rbp
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %rbx
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %r13
- cfi_adjust_cfa_offset(-8)
- cfi_restore(r13)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
ret
END(_ZGVdN8v_tanhf_avx2)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.S
deleted file mode 100644
index 904fe5f588..0000000000
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.S
+++ /dev/null
@@ -1,621 +0,0 @@
-/* Datatables for tanhf AVX2 and tanhf SSE4.
- Copyright (C) 2021-2022 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
-
- The GNU C Library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- The GNU C Library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with the GNU C Library; if not, see
- https://www.gnu.org/licenses/. */
-
-/* Offsets are ordered by use in the function. On cold-starts this
- might help the prefetcher. If the streaming prefetchers kick in it
- will prefetch into the lookup table. */
-#define _iExpMantMask 0
-#define _iMinIdxOfsMask 32
-#define _iMaxIdxMask 64
-#define _sAbsMask 96
-#define _iExpMask 128
-#define _lookupTable 160
-
-#define TANHF_DATA(offset) ((offset)+__svml_stanh_data_internal_avx2)
-#ifndef ONLY_DECL_OFFSET
- .section .rodata, "a"
- .align 32
-
-# ifdef __svml_stanh_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct
- {
- __declspec(align(32)) VUINT32 _iExpMantMask[8][1];
- __declspec(align(32)) VUINT32 _iMinIdxOfsMask[8][1];
- __declspec(align(32)) VUINT32 _iMaxIdxMask[8][1];
- __declspec(align(32)) VUINT32 _sAbsMask[8][1];
- __declspec(align(32)) VUINT32 _iExpMask[8][1];
- __declspec(align(32)) VUINT32 _lookupTable[(134*4)][2];
-} __svml_stanh_data_internal;
-# endif
-
-
-__svml_stanh_data_internal:
- .globl __svml_stanh_data_internal_avx2
-__svml_stanh_data_internal_avx2:
- .align 32
- /* _iExpMantMask. */
- .long 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000
- .long 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000
-
- .align 32
- /* _iMinIdxOfsMask. */
- .long 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000
- .long 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000
-
- .align 32
- /* _iMaxIdxMask. */
- .long 0x04280000, 0x04280000, 0x04280000, 0x04280000
- .long 0x04280000, 0x04280000, 0x04280000, 0x04280000
-
- .align 32
- /* _sAbsMask. */
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
-
- .align 32
- /* _iExpMask. */
- .long 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000
- .long 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000
-
- .align 32
- /* _lookupTable. */
- /* Pol_000: err=7.93e-09, x in [0.0000000; 0.0312500]. */
- .quad 0x0000000000000000 /* A00 = +0.000000000000000000000e-01. */
- .quad 0x3FF00000022C70EB /* A01 = +1.000000008097283510367e+00. */
- .quad 0xBED00E878CFFA194 /* A02 = -3.828228912518614443549e-06. */
- .quad 0xBFD551766D0607A9 /* A03 = -3.330970825846813476723e-01. */
- .quad 0xBE53D60CE3E4C297 /* A00 = -1.847383956330407336230e-08. */
- .quad 0x3FF000024177CF5C /* A01 = +1.000002151235967140508e+00. */
- .quad 0xBF1758BC94A51A25 /* A02 = -8.906031613262943753568e-05. */
- .quad 0xBFD53EAE67E0D4F0 /* A03 = -3.319507612644221339337e-01. */
- .quad 0xBE5A9E47EF32D6FE /* A00 = -2.479020984039698285657e-08. */
- .quad 0x3FF00002DA983057 /* A01 = +1.000002721676556793895e+00. */
- .quad 0xBF1BD953509E94AA /* A02 = -1.062352277175377670507e-04. */
- .quad 0xBFD53BDB562EEDD5 /* A03 = -3.317783681520414806876e-01. */
- .quad 0xBE6191BBE496D294 /* A00 = -3.272532162914017685901e-08. */
- .quad 0x3FF0000390492017 /* A01 = +1.000003398528866105366e+00. */
- .quad 0xBF20727E814A57CE /* A02 = -1.254825043772153972919e-04. */
- .quad 0xBFD538DE060A6F22 /* A03 = -3.315959033004550748913e-01. */
- .quad 0xBE66DAFA2A893A25 /* A00 = -4.257146219278012568149e-08. */
- .quad 0x3FF0000465E08CD1 /* A01 = +1.000004194219219266770e+00. */
- .quad 0xBF2341C765EF91B6 /* A02 = -1.469188600530365522261e-04. */
- .quad 0xBFD535B6841FAF9E /* A03 = -3.314033785124993469751e-01. */
- .quad 0xBE6D5794E361E964 /* A00 = -5.465394929765249413434e-08. */
- .quad 0x3FF000055EE2A0CB /* A01 = +1.000005121846742950353e+00. */
- .quad 0xBF265E6C77E66C8B /* A02 = -1.706607253709506650304e-04. */
- .quad 0xBFD53264DDCCEDA6 /* A03 = -3.312008062382240103361e-01. */
- .quad 0xBE729C844D374A6E /* A00 = -6.933284462462096107184e-08. */
- .quad 0x3FF000067F019093 /* A01 = +1.000006195180536350264e+00. */
- .quad 0xBF29CC5348D6DCE5 /* A02 = -1.968242326435338705130e-04. */
- .quad 0xBFD52EE92121ED35 /* A03 = -3.309881995734998416658e-01. */
- .quad 0xBE775AEA17EAA872 /* A00 = -8.700465590574974405858e-08. */
- .quad 0x3FF00007CA1D66B8 /* A01 = +1.000007428656699559610e+00. */
- .quad 0xBF2D8F5EB98A2637 /* A02 = -2.255252009216044881395e-04. */
- .quad 0xBFD52B435CDF9128 /* A03 = -3.307655722585587376727e-01. */
- .quad 0xBE7D04DA28C343F0 /* A00 = -1.081040272327705484794e-07. */
- .quad 0x3FF000094443CCF5 /* A01 = +1.000008837375216730337e+00. */
- .quad 0xBF30D5B76C947AE5 /* A02 = -2.568791210978817814332e-04. */
- .quad 0xBFD52773A0776FAD /* A03 = -3.305329386764651045105e-01. */
- .quad 0xBE81DD77A12C51C7 /* A00 = -1.331054169875768625701e-07. */
- .quad 0x3FF0000AF1AFD2DA /* A01 = +1.000010437096696680470e+00. */
- .quad 0xBF331230624C1680 /* A02 = -2.910011410651516805537e-04. */
- .quad 0xBFD52379FC0B61DF /* A03 = -3.302903138515186909352e-01. */
- .quad 0xBE85D04EEEB3C435 /* A00 = -1.625247628488202841012e-07. */
- .quad 0x3FF0000CD6C9B1F2 /* A01 = +1.000012244238970726684e+00. */
- .quad 0xBF357F0742FADDD4 /* A02 = -3.280060509313874068243e-04. */
- .quad 0xBFD51F56806D0E81 /* A03 = -3.300377134475880880338e-01. */
- .quad 0xBE8A6E289B59681B /* A00 = -1.969211333326924655065e-07. */
- .quad 0x3FF0000EF8268F72 /* A01 = +1.000014275873550406715e+00. */
- .quad 0xBF381E277A1B747A /* A02 = -3.680082682942575423093e-04. */
- .quad 0xBFD51B093F1D6FD4 /* A03 = -3.297751537663746734808e-01. */
- .quad 0xBE8FCBC40EE9ABD5 /* A00 = -2.368983653301529373887e-07. */
- .quad 0x3FF000115A883B6C /* A01 = +1.000016549721943981410e+00. */
- .quad 0xBF3AF17AC974B3D9 /* A02 = -4.111218235774406434303e-04. */
- .quad 0xBFD516924A4C549C /* A03 = -3.295026517456081105450e-01. */
- .quad 0xBE92FFBC60A3F956 /* A00 = -2.831066871072026054144e-07. */
- .quad 0x3FF0001402DCED8A /* A01 = +1.000019084151832604590e+00. */
- .quad 0xBF3DFAE9390C4801 /* A02 = -4.574603454311488280083e-04. */
- .quad 0xBFD511F1B4D7DC3A /* A03 = -3.292202249571719585575e-01. */
- .quad 0xBE9690A22F96D5AD /* A00 = -3.362443262393081632612e-07. */
- .quad 0x3FF00016F63EFF5D /* A01 = +1.000021898173108825247e+00. */
- .quad 0xBF409E2C839605BB /* A02 = -5.071370461992499986334e-04. */
- .quad 0xBFD50D27924BEE00 /* A03 = -3.289278916051614487515e-01. */
- .quad 0xBE9AA56C65E72A73 /* A00 = -3.970591019557469835586e-07. */
- .quad 0x3FF0001A39F4A43E /* A01 = +1.000025011433776978009e+00. */
- .quad 0xBF425BD74C3D6667 /* A02 = -5.602647074553602319844e-04. */
- .quad 0xBFD50833F6E1ABA2 /* A03 = -3.286256705238718156536e-01. */
- .quad 0xBE9F4BD4FF1A83B0 /* A00 = -4.663500013744687071912e-07. */
- .quad 0x3FF0001DD36F9EC2 /* A01 = +1.000028444215715683896e+00. */
- .quad 0xBF44376634149405 /* A02 = -6.169556656102642569831e-04. */
- .quad 0xBFD50316F77EDEE5 /* A03 = -3.283135811757190158922e-01. */
- .quad 0xBEA3B625387BB079 /* A00 = -5.874486399249461304297e-07. */
- .quad 0x3FF00023E14CFBA9 /* A01 = +1.000034217911642153709e+00. */
- .quad 0xBF47392F923218D2 /* A02 = -7.087213783883111826306e-04. */
- .quad 0xBFD4FB1FACDEB938 /* A03 = -3.278273761924483942209e-01. */
- .quad 0xBEAA6E24F543500A /* A00 = -7.876828740601738750574e-07. */
- .quad 0x3FF0002D5C6E8412 /* A01 = +1.000043259679163742959e+00. */
- .quad 0xBF4BAF02BD7FDD70 /* A02 = -8.448375110664940040861e-04. */
- .quad 0xBFD4EFEE6527A7DE /* A03 = -3.271442401734229177279e-01. */
- .quad 0xBEB16E3EBE2157D0 /* A00 = -1.038947396133402500647e-06. */
- .quad 0x3FF00038990FEE2F /* A01 = +1.000053975962952312884e+00. */
- .quad 0xBF50569481C574CB /* A02 = -9.972048056490652716971e-04. */
- .quad 0xBFD4E419278DA2B4 /* A03 = -3.264220129263251113372e-01. */
- .quad 0xBEB6A7B6723165D4 /* A00 = -1.350350836279403750524e-06. */
- .quad 0x3FF00045CAB4158E /* A01 = +1.000066558657042303793e+00. */
- .quad 0xBF531D7C9C849108 /* A02 = -1.166698160951775212202e-03. */
- .quad 0xBFD4D7A0BB33B152 /* A03 = -3.256608799117844954552e-01. */
- .quad 0xBEBD0EE2A8654AFD /* A00 = -1.732000471561702711532e-06. */
- .quad 0x3FF00055276F18D6 /* A01 = +1.000081209219890521211e+00. */
- .quad 0xBF562FDBA3FB6C6C /* A02 = -1.354183666925102939860e-03. */
- .quad 0xBFD4CA85F1B93DB2 /* A03 = -3.248610363561638125773e-01. */
- .quad 0xBEC269D4036A207E /* A00 = -2.195047297096822741730e-06. */
- .quad 0x3FF00066E7DA6E4E /* A01 = +1.000098138500919997540e+00. */
- .quad 0xBF5991499FC36B3A /* A02 = -1.560518167983372759405e-03. */
- .quad 0xBFD4BCC9A72283D6 /* A03 = -3.240226871658341556426e-01. */
- .quad 0xBEC7154B6C09CFE1 /* A00 = -2.751729738565190291276e-06. */
- .quad 0x3FF0007B47086B80 /* A01 = +1.000117566559055148900e+00. */
- .quad 0xBF5D455433B4F8F4 /* A02 = -1.786548832412968197680e-03. */
- .quad 0xBFD4AE6CC1BFE145 /* A03 = -3.231460468373550942722e-01. */
- .quad 0xBECCA68CC64A0F8A /* A00 = -3.415415948561670285790e-06. */
- .quad 0x3FF00092827742F7 /* A01 = +1.000139722473418535387e+00. */
- .quad 0xBF60A7BF15A527AF /* A02 = -2.033112728132522705610e-03. */
- .quad 0xBFD49F703214084C /* A03 = -3.222313393636155876010e-01. */
- .quad 0xBED19E68676B241B /* A00 = -4.200644630977303616698e-06. */
- .quad 0x3FF000ACDA037B26 /* A01 = +1.000164844146362863597e+00. */
- .quad 0xBF62D99F836A02F8 /* A02 = -2.301036405072284102280e-03. */
- .quad 0xBFD48FD4F2B91B28 /* A03 = -3.212787981359945810311e-01. */
- .quad 0xBED57CF4B0C7AA54 /* A00 = -5.123164339408145209103e-06. */
- .quad 0x3FF000CA8FD9E1A1 /* A01 = +1.000193178099017865534e+00. */
- .quad 0xBF653A014548E686 /* A02 = -2.591135484433962181405e-03. */
- .quad 0xBFD47F9C0844B38F /* A03 = -3.202886658426046806447e-01. */
- .quad 0xBEDA012B1B1A41E2 /* A00 = -6.199971197454598722328e-06. */
- .quad 0x3FF000EBE868FDF4 /* A01 = +1.000224979259539459520e+00. */
- .quad 0xBF67CA9427E0A544 /* A02 = -2.904214255086275467410e-03. */
- .quad 0xBFD46EC6812ADB37 /* A03 = -3.192611943626845749655e-01. */
- .quad 0xBEDF3EAC5BF12194 /* A00 = -7.449344990702664567927e-06. */
- .quad 0x3FF001112A520784 /* A01 = +1.000260510744255704196e+00. */
- .quad 0xBF6A8D01ABDA4DC4 /* A02 = -3.241065277345108255891e-03. */
- .quad 0xBFD45D55759FFA4A /* A03 = -3.181966446572103146551e-01. */
- .quad 0xBEE2A541BC274267 /* A00 = -8.890883582164319970972e-06. */
- .quad 0x3FF0013A9E5961F2 /* A01 = +1.000300043631906721231e+00. */
- .quad 0xBF6D82ECD080C540 /* A02 = -3.602468994380686462264e-03. */
- .quad 0xBFD44B4A0779C0AD /* A03 = -3.170952866557950611259e-01. */
- .quad 0xBEE61D97609A27F4 /* A00 = -1.054553560499505625520e-05. */
- .quad 0x3FF001688F56A3AF /* A01 = +1.000343856731187974773e+00. */
- .quad 0xBF7056F8EFB683EC /* A02 = -3.989193351487490407647e-03. */
- .quad 0xBFD438A5620F0F74 /* A03 = -3.159573991399533543500e-01. */
- .quad 0xBEEA145429EDD370 /* A00 = -1.243563138839952927732e-05. */
- .quad 0x3FF0019B4A242A67 /* A01 = +1.000392236341804297339e+00. */
- .quad 0xBF7207D31CA78D9B /* A02 = -4.401993423445739288258e-03. */
- .quad 0xBFD42568BA16E7CD /* A03 = -3.147832696228050619602e-01. */
- .quad 0xBEEE96370D52680F /* A00 = -1.458491207477835326165e-05. */
- .quad 0x3FF001D31D8E4115 /* A01 = +1.000445476009251821736e+00. */
- .quad 0xBF73D4CC11EDC094 /* A02 = -4.841611050196221316400e-03. */
- .quad 0xBFD411954D8664E7 /* A03 = -3.135731942252974469021e-01. */
- .quad 0xBEF338C046215EF8 /* A00 = -1.833122622260562810219e-05. */
- .quad 0x3FF00230C32C2EC1 /* A01 = +1.000534784691737621998e+00. */
- .quad 0xBF76BD019BCC5DAF /* A02 = -5.551344188254799492943e-03. */
- .quad 0xBFD3F2C7156DC21E /* A03 = -3.116929730668135389848e-01. */
- .quad 0xBEF9B15EAE411EAE /* A00 = -2.450261207822986676092e-05. */
- .quad 0x3FF002C2DF057A4D /* A01 = +1.000674124886830940184e+00. */
- .quad 0xBF7B08CCD9AC1E30 /* A02 = -6.600189396301511801646e-03. */
- .quad 0xBFD3C7A7A114FED8 /* A03 = -3.090609620157755976777e-01. */
- .quad 0xBF00E36483C373B3 /* A00 = -3.221178528332122595812e-05. */
- .quad 0x3FF0036F419480D7 /* A01 = +1.000838524028997644777e+00. */
- .quad 0xBF7FD255D1777007 /* A02 = -7.768950679260206403087e-03. */
- .quad 0xBFD39A453911D6CE /* A03 = -3.062909180947429588215e-01. */
- .quad 0xBF05DFA04DD12059 /* A00 = -4.172046622180685472624e-05. */
- .quad 0x3FF00438B2A03D8D /* A01 = +1.001030633695197069599e+00. */
- .quad 0xBF828F8DBB4A9D10 /* A02 = -9.062869337255224921890e-03. */
- .quad 0xBFD36AAB704697D9 /* A03 = -3.033856007044711255993e-01. */
- .quad 0xBF0BF3E0C647DEFB /* A00 = -5.331544597092331081714e-05. */
- .quad 0x3FF005221063D36D /* A01 = +1.001253189109060359741e+00. */
- .quad 0xBF857A2CB3C96102 /* A02 = -1.048693584122917590862e-02. */
- .quad 0xBFD338E65BBB4FEC /* A03 = -3.003478904549854444639e-01. */
- .quad 0xBF11A506ED7C9D31 /* A00 = -6.730894835681591541979e-05. */
- .quad 0x3FF0062E4D0EA92A /* A01 = +1.001508999829250345925e+00. */
- .quad 0xBF88AB82C2761AF3 /* A02 = -1.204588085125866091241e-02. */
- .quad 0xBFD305028D6BD206 /* A03 = -2.971807843271395688234e-01. */
- .quad 0xBF1607C0922D9BF1 /* A00 = -8.403885708006799337092e-05. */
- .quad 0x3FF007606C341961 /* A01 = +1.001800940198869449560e+00. */
- .quad 0xBF8C25E6DA487BCF /* A02 = -1.374416688582682892494e-02. */
- .quad 0xBFD2CF0D0EE8F7B5 /* A03 = -2.938873906713255768075e-01. */
- .quad 0xBF1B3A8480A0A16D /* A00 = -1.038688061788578038307e-04. */
- .quad 0x3FF008BB802D02D6 /* A01 = +1.002131939589323561535e+00. */
- .quad 0xBF8FEB8AE99FD100 /* A02 = -1.558598065819483124983e-02. */
- .quad 0xBFD297135BD0911B /* A03 = -2.904709240558688843059e-01. */
- .quad 0xBF20ABB9BDB75C65 /* A00 = -1.271881327357976163798e-04. */
- .quad 0x3FF00A42A76D8CD1 /* A01 = +1.002504972472525901495e+00. */
- .quad 0xBF91FF3D752BB9E6 /* A02 = -1.757522609380570560722e-02. */
- .quad 0xBFD25D235C1F88B4 /* A03 = -2.869346999779154305799e-01. */
- .quad 0xBF243D3254425461 /* A00 = -1.544116913733432829448e-04. */
- .quad 0x3FF00BF909D1795E /* A01 = +1.002923048355647051011e+00. */
- .quad 0xBF94304E04D44942 /* A02 = -1.971551804042204897316e-02. */
- .quad 0xBFD2214B5E61CFA6 /* A03 = -2.832821294498394371075e-01. */
- .quad 0xBF286070011B61CE /* A00 = -1.859795307186510085994e-04. */
- .quad 0x3FF00DE1D5E1627E /* A01 = +1.003389201612804537689e+00. */
- .quad 0xBF9689D5F4163F59 /* A02 = -2.201017668045266231780e-02. */
- .quad 0xBFD1E39A11C3B42C /* A03 = -2.795167134743816728104e-01. */
- .quad 0xBF2D250B366A79E8 /* A00 = -2.223564326486314902259e-04. */
- .quad 0x3FF010003E134001 /* A01 = +1.003906481248123094829e+00. */
- .quad 0xBF990C9FF91F6F81 /* A02 = -2.446222265267250853271e-02. */
- .quad 0xBFD1A41E80084CDC /* A03 = -2.756420374218586655246e-01. */
- .quad 0xBF314DB5DDC2A30E /* A00 = -2.640313157465248123865e-04. */
- .quad 0x3FF012577608921B /* A01 = +1.004477940624503018441e+00. */
- .quad 0xBF9BB9626875B0C9 /* A02 = -2.707437288829409385849e-02. */
- .quad 0xBFD162E80768A9D0 /* A03 = -2.716617653228725615122e-01. */
- .quad 0xBF346A6133808864 /* A00 = -3.115165050094957730625e-04. */
- .quad 0x3FF014EAAFCC88A3 /* A01 = +1.005106627192198898157e+00. */
- .quad 0xBF9E90BEF9BF7419 /* A02 = -2.984903716411588595059e-02. */
- .quad 0xBFD12006545F7FAD /* A03 = -2.675796340899932457269e-01. */
- .quad 0xBF37F180DC3848EA /* A00 = -3.653468704395550778821e-04. */
- .quad 0x3FF017BD19147861 /* A01 = +1.005795572250939295955e+00. */
- .quad 0xBFA0C9A14C702E07 /* A02 = -3.278831537326359207851e-02. */
- .quad 0xBFD0DB895B650092 /* A03 = -2.633994476818851682154e-01. */
- .quad 0xBF3BEC6AAC6D7635 /* A00 = -4.260788377246944457107e-04. */
- .quad 0x3FF01AD1D884E719 /* A01 = +1.006547780778822565040e+00. */
- .quad 0xBFA260B2A1B1434A /* A02 = -3.589399551186163439542e-02. */
- .quad 0xBFD09581529E93D6 /* A03 = -2.591250712233067465817e-01. */
- .quad 0xBF4164E26167882B /* A00 = -5.308251737086202562063e-04. */
- .quad 0x3FF01FEF14B62B81 /* A01 = +1.007796364693348545316e+00. */
- .quad 0xBFA4EB014538AA42 /* A02 = -4.085544557559163403315e-02. */
- .quad 0xBFD029D36FEAF41F /* A03 = -2.525528519580024222613e-01. */
- .quad 0xBF46F6FFF4E53DC8 /* A00 = -7.008313930700277652464e-04. */
- .quad 0x3FF027CBB51CBBA0 /* A01 = +1.009715754956893363214e+00. */
- .quad 0xBFA89DEC9FEC112E /* A02 = -4.807986690687680864098e-02. */
- .quad 0xBFCF2A99464D0DB4 /* A03 = -2.434875100390009317053e-01. */
- .quad 0xBF4DCC9C4F66A4D9 /* A00 = -9.094012482836712945103e-04. */
- .quad 0x3FF030E7CFCCD583 /* A01 = +1.011939822882909068014e+00. */
- .quad 0xBFACAA3B95814081 /* A02 = -5.598627281199331645611e-02. */
- .quad 0xBFCDF78F156BE7CF /* A03 = -2.341173987004467604844e-01. */
- .quad 0xBF5308ED74E5C7A6 /* A00 = -1.161796466103906435435e-03. */
- .quad 0x3FF03B5986412ECB /* A01 = +1.014489674026594512313e+00. */
- .quad 0xBFB087EBA88DCC3F /* A02 = -6.457398285947223148806e-02. */
- .quad 0xBFCCBB9BD134862F /* A03 = -2.244753619680052991736e-01. */
- .quad 0xBF57FA23C00DF4B5 /* A00 = -1.463446533505758208674e-03. */
- .quad 0x3FF0473558A1BCC0 /* A01 = +1.017384859292903342975e+00. */
- .quad 0xBFB2E702BC6360EF /* A02 = -7.383744334527241048871e-02. */
- .quad 0xBFCB77D546379288 /* A03 = -2.145945160729250122955e-01. */
- .quad 0xBF5DD12971557F71 /* A00 = -1.819887610814388068450e-03. */
- .quad 0x3FF0548DDF5000A8 /* A01 = +1.020643112482540360020e+00. */
- .quad 0xBFB571B63DA186E1 /* A02 = -8.376635555898871710045e-02. */
- .quad 0xBFCA2D5202605148 /* A03 = -2.045080672838912594358e-01. */
- .quad 0xBF6252B1AD5D4F17 /* A00 = -2.236697221556737096709e-03. */
- .quad 0x3FF063738A910BF7 /* A01 = +1.024280110622155737232e+00. */
- .quad 0xBFB8270C8E6B601B /* A02 = -9.434584118878357184013e-02. */
- .quad 0xBFC8DD27D950A07E /* A03 = -1.942491351230763441116e-01. */
- .quad 0xBF66470C91730CFC /* A00 = -2.719425723258004842786e-03. */
- .quad 0x3FF073F468FCF331 /* A01 = +1.028309259519300633556e+00. */
- .quad 0xBFBB05C2952191E4 /* A02 = -1.055566419686964629854e-01. */
- .quad 0xBFC7886A770DE2BD /* A03 = -1.838505822486435070662e-01. */
- .quad 0xBF6AD114AC8E98EC /* A00 = -3.273525599485007861467e-03. */
- .quad 0x3FF0861BF53E5226 /* A01 = +1.032741506559554434119e+00. */
- .quad 0xBFBE0C4F9B461507 /* A02 = -1.173753503881763554650e-01. */
- .quad 0xBFC6302A037CDE3A /* A03 = -1.733448521642786954722e-01. */
- .quad 0xBF6FFBDE2A6C2AF8 /* A00 = -3.904279630096648551207e-03. */
- .quad 0x3FF099F2EB8E7DA3 /* A01 = +1.037585182326304034106e+00. */
- .quad 0xBFC09C74D192DDF0 /* A02 = -1.297746680554463516444e-01. */
- .quad 0xBFC4D571D8E3079F /* A03 = -1.627638157861470424859e-01. */
- .quad 0xBF72E8FDC0B952AA /* A00 = -4.616728994353872309042e-03. */
- .quad 0x3FF0AF7F273C9533 /* A01 = +1.042845872181101141152e+00. */
- .quad 0xBFC244C512736F10 /* A02 = -1.427236881344176033792e-01. */
- .quad 0xBFC379474F58B902 /* A03 = -1.521386277613104298645e-01. */
- .quad 0xBF762EABAF17395B /* A00 = -5.415602341101023557701e-03. */
- .quad 0x3FF0C6C3886F63FB /* A01 = +1.048526318502125631582e+00. */
- .quad 0xBFC3FDF9918EA12A /* A02 = -1.561881981590514389957e-01. */
- .quad 0xBFC21CA89ECAB895 /* A03 = -1.414995932913753196036e-01. */
- .quad 0xBF79D387CE5B2BAE /* A00 = -6.305246822828998107258e-03. */
- .quad 0x3FF0DFBFE2346376 /* A01 = +1.054626353847394337748e+00. */
- .quad 0xBFC5C6DA43602620 /* A02 = -1.701309994680721970894e-01. */
- .quad 0xBFC0C08BD8DB6631 /* A03 = -1.308760460731704100557e-01. */
- .quad 0xBF7DDBA8E8DA9060 /* A00 = -7.289562037531366334164e-03. */
- .quad 0x3FF0FA70F0D1B464 /* A01 = +1.061142864894713433443e+00. */
- .quad 0xBFC79E18D92BAA7C /* A02 = -1.845122394946264732241e-01. */
- .quad 0xBFBECBBBF74C2669 /* A03 = -1.202962378266875381749e-01. */
- .quad 0xBF81254E76EA25DA /* A00 = -8.371937755572145950511e-03. */
- .quad 0x3FF116D05835EBD0 /* A01 = +1.068069786618014660462e+00. */
- .quad 0xBFC982539E2ED224 /* A02 = -1.992897531869327609755e-01. */
- .quad 0xBFBC1B043C350159 /* A03 = -1.097872397413132278254e-01. */
- .quad 0xBF8391ACBA863403 /* A00 = -9.555196230190082448686e-03. */
- .quad 0x3FF134D4AA477FE2 /* A01 = +1.075398125794884141015e+00. */
- .quad 0xBFCB7218609FEAFB /* A02 = -2.144194099235717521079e-01. */
- .quad 0xBFB970A16CB88329 /* A03 = -9.937485603633135211599e-02. */
- .quad 0xBF87935088E48E8B /* A00 = -1.151144902957603431692e-02. */
- .quad 0x3FF1649892AD7DD3 /* A01 = +1.087059567413110938716e+00. */
- .quad 0xBFCE6971DDE75409 /* A02 = -2.375929196847723912089e-01. */
- .quad 0xBFB58291E88CB251 /* A03 = -8.402358939628952472223e-02. */
- .quad 0xBF8DB3A62C325325 /* A00 = -1.450280973794233242702e-02. */
- .quad 0x3FF1A9C900C6DEEA /* A01 = +1.103951457056548068891e+00. */
- .quad 0xBFD13DBC65B0E08E /* A02 = -2.693930619311765140012e-01. */
- .quad 0xBFB06696F62696D1 /* A03 = -6.406539449252625362252e-02. */
- .quad 0xBF92583699F2E27A /* A00 = -1.791463198307716858659e-02. */
- .quad 0x3FF1F451B85AA9F0 /* A01 = +1.122148246892376022288e+00. */
- .quad 0xBFD34FD5F8288180 /* A02 = -3.017477916164565954205e-01. */
- .quad 0xBFA6FB692825B683 /* A03 = -4.488686194495718900788e-02. */
- .quad 0xBF9641C26E673D6F /* A00 = -2.173522757385398448959e-02. */
- .quad 0x3FF24364DA5E2B07 /* A01 = +1.141453602790251542487e+00. */
- .quad 0xBFD564A5A5EF5890 /* A02 = -3.342680092295120530821e-01. */
- .quad 0xBF9B43712011A982 /* A03 = -2.662445791467283467968e-02. */
- .quad 0xBF9A901038EC2F39 /* A00 = -2.594018313816024226548e-02. */
- .quad 0x3FF2961356DFFEBA /* A01 = +1.161639537196534011088e+00. */
- .quad 0xBFD775EBB17198C7 /* A02 = -3.665723069046972759644e-01. */
- .quad 0xBF833B1A926CD462 /* A03 = -9.390075295963199591975e-03. */
- .quad 0xBF9F396A6A461B91 /* A00 = -3.049246095317987084727e-02. */
- .quad 0x3FF2EB53BAEF534B /* A01 = +1.182452898229899629357e+00. */
- .quad 0xBFD97DABF8AD8BBD /* A02 = -3.982953957076310058660e-01. */
- .quad 0x3F7B8F6A3E0F8837 /* A03 = +6.728568086119371925713e-03. */
- .quad 0xBFA21878590F8BAA /* A00 = -3.534294211546946951064e-02. */
- .quad 0x3FF34209790236E1 /* A01 = +1.203622315111197105253e+00. */
- .quad 0xBFDB764C0E71BECB /* A02 = -4.290952817018306997277e-01. */
- .quad 0x3F962FE0C03F84C0 /* A03 = +2.166701482190513949888e-02. */
- .quad 0xBFA4B36B9AD27ECC /* A00 = -4.043136849327097492868e-02. */
- .quad 0x3FF3990C5B12FC16 /* A01 = +1.224865298994477935679e+00. */
- .quad 0xBFDD5AABB0D01390 /* A02 = -4.586590983092770912322e-01. */
- .quad 0x3FA21DAF5CA162DB /* A03 = +3.538272863142363083844e-02. */
- .quad 0xBFA7645E4D7BF28B /* A00 = -4.568762489177399105378e-02. */
- .quad 0x3FF3EF2FD51C0D9F /* A01 = +1.245895225962932562069e+00. */
- .quad 0xBFDF26377E1B686E /* A02 = -4.867075664057044503963e-01. */
- .quad 0x3FA8803E756EE812 /* A03 = +4.785342391501513914509e-02. */
- .quad 0xBFAA210925C64413 /* A00 = -5.103329263796054643398e-02. */
- .quad 0x3FF44349F897D8E7 /* A01 = +1.266427966181760345066e+00. */
- .quad 0xBFE06A7B02C6D8E2 /* A02 = -5.129981092675530707226e-01. */
- .quad 0x3FAE3F194734F5D0 /* A03 = +5.907515520309980505687e-02. */
- .quad 0xBFACDE48F8A19BBB /* A00 = -5.638340029764018351832e-02. */
- .quad 0x3FF49439D5466582 /* A01 = +1.286187966447272845727e+00. */
- .quad 0xBFE131C7C1063DDC /* A02 = -5.373266954429101183166e-01. */
- .quad 0x3FB1ADEEC36AD805 /* A03 = +6.906025191241844940482e-02. */
- .quad 0xBFAF905D8F585680 /* A00 = -6.164829611604449866036e-02. */
- .quad 0x3FF4E0ED1FD27F99 /* A01 = +1.304913639360142818546e+00. */
- .quad 0xBFE1E7A859DC1D3D /* A02 = -5.595285182070380836095e-01. */
- .quad 0x3FB3ED018E4642A1 /* A03 = +7.783517573831001679086e-02. */
- .quad 0xBFB11595104160BA /* A00 = -6.673556944713512906198e-02. */
- .quad 0x3FF528650340490B /* A01 = +1.322361958217302513319e+00. */
- .quad 0xBFE28B14B40BC974 /* A02 = -5.794776455425521000109e-01. */
- .quad 0x3FB5DF49F5BAF6D7 /* A03 = +8.543836831355676453281e-02. */
- .quad 0xBFB2513A97344BA4 /* A00 = -7.155195418844911836587e-02. */
- .quad 0x3FF569BA0DB5EE14 /* A01 = +1.338312200124055273420e+00. */
- .quad 0xBFE31B53A8B67B20 /* A02 = -5.970857901737396389308e-01. */
- .quad 0x3FB787F297BB0544 /* A03 = +9.191814617499455275507e-02. */
- .quad 0xBFB37512E848FAFA /* A00 = -7.600515528700305112331e-02. */
- .quad 0x3FF5A41F33B403C8 /* A01 = +1.352568819013173495591e+00. */
- .quad 0xBFE397F6EA9A58A5 /* A02 = -6.123003561103997904880e-01. */
- .quad 0x3FB8EAA9FF25CA06 /* A03 = +9.733068923177520814782e-02. */
- .quad 0xBFB47B3E603AFC5D /* A00 = -8.000554894805263217439e-02. */
- .quad 0x3FF5D6E3EDE40487 /* A01 = +1.364963464031718975988e+00. */
- .quad 0xBFE400D5BCA6D631 /* A02 = -6.251019177058819709103e-01. */
- .quad 0x3FBA0B830ED567FE /* A03 = +1.017381583418739132707e-01. */
- .quad 0xBFB5BBFE8AC90496 /* A00 = -8.489981544791400103200e-02. */
- .quad 0x3FF612BA70107E95 /* A01 = +1.379572332145390989311e+00. */
- .quad 0xBFE477EAF1FA7693 /* A02 = -6.396383978023599814478e-01. */
- .quad 0x3FBB4784B7C08A95 /* A03 = +1.065600346196709652391e-01. */
- .quad 0xBFB6D5D940743939 /* A00 = -8.920057128509463473254e-02. */
- .quad 0x3FF644A8748F70CE /* A01 = +1.391762214006166953340e+00. */
- .quad 0xBFE4D646AB07EA37 /* A02 = -6.511567440459832267763e-01. */
- .quad 0x3FBC354F4E1D5292 /* A03 = +1.101884427747086558913e-01. */
- .quad 0xBFB7223D19E4F3D1 /* A00 = -9.036619074045339206069e-02. */
- .quad 0x3FF6518FEB42B7FA /* A01 = +1.394912642466350494175e+00. */
- .quad 0xBFE4ED86CB87498C /* A02 = -6.539949393430091184598e-01. */
- .quad 0x3FBC6D29F28CCA9B /* A03 = +1.110407082713131127205e-01. */
- .quad 0xBFB6878652FF6312 /* A00 = -8.800544287022329936754e-02. */
- .quad 0x3FF63948C302D040 /* A01 = +1.388985406648330922508e+00. */
- .quad 0xBFE4C4E2E7904E17 /* A02 = -6.490339777687407218920e-01. */
- .quad 0x3FBC127356CA1ABE /* A03 = +1.096565329445224612481e-01. */
- .quad 0xBFB4F5D18B0C91D6 /* A00 = -8.187589306596207427980e-02. */
- .quad 0x3FF5FD27EB7DD0B8 /* A01 = +1.374305648697413673176e+00. */
- .quad 0xBFE464E01A2B2FC6 /* A02 = -6.373138915164353601739e-01. */
- .quad 0x3FBB460547674A30 /* A03 = +1.065371798825160976065e-01. */
- .quad 0xBFB26642FA16A685 /* A00 = -7.187288861919156890412e-02. */
- .quad 0x3FF59F9BEDE1C95A /* A01 = +1.351467065073470141812e+00. */
- .quad 0xBFE3D67920C8FBEA /* A02 = -6.199308052381387046381e-01. */
- .quad 0x3FBA24F6A8D3CBC1 /* A03 = +1.021265184570401413078e-01. */
- .quad 0xBFADB5294794F097 /* A00 = -5.802277563859197656582e-02. */
- .quad 0x3FF523EA7B9CF453 /* A01 = +1.321268542159732772845e+00. */
- .quad 0xBFE322A8B55E35DB /* A02 = -5.979808370918208160205e-01. */
- .quad 0x3FB8C8673B1B3E37 /* A03 = +9.680791085269722928697e-02. */
- .quad 0xBFA4B7D661965C6A /* A00 = -4.046506825687219699450e-02. */
- .quad 0x3FF48DE3E2CE3122 /* A01 = +1.284641157110919085227e+00. */
- .quad 0xBFE251FED1A7F445 /* A02 = -5.725092024655472622285e-01. */
- .quad 0x3FB745699FCABDB9 /* A03 = +9.090290213747821701507e-02. */
- .quad 0xBF93E60456E4EE1D /* A00 = -1.943213253365004902773e-02. */
- .quad 0x3FF3E1A14E628A59 /* A01 = +1.242585474196536532432e+00. */
- .quad 0xBFE16C5AB660E876 /* A02 = -5.444768488007543094653e-01. */
- .quad 0x3FB5AD33AA8C188F /* A03 = +8.467410005332197397987e-02. */
- .quad 0x3F738C17C47C7961 /* A00 = +4.772274820224659853951e-03. */
- .quad 0x3FF3234DDE3BD146 /* A01 = +1.196119182682268355933e+00. */
- .quad 0xBFE078C0D77A9D3B /* A02 = -5.147403915952176722826e-01. */
- .quad 0x3FB40D74B3E276B8 /* A03 = +7.833032027925923568290e-02. */
- .quad 0x3FA0474BECC689C7 /* A00 = +3.179394975019849550746e-02. */
- .quad 0x3FF256FB4FA7D18A /* A01 = +1.146235762743432307076e+00. */
- .quad 0xBFDEFA8E3FB285E2 /* A02 = -4.840427038235174395098e-01. */
- .quad 0x3FB270C007493D59 /* A03 = +7.203293016322244446403e-02. */
- .quad 0x3FAF5BD51E479BDC /* A00 = +6.124750132203590768931e-02. */
- .quad 0x3FF18081D0B53BC5 /* A01 = +1.093873801484492647162e+00. */
- .quad 0xBFDCFE2439BD0C03 /* A02 = -4.530115665294831006626e-01. */
- .quad 0x3FB0DEFE5A45AFDD /* A03 = +6.590261176978580437424e-02. */
- .quad 0x3FB7BD5D2806EA26 /* A00 = +9.273321368429118805032e-02. */
- .quad 0x3FF0A369E35B4440 /* A01 = +1.039895904647224256223e+00. */
- .quad 0xBFDB04BC5C9951E7 /* A02 = -4.221640495573226181669e-01. */
- .quad 0x3FAEBBBAA9D6DEEF /* A03 = +6.002600978120919278380e-02. */
- .quad 0x3FC01BE411098DBC /* A00 = +1.258511622610124502941e-01. */
- .quad 0x3FEF85BDABC031C1 /* A01 = +9.850757936961188621083e-01. */
- .quad 0xBFD91521375097C2 /* A02 = -3.919146576102968682065e-01. */
- .quad 0x3FABE26F0086D982 /* A03 = +5.446192628317005068883e-02. */
- .quad 0x3FC481D7FF5776B9 /* A00 = +1.602125164781023347604e-01. */
- .quad 0x3FEDC3506C1E7218 /* A01 = +9.300920592973538347792e-01. */
- .quad 0xBFD7349A88DA7D4F /* A02 = -3.625856720409119104964e-01. */
- .quad 0x3FA936E2DFF8E2AE /* A03 = +4.924687370334389358018e-02. */
- .quad 0x3FC90471F96FA27A /* A00 = +1.954481571149420671141e-01. */
- .quad 0x3FEC0451601987A2 /* A01 = +8.755270840595026360376e-01. */
- .quad 0xBFD5671CD4B898DC /* A02 = -3.344184949259110251063e-01. */
- .quad 0x3FA6BB9594603B67 /* A03 = +4.439990459660841243261e-02. */
- .quad 0x3FCFD8ADB9ED944C /* A00 = +2.488000066615846384011e-01. */
- .quad 0x3FE978C073F6809A /* A01 = +7.959902062321078108909e-01. */
- .quad 0xBFD2DF7E00BCD5A9 /* A02 = -2.948908812716931060471e-01. */
- .quad 0x3FA3614033D490B2 /* A03 = +3.785133965200894456959e-02. */
- .quad 0x3FD4846A12AFE5A0 /* A00 = +3.205819303981005674586e-01. */
- .quad 0x3FE63A1147D40472 /* A01 = +6.945883181471244061100e-01. */
- .quad 0xBFCFA2268AD34450 /* A02 = -2.471359422548027318101e-01. */
- .quad 0x3F9F150201D9FFE0 /* A03 = +3.035357605267552383310e-02. */
- .quad 0x3FD9018641F82BEB /* A00 = +3.907180446846598154131e-01. */
- .quad 0x3FE33B7C220FFBDC /* A01 = +6.010113396913498995389e-01. */
- .quad 0xBFCA4E4187E29C86 /* A02 = -2.055131829740483584423e-01. */
- .quad 0x3F98C30CED19F8F4 /* A03 = +2.418155858185229434287e-02. */
- .quad 0x3FDD4B8255BEB078 /* A00 = +4.577337109901757905561e-01. */
- .quad 0x3FE0858B19D3A49B /* A01 = +5.163016800335243905451e-01. */
- .quad 0xBFC5BC929EACE564 /* A02 = -1.698172831327539045176e-01. */
- .quad 0x3F93A083CE57DE2B /* A03 = +1.916700312537337677621e-02. */
- .quad 0x3FE0A8E5E039295C /* A00 = +5.206174258576470315063e-01. */
- .quad 0x3FDC35E1234583FE /* A01 = +4.407885403107342225937e-01. */
- .quad 0xBFC1DE034E31AEB9 /* A02 = -1.395877963835710222629e-01. */
- .quad 0x3F8EFDEBB3471BDC /* A03 = +1.513275280821162888101e-02. */
- .quad 0x3FE2851B603CB2A5 /* A00 = +5.787484054213406503564e-01. */
- .quad 0x3FD7F4A44ABBB286 /* A01 = +3.743067483726821853551e-01. */
- .quad 0xBFBD3EEB67087DE7 /* A02 = -1.142413260026767657385e-01. */
- .quad 0x3F8864F38329E8BD /* A03 = +1.191129917173260922836e-02. */
- .quad 0x3FE437DBE3C34AC1 /* A00 = +6.318187187665317283702e-01. */
- .quad 0x3FD43F6F789441B5 /* A01 = +3.163717916040938438194e-01. */
- .quad 0xBFB7D92E7901B9A4 /* A02 = -9.315767721429907277653e-02. */
- .quad 0x3F8327ED342308E1 /* A03 = +9.353497651663324544136e-03. */
- .quad 0x3FE5C0977766D55C /* A00 = +6.797597248138731451661e-01. */
- .quad 0x3FD10B42A764D8F9 /* A01 = +2.663122782427219115142e-01. */
- .quad 0xBFB3633351D3D70F /* A02 = -7.573242900602060456716e-02. */
- .quad 0x3F7E079E30FF899C /* A03 = +7.331483779099558922843e-03. */
- .quad 0x3FE7202CE08A88C4 /* A00 = +7.226776490754436288455e-01. */
- .quad 0x3FCC973EB5662B01 /* A01 = +2.233656297433626314319e-01. */
- .quad 0xBFAF70A455F9920B /* A02 = -6.140626477716545211782e-02. */
- .quad 0x3F77812411CE99B6 /* A03 = +5.738392731393584730859e-03. */
- .quad 0x3FE85879424095B1 /* A00 = +7.608000082006382003286e-01. */
- .quad 0x3FC7E73BD1674D84 /* A01 = +1.867441914060742336190e-01. */
- .quad 0xBFA96F84E4BF333B /* A02 = -4.967894832916504993525e-02. */
- .quad 0x3F72606DDCA6E117 /* A03 = +4.486493251924870105662e-03. */
- .quad 0x3FE96BFE4957F4DD /* A00 = +7.944327766887472330737e-01. */
- .quad 0x3FC3ED4780D25478 /* A01 = +1.556786898624158421711e-01. */
- .quad 0xBFA489C5F9A56B58 /* A02 = -4.011362717093075458408e-02. */
- .quad 0x3F6CB5DC17E9AD2A /* A03 = +3.504686231556104931972e-03. */
- .quad 0x3FEA5D9CB2F41234 /* A00 = +8.239272589858672724006e-01. */
- .quad 0x3FC091A758374DCF /* A01 = +1.294449978582705440555e-01. */
- .quad 0xBFA08E436D4B5CE0 /* A02 = -3.233538350257858517978e-02. */
- .quad 0x3F666997AD53E6B7 /* A03 = +2.735897297154145629133e-03. */
- .quad 0x3FEB3060342CB850 /* A00 = +8.496552485501158713532e-01. */
- .quad 0x3FBB7D30BBC7DC1B /* A01 = +1.073790033768634993860e-01. */
- .quad 0xBF9AA6BA3443D9E3 /* A02 = -2.602663940430173170060e-02. */
- .quad 0x3F617CA764B7850B /* A03 = +2.134634914668814050648e-03. */
- .quad 0x3FEBE759A6A0C7B8 /* A00 = +8.719909910635044170135e-01. */
- .quad 0x3FB6C10DE6A703FF /* A01 = +8.888327485239243264115e-02. */
- .quad 0xBF956C566D8BE1F6 /* A02 = -2.092108768099084498138e-02. */
- .quad 0x3F5B46D1A4A59CF8 /* A03 = +1.664833764687232917079e-03. */
- .quad 0x3FEC858494887A04 /* A00 = +8.912985707318630268503e-01. */
- .quad 0x3FB2CC31F543394D /* A01 = +7.342827070099140762682e-02. */
- .quad 0xBF9133477FF69137 /* A02 = -1.679717749142747504343e-02. */
- .quad 0x3F5544482FBB4DA5 /* A03 = +1.298017973501022466823e-03. */
- .quad 0x3FED0DB59D0E32E9 /* A00 = +9.079235141267335551518e-01. */
- .quad 0x3FAF006BAFFC6EF4 /* A01 = +6.055008433597022787787e-02. */
- .quad 0xBF8B97146FA2B97A /* A02 = -1.347175565419144252499e-02. */
- .quad 0x3F5093B01F4CDC69 /* A03 = +1.011774057770665211434e-03. */
- .quad 0x3FEDB487C3EC457C /* A00 = +9.282873942012623835751e-01. */
- .quad 0x3FA7390C09D0BD1D /* A01 = +4.535710925881118044112e-02. */
- .quad 0xBF83D9F7C3181106 /* A02 = -9.693084374710735778846e-03. */
- .quad 0x3F46E34A0A3C0E64 /* A03 = +6.984817050299072134500e-04. */
- .quad 0x3FEE5FFCB4E6EB00 /* A00 = +9.492171796076434020506e-01. */
- .quad 0x3F9F4913ED00AADF /* A01 = +3.055220731782070861526e-02. */
- .quad 0xBF79670BD0E59B5C /* A02 = -6.201788097633133961528e-03. */
- .quad 0x3F3BC998EBCAF96D /* A03 = +4.240034429975534616304e-04. */
- .quad 0x3FEEDBA41E9542FE /* A00 = +9.643116566968215064293e-01. */
- .quad 0x3F94F5DD18D9C24D /* A01 = +2.046914543319848858727e-02. */
- .quad 0xBF7034896AA122B9 /* A02 = -3.956352980886528904192e-03. */
- .quad 0x3F30DCCB47810B39 /* A03 = +2.573009765038273091199e-04. */
- .quad 0x3FEF33F2882520ED /* A00 = +9.750912341196716903724e-01. */
- .quad 0x3F8BF37F2CF553FF /* A01 = +1.364802699996836392315e-02. */
- .quad 0xBF649F6F05A69619 /* A02 = -2.517430152880317534986e-03. */
- .quad 0x3F247623C950AAC9 /* A03 = +1.561087307505231250044e-04. */
- .quad 0x3FEF727757751741 /* A00 = +9.827229221489021115943e-01. */
- .quad 0x3F828E67912C4400 /* A01 = +9.060677640748693306705e-03. */
- .quad 0xBF5A2F51A806CC2C /* A02 = -1.598195784123355826789e-03. */
- .quad 0x3F18D35D7687E613 /* A03 = +9.470231965016282719549e-05. */
- .quad 0x3FEF9E6325C5942A /* A00 = +9.880843866091073568469e-01. */
- .quad 0x3F788AB117618F76 /* A01 = +5.991641772286606867914e-03. */
- .quad 0xBF5096EAB0B1EA89 /* A02 = -1.012543859160305046233e-03. */
- .quad 0x3F0E1E50EC4435AB /* A03 = +5.744633156910412119652e-05. */
- .quad 0x3FEFBD0784049369 /* A00 = +9.918248728250605994461e-01. */
- .quad 0x3F702BBD8294035F /* A01 = +3.947963975634432264028e-03. */
- .quad 0xBF44FB55E0F00593 /* A02 = -6.403130845457509273330e-04. */
- .quad 0x3F0244DCD723230A /* A03 = +3.484534217219031730379e-05. */
- .quad 0x3FEFD245E2366A43 /* A00 = +9.944180887426415926811e-01. */
- .quad 0x3F653D82EC088433 /* A01 = +2.592807490387838333795e-03. */
- .quad 0xBF3A7DF75E013CB8 /* A02 = -4.042366908878036561859e-04. */
- .quad 0x3EF6298E69F991CD /* A03 = +2.113564425911141559972e-05. */
- .quad 0x3FEFE0EAA508BC69 /* A00 = +9.962056372950317539861e-01. */
- .quad 0x3F5BD0771AF3FDDA /* A01 = +1.697651208644282514598e-03. */
- .quad 0xBF30B2E1254DE571 /* A02 = -2.548026725928887099328e-04. */
- .quad 0x3EEAE28B70EC0256 /* A03 = +1.281973848454955042307e-05. */
- .quad 0x3FEFEAF5303D7F96 /* A00 = +9.974313680831865536192e-01. */
- .quad 0x3F5229111365657E /* A01 = +1.108423877289460134782e-03. */
- .quad 0xBF250572D04DFE66 /* A02 = -1.603796628408704519168e-04. */
- .quad 0x3EE04E89BB57C981 /* A03 = +7.775682983689149966743e-06. */
- .quad 0x3FEFF1CF52F1CF44 /* A00 = +9.982678051005469122003e-01. */
- .quad 0x3F47A71316147CEB /* A01 = +7.218211359577819110842e-04. */
- .quad 0xBF1A6D7604055719 /* A02 = -1.008132248946049582547e-04. */
- .quad 0x3ED3C8047586A85C /* A03 = +4.716233739913014633626e-06. */
- .quad 0x3FEFF6770369EF69 /* A00 = +9.988360468555416149528e-01. */
- .quad 0x3F3EBB261180FBF0 /* A01 = +4.689186039321105101130e-04. */
- .quad 0xBF1097754FE19D7F /* A02 = -6.329206004950480057066e-05. */
- .quad 0x3EC7FEFF83BCA0A7 /* A03 = +2.860556404988488738366e-06. */
- .quad 0x3FEFF99D42371AC4 /* A00 = +9.992204945818561334647e-01. */
- .quad 0x3F33EB2AEC271F59 /* A01 = +3.039340773764907474054e-04. */
- .quad 0xBF04CF18E0FC0D79 /* A02 = -3.968996690952969588805e-05. */
- .quad 0x3EBD1BDBD6019BE9 /* A03 = +1.735021065507727833886e-06. */
- .quad 0x3FEFFBBCA32B0D91 /* A00 = +9.994795977476532700123e-01. */
- .quad 0x3F29C41E1615110A /* A01 = +1.965796209707565346710e-04. */
- .quad 0xBEFA11F93D9DCB5A /* A02 = -2.486248909101414873235e-05. */
- .quad 0x3EB1A7CA4546F7A7 /* A03 = +1.052345642723709228769e-06. */
- .quad 0x3FEFFD298B8E8DE2 /* A00 = +9.996535993308806045121e-01. */
- .quad 0x3F20A1C42D523C5B /* A01 = +1.268913244172078754520e-04. */
- .quad 0xBEF0507A364AFAE4 /* A02 = -1.555859070622834605755e-05. */
- .quad 0x3EA56ACA17E7CDF4 /* A03 = +6.382806956848098872313e-07. */
- .quad 0x3FEFFE1DC82BA5A3 /* A00 = +9.997700604991915929176e-01. */
- .quad 0x3F156E73B90F1769 /* A01 = +8.175450626798714452801e-05. */
- .quad 0xBEE4663579D0A09F /* A02 = -9.727122057226747625365e-06. */
- .quad 0x3E99FAF6FEC5D4C1 /* A03 = +3.871371052824002996020e-07. */
- .quad 0x3FEFFEF8D0BB5E81 /* A00 = +9.998745037837154514548e-01. */
- .quad 0x3F06686DA18D39C3 /* A01 = +4.273972098777251447726e-05. */
- .quad 0xBED46BC298073E90 /* A02 = -4.868731025855742842491e-06. */
- .quad 0x3E88E42286B9D0FD /* A03 = +1.854535328530838170114e-07. */
- .quad 0x3FEFFF8DBC68DDC7 /* A00 = +9.999455146670975791423e-01. */
- .quad 0x3EF26B2953A80AF0 /* A01 = +1.756534514108903368909e-05. */
- .quad 0xBEBFC4472D580F83 /* A02 = -1.893443529411295465239e-06. */
- .quad 0x3E72505B4553D19F /* A03 = +6.822456673547912277047e-08. */
- .quad 0x3FEFFFCED1276609 /* A00 = +9.999765477215883935358e-01. */
- .quad 0x3EDE1A94C7CC58F5 /* A01 = +7.177313020153979672606e-06. */
- .quad 0xBEA8A2C988744E57 /* A02 = -7.342066660497443762363e-07. */
- .quad 0x3E5AF30036BBBAF4 /* A03 = +2.509841882843541084885e-08. */
- .quad 0x3FEFFFEAFE70FCFC /* A00 = +9.999899835164849370983e-01. */
- .quad 0x3EC879175E3549F5 /* A01 = +2.917410471128503564412e-06. */
- .quad 0xBE930E36677D1813 /* A02 = -2.839493400307523115929e-07. */
- .quad 0x3E43D4005B42D48F /* A03 = +9.233192745401904898013e-09. */
- .quad 0x3ff0000000000000
- .quad 0x0000000000000000
- .quad 0x0000000000000000
- .quad 0x0000000000000000
-
- .align 32
- .type __svml_stanh_data_internal_avx2, @object
- .size __svml_stanh_data_internal_avx2, .-__svml_stanh_data_internal_avx2
- .type __svml_stanh_data_internal, @object
- .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
-#endif
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.h.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.h.S
new file mode 100644
index 0000000000..3634950e97
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf_rodata.h.S
@@ -0,0 +1,591 @@
+/* Datatables for tanhf_{avx2,sse4}
+ Copyright (C) 2021-2022 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ https://www.gnu.org/licenses/. */
+
+#include "svml_common_data_macros.h.S"
+
+#if (defined AVX2_SHARED_OFFSETS) || (defined AVX2_SHARED_TABLE)
+
+/* Offsets are ordered by use in the function. On cold-starts this
+ might help the prefetcher. If the streaming prefetchers kick in it
+ will prefetch into the lookup table. */
+# define _iExpMantMask 0
+# define _iMinIdxOfsMask 32
+# define _iMaxIdxMask 64
+# define _iExpMask 96
+# define _lookupTable 128
+
+# define AVX2_SHARED_DATA(offset) ((offset) + __svml_stanh_common_data_avx2)
+
+# if (defined AVX2_SHARED_TABLE)
+
+ .section .rodata.avx2, "a"
+
+ .align 32
+ .globl __svml_stanh_common_data_avx2
+__svml_stanh_common_data_avx2:
+ /* _iExpMantMask. */
+ float_vector32 (__svml_stanh_common_data_avx2, _iExpMantMask, 0x7ff80000)
+ float_vector32 (__svml_stanh_common_data_avx2, _iMinIdxOfsMask, 0x3cf80000)
+ float_vector32 (__svml_stanh_common_data_avx2, _iMaxIdxMask, 0x04280000)
+ float_vector32 (__svml_stanh_common_data_avx2, _iExpMask, 0x7f000000)
+
+ /* _lookupTable. */
+ /* Pol_000: err=7.93e-09, x in [0.0000000; 0.0312500]. */
+ float_block (__svml_stanh_common_data_avx2, _lookupTable,
+ 0x00000000, 0x00000000, /* A00 = +0.000000000000000000000e-01. */
+ 0x022C70EB, 0x3FF00000, /* A01 = +1.000000008097283510367e+00. */
+ 0x8CFFA194, 0xBED00E87, /* A02 = -3.828228912518614443549e-06. */
+ 0x6D0607A9, 0xBFD55176, /* A03 = -3.330970825846813476723e-01. */
+ 0xE3E4C297, 0xBE53D60C, /* A00 = -1.847383956330407336230e-08. */
+ 0x4177CF5C, 0x3FF00002, /* A01 = +1.000002151235967140508e+00. */
+ 0x94A51A25, 0xBF1758BC, /* A02 = -8.906031613262943753568e-05. */
+ 0x67E0D4F0, 0xBFD53EAE, /* A03 = -3.319507612644221339337e-01. */
+ 0xEF32D6FE, 0xBE5A9E47, /* A00 = -2.479020984039698285657e-08. */
+ 0xDA983057, 0x3FF00002, /* A01 = +1.000002721676556793895e+00. */
+ 0x509E94AA, 0xBF1BD953, /* A02 = -1.062352277175377670507e-04. */
+ 0x562EEDD5, 0xBFD53BDB, /* A03 = -3.317783681520414806876e-01. */
+ 0xE496D294, 0xBE6191BB, /* A00 = -3.272532162914017685901e-08. */
+ 0x90492017, 0x3FF00003, /* A01 = +1.000003398528866105366e+00. */
+ 0x814A57CE, 0xBF20727E, /* A02 = -1.254825043772153972919e-04. */
+ 0x060A6F22, 0xBFD538DE, /* A03 = -3.315959033004550748913e-01. */
+ 0x2A893A25, 0xBE66DAFA, /* A00 = -4.257146219278012568149e-08. */
+ 0x65E08CD1, 0x3FF00004, /* A01 = +1.000004194219219266770e+00. */
+ 0x65EF91B6, 0xBF2341C7, /* A02 = -1.469188600530365522261e-04. */
+ 0x841FAF9E, 0xBFD535B6, /* A03 = -3.314033785124993469751e-01. */
+ 0xE361E964, 0xBE6D5794, /* A00 = -5.465394929765249413434e-08. */
+ 0x5EE2A0CB, 0x3FF00005, /* A01 = +1.000005121846742950353e+00. */
+ 0x77E66C8B, 0xBF265E6C, /* A02 = -1.706607253709506650304e-04. */
+ 0xDDCCEDA6, 0xBFD53264, /* A03 = -3.312008062382240103361e-01. */
+ 0x4D374A6E, 0xBE729C84, /* A00 = -6.933284462462096107184e-08. */
+ 0x7F019093, 0x3FF00006, /* A01 = +1.000006195180536350264e+00. */
+ 0x48D6DCE5, 0xBF29CC53, /* A02 = -1.968242326435338705130e-04. */
+ 0x2121ED35, 0xBFD52EE9, /* A03 = -3.309881995734998416658e-01. */
+ 0x17EAA872, 0xBE775AEA, /* A00 = -8.700465590574974405858e-08. */
+ 0xCA1D66B8, 0x3FF00007, /* A01 = +1.000007428656699559610e+00. */
+ 0xB98A2637, 0xBF2D8F5E, /* A02 = -2.255252009216044881395e-04. */
+ 0x5CDF9128, 0xBFD52B43, /* A03 = -3.307655722585587376727e-01. */
+ 0x28C343F0, 0xBE7D04DA, /* A00 = -1.081040272327705484794e-07. */
+ 0x4443CCF5, 0x3FF00009, /* A01 = +1.000008837375216730337e+00. */
+ 0x6C947AE5, 0xBF30D5B7, /* A02 = -2.568791210978817814332e-04. */
+ 0xA0776FAD, 0xBFD52773, /* A03 = -3.305329386764651045105e-01. */
+ 0xA12C51C7, 0xBE81DD77, /* A00 = -1.331054169875768625701e-07. */
+ 0xF1AFD2DA, 0x3FF0000A, /* A01 = +1.000010437096696680470e+00. */
+ 0x624C1680, 0xBF331230, /* A02 = -2.910011410651516805537e-04. */
+ 0xFC0B61DF, 0xBFD52379, /* A03 = -3.302903138515186909352e-01. */
+ 0xEEB3C435, 0xBE85D04E, /* A00 = -1.625247628488202841012e-07. */
+ 0xD6C9B1F2, 0x3FF0000C, /* A01 = +1.000012244238970726684e+00. */
+ 0x42FADDD4, 0xBF357F07, /* A02 = -3.280060509313874068243e-04. */
+ 0x806D0E81, 0xBFD51F56, /* A03 = -3.300377134475880880338e-01. */
+ 0x9B59681B, 0xBE8A6E28, /* A00 = -1.969211333326924655065e-07. */
+ 0xF8268F72, 0x3FF0000E, /* A01 = +1.000014275873550406715e+00. */
+ 0x7A1B747A, 0xBF381E27, /* A02 = -3.680082682942575423093e-04. */
+ 0x3F1D6FD4, 0xBFD51B09, /* A03 = -3.297751537663746734808e-01. */
+ 0x0EE9ABD5, 0xBE8FCBC4, /* A00 = -2.368983653301529373887e-07. */
+ 0x5A883B6C, 0x3FF00011, /* A01 = +1.000016549721943981410e+00. */
+ 0xC974B3D9, 0xBF3AF17A, /* A02 = -4.111218235774406434303e-04. */
+ 0x4A4C549C, 0xBFD51692, /* A03 = -3.295026517456081105450e-01. */
+ 0x60A3F956, 0xBE92FFBC, /* A00 = -2.831066871072026054144e-07. */
+ 0x02DCED8A, 0x3FF00014, /* A01 = +1.000019084151832604590e+00. */
+ 0x390C4801, 0xBF3DFAE9, /* A02 = -4.574603454311488280083e-04. */
+ 0xB4D7DC3A, 0xBFD511F1, /* A03 = -3.292202249571719585575e-01. */
+ 0x2F96D5AD, 0xBE9690A2, /* A00 = -3.362443262393081632612e-07. */
+ 0xF63EFF5D, 0x3FF00016, /* A01 = +1.000021898173108825247e+00. */
+ 0x839605BB, 0xBF409E2C, /* A02 = -5.071370461992499986334e-04. */
+ 0x924BEE00, 0xBFD50D27, /* A03 = -3.289278916051614487515e-01. */
+ 0x65E72A73, 0xBE9AA56C, /* A00 = -3.970591019557469835586e-07. */
+ 0x39F4A43E, 0x3FF0001A, /* A01 = +1.000025011433776978009e+00. */
+ 0x4C3D6667, 0xBF425BD7, /* A02 = -5.602647074553602319844e-04. */
+ 0xF6E1ABA2, 0xBFD50833, /* A03 = -3.286256705238718156536e-01. */
+ 0xFF1A83B0, 0xBE9F4BD4, /* A00 = -4.663500013744687071912e-07. */
+ 0xD36F9EC2, 0x3FF0001D, /* A01 = +1.000028444215715683896e+00. */
+ 0x34149405, 0xBF443766, /* A02 = -6.169556656102642569831e-04. */
+ 0xF77EDEE5, 0xBFD50316, /* A03 = -3.283135811757190158922e-01. */
+ 0x387BB079, 0xBEA3B625, /* A00 = -5.874486399249461304297e-07. */
+ 0xE14CFBA9, 0x3FF00023, /* A01 = +1.000034217911642153709e+00. */
+ 0x923218D2, 0xBF47392F, /* A02 = -7.087213783883111826306e-04. */
+ 0xACDEB938, 0xBFD4FB1F, /* A03 = -3.278273761924483942209e-01. */
+ 0xF543500A, 0xBEAA6E24, /* A00 = -7.876828740601738750574e-07. */
+ 0x5C6E8412, 0x3FF0002D, /* A01 = +1.000043259679163742959e+00. */
+ 0xBD7FDD70, 0xBF4BAF02, /* A02 = -8.448375110664940040861e-04. */
+ 0x6527A7DE, 0xBFD4EFEE, /* A03 = -3.271442401734229177279e-01. */
+ 0xBE2157D0, 0xBEB16E3E, /* A00 = -1.038947396133402500647e-06. */
+ 0x990FEE2F, 0x3FF00038, /* A01 = +1.000053975962952312884e+00. */
+ 0x81C574CB, 0xBF505694, /* A02 = -9.972048056490652716971e-04. */
+ 0x278DA2B4, 0xBFD4E419, /* A03 = -3.264220129263251113372e-01. */
+ 0x723165D4, 0xBEB6A7B6, /* A00 = -1.350350836279403750524e-06. */
+ 0xCAB4158E, 0x3FF00045, /* A01 = +1.000066558657042303793e+00. */
+ 0x9C849108, 0xBF531D7C, /* A02 = -1.166698160951775212202e-03. */
+ 0xBB33B152, 0xBFD4D7A0, /* A03 = -3.256608799117844954552e-01. */
+ 0xA8654AFD, 0xBEBD0EE2, /* A00 = -1.732000471561702711532e-06. */
+ 0x276F18D6, 0x3FF00055, /* A01 = +1.000081209219890521211e+00. */
+ 0xA3FB6C6C, 0xBF562FDB, /* A02 = -1.354183666925102939860e-03. */
+ 0xF1B93DB2, 0xBFD4CA85, /* A03 = -3.248610363561638125773e-01. */
+ 0x036A207E, 0xBEC269D4, /* A00 = -2.195047297096822741730e-06. */
+ 0xE7DA6E4E, 0x3FF00066, /* A01 = +1.000098138500919997540e+00. */
+ 0x9FC36B3A, 0xBF599149, /* A02 = -1.560518167983372759405e-03. */
+ 0xA72283D6, 0xBFD4BCC9, /* A03 = -3.240226871658341556426e-01. */
+ 0x6C09CFE1, 0xBEC7154B, /* A00 = -2.751729738565190291276e-06. */
+ 0x47086B80, 0x3FF0007B, /* A01 = +1.000117566559055148900e+00. */
+ 0x33B4F8F4, 0xBF5D4554, /* A02 = -1.786548832412968197680e-03. */
+ 0xC1BFE145, 0xBFD4AE6C, /* A03 = -3.231460468373550942722e-01. */
+ 0xC64A0F8A, 0xBECCA68C, /* A00 = -3.415415948561670285790e-06. */
+ 0x827742F7, 0x3FF00092, /* A01 = +1.000139722473418535387e+00. */
+ 0x15A527AF, 0xBF60A7BF, /* A02 = -2.033112728132522705610e-03. */
+ 0x3214084C, 0xBFD49F70, /* A03 = -3.222313393636155876010e-01. */
+ 0x676B241B, 0xBED19E68, /* A00 = -4.200644630977303616698e-06. */
+ 0xDA037B26, 0x3FF000AC, /* A01 = +1.000164844146362863597e+00. */
+ 0x836A02F8, 0xBF62D99F, /* A02 = -2.301036405072284102280e-03. */
+ 0xF2B91B28, 0xBFD48FD4, /* A03 = -3.212787981359945810311e-01. */
+ 0xB0C7AA54, 0xBED57CF4, /* A00 = -5.123164339408145209103e-06. */
+ 0x8FD9E1A1, 0x3FF000CA, /* A01 = +1.000193178099017865534e+00. */
+ 0x4548E686, 0xBF653A01, /* A02 = -2.591135484433962181405e-03. */
+ 0x0844B38F, 0xBFD47F9C, /* A03 = -3.202886658426046806447e-01. */
+ 0x1B1A41E2, 0xBEDA012B, /* A00 = -6.199971197454598722328e-06. */
+ 0xE868FDF4, 0x3FF000EB, /* A01 = +1.000224979259539459520e+00. */
+ 0x27E0A544, 0xBF67CA94, /* A02 = -2.904214255086275467410e-03. */
+ 0x812ADB37, 0xBFD46EC6, /* A03 = -3.192611943626845749655e-01. */
+ 0x5BF12194, 0xBEDF3EAC, /* A00 = -7.449344990702664567927e-06. */
+ 0x2A520784, 0x3FF00111, /* A01 = +1.000260510744255704196e+00. */
+ 0xABDA4DC4, 0xBF6A8D01, /* A02 = -3.241065277345108255891e-03. */
+ 0x759FFA4A, 0xBFD45D55, /* A03 = -3.181966446572103146551e-01. */
+ 0xBC274267, 0xBEE2A541, /* A00 = -8.890883582164319970972e-06. */
+ 0x9E5961F2, 0x3FF0013A, /* A01 = +1.000300043631906721231e+00. */
+ 0xD080C540, 0xBF6D82EC, /* A02 = -3.602468994380686462264e-03. */
+ 0x0779C0AD, 0xBFD44B4A, /* A03 = -3.170952866557950611259e-01. */
+ 0x609A27F4, 0xBEE61D97, /* A00 = -1.054553560499505625520e-05. */
+ 0x8F56A3AF, 0x3FF00168, /* A01 = +1.000343856731187974773e+00. */
+ 0xEFB683EC, 0xBF7056F8, /* A02 = -3.989193351487490407647e-03. */
+ 0x620F0F74, 0xBFD438A5, /* A03 = -3.159573991399533543500e-01. */
+ 0x29EDD370, 0xBEEA1454, /* A00 = -1.243563138839952927732e-05. */
+ 0x4A242A67, 0x3FF0019B, /* A01 = +1.000392236341804297339e+00. */
+ 0x1CA78D9B, 0xBF7207D3, /* A02 = -4.401993423445739288258e-03. */
+ 0xBA16E7CD, 0xBFD42568, /* A03 = -3.147832696228050619602e-01. */
+ 0x0D52680F, 0xBEEE9637, /* A00 = -1.458491207477835326165e-05. */
+ 0x1D8E4115, 0x3FF001D3, /* A01 = +1.000445476009251821736e+00. */
+ 0x11EDC094, 0xBF73D4CC, /* A02 = -4.841611050196221316400e-03. */
+ 0x4D8664E7, 0xBFD41195, /* A03 = -3.135731942252974469021e-01. */
+ 0x46215EF8, 0xBEF338C0, /* A00 = -1.833122622260562810219e-05. */
+ 0xC32C2EC1, 0x3FF00230, /* A01 = +1.000534784691737621998e+00. */
+ 0x9BCC5DAF, 0xBF76BD01, /* A02 = -5.551344188254799492943e-03. */
+ 0x156DC21E, 0xBFD3F2C7, /* A03 = -3.116929730668135389848e-01. */
+ 0xAE411EAE, 0xBEF9B15E, /* A00 = -2.450261207822986676092e-05. */
+ 0xDF057A4D, 0x3FF002C2, /* A01 = +1.000674124886830940184e+00. */
+ 0xD9AC1E30, 0xBF7B08CC, /* A02 = -6.600189396301511801646e-03. */
+ 0xA114FED8, 0xBFD3C7A7, /* A03 = -3.090609620157755976777e-01. */
+ 0x83C373B3, 0xBF00E364, /* A00 = -3.221178528332122595812e-05. */
+ 0x419480D7, 0x3FF0036F, /* A01 = +1.000838524028997644777e+00. */
+ 0xD1777007, 0xBF7FD255, /* A02 = -7.768950679260206403087e-03. */
+ 0x3911D6CE, 0xBFD39A45, /* A03 = -3.062909180947429588215e-01. */
+ 0x4DD12059, 0xBF05DFA0, /* A00 = -4.172046622180685472624e-05. */
+ 0xB2A03D8D, 0x3FF00438, /* A01 = +1.001030633695197069599e+00. */
+ 0xBB4A9D10, 0xBF828F8D, /* A02 = -9.062869337255224921890e-03. */
+ 0x704697D9, 0xBFD36AAB, /* A03 = -3.033856007044711255993e-01. */
+ 0xC647DEFB, 0xBF0BF3E0, /* A00 = -5.331544597092331081714e-05. */
+ 0x1063D36D, 0x3FF00522, /* A01 = +1.001253189109060359741e+00. */
+ 0xB3C96102, 0xBF857A2C, /* A02 = -1.048693584122917590862e-02. */
+ 0x5BBB4FEC, 0xBFD338E6, /* A03 = -3.003478904549854444639e-01. */
+ 0xED7C9D31, 0xBF11A506, /* A00 = -6.730894835681591541979e-05. */
+ 0x4D0EA92A, 0x3FF0062E, /* A01 = +1.001508999829250345925e+00. */
+ 0xC2761AF3, 0xBF88AB82, /* A02 = -1.204588085125866091241e-02. */
+ 0x8D6BD206, 0xBFD30502, /* A03 = -2.971807843271395688234e-01. */
+ 0x922D9BF1, 0xBF1607C0, /* A00 = -8.403885708006799337092e-05. */
+ 0x6C341961, 0x3FF00760, /* A01 = +1.001800940198869449560e+00. */
+ 0xDA487BCF, 0xBF8C25E6, /* A02 = -1.374416688582682892494e-02. */
+ 0x0EE8F7B5, 0xBFD2CF0D, /* A03 = -2.938873906713255768075e-01. */
+ 0x80A0A16D, 0xBF1B3A84, /* A00 = -1.038688061788578038307e-04. */
+ 0x802D02D6, 0x3FF008BB, /* A01 = +1.002131939589323561535e+00. */
+ 0xE99FD100, 0xBF8FEB8A, /* A02 = -1.558598065819483124983e-02. */
+ 0x5BD0911B, 0xBFD29713, /* A03 = -2.904709240558688843059e-01. */
+ 0xBDB75C65, 0xBF20ABB9, /* A00 = -1.271881327357976163798e-04. */
+ 0xA76D8CD1, 0x3FF00A42, /* A01 = +1.002504972472525901495e+00. */
+ 0x752BB9E6, 0xBF91FF3D, /* A02 = -1.757522609380570560722e-02. */
+ 0x5C1F88B4, 0xBFD25D23, /* A03 = -2.869346999779154305799e-01. */
+ 0x54425461, 0xBF243D32, /* A00 = -1.544116913733432829448e-04. */
+ 0x09D1795E, 0x3FF00BF9, /* A01 = +1.002923048355647051011e+00. */
+ 0x04D44942, 0xBF94304E, /* A02 = -1.971551804042204897316e-02. */
+ 0x5E61CFA6, 0xBFD2214B, /* A03 = -2.832821294498394371075e-01. */
+ 0x011B61CE, 0xBF286070, /* A00 = -1.859795307186510085994e-04. */
+ 0xD5E1627E, 0x3FF00DE1, /* A01 = +1.003389201612804537689e+00. */
+ 0xF4163F59, 0xBF9689D5, /* A02 = -2.201017668045266231780e-02. */
+ 0x11C3B42C, 0xBFD1E39A, /* A03 = -2.795167134743816728104e-01. */
+ 0x366A79E8, 0xBF2D250B, /* A00 = -2.223564326486314902259e-04. */
+ 0x3E134001, 0x3FF01000, /* A01 = +1.003906481248123094829e+00. */
+ 0xF91F6F81, 0xBF990C9F, /* A02 = -2.446222265267250853271e-02. */
+ 0x80084CDC, 0xBFD1A41E, /* A03 = -2.756420374218586655246e-01. */
+ 0xDDC2A30E, 0xBF314DB5, /* A00 = -2.640313157465248123865e-04. */
+ 0x7608921B, 0x3FF01257, /* A01 = +1.004477940624503018441e+00. */
+ 0x6875B0C9, 0xBF9BB962, /* A02 = -2.707437288829409385849e-02. */
+ 0x0768A9D0, 0xBFD162E8, /* A03 = -2.716617653228725615122e-01. */
+ 0x33808864, 0xBF346A61, /* A00 = -3.115165050094957730625e-04. */
+ 0xAFCC88A3, 0x3FF014EA, /* A01 = +1.005106627192198898157e+00. */
+ 0xF9BF7419, 0xBF9E90BE, /* A02 = -2.984903716411588595059e-02. */
+ 0x545F7FAD, 0xBFD12006, /* A03 = -2.675796340899932457269e-01. */
+ 0xDC3848EA, 0xBF37F180, /* A00 = -3.653468704395550778821e-04. */
+ 0x19147861, 0x3FF017BD, /* A01 = +1.005795572250939295955e+00. */
+ 0x4C702E07, 0xBFA0C9A1, /* A02 = -3.278831537326359207851e-02. */
+ 0x5B650092, 0xBFD0DB89, /* A03 = -2.633994476818851682154e-01. */
+ 0xAC6D7635, 0xBF3BEC6A, /* A00 = -4.260788377246944457107e-04. */
+ 0xD884E719, 0x3FF01AD1, /* A01 = +1.006547780778822565040e+00. */
+ 0xA1B1434A, 0xBFA260B2, /* A02 = -3.589399551186163439542e-02. */
+ 0x529E93D6, 0xBFD09581, /* A03 = -2.591250712233067465817e-01. */
+ 0x6167882B, 0xBF4164E2, /* A00 = -5.308251737086202562063e-04. */
+ 0x14B62B81, 0x3FF01FEF, /* A01 = +1.007796364693348545316e+00. */
+ 0x4538AA42, 0xBFA4EB01, /* A02 = -4.085544557559163403315e-02. */
+ 0x6FEAF41F, 0xBFD029D3, /* A03 = -2.525528519580024222613e-01. */
+ 0xF4E53DC8, 0xBF46F6FF, /* A00 = -7.008313930700277652464e-04. */
+ 0xB51CBBA0, 0x3FF027CB, /* A01 = +1.009715754956893363214e+00. */
+ 0x9FEC112E, 0xBFA89DEC, /* A02 = -4.807986690687680864098e-02. */
+ 0x464D0DB4, 0xBFCF2A99, /* A03 = -2.434875100390009317053e-01. */
+ 0x4F66A4D9, 0xBF4DCC9C, /* A00 = -9.094012482836712945103e-04. */
+ 0xCFCCD583, 0x3FF030E7, /* A01 = +1.011939822882909068014e+00. */
+ 0x95814081, 0xBFACAA3B, /* A02 = -5.598627281199331645611e-02. */
+ 0x156BE7CF, 0xBFCDF78F, /* A03 = -2.341173987004467604844e-01. */
+ 0x74E5C7A6, 0xBF5308ED, /* A00 = -1.161796466103906435435e-03. */
+ 0x86412ECB, 0x3FF03B59, /* A01 = +1.014489674026594512313e+00. */
+ 0xA88DCC3F, 0xBFB087EB, /* A02 = -6.457398285947223148806e-02. */
+ 0xD134862F, 0xBFCCBB9B, /* A03 = -2.244753619680052991736e-01. */
+ 0xC00DF4B5, 0xBF57FA23, /* A00 = -1.463446533505758208674e-03. */
+ 0x58A1BCC0, 0x3FF04735, /* A01 = +1.017384859292903342975e+00. */
+ 0xBC6360EF, 0xBFB2E702, /* A02 = -7.383744334527241048871e-02. */
+ 0x46379288, 0xBFCB77D5, /* A03 = -2.145945160729250122955e-01. */
+ 0x71557F71, 0xBF5DD129, /* A00 = -1.819887610814388068450e-03. */
+ 0xDF5000A8, 0x3FF0548D, /* A01 = +1.020643112482540360020e+00. */
+ 0x3DA186E1, 0xBFB571B6, /* A02 = -8.376635555898871710045e-02. */
+ 0x02605148, 0xBFCA2D52, /* A03 = -2.045080672838912594358e-01. */
+ 0xAD5D4F17, 0xBF6252B1, /* A00 = -2.236697221556737096709e-03. */
+ 0x8A910BF7, 0x3FF06373, /* A01 = +1.024280110622155737232e+00. */
+ 0x8E6B601B, 0xBFB8270C, /* A02 = -9.434584118878357184013e-02. */
+ 0xD950A07E, 0xBFC8DD27, /* A03 = -1.942491351230763441116e-01. */
+ 0x91730CFC, 0xBF66470C, /* A00 = -2.719425723258004842786e-03. */
+ 0x68FCF331, 0x3FF073F4, /* A01 = +1.028309259519300633556e+00. */
+ 0x952191E4, 0xBFBB05C2, /* A02 = -1.055566419686964629854e-01. */
+ 0x770DE2BD, 0xBFC7886A, /* A03 = -1.838505822486435070662e-01. */
+ 0xAC8E98EC, 0xBF6AD114, /* A00 = -3.273525599485007861467e-03. */
+ 0xF53E5226, 0x3FF0861B, /* A01 = +1.032741506559554434119e+00. */
+ 0x9B461507, 0xBFBE0C4F, /* A02 = -1.173753503881763554650e-01. */
+ 0x037CDE3A, 0xBFC6302A, /* A03 = -1.733448521642786954722e-01. */
+ 0x2A6C2AF8, 0xBF6FFBDE, /* A00 = -3.904279630096648551207e-03. */
+ 0xEB8E7DA3, 0x3FF099F2, /* A01 = +1.037585182326304034106e+00. */
+ 0xD192DDF0, 0xBFC09C74, /* A02 = -1.297746680554463516444e-01. */
+ 0xD8E3079F, 0xBFC4D571, /* A03 = -1.627638157861470424859e-01. */
+ 0xC0B952AA, 0xBF72E8FD, /* A00 = -4.616728994353872309042e-03. */
+ 0x273C9533, 0x3FF0AF7F, /* A01 = +1.042845872181101141152e+00. */
+ 0x12736F10, 0xBFC244C5, /* A02 = -1.427236881344176033792e-01. */
+ 0x4F58B902, 0xBFC37947, /* A03 = -1.521386277613104298645e-01. */
+ 0xAF17395B, 0xBF762EAB, /* A00 = -5.415602341101023557701e-03. */
+ 0x886F63FB, 0x3FF0C6C3, /* A01 = +1.048526318502125631582e+00. */
+ 0x918EA12A, 0xBFC3FDF9, /* A02 = -1.561881981590514389957e-01. */
+ 0x9ECAB895, 0xBFC21CA8, /* A03 = -1.414995932913753196036e-01. */
+ 0xCE5B2BAE, 0xBF79D387, /* A00 = -6.305246822828998107258e-03. */
+ 0xE2346376, 0x3FF0DFBF, /* A01 = +1.054626353847394337748e+00. */
+ 0x43602620, 0xBFC5C6DA, /* A02 = -1.701309994680721970894e-01. */
+ 0xD8DB6631, 0xBFC0C08B, /* A03 = -1.308760460731704100557e-01. */
+ 0xE8DA9060, 0xBF7DDBA8, /* A00 = -7.289562037531366334164e-03. */
+ 0xF0D1B464, 0x3FF0FA70, /* A01 = +1.061142864894713433443e+00. */
+ 0xD92BAA7C, 0xBFC79E18, /* A02 = -1.845122394946264732241e-01. */
+ 0xF74C2669, 0xBFBECBBB, /* A03 = -1.202962378266875381749e-01. */
+ 0x76EA25DA, 0xBF81254E, /* A00 = -8.371937755572145950511e-03. */
+ 0x5835EBD0, 0x3FF116D0, /* A01 = +1.068069786618014660462e+00. */
+ 0x9E2ED224, 0xBFC98253, /* A02 = -1.992897531869327609755e-01. */
+ 0x3C350159, 0xBFBC1B04, /* A03 = -1.097872397413132278254e-01. */
+ 0xBA863403, 0xBF8391AC, /* A00 = -9.555196230190082448686e-03. */
+ 0xAA477FE2, 0x3FF134D4, /* A01 = +1.075398125794884141015e+00. */
+ 0x609FEAFB, 0xBFCB7218, /* A02 = -2.144194099235717521079e-01. */
+ 0x6CB88329, 0xBFB970A1, /* A03 = -9.937485603633135211599e-02. */
+ 0x88E48E8B, 0xBF879350, /* A00 = -1.151144902957603431692e-02. */
+ 0x92AD7DD3, 0x3FF16498, /* A01 = +1.087059567413110938716e+00. */
+ 0xDDE75409, 0xBFCE6971, /* A02 = -2.375929196847723912089e-01. */
+ 0xE88CB251, 0xBFB58291, /* A03 = -8.402358939628952472223e-02. */
+ 0x2C325325, 0xBF8DB3A6, /* A00 = -1.450280973794233242702e-02. */
+ 0x00C6DEEA, 0x3FF1A9C9, /* A01 = +1.103951457056548068891e+00. */
+ 0x65B0E08E, 0xBFD13DBC, /* A02 = -2.693930619311765140012e-01. */
+ 0xF62696D1, 0xBFB06696, /* A03 = -6.406539449252625362252e-02. */
+ 0x99F2E27A, 0xBF925836, /* A00 = -1.791463198307716858659e-02. */
+ 0xB85AA9F0, 0x3FF1F451, /* A01 = +1.122148246892376022288e+00. */
+ 0xF8288180, 0xBFD34FD5, /* A02 = -3.017477916164565954205e-01. */
+ 0x2825B683, 0xBFA6FB69, /* A03 = -4.488686194495718900788e-02. */
+ 0x6E673D6F, 0xBF9641C2, /* A00 = -2.173522757385398448959e-02. */
+ 0xDA5E2B07, 0x3FF24364, /* A01 = +1.141453602790251542487e+00. */
+ 0xA5EF5890, 0xBFD564A5, /* A02 = -3.342680092295120530821e-01. */
+ 0x2011A982, 0xBF9B4371, /* A03 = -2.662445791467283467968e-02. */
+ 0x38EC2F39, 0xBF9A9010, /* A00 = -2.594018313816024226548e-02. */
+ 0x56DFFEBA, 0x3FF29613, /* A01 = +1.161639537196534011088e+00. */
+ 0xB17198C7, 0xBFD775EB, /* A02 = -3.665723069046972759644e-01. */
+ 0x926CD462, 0xBF833B1A, /* A03 = -9.390075295963199591975e-03. */
+ 0x6A461B91, 0xBF9F396A, /* A00 = -3.049246095317987084727e-02. */
+ 0xBAEF534B, 0x3FF2EB53, /* A01 = +1.182452898229899629357e+00. */
+ 0xF8AD8BBD, 0xBFD97DAB, /* A02 = -3.982953957076310058660e-01. */
+ 0x3E0F8837, 0x3F7B8F6A, /* A03 = +6.728568086119371925713e-03. */
+ 0x590F8BAA, 0xBFA21878, /* A00 = -3.534294211546946951064e-02. */
+ 0x790236E1, 0x3FF34209, /* A01 = +1.203622315111197105253e+00. */
+ 0x0E71BECB, 0xBFDB764C, /* A02 = -4.290952817018306997277e-01. */
+ 0xC03F84C0, 0x3F962FE0, /* A03 = +2.166701482190513949888e-02. */
+ 0x9AD27ECC, 0xBFA4B36B, /* A00 = -4.043136849327097492868e-02. */
+ 0x5B12FC16, 0x3FF3990C, /* A01 = +1.224865298994477935679e+00. */
+ 0xB0D01390, 0xBFDD5AAB, /* A02 = -4.586590983092770912322e-01. */
+ 0x5CA162DB, 0x3FA21DAF, /* A03 = +3.538272863142363083844e-02. */
+ 0x4D7BF28B, 0xBFA7645E, /* A00 = -4.568762489177399105378e-02. */
+ 0xD51C0D9F, 0x3FF3EF2F, /* A01 = +1.245895225962932562069e+00. */
+ 0x7E1B686E, 0xBFDF2637, /* A02 = -4.867075664057044503963e-01. */
+ 0x756EE812, 0x3FA8803E, /* A03 = +4.785342391501513914509e-02. */
+ 0x25C64413, 0xBFAA2109, /* A00 = -5.103329263796054643398e-02. */
+ 0xF897D8E7, 0x3FF44349, /* A01 = +1.266427966181760345066e+00. */
+ 0x02C6D8E2, 0xBFE06A7B, /* A02 = -5.129981092675530707226e-01. */
+ 0x4734F5D0, 0x3FAE3F19, /* A03 = +5.907515520309980505687e-02. */
+ 0xF8A19BBB, 0xBFACDE48, /* A00 = -5.638340029764018351832e-02. */
+ 0xD5466582, 0x3FF49439, /* A01 = +1.286187966447272845727e+00. */
+ 0xC1063DDC, 0xBFE131C7, /* A02 = -5.373266954429101183166e-01. */
+ 0xC36AD805, 0x3FB1ADEE, /* A03 = +6.906025191241844940482e-02. */
+ 0x8F585680, 0xBFAF905D, /* A00 = -6.164829611604449866036e-02. */
+ 0x1FD27F99, 0x3FF4E0ED, /* A01 = +1.304913639360142818546e+00. */
+ 0x59DC1D3D, 0xBFE1E7A8, /* A02 = -5.595285182070380836095e-01. */
+ 0x8E4642A1, 0x3FB3ED01, /* A03 = +7.783517573831001679086e-02. */
+ 0x104160BA, 0xBFB11595, /* A00 = -6.673556944713512906198e-02. */
+ 0x0340490B, 0x3FF52865, /* A01 = +1.322361958217302513319e+00. */
+ 0xB40BC974, 0xBFE28B14, /* A02 = -5.794776455425521000109e-01. */
+ 0xF5BAF6D7, 0x3FB5DF49, /* A03 = +8.543836831355676453281e-02. */
+ 0x97344BA4, 0xBFB2513A, /* A00 = -7.155195418844911836587e-02. */
+ 0x0DB5EE14, 0x3FF569BA, /* A01 = +1.338312200124055273420e+00. */
+ 0xA8B67B20, 0xBFE31B53, /* A02 = -5.970857901737396389308e-01. */
+ 0x97BB0544, 0x3FB787F2, /* A03 = +9.191814617499455275507e-02. */
+ 0xE848FAFA, 0xBFB37512, /* A00 = -7.600515528700305112331e-02. */
+ 0x33B403C8, 0x3FF5A41F, /* A01 = +1.352568819013173495591e+00. */
+ 0xEA9A58A5, 0xBFE397F6, /* A02 = -6.123003561103997904880e-01. */
+ 0xFF25CA06, 0x3FB8EAA9, /* A03 = +9.733068923177520814782e-02. */
+ 0x603AFC5D, 0xBFB47B3E, /* A00 = -8.000554894805263217439e-02. */
+ 0xEDE40487, 0x3FF5D6E3, /* A01 = +1.364963464031718975988e+00. */
+ 0xBCA6D631, 0xBFE400D5, /* A02 = -6.251019177058819709103e-01. */
+ 0x0ED567FE, 0x3FBA0B83, /* A03 = +1.017381583418739132707e-01. */
+ 0x8AC90496, 0xBFB5BBFE, /* A00 = -8.489981544791400103200e-02. */
+ 0x70107E95, 0x3FF612BA, /* A01 = +1.379572332145390989311e+00. */
+ 0xF1FA7693, 0xBFE477EA, /* A02 = -6.396383978023599814478e-01. */
+ 0xB7C08A95, 0x3FBB4784, /* A03 = +1.065600346196709652391e-01. */
+ 0x40743939, 0xBFB6D5D9, /* A00 = -8.920057128509463473254e-02. */
+ 0x748F70CE, 0x3FF644A8, /* A01 = +1.391762214006166953340e+00. */
+ 0xAB07EA37, 0xBFE4D646, /* A02 = -6.511567440459832267763e-01. */
+ 0x4E1D5292, 0x3FBC354F, /* A03 = +1.101884427747086558913e-01. */
+ 0x19E4F3D1, 0xBFB7223D, /* A00 = -9.036619074045339206069e-02. */
+ 0xEB42B7FA, 0x3FF6518F, /* A01 = +1.394912642466350494175e+00. */
+ 0xCB87498C, 0xBFE4ED86, /* A02 = -6.539949393430091184598e-01. */
+ 0xF28CCA9B, 0x3FBC6D29, /* A03 = +1.110407082713131127205e-01. */
+ 0x52FF6312, 0xBFB68786, /* A00 = -8.800544287022329936754e-02. */
+ 0xC302D040, 0x3FF63948, /* A01 = +1.388985406648330922508e+00. */
+ 0xE7904E17, 0xBFE4C4E2, /* A02 = -6.490339777687407218920e-01. */
+ 0x56CA1ABE, 0x3FBC1273, /* A03 = +1.096565329445224612481e-01. */
+ 0x8B0C91D6, 0xBFB4F5D1, /* A00 = -8.187589306596207427980e-02. */
+ 0xEB7DD0B8, 0x3FF5FD27, /* A01 = +1.374305648697413673176e+00. */
+ 0x1A2B2FC6, 0xBFE464E0, /* A02 = -6.373138915164353601739e-01. */
+ 0x47674A30, 0x3FBB4605, /* A03 = +1.065371798825160976065e-01. */
+ 0xFA16A685, 0xBFB26642, /* A00 = -7.187288861919156890412e-02. */
+ 0xEDE1C95A, 0x3FF59F9B, /* A01 = +1.351467065073470141812e+00. */
+ 0x20C8FBEA, 0xBFE3D679, /* A02 = -6.199308052381387046381e-01. */
+ 0xA8D3CBC1, 0x3FBA24F6, /* A03 = +1.021265184570401413078e-01. */
+ 0x4794F097, 0xBFADB529, /* A00 = -5.802277563859197656582e-02. */
+ 0x7B9CF453, 0x3FF523EA, /* A01 = +1.321268542159732772845e+00. */
+ 0xB55E35DB, 0xBFE322A8, /* A02 = -5.979808370918208160205e-01. */
+ 0x3B1B3E37, 0x3FB8C867, /* A03 = +9.680791085269722928697e-02. */
+ 0x61965C6A, 0xBFA4B7D6, /* A00 = -4.046506825687219699450e-02. */
+ 0xE2CE3122, 0x3FF48DE3, /* A01 = +1.284641157110919085227e+00. */
+ 0xD1A7F445, 0xBFE251FE, /* A02 = -5.725092024655472622285e-01. */
+ 0x9FCABDB9, 0x3FB74569, /* A03 = +9.090290213747821701507e-02. */
+ 0x56E4EE1D, 0xBF93E604, /* A00 = -1.943213253365004902773e-02. */
+ 0x4E628A59, 0x3FF3E1A1, /* A01 = +1.242585474196536532432e+00. */
+ 0xB660E876, 0xBFE16C5A, /* A02 = -5.444768488007543094653e-01. */
+ 0xAA8C188F, 0x3FB5AD33, /* A03 = +8.467410005332197397987e-02. */
+ 0xC47C7961, 0x3F738C17, /* A00 = +4.772274820224659853951e-03. */
+ 0xDE3BD146, 0x3FF3234D, /* A01 = +1.196119182682268355933e+00. */
+ 0xD77A9D3B, 0xBFE078C0, /* A02 = -5.147403915952176722826e-01. */
+ 0xB3E276B8, 0x3FB40D74, /* A03 = +7.833032027925923568290e-02. */
+ 0xECC689C7, 0x3FA0474B, /* A00 = +3.179394975019849550746e-02. */
+ 0x4FA7D18A, 0x3FF256FB, /* A01 = +1.146235762743432307076e+00. */
+ 0x3FB285E2, 0xBFDEFA8E, /* A02 = -4.840427038235174395098e-01. */
+ 0x07493D59, 0x3FB270C0, /* A03 = +7.203293016322244446403e-02. */
+ 0x1E479BDC, 0x3FAF5BD5, /* A00 = +6.124750132203590768931e-02. */
+ 0xD0B53BC5, 0x3FF18081, /* A01 = +1.093873801484492647162e+00. */
+ 0x39BD0C03, 0xBFDCFE24, /* A02 = -4.530115665294831006626e-01. */
+ 0x5A45AFDD, 0x3FB0DEFE, /* A03 = +6.590261176978580437424e-02. */
+ 0x2806EA26, 0x3FB7BD5D, /* A00 = +9.273321368429118805032e-02. */
+ 0xE35B4440, 0x3FF0A369, /* A01 = +1.039895904647224256223e+00. */
+ 0x5C9951E7, 0xBFDB04BC, /* A02 = -4.221640495573226181669e-01. */
+ 0xA9D6DEEF, 0x3FAEBBBA, /* A03 = +6.002600978120919278380e-02. */
+ 0x11098DBC, 0x3FC01BE4, /* A00 = +1.258511622610124502941e-01. */
+ 0xABC031C1, 0x3FEF85BD, /* A01 = +9.850757936961188621083e-01. */
+ 0x375097C2, 0xBFD91521, /* A02 = -3.919146576102968682065e-01. */
+ 0x0086D982, 0x3FABE26F, /* A03 = +5.446192628317005068883e-02. */
+ 0xFF5776B9, 0x3FC481D7, /* A00 = +1.602125164781023347604e-01. */
+ 0x6C1E7218, 0x3FEDC350, /* A01 = +9.300920592973538347792e-01. */
+ 0x88DA7D4F, 0xBFD7349A, /* A02 = -3.625856720409119104964e-01. */
+ 0xDFF8E2AE, 0x3FA936E2, /* A03 = +4.924687370334389358018e-02. */
+ 0xF96FA27A, 0x3FC90471, /* A00 = +1.954481571149420671141e-01. */
+ 0x601987A2, 0x3FEC0451, /* A01 = +8.755270840595026360376e-01. */
+ 0xD4B898DC, 0xBFD5671C, /* A02 = -3.344184949259110251063e-01. */
+ 0x94603B67, 0x3FA6BB95, /* A03 = +4.439990459660841243261e-02. */
+ 0xB9ED944C, 0x3FCFD8AD, /* A00 = +2.488000066615846384011e-01. */
+ 0x73F6809A, 0x3FE978C0, /* A01 = +7.959902062321078108909e-01. */
+ 0x00BCD5A9, 0xBFD2DF7E, /* A02 = -2.948908812716931060471e-01. */
+ 0x33D490B2, 0x3FA36140, /* A03 = +3.785133965200894456959e-02. */
+ 0x12AFE5A0, 0x3FD4846A, /* A00 = +3.205819303981005674586e-01. */
+ 0x47D40472, 0x3FE63A11, /* A01 = +6.945883181471244061100e-01. */
+ 0x8AD34450, 0xBFCFA226, /* A02 = -2.471359422548027318101e-01. */
+ 0x01D9FFE0, 0x3F9F1502, /* A03 = +3.035357605267552383310e-02. */
+ 0x41F82BEB, 0x3FD90186, /* A00 = +3.907180446846598154131e-01. */
+ 0x220FFBDC, 0x3FE33B7C, /* A01 = +6.010113396913498995389e-01. */
+ 0x87E29C86, 0xBFCA4E41, /* A02 = -2.055131829740483584423e-01. */
+ 0xED19F8F4, 0x3F98C30C, /* A03 = +2.418155858185229434287e-02. */
+ 0x55BEB078, 0x3FDD4B82, /* A00 = +4.577337109901757905561e-01. */
+ 0x19D3A49B, 0x3FE0858B, /* A01 = +5.163016800335243905451e-01. */
+ 0x9EACE564, 0xBFC5BC92, /* A02 = -1.698172831327539045176e-01. */
+ 0xCE57DE2B, 0x3F93A083, /* A03 = +1.916700312537337677621e-02. */
+ 0xE039295C, 0x3FE0A8E5, /* A00 = +5.206174258576470315063e-01. */
+ 0x234583FE, 0x3FDC35E1, /* A01 = +4.407885403107342225937e-01. */
+ 0x4E31AEB9, 0xBFC1DE03, /* A02 = -1.395877963835710222629e-01. */
+ 0xB3471BDC, 0x3F8EFDEB, /* A03 = +1.513275280821162888101e-02. */
+ 0x603CB2A5, 0x3FE2851B, /* A00 = +5.787484054213406503564e-01. */
+ 0x4ABBB286, 0x3FD7F4A4, /* A01 = +3.743067483726821853551e-01. */
+ 0x67087DE7, 0xBFBD3EEB, /* A02 = -1.142413260026767657385e-01. */
+ 0x8329E8BD, 0x3F8864F3, /* A03 = +1.191129917173260922836e-02. */
+ 0xE3C34AC1, 0x3FE437DB, /* A00 = +6.318187187665317283702e-01. */
+ 0x789441B5, 0x3FD43F6F, /* A01 = +3.163717916040938438194e-01. */
+ 0x7901B9A4, 0xBFB7D92E, /* A02 = -9.315767721429907277653e-02. */
+ 0x342308E1, 0x3F8327ED, /* A03 = +9.353497651663324544136e-03. */
+ 0x7766D55C, 0x3FE5C097, /* A00 = +6.797597248138731451661e-01. */
+ 0xA764D8F9, 0x3FD10B42, /* A01 = +2.663122782427219115142e-01. */
+ 0x51D3D70F, 0xBFB36333, /* A02 = -7.573242900602060456716e-02. */
+ 0x30FF899C, 0x3F7E079E, /* A03 = +7.331483779099558922843e-03. */
+ 0xE08A88C4, 0x3FE7202C, /* A00 = +7.226776490754436288455e-01. */
+ 0xB5662B01, 0x3FCC973E, /* A01 = +2.233656297433626314319e-01. */
+ 0x55F9920B, 0xBFAF70A4, /* A02 = -6.140626477716545211782e-02. */
+ 0x11CE99B6, 0x3F778124, /* A03 = +5.738392731393584730859e-03. */
+ 0x424095B1, 0x3FE85879, /* A00 = +7.608000082006382003286e-01. */
+ 0xD1674D84, 0x3FC7E73B, /* A01 = +1.867441914060742336190e-01. */
+ 0xE4BF333B, 0xBFA96F84, /* A02 = -4.967894832916504993525e-02. */
+ 0xDCA6E117, 0x3F72606D, /* A03 = +4.486493251924870105662e-03. */
+ 0x4957F4DD, 0x3FE96BFE, /* A00 = +7.944327766887472330737e-01. */
+ 0x80D25478, 0x3FC3ED47, /* A01 = +1.556786898624158421711e-01. */
+ 0xF9A56B58, 0xBFA489C5, /* A02 = -4.011362717093075458408e-02. */
+ 0x17E9AD2A, 0x3F6CB5DC, /* A03 = +3.504686231556104931972e-03. */
+ 0xB2F41234, 0x3FEA5D9C, /* A00 = +8.239272589858672724006e-01. */
+ 0x58374DCF, 0x3FC091A7, /* A01 = +1.294449978582705440555e-01. */
+ 0x6D4B5CE0, 0xBFA08E43, /* A02 = -3.233538350257858517978e-02. */
+ 0xAD53E6B7, 0x3F666997, /* A03 = +2.735897297154145629133e-03. */
+ 0x342CB850, 0x3FEB3060, /* A00 = +8.496552485501158713532e-01. */
+ 0xBBC7DC1B, 0x3FBB7D30, /* A01 = +1.073790033768634993860e-01. */
+ 0x3443D9E3, 0xBF9AA6BA, /* A02 = -2.602663940430173170060e-02. */
+ 0x64B7850B, 0x3F617CA7, /* A03 = +2.134634914668814050648e-03. */
+ 0xA6A0C7B8, 0x3FEBE759, /* A00 = +8.719909910635044170135e-01. */
+ 0xE6A703FF, 0x3FB6C10D, /* A01 = +8.888327485239243264115e-02. */
+ 0x6D8BE1F6, 0xBF956C56, /* A02 = -2.092108768099084498138e-02. */
+ 0xA4A59CF8, 0x3F5B46D1, /* A03 = +1.664833764687232917079e-03. */
+ 0x94887A04, 0x3FEC8584, /* A00 = +8.912985707318630268503e-01. */
+ 0xF543394D, 0x3FB2CC31, /* A01 = +7.342827070099140762682e-02. */
+ 0x7FF69137, 0xBF913347, /* A02 = -1.679717749142747504343e-02. */
+ 0x2FBB4DA5, 0x3F554448, /* A03 = +1.298017973501022466823e-03. */
+ 0x9D0E32E9, 0x3FED0DB5, /* A00 = +9.079235141267335551518e-01. */
+ 0xAFFC6EF4, 0x3FAF006B, /* A01 = +6.055008433597022787787e-02. */
+ 0x6FA2B97A, 0xBF8B9714, /* A02 = -1.347175565419144252499e-02. */
+ 0x1F4CDC69, 0x3F5093B0, /* A03 = +1.011774057770665211434e-03. */
+ 0xC3EC457C, 0x3FEDB487, /* A00 = +9.282873942012623835751e-01. */
+ 0x09D0BD1D, 0x3FA7390C, /* A01 = +4.535710925881118044112e-02. */
+ 0xC3181106, 0xBF83D9F7, /* A02 = -9.693084374710735778846e-03. */
+ 0x0A3C0E64, 0x3F46E34A, /* A03 = +6.984817050299072134500e-04. */
+ 0xB4E6EB00, 0x3FEE5FFC, /* A00 = +9.492171796076434020506e-01. */
+ 0xED00AADF, 0x3F9F4913, /* A01 = +3.055220731782070861526e-02. */
+ 0xD0E59B5C, 0xBF79670B, /* A02 = -6.201788097633133961528e-03. */
+ 0xEBCAF96D, 0x3F3BC998, /* A03 = +4.240034429975534616304e-04. */
+ 0x1E9542FE, 0x3FEEDBA4, /* A00 = +9.643116566968215064293e-01. */
+ 0x18D9C24D, 0x3F94F5DD, /* A01 = +2.046914543319848858727e-02. */
+ 0x6AA122B9, 0xBF703489, /* A02 = -3.956352980886528904192e-03. */
+ 0x47810B39, 0x3F30DCCB, /* A03 = +2.573009765038273091199e-04. */
+ 0x882520ED, 0x3FEF33F2, /* A00 = +9.750912341196716903724e-01. */
+ 0x2CF553FF, 0x3F8BF37F, /* A01 = +1.364802699996836392315e-02. */
+ 0x05A69619, 0xBF649F6F, /* A02 = -2.517430152880317534986e-03. */
+ 0xC950AAC9, 0x3F247623, /* A03 = +1.561087307505231250044e-04. */
+ 0x57751741, 0x3FEF7277, /* A00 = +9.827229221489021115943e-01. */
+ 0x912C4400, 0x3F828E67, /* A01 = +9.060677640748693306705e-03. */
+ 0xA806CC2C, 0xBF5A2F51, /* A02 = -1.598195784123355826789e-03. */
+ 0x7687E613, 0x3F18D35D, /* A03 = +9.470231965016282719549e-05. */
+ 0x25C5942A, 0x3FEF9E63, /* A00 = +9.880843866091073568469e-01. */
+ 0x17618F76, 0x3F788AB1, /* A01 = +5.991641772286606867914e-03. */
+ 0xB0B1EA89, 0xBF5096EA, /* A02 = -1.012543859160305046233e-03. */
+ 0xEC4435AB, 0x3F0E1E50, /* A03 = +5.744633156910412119652e-05. */
+ 0x84049369, 0x3FEFBD07, /* A00 = +9.918248728250605994461e-01. */
+ 0x8294035F, 0x3F702BBD, /* A01 = +3.947963975634432264028e-03. */
+ 0xE0F00593, 0xBF44FB55, /* A02 = -6.403130845457509273330e-04. */
+ 0xD723230A, 0x3F0244DC, /* A03 = +3.484534217219031730379e-05. */
+ 0xE2366A43, 0x3FEFD245, /* A00 = +9.944180887426415926811e-01. */
+ 0xEC088433, 0x3F653D82, /* A01 = +2.592807490387838333795e-03. */
+ 0x5E013CB8, 0xBF3A7DF7, /* A02 = -4.042366908878036561859e-04. */
+ 0x69F991CD, 0x3EF6298E, /* A03 = +2.113564425911141559972e-05. */
+ 0xA508BC69, 0x3FEFE0EA, /* A00 = +9.962056372950317539861e-01. */
+ 0x1AF3FDDA, 0x3F5BD077, /* A01 = +1.697651208644282514598e-03. */
+ 0x254DE571, 0xBF30B2E1, /* A02 = -2.548026725928887099328e-04. */
+ 0x70EC0256, 0x3EEAE28B, /* A03 = +1.281973848454955042307e-05. */
+ 0x303D7F96, 0x3FEFEAF5, /* A00 = +9.974313680831865536192e-01. */
+ 0x1365657E, 0x3F522911, /* A01 = +1.108423877289460134782e-03. */
+ 0xD04DFE66, 0xBF250572, /* A02 = -1.603796628408704519168e-04. */
+ 0xBB57C981, 0x3EE04E89, /* A03 = +7.775682983689149966743e-06. */
+ 0x52F1CF44, 0x3FEFF1CF, /* A00 = +9.982678051005469122003e-01. */
+ 0x16147CEB, 0x3F47A713, /* A01 = +7.218211359577819110842e-04. */
+ 0x04055719, 0xBF1A6D76, /* A02 = -1.008132248946049582547e-04. */
+ 0x7586A85C, 0x3ED3C804, /* A03 = +4.716233739913014633626e-06. */
+ 0x0369EF69, 0x3FEFF677, /* A00 = +9.988360468555416149528e-01. */
+ 0x1180FBF0, 0x3F3EBB26, /* A01 = +4.689186039321105101130e-04. */
+ 0x4FE19D7F, 0xBF109775, /* A02 = -6.329206004950480057066e-05. */
+ 0x83BCA0A7, 0x3EC7FEFF, /* A03 = +2.860556404988488738366e-06. */
+ 0x42371AC4, 0x3FEFF99D, /* A00 = +9.992204945818561334647e-01. */
+ 0xEC271F59, 0x3F33EB2A, /* A01 = +3.039340773764907474054e-04. */
+ 0xE0FC0D79, 0xBF04CF18, /* A02 = -3.968996690952969588805e-05. */
+ 0xD6019BE9, 0x3EBD1BDB, /* A03 = +1.735021065507727833886e-06. */
+ 0xA32B0D91, 0x3FEFFBBC, /* A00 = +9.994795977476532700123e-01. */
+ 0x1615110A, 0x3F29C41E, /* A01 = +1.965796209707565346710e-04. */
+ 0x3D9DCB5A, 0xBEFA11F9, /* A02 = -2.486248909101414873235e-05. */
+ 0x4546F7A7, 0x3EB1A7CA, /* A03 = +1.052345642723709228769e-06. */
+ 0x8B8E8DE2, 0x3FEFFD29, /* A00 = +9.996535993308806045121e-01. */
+ 0x2D523C5B, 0x3F20A1C4, /* A01 = +1.268913244172078754520e-04. */
+ 0x364AFAE4, 0xBEF0507A, /* A02 = -1.555859070622834605755e-05. */
+ 0x17E7CDF4, 0x3EA56ACA, /* A03 = +6.382806956848098872313e-07. */
+ 0xC82BA5A3, 0x3FEFFE1D, /* A00 = +9.997700604991915929176e-01. */
+ 0xB90F1769, 0x3F156E73, /* A01 = +8.175450626798714452801e-05. */
+ 0x79D0A09F, 0xBEE46635, /* A02 = -9.727122057226747625365e-06. */
+ 0xFEC5D4C1, 0x3E99FAF6, /* A03 = +3.871371052824002996020e-07. */
+ 0xD0BB5E81, 0x3FEFFEF8, /* A00 = +9.998745037837154514548e-01. */
+ 0xA18D39C3, 0x3F06686D, /* A01 = +4.273972098777251447726e-05. */
+ 0x98073E90, 0xBED46BC2, /* A02 = -4.868731025855742842491e-06. */
+ 0x86B9D0FD, 0x3E88E422, /* A03 = +1.854535328530838170114e-07. */
+ 0xBC68DDC7, 0x3FEFFF8D, /* A00 = +9.999455146670975791423e-01. */
+ 0x53A80AF0, 0x3EF26B29, /* A01 = +1.756534514108903368909e-05. */
+ 0x2D580F83, 0xBEBFC447, /* A02 = -1.893443529411295465239e-06. */
+ 0x4553D19F, 0x3E72505B, /* A03 = +6.822456673547912277047e-08. */
+ 0xD1276609, 0x3FEFFFCE, /* A00 = +9.999765477215883935358e-01. */
+ 0xC7CC58F5, 0x3EDE1A94, /* A01 = +7.177313020153979672606e-06. */
+ 0x88744E57, 0xBEA8A2C9, /* A02 = -7.342066660497443762363e-07. */
+ 0x36BBBAF4, 0x3E5AF300, /* A03 = +2.509841882843541084885e-08. */
+ 0xFE70FCFC, 0x3FEFFFEA, /* A00 = +9.999899835164849370983e-01. */
+ 0x5E3549F5, 0x3EC87917, /* A01 = +2.917410471128503564412e-06. */
+ 0x677D1813, 0xBE930E36, /* A02 = -2.839493400307523115929e-07. */
+ 0x5B42D48F, 0x3E43D400, /* A03 = +9.233192745401904898013e-09. */
+ 0x00000000, 0x3ff00000,
+ 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000)
+
+ .align 32
+ .type __svml_stanh_common_data_avx2, @object
+ .size __svml_stanh_common_data_avx2, .-__svml_stanh_common_data_avx2
+# endif
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (4 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 06/27] x86/fpu: Update rodata usage in svml_s_tanhf_*_{avx2, sse4} Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-16 17:05 ` H.J. Lu via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 08/27] x86/fpu: Update rodata usage in svml_s_atanhf16_core_avx512.S Noah Goldstein via Libc-alpha
` (20 subsequent siblings)
26 siblings, 1 reply; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
No changes to the logic, just change how rodata is handled.
1. Define the rodatas using the new macros so they check that the
offset is correct.
2. Use common data where applicable.
---
.../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
1 file changed, 197 insertions(+), 253 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
index d74fc7731d..765e9ed7f7 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
@@ -70,94 +70,99 @@
*
*/
-/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
- by use in the function. On cold-starts this might help the
- prefetcher. Possibly a better idea is to interleave start/end so
- that the prefetcher is less likely to detect a stream and pull
- irrelivant lines into cache. */
-/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
- */
+
+#define LOCAL_DATA_NAME __svml_stanh_data_internal
+#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+/* Offsets for data table __svml_stanh_data_internal_unaligned.
+ 4 bytes each. */
#define _iExpMantMask_UISA 0
#define _iMinIdxOfsMask_UISA 4
#define _iMaxIdxMask_UISA 8
#define _iExpMask 12
-/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
- each. */
-#define _sC_lo 0
-#define _sC_hi 64
-#define _sP7_lo 128
-#define _sP7_hi 192
-#define _sSignMask 256
-#define _sP6_lo 320
-#define _sP6_hi 384
-#define _sP5_lo 448
-#define _sP5_hi 512
-#define _sP4_lo 576
-#define _sP4_hi 640
-#define _sP3_lo 704
-#define _sP3_hi 768
-#define _sP2_lo 832
-#define _sP2_hi 896
-#define _sP0_lo 960
-#define _sP0_hi 1024
+/* Offsets for data table __svml_stanh_data_internal. Ordered
+ by use in the function. On cold-starts this might help the
+ prefetcher. Possibly a better idea is to interleave start/end so
+ that the prefetcher is less likely to detect a stream and pull
+ irrelivant lines into cache. */
+
+/* Offsets for data table __svml_stanh_data_internal.
+ 64 bytes each. */
+#define _sC_lo 0
+#define _sC_hi 64
+#define _sP7_lo 128
+#define _sP7_hi 192
+#define _sP6_lo 256
+#define _sP6_hi 320
+#define _sP5_lo 384
+#define _sP5_hi 448
+#define _sP4_lo 512
+#define _sP4_hi 576
+#define _sP3_lo 640
+#define _sP3_hi 704
+#define _sP2_lo 768
+#define _sP2_hi 832
+#define _sP0_lo 896
+#define _sP0_hi 960
+
#include <sysdep.h>
-#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
-#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_tanhf_skx)
- /* Here huge arguments, INF and NaNs are filtered out to callout. */
- vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
- vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
+ /* Here huge arguments, INF and NaNs are filtered out to
+ callout. */
+ vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
+ vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
/* Selection arguments between [0, 0x03e00000] into zmm3. */
vpxord %zmm3, %zmm3, %zmm3
vpmaxsd %zmm3, %zmm2, %zmm3
- vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
+ vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
/* Setup permute indices in zmm3. */
vpsrld $21, %zmm3, %zmm3
/* Store if there are any special cases in k1. */
- vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
+ vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
- vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
- vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
+ vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
+ vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
- vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
- vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
+ vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
+ vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
/* Store absolute values of inputs in zmm1. */
- vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
+ vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
vandnps %zmm0, %zmm4, %zmm1
vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
- vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
- vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
+ vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
+ vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
- vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
- vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
+ vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
+ vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
- vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
- vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
+ vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
+ vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
- vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
- vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
+ vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
+ vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
- vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
- vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
+ vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
+ vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
- vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
- vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
+ vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
+ vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
@@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
/* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
+
/* Wait until after branch of write over zmm0. */
vpternlogd $0xec, %zmm4, %zmm2, %zmm0
@@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a tanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
- /* Use r13 to save/restore the stack. This allows us to use rbp as
- callee save register saving code size. */
+
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
pushq %r13
- cfi_adjust_cfa_offset(8)
- cfi_offset(r13, -16)
- /* Need to callee save registers to preserve state across tanhf calls.
- */
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
pushq %rbx
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbx, -24)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
pushq %rbp
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbp, -32)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
movq %rsp, %r13
- cfi_def_cfa_register(r13)
+ cfi_def_cfa_register (r13)
/* Align stack and make room for 2x zmm vectors. */
andq $-64, %rsp
@@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
vzeroupper
- /* edx has 1s where there was a special value that needs to be handled
- by a tanhf call. */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- tanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 56] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. Realigning also costs more code size. */
+
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
xorl %ebp, %ebp
tzcntl %ebx, %ebp
@@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
vmovss 64(%rsp, %rbp, 4), %xmm0
call tanhf@PLT
- /* No good way to avoid the store-forwarding fault this will cause on
- return. `lfence` avoids the SF fault but at greater cost as it
- serialized stack/callee save restoration. */
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
vmovss %xmm0, (%rsp, %rbp, 4)
- blsrl %ebx, %ebx
+ blsrl %ebx, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
+
/* All results have been written to (%rsp). */
vmovaps (%rsp), %zmm0
/* Restore rsp. */
movq %r13, %rsp
- cfi_def_cfa_register(rsp)
+ cfi_def_cfa_register (rsp)
/* Restore callee save registers. */
popq %rbp
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %rbx
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %r13
- cfi_adjust_cfa_offset(-8)
- cfi_restore(r13)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
ret
END(_ZGVeN16v_tanhf_skx)
- .section .rodata, "a"
+ .section .rodata.evex512, "a"
.align 16
-#ifdef __svml_stanh_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct
- {
- __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
- __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
- __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
- __declspec(align(4)) VUINT32 _iExpMask[1][1];
- __declspec(align(64)) VUINT32 _sC_lo[16][1];
- __declspec(align(64)) VUINT32 _sC_hi[16][1];
- __declspec(align(64)) VUINT32 _sP7_lo[16][1];
- __declspec(align(64)) VUINT32 _sP7_hi[16][1];
- __declspec(align(64)) VUINT32 _sSignMask[16][1];
- __declspec(align(64)) VUINT32 _sP6_lo[16][1];
- __declspec(align(64)) VUINT32 _sP6_hi[16][1];
- __declspec(align(64)) VUINT32 _sP5_lo[16][1];
- __declspec(align(64)) VUINT32 _sP5_hi[16][1];
- __declspec(align(64)) VUINT32 _sP4_lo[16][1];
- __declspec(align(64)) VUINT32 _sP4_hi[16][1];
- __declspec(align(64)) VUINT32 _sP3_lo[16][1];
- __declspec(align(64)) VUINT32 _sP3_hi[16][1];
- __declspec(align(64)) VUINT32 _sP2_lo[16][1];
- __declspec(align(64)) VUINT32 _sP2_hi[16][1];
- __declspec(align(64)) VUINT32 _sP0_lo[16][1];
- __declspec(align(64)) VUINT32 _sP0_hi[16][1];
-} __svml_stanh_data_internal;
-#endif
-
-__svml_stanh_data_internal:
- .align 4
- /* _iExpMantMask_UISA */
- .long 0x7fe00000
-
- .align 4
- /* _iMinIdxOfsMask_UISA */
- .long 0x3d400000
-
- .align 4
- /* _iMaxIdxMask_UISA */
- .long 0x03e00000
-
- .align 4
- /* _iExpMask */
- .long 0x7f000000
-
- .align 64
-__svml_stanh_data_internal_al64:
- .align 64
- /* _sC_lo */
- .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
- .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
- .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
- .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
-
- .align 64
- /* _sC_hi */
- .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
- .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
- .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
- .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
-
- .align 64
- /* _sP7_lo */
- .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
- .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
- .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
- .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
-
- .align 64
- /* _sP7_hi */
- .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
- .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
- .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
- .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
- .align 64
- /* _sSignMask */
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
-
- .align 64
- /* _sP6_lo */
- .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
- .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
- .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
- .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
-
- .align 64
- /* _sP6_hi */
- .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
- .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
- .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
- .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
-
- .align 64
- /* _sP5_lo */
- .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
- .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
- .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
- .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
-
- .align 64
- /* _sP5_hi */
- .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
- .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
- .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
- .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
-
- .align 64
- /* _sP4_lo */
- .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
- .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
- .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
- .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
-
- .align 64
- /* _sP4_hi */
- .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
- .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
- .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
- .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
-
- .align 64
- /* _sP3_lo */
- .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
- .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
- .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
- .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
-
- .align 64
- /* _sP3_hi */
- .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
- .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
- .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
- .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
-
- .align 64
- /* _sP2_lo */
- .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
- .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
- .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
- .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
-
- .align 64
- /* _sP2_hi */
- .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
- .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
- .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
- .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
-
- .align 64
- /* _sP0_lo */
- .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
- .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
- .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
- .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
-
- .align 64
- /* _sP0_hi */
- .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
- .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
- .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
- .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
+LOCAL_DATA_NAME_UNALIGNED:
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
+ .type LOCAL_DATA_NAME_UNALIGNED, @object
+ .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
.align 64
- .type __svml_stanh_data_internal_al64, @object
- .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
- .type __svml_stanh_data_internal, @object
- .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
+LOCAL_DATA_NAME:
+ float_block (LOCAL_DATA_NAME, _sC_lo,
+ 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
+ 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
+ 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
+ 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
+
+ float_block (LOCAL_DATA_NAME, _sC_hi,
+ 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
+ 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
+ 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
+ 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP7_lo,
+ 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
+ 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
+ 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
+ 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
+
+ float_block (LOCAL_DATA_NAME, _sP7_hi,
+ 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
+ 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
+ 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
+ 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP6_lo,
+ 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
+ 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
+ 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
+ 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
+
+ float_block (LOCAL_DATA_NAME, _sP6_hi,
+ 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
+ 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
+ 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
+ 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP5_lo,
+ 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
+ 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
+ 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
+ 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
+
+ float_block (LOCAL_DATA_NAME, _sP5_hi,
+ 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
+ 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
+ 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
+ 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP4_lo,
+ 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
+ 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
+ 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
+ 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
+
+ float_block (LOCAL_DATA_NAME, _sP4_hi,
+ 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
+ 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
+ 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
+ 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP3_lo,
+ 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
+ 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
+ 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
+ 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
+
+ float_block (LOCAL_DATA_NAME, _sP3_hi,
+ 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
+ 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
+ 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
+ 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP2_lo,
+ 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
+ 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
+ 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
+ 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
+
+ float_block (LOCAL_DATA_NAME, _sP2_hi,
+ 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
+ 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
+ 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
+ 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
+
+ float_block (LOCAL_DATA_NAME, _sP0_lo,
+ 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
+ 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
+ 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
+ 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
+
+ float_block (LOCAL_DATA_NAME, _sP0_hi,
+ 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
+ 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
+ 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
+ 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 08/27] x86/fpu: Update rodata usage in svml_s_atanhf16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (5 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 09/27] x86/fpu: Update rodata usage in svml_s_atanhf4_core_sse4.S Noah Goldstein via Libc-alpha
` (19 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
No changes to the logic, just change how rodata is handled.
1. Define the rodatas using the new macros so they check that the
offset is correct.
2. Use common data where applicable.
---
.../multiarch/svml_s_atanhf16_core_avx512.S | 416 +++++++-----------
1 file changed, 171 insertions(+), 245 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S
index 07094cc82f..4e6af8ddf9 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S
@@ -31,101 +31,96 @@
*
*/
-/* Offsets for data table __svml_satanh_data_internal_avx512 and
- __svml_satanh_data_internal_avx512_al64. Ordered by use in the
- function. On cold-starts this might help the prefetcher. Possibly
- a better idea is to interleave start/end so that the prefetcher is
- less likely to detect a stream and pull irrelivant lines into
- cache. */
-
-/* Offset into __svml_satanh_data_internal_avx512. 4-byte aligned as
- the memory is broadcast to {1to16}. */
-#define AbsMask 0
-
-/* Offset into __svml_satanh_data_internal_avx512_al64. The full value
- is used here. */
-#define One 0
-#define AddB5 64
-#define RcpBitMask 128
-#define Log_tbl_L_lo 192
-#define Log_tbl_L_hi 256
-#define Log_tbl_H_lo 320
-#define Log_tbl_H_hi 384
-#define L2H 448
-#define L2L 512
-#define poly_coeff3 576
-#define poly_coeff2 640
-#define poly_coeff1 704
+#define LOCAL_DATA_NAME __svml_satanh_data_internal
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+/* Offsets for data table __svml_satanh_data_internal are Ordered by
+ use in the function. On cold-starts this might help the
+ prefetcher. Possibly a better idea is to interleave start/end so
+ that the prefetcher is less likely to detect a stream and pull
+ irrelivant lines into cache. */
+
+/* Offset into __svml_satanh_data_internal. 64 bytes each. */
+#define AddB5 0
+#define RcpBitMask 64
+#define Log_tbl_L_lo 128
+#define Log_tbl_L_hi 192
+#define Log_tbl_H_lo 256
+#define Log_tbl_H_hi 320
+#define L2H 384
+#define L2L 448
+#define poly_coeff3 512
+#define poly_coeff2 576
+#define poly_coeff1 640
-#include <sysdep.h>
-#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal_avx512_al64)
+#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_atanhf_skx)
- vandps AbsMask+__svml_satanh_data_internal_avx512(%rip){1to16}, %zmm0, %zmm6
- vmovups ATANHF_DATA(One)(%rip), %zmm4
+ vandps COMMON_DATA(_AbsMask)(%rip){1to16}, %zmm0, %zmm6
+ vmovups COMMON_DATA(_OneF)(%rip), %zmm4
- /* 1+y */
+ /* 1+y. */
vaddps {rn-sae}, %zmm4, %zmm6, %zmm9
- /* 1-y */
+ /* 1-y. */
vsubps {rn-sae}, %zmm6, %zmm4, %zmm8
- /* round reciprocals to 1+5b mantissas */
- vmovups ATANHF_DATA(AddB5)(%rip), %zmm14
- vmovups ATANHF_DATA(RcpBitMask)(%rip), %zmm1
+ /* round reciprocals to 1+5b mantissas. */
+ vmovups LOCAL_DATA(AddB5)(%rip), %zmm14
+ vmovups LOCAL_DATA(RcpBitMask)(%rip), %zmm1
- /* RcpP ~ 1/Yp */
+ /* RcpP ~ 1/Yp. */
vrcp14ps %zmm9, %zmm12
- /* RcpM ~ 1/Ym */
+ /* RcpM ~ 1/Ym. */
vrcp14ps %zmm8, %zmm13
- /* Yp_high */
+ /* Yp_high. */
vsubps {rn-sae}, %zmm4, %zmm9, %zmm2
- /* -Ym_high */
+ /* -Ym_high. */
vsubps {rn-sae}, %zmm4, %zmm8, %zmm5
- /* input outside (-1, 1) ? */
+ /* input outside (-1, 1) ? */
vpaddd %zmm14, %zmm12, %zmm15
vpaddd %zmm14, %zmm13, %zmm12
- /* Yp_low */
+ /* Yp_low. */
vsubps {rn-sae}, %zmm2, %zmm6, %zmm3
vandps %zmm1, %zmm15, %zmm7
vandps %zmm1, %zmm12, %zmm12
- /* Ym_low */
+ /* Ym_low. */
vaddps {rn-sae}, %zmm5, %zmm6, %zmm5
- /* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low */
+ /* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low. */
vfmsub213ps {rn-sae}, %zmm4, %zmm7, %zmm9
- /* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low */
+ /* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low. */
vfmsub213ps {rn-sae}, %zmm4, %zmm12, %zmm8
- vmovups ATANHF_DATA(Log_tbl_L_lo)(%rip), %zmm10
- vmovups ATANHF_DATA(Log_tbl_L_hi)(%rip), %zmm13
+ vmovups LOCAL_DATA(Log_tbl_L_lo)(%rip), %zmm10
+ vmovups LOCAL_DATA(Log_tbl_L_hi)(%rip), %zmm13
- /* exponents */
+ /* exponents. */
vfmadd231ps {rn-sae}, %zmm7, %zmm3, %zmm9
vgetexpps {sae}, %zmm7, %zmm15
- /* Table lookups */
+ /* Table lookups. */
vfnmadd231ps {rn-sae}, %zmm12, %zmm5, %zmm8
vgetexpps {sae}, %zmm12, %zmm14
- /* Prepare table index */
+ /* Prepare table index. */
vpsrld $18, %zmm7, %zmm3
vpsrld $18, %zmm12, %zmm2
- vmovups ATANHF_DATA(Log_tbl_H_lo)(%rip), %zmm11
- vmovups ATANHF_DATA(Log_tbl_H_hi)(%rip), %zmm7
- /* Km-Kp */
+ vmovups LOCAL_DATA(Log_tbl_H_lo)(%rip), %zmm11
+ vmovups LOCAL_DATA(Log_tbl_H_hi)(%rip), %zmm7
+ /* Km-Kp. */
vmovaps %zmm3, %zmm5
vpermi2ps %zmm13, %zmm10, %zmm3
@@ -135,35 +130,35 @@ ENTRY(_ZGVeN16v_atanhf_skx)
vsubps {rn-sae}, %zmm15, %zmm14, %zmm1
vsubps {rn-sae}, %zmm3, %zmm10, %zmm7
- /* K*L2H + Th */
- vmovups ATANHF_DATA(L2H)(%rip), %zmm2
+ /* K*L2H + Th. */
+ vmovups LOCAL_DATA(L2H)(%rip), %zmm2
- /* K*L2L + Tl */
- vmovups ATANHF_DATA(L2L)(%rip), %zmm3
+ /* K*L2L + Tl. */
+ vmovups LOCAL_DATA(L2L)(%rip), %zmm3
- /* table values */
+ /* table values. */
vsubps {rn-sae}, %zmm5, %zmm11, %zmm5
vfmadd231ps {rn-sae}, %zmm1, %zmm2, %zmm5
vfmadd213ps {rn-sae}, %zmm7, %zmm3, %zmm1
- /* polynomials */
- vmovups ATANHF_DATA(poly_coeff3)(%rip), %zmm7
- vmovups ATANHF_DATA(poly_coeff2)(%rip), %zmm10
+ /* polynomials. */
+ vmovups LOCAL_DATA(poly_coeff3)(%rip), %zmm7
+ vmovups LOCAL_DATA(poly_coeff2)(%rip), %zmm10
vmovaps %zmm10, %zmm14
vfmadd231ps {rn-sae}, %zmm9, %zmm7, %zmm10
vfmadd231ps {rn-sae}, %zmm8, %zmm7, %zmm14
- vmovups ATANHF_DATA(poly_coeff1)(%rip), %zmm12
+ vmovups COMMON_DATA(_Neg5F)(%rip), %zmm12
vfmadd213ps {rn-sae}, %zmm12, %zmm9, %zmm10
vfmadd213ps {rn-sae}, %zmm12, %zmm8, %zmm14
vfmadd213ps {rn-sae}, %zmm4, %zmm9, %zmm10
vfmadd213ps {rn-sae}, %zmm4, %zmm8, %zmm14
- /* (K*L2L + Tl) + Rp*PolyP */
+ /* (K*L2L + Tl) + Rp*PolyP. */
vfmadd213ps {rn-sae}, %zmm1, %zmm9, %zmm10
/* zmm12 = zmm12 & (zmm4 | zmm0). */
vpternlogq $0xe0, %zmm0, %zmm4, %zmm12
- /* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM */
+ /* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM. */
vfnmadd213ps {rn-sae}, %zmm5, %zmm8, %zmm14
vaddps {rn-sae}, %zmm14, %zmm10, %zmm8
@@ -171,9 +166,9 @@ ENTRY(_ZGVeN16v_atanhf_skx)
kmovw %k0, %edx
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 zmm0 zmm8 zmm12
+
vmulps {rn-sae}, %zmm12, %zmm8, %zmm0
/* No register to restore on fast path. */
@@ -181,24 +176,24 @@ ENTRY(_ZGVeN16v_atanhf_skx)
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a atanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm8 zmm12
- /* Use r13 to save/restore the stack. This allows us to use rbp as
- callee save register saving code size. */
+
+ /* Use r13 to save/restore the stack. This allows us to use rbp as
+ callee save register saving code size. */
pushq %r13
- cfi_adjust_cfa_offset(8)
- cfi_offset(r13, -16)
- /* Need to callee save registers to preserve state across tanhf calls.
- */
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
pushq %rbx
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbx, -24)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
pushq %rbp
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbp, -32)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
movq %rsp, %r13
- cfi_def_cfa_register(r13)
+ cfi_def_cfa_register (r13)
/* Align stack and make room for 2x zmm vectors. */
andq $-64, %rsp
@@ -208,16 +203,17 @@ L(SPECIAL_VALUES_BRANCH):
vmovaps %zmm0, 64(%rsp)
vzeroupper
- /* edx has 1s where there was a special value that needs to be handled
- by a atanhf call. */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a atanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- atanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 56] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. Realigning also costs more code size. */
+
+ /* use rbp as index for special value that is saved across calls
+ to atanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
xorl %ebp, %ebp
tzcntl %ebx, %ebp
@@ -230,177 +226,107 @@ L(SPECIAL_VALUES_LOOP):
serialized stack/callee save restoration. */
vmovss %xmm0, (%rsp, %rbp, 4)
- blsrl %ebx, %ebx
+ blsrl %ebx, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
+
/* All results have been written to (%rsp). */
vmovaps (%rsp), %zmm0
/* Restore rsp. */
movq %r13, %rsp
- cfi_def_cfa_register(rsp)
+ cfi_def_cfa_register (rsp)
/* Restore callee save registers. */
popq %rbp
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %rbx
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %r13
- cfi_adjust_cfa_offset(-8)
- cfi_restore(r13)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
ret
END(_ZGVeN16v_atanhf_skx)
- .section .rodata, "a"
- .align 4
-#ifdef __svml_satanh_data_internal_avx512_typedef
-typedef unsigned int VUINT32;
-typedef struct{
- __declspec(align(4)) VUINT32 AbsMask[1][1];
- __declspec(align(64)) VUINT32 One[16][1];
- __declspec(align(64)) VUINT32 AddB5[16][1];
- __declspec(align(64)) VUINT32 RcpBitMask[16][1];
- __declspec(align(64)) VUINT32 Log_tbl_L_lo[16][1];
- __declspec(align(64)) VUINT32 Log_tbl_L_hi[16][1];
- __declspec(align(64)) VUINT32 Log_tbl_H_lo[16][1];
- __declspec(align(64)) VUINT32 Log_tbl_H_hi[16][1];
- __declspec(align(64)) VUINT32 L2H[16][1];
- __declspec(align(64)) VUINT32 L2L[16][1];
- __declspec(align(64)) VUINT32 poly_coeff3[16][1];
- __declspec(align(64)) VUINT32 poly_coeff2[16][1];
- __declspec(align(64)) VUINT32 poly_coeff1[16][1];
-} __svml_satanh_data_internal_avx512;
-#endif
-__svml_satanh_data_internal_avx512:
- /* Leave this at front so we can potentially save space due to
- smaller alignment constraint. */
- .align 4
- /* AbsMask */
- .long 0x7fffffff
- .align 64
-__svml_satanh_data_internal_avx512_al64:
- /* One */
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* AddB5 */
- .align 64
- .long 0x00020000, 0x00020000, 0x00020000, 0x00020000
- .long 0x00020000, 0x00020000, 0x00020000, 0x00020000
- .long 0x00020000, 0x00020000, 0x00020000, 0x00020000
- .long 0x00020000, 0x00020000, 0x00020000, 0x00020000
- /* RcpBitMask */
- .align 64
- .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
- .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
- .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
- .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
- /* Log_tbl_L_lo */
- .align 64
- .long 0x00000000
- .long 0x3726c39e
- .long 0x38a30c01
- .long 0x37528ae5
- .long 0x38e0edc5
- .long 0xb8ab41f8
- .long 0xb7cf8f58
- .long 0x3896a73d
- .long 0xb5838656
- .long 0x380c36af
- .long 0xb8235454
- .long 0x3862bae1
- .long 0x38c5e10e
- .long 0x38dedfac
- .long 0x38ebfb5e
- .long 0xb8e63c9f
- /* Log_tbl_L_hi */
- .align 64
- .long 0xb85c1340
- .long 0x38777bcd
- .long 0xb6038656
- .long 0x37d40984
- .long 0xb8b85028
- .long 0xb8ad5a5a
- .long 0x3865c84a
- .long 0x38c3d2f5
- .long 0x383ebce1
- .long 0xb8a1ed76
- .long 0xb7a332c4
- .long 0xb779654f
- .long 0xb8602f73
- .long 0x38f85db0
- .long 0x37b4996f
- .long 0xb8bfb3ca
- /* Log_tbl_H_lo */
- .align 64
- .long 0x00000000
- .long 0x3cfc0000
- .long 0x3d780000
- .long 0x3db78000
- .long 0x3df10000
- .long 0x3e14c000
- .long 0x3e300000
- .long 0x3e4a8000
- .long 0x3e648000
- .long 0x3e7dc000
- .long 0x3e8b4000
- .long 0x3e974000
- .long 0x3ea30000
- .long 0x3eae8000
- .long 0x3eb9c000
- .long 0x3ec4e000
- /* Log_tbl_H_hi */
- .align 64
- .long 0x3ecfa000
- .long 0x3eda2000
- .long 0x3ee48000
- .long 0x3eeea000
- .long 0x3ef8a000
- .long 0x3f013000
- .long 0x3f05f000
- .long 0x3f0aa000
- .long 0x3f0f4000
- .long 0x3f13d000
- .long 0x3f184000
- .long 0x3f1ca000
- .long 0x3f20f000
- .long 0x3f252000
- .long 0x3f295000
- .long 0x3f2d7000
- /* L2H = log(2)_high */
- .align 64
- .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
- .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
- .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
- .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
- /* L2L = log(2)_low */
- .align 64
- .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
- .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
- .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
- .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
- /* poly_coeff3 */
- .align 64
- .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
- .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
- .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
- .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
- /* poly_coeff2 */
- .align 64
- .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
- .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
- .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
- .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
- /* poly_coeff1 */
- .align 64
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
+ .section .rodata.evex512, "a"
.align 64
- .type __svml_satanh_data_internal_avx512_al64, @object
- .size __svml_satanh_data_internal_avx512_al64, .-__svml_satanh_data_internal_avx512_al64
- .type __svml_satanh_data_internal_avx512, @object
- .size __svml_satanh_data_internal_avx512, .-__svml_satanh_data_internal_avx512
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, AddB5, 0x00020000)
+ DATA_VEC (LOCAL_DATA_NAME, RcpBitMask, 0xfffc0000)
+
+ float_block (LOCAL_DATA_NAME, Log_tbl_L_lo,
+ 0x00000000,
+ 0x3726c39e,
+ 0x38a30c01,
+ 0x37528ae5,
+ 0x38e0edc5,
+ 0xb8ab41f8,
+ 0xb7cf8f58,
+ 0x3896a73d,
+ 0xb5838656,
+ 0x380c36af,
+ 0xb8235454,
+ 0x3862bae1,
+ 0x38c5e10e,
+ 0x38dedfac,
+ 0x38ebfb5e,
+ 0xb8e63c9f)
+ float_block (LOCAL_DATA_NAME, Log_tbl_L_hi,
+ 0xb85c1340,
+ 0x38777bcd,
+ 0xb6038656,
+ 0x37d40984,
+ 0xb8b85028,
+ 0xb8ad5a5a,
+ 0x3865c84a,
+ 0x38c3d2f5,
+ 0x383ebce1,
+ 0xb8a1ed76,
+ 0xb7a332c4,
+ 0xb779654f,
+ 0xb8602f73,
+ 0x38f85db0,
+ 0x37b4996f,
+ 0xb8bfb3ca)
+ float_block (LOCAL_DATA_NAME, Log_tbl_H_lo,
+ 0x00000000,
+ 0x3cfc0000,
+ 0x3d780000,
+ 0x3db78000,
+ 0x3df10000,
+ 0x3e14c000,
+ 0x3e300000,
+ 0x3e4a8000,
+ 0x3e648000,
+ 0x3e7dc000,
+ 0x3e8b4000,
+ 0x3e974000,
+ 0x3ea30000,
+ 0x3eae8000,
+ 0x3eb9c000,
+ 0x3ec4e000)
+ float_block (LOCAL_DATA_NAME, Log_tbl_H_hi,
+ 0x3ecfa000,
+ 0x3eda2000,
+ 0x3ee48000,
+ 0x3eeea000,
+ 0x3ef8a000,
+ 0x3f013000,
+ 0x3f05f000,
+ 0x3f0aa000,
+ 0x3f0f4000,
+ 0x3f13d000,
+ 0x3f184000,
+ 0x3f1ca000,
+ 0x3f20f000,
+ 0x3f252000,
+ 0x3f295000,
+ 0x3f2d7000)
+
+ DATA_VEC (LOCAL_DATA_NAME, L2H, 0x3f317000)
+ DATA_VEC (LOCAL_DATA_NAME, L2L, 0x3805fdf4)
+ DATA_VEC (LOCAL_DATA_NAME, poly_coeff3, 0xbe800810)
+ DATA_VEC (LOCAL_DATA_NAME, poly_coeff2, 0x3eaab11e)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 09/27] x86/fpu: Update rodata usage in svml_s_atanhf4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (6 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 08/27] x86/fpu: Update rodata usage in svml_s_atanhf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 10/27] x86/fpu: Update rodata usage in svml_s_atanhf8_core_avx2.S Noah Goldstein via Libc-alpha
` (18 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
No changes to the logic, just change how rodata is handled.
1. Define the rodatas using the new macros so they check that the
offset is correct.
2. Use common data where applicable.
---
.../fpu/multiarch/svml_s_atanhf4_core_sse4.S | 240 ++++++++----------
1 file changed, 102 insertions(+), 138 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S
index 37200b3601..da5744506f 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S
@@ -30,46 +30,45 @@
*
*/
-/* Offsets for data table __svml_satanh_data_internal_avx512. Ordered
- by use in the function. On cold-starts this might help the
- prefetcher. Possibly a better idea is to interleave start/end so
- that the prefetcher is less likely to detect a stream and pull
- irrelivant lines into cache. */
-#define sOne 0
-#define SgnMask 16
-#define sTopMask12 32
-#define iBrkValue 48
-#define iOffExpoMask 64
-#define sPoly 80
-#define sLn2 208
-#define TinyRange 224
+#define LOCAL_DATA_NAME __svml_satanh_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+
+/* Offsets for data table __svml_stan_data_internal. */
+#define _Poly_1 0
+#define _Poly_2 16
+#define _Poly_3 32
+#define _Poly_4 48
+#define _Poly_5 64
+#define _Poly_6 80
+#define _Poly_7 96
+#define _TinyRange 112
#include <sysdep.h>
-#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_atanhf_sse4)
movaps %xmm0, %xmm5
- /* Load constants including One = 1 */
- movups ATANHF_DATA(sOne)(%rip), %xmm4
+ /* Load constants including One = 1. */
+ movups COMMON_DATA(_OneF)(%rip), %xmm4
movaps %xmm5, %xmm3
- /* Strip off the sign, so treat X as positive until right at the end */
- movups ATANHF_DATA(SgnMask)(%rip), %xmm1
+ /* Strip off the sign, so treat X as positive until right at the
+ end. */
+ movups COMMON_DATA(_AbsMask)(%rip), %xmm1
movaps %xmm4, %xmm2
andps %xmm1, %xmm0
movaps %xmm4, %xmm10
- movups ATANHF_DATA(sTopMask12)(%rip), %xmm11
+ movups COMMON_DATA(_Neg4096)(%rip), %xmm11
movaps %xmm4, %xmm14
movaps %xmm11, %xmm9
- /*
- * Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
- * the upper part UHi being <= 12 bits long. Then we have
- * atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
- */
+ /* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two
+ pieces, the upper part UHi being <= 12 bits long. Then we
+ have:
+ atanh(X) = 1/2 * log((1 + X) / (1 - X))
+ = 1/2 * log1p(V / (UHi + ULo)). */
movaps %xmm0, %xmm6
mulps %xmm5, %xmm3
subps %xmm0, %xmm2
@@ -80,65 +79,61 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
andps %xmm2, %xmm9
- /*
- * Check whether |X| < 1, in which case we use the main function.
- * Otherwise set the rangemask so that the callout will get used.
- * Note that this will also use the callout for NaNs since not(NaN < 1).
- */
+ /* Check whether |X| < 1, in which case we use the main
+ function. Otherwise set the rangemask so that the callout
+ will get used. Note that this will also use the callout for
+ NaNs since not(NaN < 1). */
rcpps %xmm9, %xmm7
subps %xmm9, %xmm2
andps %xmm11, %xmm7
- /*
- * Split V as well into upper 12 bits and lower part, so that we can get
- * a preliminary quotient estimate without rounding error.
- */
+ /* Split V as well into upper 12 bits and lower part, so that we
+ can get a preliminary quotient estimate without rounding
+ error. */
andps %xmm6, %xmm11
mulps %xmm7, %xmm9
addps %xmm2, %xmm10
subps %xmm11, %xmm6
- /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
+ /* Hence get initial quotient estimate:
+ QHi + QLo = R * VHi + R * VLo. */
mulps %xmm7, %xmm11
mulps %xmm7, %xmm10
subps %xmm9, %xmm14
mulps %xmm6, %xmm7
subps %xmm10, %xmm14
- /* Compute D = E + E^2 */
+ /* Compute D = E + E^2. */
movaps %xmm14, %xmm13
movaps %xmm4, %xmm8
mulps %xmm14, %xmm13
- /* reduction: compute r,n */
- movdqu ATANHF_DATA(iBrkValue)(%rip), %xmm9
+ /* reduction: compute r,n. */
+ movdqu COMMON_DATA(_IBrkValue)(%rip), %xmm9
addps %xmm13, %xmm14
- /*
- * Compute R * (VHi + VLo) * (1 + E + E^2)
- * = R * (VHi + VLo) * (1 + D)
- * = QHi + (QHi * D + QLo + QLo * D)
- */
+ /* Compute R * (VHi + VLo) * (1 + E + E^2)
+ = R * (VHi + VLo) * (1 + D)
+ = QHi + (QHi * D + QLo + QLo * D). */
movaps %xmm14, %xmm2
mulps %xmm7, %xmm14
mulps %xmm11, %xmm2
addps %xmm14, %xmm7
- movdqu ATANHF_DATA(iOffExpoMask)(%rip), %xmm12
+ movdqu COMMON_DATA(_NotiOffExpoMask)(%rip), %xmm12
movaps %xmm4, %xmm14
- /* Record the sign for eventual reincorporation. */
+ /* Record the sign for eventual reincorporation. */
addps %xmm7, %xmm2
- /*
- * Now finally accumulate the high and low parts of the
- * argument to log1p, H + L, with a final compensated summation.
- */
+ /* Now finally accumulate the high and low parts of the
+ argument to log1p, H + L, with a final compensated summation. */
movaps %xmm2, %xmm6
andnps %xmm5, %xmm1
movaps %xmm4, %xmm7
- /* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
+ /* Or the sign bit in with the tiny result to handle atanh(-0)
+ correctly. */
addps %xmm11, %xmm6
maxps %xmm6, %xmm7
minps %xmm6, %xmm8
@@ -149,43 +144,43 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
subps %xmm10, %xmm7
psubd %xmm9, %xmm10
addps %xmm8, %xmm7
- pand %xmm10, %xmm12
+ pandn %xmm10, %xmm12
psrad $23, %xmm10
cvtdq2ps %xmm10, %xmm13
addps %xmm7, %xmm2
- /* final reconstruction */
+ /* final reconstruction. */
pslld $23, %xmm10
paddd %xmm9, %xmm12
psubd %xmm10, %xmm14
- /* polynomial evaluation */
+ /* polynomial evaluation. */
subps %xmm4, %xmm12
mulps %xmm14, %xmm2
- movups ATANHF_DATA(sPoly+0)(%rip), %xmm7
+ movups LOCAL_DATA(_Poly_1)(%rip), %xmm7
addps %xmm12, %xmm2
mulps %xmm2, %xmm7
- /* Finally, halve the result and reincorporate the sign */
- addps ATANHF_DATA(sPoly+16)(%rip), %xmm7
+ /* Finally, halve the result and reincorporate the sign. */
+ addps LOCAL_DATA(_Poly_2)(%rip), %xmm7
mulps %xmm2, %xmm7
- addps ATANHF_DATA(sPoly+32)(%rip), %xmm7
+ addps LOCAL_DATA(_Poly_3)(%rip), %xmm7
mulps %xmm2, %xmm7
- addps ATANHF_DATA(sPoly+48)(%rip), %xmm7
+ addps LOCAL_DATA(_Poly_4)(%rip), %xmm7
mulps %xmm2, %xmm7
- addps ATANHF_DATA(sPoly+64)(%rip), %xmm7
+ addps LOCAL_DATA(_Poly_5)(%rip), %xmm7
mulps %xmm2, %xmm7
- addps ATANHF_DATA(sPoly+80)(%rip), %xmm7
+ addps LOCAL_DATA(_Poly_6)(%rip), %xmm7
mulps %xmm2, %xmm7
- addps ATANHF_DATA(sPoly+96)(%rip), %xmm7
+ addps LOCAL_DATA(_Poly_7)(%rip), %xmm7
mulps %xmm2, %xmm7
- movaps ATANHF_DATA(sPoly+112)(%rip), %xmm6
+ movaps COMMON_DATA(_Neg5F)(%rip), %xmm6
addps %xmm6, %xmm7
mulps %xmm2, %xmm7
mulps %xmm2, %xmm7
- mulps ATANHF_DATA(sLn2)(%rip), %xmm13
- /* We can build `sHalf` with `sPoly & sOne`. */
+ mulps COMMON_DATA(_Ln2)(%rip), %xmm13
+ /* We can build `sHalf` with `_Poly & sOne`. */
andps %xmm4, %xmm6
orps %xmm1, %xmm3
xorps %xmm6, %xmm1
@@ -197,7 +192,7 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
/* Finish check of NaNs. */
cmpleps %xmm0, %xmm4
movmskps %xmm4, %edx
- cmpltps ATANHF_DATA(TinyRange)(%rip), %xmm0
+ cmpltps LOCAL_DATA(_TinyRange)(%rip), %xmm0
andps %xmm0, %xmm3
andnps %xmm1, %xmm0
@@ -206,115 +201,84 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
testl %edx, %edx
/* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 xmm0
+
/* No registers to restore on fast path. */
ret
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a atanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx rbp r12 r13 r14 r15 xmm0 xmm5
+
/* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
- call entry will be 16-byte aligned. */
+ call entry will be 16-byte aligned. */
subq $56, %rsp
- cfi_def_cfa_offset(64)
+ cfi_def_cfa_offset (64)
movups %xmm0, 24(%rsp)
movups %xmm5, 40(%rsp)
/* Use rbx/rbp for callee save registers as they get short
- encoding for many instructions (as compared with r12/r13). */
+ encoding for many instructions (as compared with r12/r13). */
movq %rbx, (%rsp)
- cfi_offset(rbx, -64)
+ cfi_offset (rbx, -64)
movq %rbp, 8(%rsp)
- cfi_offset(rbp, -56)
- /* edx has 1s where there was a special value that needs to be handled
- by a tanhf call. */
+ cfi_offset (rbp, -56)
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- tanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 12] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. */
+
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
xorl %ebp, %ebp
bsfl %ebx, %ebp
/* Scalar math fucntion call to process special input. */
movss 40(%rsp, %rbp, 4), %xmm0
call atanhf@PLT
- /* No good way to avoid the store-forwarding fault this will cause on
- return. `lfence` avoids the SF fault but at greater cost as it
- serialized stack/callee save restoration. */
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
movss %xmm0, 24(%rsp, %rbp, 4)
leal -1(%rbx), %eax
andl %eax, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
+
/* All results have been written to 24(%rsp). */
movups 24(%rsp), %xmm0
movq (%rsp), %rbx
- cfi_restore(rbx)
+ cfi_restore (rbx)
movq 8(%rsp), %rbp
- cfi_restore(rbp)
+ cfi_restore (rbp)
addq $56, %rsp
- cfi_def_cfa_offset(8)
+ cfi_def_cfa_offset (8)
ret
END(_ZGVbN4v_atanhf_sse4)
- .section .rodata, "a"
+ .section .rodata.sse4, "a"
.align 16
-#ifdef __svml_satanh_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct{
- __declspec(align(16)) VUINT32 sOne[4][1];
- __declspec(align(16)) VUINT32 SgnMask[4][1];
- __declspec(align(16)) VUINT32 sTopMask12[4][1];
- __declspec(align(16)) VUINT32 iBrkValue[4][1];
- __declspec(align(16)) VUINT32 iOffExpoMask[4][1];
- __declspec(align(16)) VUINT32 sPoly[8][4][1];
- __declspec(align(16)) VUINT32 sLn2[4][1];
- __declspec(align(16)) VUINT32 TinyRange[4][1];
-} __svml_satanh_data_internal;
-#endif
-
-__svml_satanh_data_internal:
- /* sOne = SP 1.0 */
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* SgnMask */
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- /* sTopMask12 */
- .align 16
- .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
- /* iBrkValue = SP 2/3 */
- .align 16
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask ==*/
- .align 16
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
-
- /* sPoly[] = SP polynomial */
- .align 16
- .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
- .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
- .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
- .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
- .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
- .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
- .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
-
- /* sLn2 = SP ln(2) */
- .align 16
- .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
- /* TinyRange */
- .align 16
- .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
- .align 16
- .type __svml_satanh_data_internal, @object
- .size __svml_satanh_data_internal, .-__svml_satanh_data_internal
+LOCAL_DATA_NAME:
+ /* _Poly[] = SP polynomial. */
+ /* 1.3820238411426544189453125e-01 P7. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_1, 0x3e0d84ed)
+ /* -1.5122179687023162841796875e-01 P6. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_2, 0xbe1ad9e3)
+ /* 1.4042308926582336425781250e-01 P5. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_3, 0x3e0fcb12)
+ /* -1.6472326219081878662109375e-01 P4. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_4, 0xbe28ad37)
+ /* 2.0007920265197753906250000e-01 P3. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_5, 0x3e4ce190)
+ /* -2.5004237890243530273437500e-01 P2. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_6, 0xbe80058e)
+ /* 3.3333265781402587890625000e-01 P1. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_7, 0x3eaaaa94)
+ DATA_VEC (LOCAL_DATA_NAME, _TinyRange, 0x0C000000)
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 10/27] x86/fpu: Update rodata usage in svml_s_atanhf8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (7 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 09/27] x86/fpu: Update rodata usage in svml_s_atanhf4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 11/27] x86/fpu: Optimize svml_s_atanf16_core_avx512.S Noah Goldstein via Libc-alpha
` (17 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
No changes to the logic, just change how rodata is handled.
1. Define the rodatas using the new macros so they check that the
offset is correct.
2. Use common data where applicable.
---
.../fpu/multiarch/svml_s_atanhf8_core_avx2.S | 308 ++++++++----------
1 file changed, 129 insertions(+), 179 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
index 49ffd7a9b2..0c93da0166 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
@@ -1,5 +1,5 @@
/* Function atanhf vectorized with AVX2.
- Copyright (C) 2021-2022 Free Software Foundation, Inc.
+n Copyright (C) 2021-2022 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@@ -30,181 +30,178 @@
*
*/
-/* Offsets for data table __svml_satanh_data_internal_avx512. Ordered
+
+#define LOCAL_DATA_NAME __svml_satan_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+
+/* Offsets for data table __svml_satanh_data_internal. Ordered
by use in the function. On cold-starts this might hhelp the
prefetcher. Possibly a better idea is to interleave start/end so
that the prefetcher is less likely to detect a stream and pull
irrelivant lines into cache. */
-#define SgnMask 0
-#define sOne 32
-#define sTopMask12 64
-#define TinyRange 96
-#define iBrkValue 128
-#define iOffExpoMask 160
-#define sPoly 192
-#define sLn2 448
-#define sHalf 480
+#define _TinyRange 0
+#define _Poly_1 32
+#define _Poly_2 64
+#define _Poly_3 96
+#define _Poly_4 128
+#define _Poly_5 160
+#define _Poly_6 192
+#define _Poly_7 224
+#define _Half 256
#include <sysdep.h>
-#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_atanhf_avx2)
- /* Strip off the sign, so treat X as positive until right at the end */
- vmovaps ATANHF_DATA(SgnMask)(%rip), %ymm2
+ /* Strip off the sign, so treat X as positive until right at the end. */
+ vmovaps COMMON_DATA(_AbsMask)(%rip), %ymm2
vandps %ymm2, %ymm0, %ymm3
- /* Load constants including One = 1 */
- vmovups ATANHF_DATA(sOne)(%rip), %ymm5
+ /* Load constants including One = 1. */
+ vmovups COMMON_DATA(_OneF)(%rip), %ymm5
vsubps %ymm3, %ymm5, %ymm1
- vmovups ATANHF_DATA(sTopMask12)(%rip), %ymm4
+ vmovups COMMON_DATA(_Neg4096)(%rip), %ymm4
vrcpps %ymm1, %ymm7
vsubps %ymm1, %ymm5, %ymm9
vandps %ymm4, %ymm7, %ymm6
vsubps %ymm3, %ymm9, %ymm7
- /* No need to split sU when FMA is available */
+ /* No need to split sU when FMA is available. */
vfnmadd213ps %ymm5, %ymm6, %ymm1
vmovaps %ymm0, %ymm8
vfmadd213ps %ymm0, %ymm0, %ymm0
vfnmadd231ps %ymm6, %ymm7, %ymm1
- /*
- * Check whether |X| < 1, in which case we use the main function.
- * Otherwise set the rangemask so that the callout will get used.
- * Note that this will also use the callout for NaNs since not(NaN < 1).
- */
+ /* Check whether |X| < 1, in which case we use the main
+ function. Otherwise set the rangemask so that the callout
+ will get used. Note that this will also use the callout for
+ NaNs since not(NaN < 1). */
vcmpnlt_uqps %ymm5, %ymm3, %ymm14
- vcmplt_oqps ATANHF_DATA(TinyRange)(%rip), %ymm3, %ymm15
+ vcmplt_oqps LOCAL_DATA(_TinyRange)(%rip), %ymm3, %ymm15
- /*
- * Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
- * the upper part UHi being <= 12 bits long. Then we have
- * atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
- */
+ /* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two
+ pieces, the upper part UHi being <= 12 bits long. Then we
+ have atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V
+ / (UHi + ULo)). */
vaddps %ymm3, %ymm3, %ymm3
- /*
- * Split V as well into upper 12 bits and lower part, so that we can get
- * a preliminary quotient estimate without rounding error.
- */
+ /* Split V as well into upper 12 bits and lower part, so that we
+ can get a preliminary quotient estimate without rounding
+ error. */
vandps %ymm4, %ymm3, %ymm4
vsubps %ymm4, %ymm3, %ymm7
- /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
+ /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo. */
vmulps %ymm4, %ymm6, %ymm4
- /* Compute D = E + E^2 */
+ /* Compute D = E + E^2. */
vfmadd213ps %ymm1, %ymm1, %ymm1
/* Record the sign for eventual reincorporation. */
vandnps %ymm8, %ymm2, %ymm3
- /* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
+ /* Or the sign bit in with the tiny result to handle atanh(-0)
+ correctly. */
vorps %ymm3, %ymm0, %ymm13
vmulps %ymm7, %ymm6, %ymm2
- /*
- * Compute R * (VHi + VLo) * (1 + E + E^2)
- * = R * (VHi + VLo) * (1 + D)
- * = QHi + (QHi * D + QLo + QLo * D)
- */
-
- /*
- * If less precision is acceptable the `vmulps %ymm1, %ymm4, %ymm9;
- * vaddps %ymm1, %ymm9, %ymm1` can be replaced with
- * `vfmadd231ps %ymm1, %ymm4, %ymm4`.
- */
+ /* Compute R * (VHi + VLo) * (1 + E + E^2)
+ = R * (VHi + VLo) * (1 + D)
+ = QHi + (QHi * D + QLo + QLo * D). */
+
+ /* If less precision is acceptable the:
+ `vmulps %ymm1, %ymm4, %ymm6; vaddps %ymm1, %ymm9, %ymm1`
+ can be replaced with:
+ `vfmadd231ps %ymm1, %ymm4, %ymm4`. */
vmulps %ymm1, %ymm4, %ymm6
vfmadd213ps %ymm2, %ymm2, %ymm1
vaddps %ymm1, %ymm6, %ymm1
- /*
- * Now finally accumulate the high and low parts of the
- * argument to log1p, H + L, with a final compensated summation.
- */
+ /* Now finally accumulate the high and low parts of the
+ argument to log1p, H + L, with a final compensated summation. */
vaddps %ymm1, %ymm4, %ymm2
- /* reduction: compute r, n */
- vmovups ATANHF_DATA(iBrkValue)(%rip), %ymm9
+ /* reduction: compute r, n. */
+ vmovups COMMON_DATA(_IBrkValue)(%rip), %ymm9
- /*
- * Now we feed into the log1p code, using H in place of _VARG1 and
- * later incorporating L into the reduced argument.
- * compute 1+x as high, low parts
- */
+ /* Now we feed into the log1p code, using H in place of _VARG1 and
+ later incorporating L into the reduced argument.
+ compute 1+x as high, low parts. */
vmaxps %ymm2, %ymm5, %ymm0
vminps %ymm2, %ymm5, %ymm6
- /* This is needed for rounding (see `vaddps %ymm1, %ymm4, %ymm2`). */
+ /* This is needed for rounding (see `vaddps %ymm1, %ymm4,
+ %ymm2`). */
vsubps %ymm2, %ymm4, %ymm2
vaddps %ymm6, %ymm0, %ymm4
vpsubd %ymm9, %ymm4, %ymm7
vsubps %ymm4, %ymm0, %ymm4
vaddps %ymm2, %ymm1, %ymm2
- vmovaps ATANHF_DATA(iOffExpoMask)(%rip), %ymm1
+ vmovaps COMMON_DATA(_NotiOffExpoMask)(%rip), %ymm1
- vandps %ymm1, %ymm7, %ymm0
+ vandnps %ymm7, %ymm1, %ymm0
vaddps %ymm4, %ymm6, %ymm4
- vandnps %ymm7, %ymm1, %ymm6
- vmovups ATANHF_DATA(sPoly+0)(%rip), %ymm1
+ vandps %ymm7, %ymm1, %ymm6
+
+ vmovups LOCAL_DATA(_Poly_1)(%rip), %ymm1
vpaddd %ymm9, %ymm0, %ymm0
vaddps %ymm4, %ymm2, %ymm4
vpsubd %ymm6, %ymm5, %ymm6
- /* polynomial evaluation */
+ /* polynomial evaluation. */
vsubps %ymm5, %ymm0, %ymm2
vfmadd231ps %ymm4, %ymm6, %ymm2
- vfmadd213ps ATANHF_DATA(sPoly+32)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+64)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+96)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+128)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+160)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+192)(%rip), %ymm2, %ymm1
- vfmadd213ps ATANHF_DATA(sPoly+224)(%rip), %ymm2, %ymm1
+
+ vfmadd213ps LOCAL_DATA(_Poly_2)(%rip), %ymm2, %ymm1
+ vfmadd213ps LOCAL_DATA(_Poly_3)(%rip), %ymm2, %ymm1
+ vfmadd213ps LOCAL_DATA(_Poly_4)(%rip), %ymm2, %ymm1
+ vfmadd213ps LOCAL_DATA(_Poly_5)(%rip), %ymm2, %ymm1
+ vfmadd213ps LOCAL_DATA(_Poly_6)(%rip), %ymm2, %ymm1
+ vfmadd213ps LOCAL_DATA(_Poly_7)(%rip), %ymm2, %ymm1
+ vfmadd213ps COMMON_DATA(_Neg5F)(%rip), %ymm2, %ymm1
vmulps %ymm1, %ymm2, %ymm1
vfmadd213ps %ymm2, %ymm2, %ymm1
- /* final reconstruction */
+ /* final reconstruction. */
vpsrad $23, %ymm7, %ymm6
vcvtdq2ps %ymm6, %ymm2
- vfmadd132ps ATANHF_DATA(sLn2)(%rip), %ymm1, %ymm2
+ vfmadd132ps COMMON_DATA(_Ln2)(%rip), %ymm1, %ymm2
- /* Finally, halve the result and reincorporate the sign */
- vxorps ATANHF_DATA(sHalf)(%rip), %ymm3, %ymm3
+ /* Finally, halve the result and reincorporate the sign. */
+ vxorps LOCAL_DATA(_Half)(%rip), %ymm3, %ymm3
vmulps %ymm2, %ymm3, %ymm2
vmovmskps %ymm14, %edx
testl %edx, %edx
vblendvps %ymm15, %ymm13, %ymm2, %ymm0
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rdx r12 r13 r14 r15 ymm0
+
/* No registers to restore on fast path. */
ret
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a atanhf call. Optimize for code size
- more so than speed here. */
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- # LOE rbx rdx r12 r13 r14 r15 ymm0 ymm8
- /* Use r13 to save/restore the stack. This allows us to use rbp as
- callee save register saving code size. */
+
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
pushq %r13
- cfi_adjust_cfa_offset(8)
- cfi_offset(r13, -16)
- /* Need to callee save registers to preserve state across tanhf calls.
- */
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
pushq %rbx
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbx, -24)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
pushq %rbp
- cfi_adjust_cfa_offset(8)
- cfi_offset(rbp, -32)
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
movq %rsp, %r13
- cfi_def_cfa_register(r13)
+ cfi_def_cfa_register (r13)
/* Align stack and make room for 2x ymm vectors. */
andq $-32, %rsp
@@ -217,16 +214,17 @@ L(SPECIAL_VALUES_BRANCH):
vzeroupper
- /* edx has 1s where there was a special value that needs to be handled
- by a atanhf call. */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a atanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- # LOE rbx rbp r12 r13 r14 r15
- /* use rbp as index for special value that is saved across calls to
- atanhf. We technically don't need a callee save register here as offset
- to rsp is always [0, 28] so we can restore rsp by realigning to 64.
- Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
- in the loop. Realigning also costs more code size. */
+
+ /* use rbp as index for special value that is saved across calls
+ to atanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
xorl %ebp, %ebp
tzcntl %ebx, %ebp
@@ -234,100 +232,52 @@ L(SPECIAL_VALUES_LOOP):
vmovss 32(%rsp, %rbp, 4), %xmm0
call atanhf@PLT
- /* No good way to avoid the store-forwarding fault this will cause on
- return. `lfence` avoids the SF fault but at greater cost as it
- serialized stack/callee save restoration. */
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
vmovss %xmm0, (%rsp, %rbp, 4)
- blsrl %ebx, %ebx
+ blsrl %ebx, %ebx
jnz L(SPECIAL_VALUES_LOOP)
- # LOE r12 r13 r14 r15
-
/* All results have been written to (%rsp). */
vmovups (%rsp), %ymm0
/* Restore rsp. */
movq %r13, %rsp
- cfi_def_cfa_register(rsp)
+ cfi_def_cfa_register (rsp)
/* Restore callee save registers. */
popq %rbp
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %rbx
- cfi_adjust_cfa_offset(-8)
- cfi_restore(rbp)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
popq %r13
- cfi_adjust_cfa_offset(-8)
- cfi_restore(r13)
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
ret
END(_ZGVdN8v_atanhf_avx2)
- .section .rodata, "a"
- .align 32
-#ifdef __svml_satanh_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct{
- __declspec(align(32)) VUINT32 SgnMask[8][1];
- __declspec(align(32)) VUINT32 sOne[8][1];
- __declspec(align(32)) VUINT32 sTopMask12[8][1];
- __declspec(align(32)) VUINT32 TinyRange[8][1];
- __declspec(align(32)) VUINT32 iBrkValue[8][1];
- __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
- __declspec(align(32)) VUINT32 sPoly[8][8][1];
- __declspec(align(32)) VUINT32 sLn2[8][1];
- __declspec(align(32)) VUINT32 sHalf[8][1];
-} __svml_satanh_data_internal;
-#endif
-__svml_satanh_data_internal:
- /* SgnMask */
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- /* sOne = SP 1.0 */
+ .section .rodata.avx2, "a"
.align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* sTopMask12 */
- .align 32
- .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
- .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
- /* TinyRange */
- .align 32
- .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
- .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
- /* iBrkValue = SP 2/3 */
- .align 32
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask */
- .align 32
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- /* sPoly[] = SP polynomial */
- .align 32
- .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed
- .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
- .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3
- .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
- .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12
- .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
- .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37
- .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
- .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190
- .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
- .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e
- .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
- .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94
- .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
- .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
- /* sLn2 = SP ln(2) */
- .align 32
- .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
- .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
- /* sHalf */
- .align 32
- .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
- .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
- .align 32
- .type __svml_satanh_data_internal, @object
- .size __svml_satanh_data_internal, .-__svml_satanh_data_internal
+
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _TinyRange, 0x0C000000)
+ /* _Poly[] = SP polynomial. */
+ /* 1.3820238411426544189453125e-01 P7. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_1, 0x3e0d84ed)
+ /* -1.5122179687023162841796875e-01 P6. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_2, 0xbe1ad9e3)
+ /* 1.4042308926582336425781250e-01 P5. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_3, 0x3e0fcb12)
+ /* -1.6472326219081878662109375e-01 P4. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_4, 0xbe28ad37)
+ /* 2.0007920265197753906250000e-01 P3. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_5, 0x3e4ce190)
+ /* -2.5004237890243530273437500e-01 P2. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_6, 0xbe80058e)
+ /* 3.3333265781402587890625000e-01 P1. */
+ DATA_VEC (LOCAL_DATA_NAME, _Poly_7, 0x3eaaaa94)
+ DATA_VEC (LOCAL_DATA_NAME, _Half, 0x3F000000)
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 11/27] x86/fpu: Optimize svml_s_atanf16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (8 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 10/27] x86/fpu: Update rodata usage in svml_s_atanhf8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 12/27] x86/fpu: Optimize svml_s_atanf4_core_sse4.S Noah Goldstein via Libc-alpha
` (16 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Change the algorithm used to match the avx2 implementation which
seems to be faster.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Changing the algorithm (1) causes a slight ULP error increase (exact
same as the avx2 version).
Before:
ulp:
0: 4127324924 (0.9610)
1: 167635550 (0.0390)
2: 6822 (0.0000)
3: 0 (0.0000)
4: 0 (0.0000)
After:
ulp:
0: 4088299128 (0.9519)
1: 206531674 (0.0481)
2: 136494 (0.0000)
3: 0 (0.0000)
4: 0 (0.0000)
Since the max ULP is the same and the distribution matches the avx2
implementation this seems like an acceptable "regression" as it
doesn't seem feasible any application could have been relying on
the precision distribution.
Code Size Change: -79 Bytes (193 - 272)
Perf Changes:
Input New Time / Old Time
0F (0x00000000) -> 0.7612
0F (0x0000ffff, Denorm) -> 1.3234
.1F (0x3dcccccd) -> 0.7690
5F (0x40a00000) -> 0.7752
2315255808F (0x4f0a0000) -> 0.7712
-NaN (0xffffffff) -> 0.7824
Note the ~32% regression in the denorm case is because of
additional micro-code assists (from the algorithm shift).
This generally seems worth it for the ~23-24% perf improvement
in other cases as denormal inputs are almost certainly cold cases.
---
.../multiarch/svml_s_atanf16_core_avx512.S | 199 ++++++------------
1 file changed, 67 insertions(+), 132 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf16_core_avx512.S
index 88b44a989c..abb3c76209 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf16_core_avx512.S
@@ -28,146 +28,81 @@
*
*/
-/* Offsets for data table __svml_satan_data_internal_avx512
- */
-#define AbsMask 0
-#define Shifter 64
-#define MaxThreshold 128
-#define MOne 192
-#define One 256
-#define LargeX 320
-#define Zero 384
-#define Tbl_H 448
-#define Pi2 576
-#define coeff_1 640
-#define coeff_2 704
-#define coeff_3 768
+#define LOCAL_DATA_NAME __svml_satan_data_internal
+#include "svml_s_common_evex512_rodata_offsets.h"
+/* Offsets for data table __svml_satan_data_internal. */
+#define _sPC8 0
+#define _sPC7 64
+#define _sPC6 128
+#define _sPC5 192
+#define _sPC4 256
+#define _sPC3 320
+#define _sPC2 384
+#define _sPC1 448
+#define _sPIO2 512
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_atanf_skx)
- vandps __svml_satan_data_internal_avx512(%rip), %zmm0, %zmm7
- vmovups MaxThreshold+__svml_satan_data_internal_avx512(%rip), %zmm3
- vmovups One+__svml_satan_data_internal_avx512(%rip), %zmm8
-
- /* round to 2 bits after binary point */
- vreduceps $40, {sae}, %zmm7, %zmm5
-
- /* saturate X range */
- vmovups LargeX+__svml_satan_data_internal_avx512(%rip), %zmm6
- vmovups Shifter+__svml_satan_data_internal_avx512(%rip), %zmm2
- vcmpps $29, {sae}, %zmm3, %zmm7, %k1
-
- /* table lookup sequence */
- vmovups Tbl_H+__svml_satan_data_internal_avx512(%rip), %zmm3
- vsubps {rn-sae}, %zmm5, %zmm7, %zmm4
- vaddps {rn-sae}, %zmm2, %zmm7, %zmm1
- vxorps %zmm0, %zmm7, %zmm0
- vfmadd231ps {rn-sae}, %zmm7, %zmm4, %zmm8
- vmovups coeff_2+__svml_satan_data_internal_avx512(%rip), %zmm4
-
- /* if|X|>=MaxThreshold, set DiffX=-1 */
- vblendmps MOne+__svml_satan_data_internal_avx512(%rip), %zmm5, %zmm9{%k1}
- vmovups coeff_3+__svml_satan_data_internal_avx512(%rip), %zmm5
-
- /* if|X|>=MaxThreshold, set Y=X */
- vminps {sae}, %zmm7, %zmm6, %zmm8{%k1}
-
- /* R+Rl = DiffX/Y */
- vgetmantps $0, {sae}, %zmm9, %zmm12
- vgetexpps {sae}, %zmm9, %zmm10
- vpermt2ps Tbl_H+64+__svml_satan_data_internal_avx512(%rip), %zmm1, %zmm3
- vgetmantps $0, {sae}, %zmm8, %zmm15
- vgetexpps {sae}, %zmm8, %zmm11
- vmovups coeff_1+__svml_satan_data_internal_avx512(%rip), %zmm1
-
- /* set table value to Pi/2 for large X */
- vblendmps Pi2+__svml_satan_data_internal_avx512(%rip), %zmm3, %zmm9{%k1}
- vrcp14ps %zmm15, %zmm13
- vsubps {rn-sae}, %zmm11, %zmm10, %zmm2
- vmulps {rn-sae}, %zmm13, %zmm12, %zmm14
- vfnmadd213ps {rn-sae}, %zmm12, %zmm14, %zmm15
- vfmadd213ps {rn-sae}, %zmm14, %zmm13, %zmm15
- vscalefps {rn-sae}, %zmm2, %zmm15, %zmm7
-
- /* polynomial evaluation */
- vmulps {rn-sae}, %zmm7, %zmm7, %zmm8
- vmulps {rn-sae}, %zmm7, %zmm8, %zmm6
- vfmadd231ps {rn-sae}, %zmm8, %zmm1, %zmm4
- vfmadd213ps {rn-sae}, %zmm5, %zmm4, %zmm8
- vfmadd213ps {rn-sae}, %zmm7, %zmm6, %zmm8
- vaddps {rn-sae}, %zmm9, %zmm8, %zmm10
- vxorps %zmm0, %zmm10, %zmm0
+ /* 1) If x>1, then r=-1/x, PIO2=Pi/2
+ 2) If -1<=x<=1, then r=x, PIO2=0
+ 3) If x<-1, then r=-1/x, PIO2=-Pi/2. */
+ vmovups COMMON_DATA(_OneF)(%rip), %zmm2
+ vmovups COMMON_DATA(_SignMask)(%rip), %zmm7
+
+
+ /* Use minud\maxud operations for argument reduction. */
+ vandnps %zmm0, %zmm7, %zmm3
+ vpcmpgtd %zmm2, %zmm3, %k1
+
+ vpmaxud %zmm3, %zmm2, %zmm4
+ vpminud %zmm3, %zmm2, %zmm5
+
+ vdivps %zmm4, %zmm5, %zmm4
+
+ vandps %zmm7, %zmm0, %zmm3
+ vmovdqa32 %zmm7, %zmm7{%k1}{z}
+
+ vmulps %zmm4, %zmm4, %zmm1
+ vpternlogq $0x96, %zmm3, %zmm4, %zmm7
+
+ /* Polynomial. */
+
+ vmovups LOCAL_DATA(_sPC8)(%rip), %zmm0
+ vmovups LOCAL_DATA(_sPC7)(%rip), %zmm4
+
+ vmulps %zmm1, %zmm1, %zmm5
+
+ vfmadd213ps LOCAL_DATA(_sPC6)(%rip), %zmm5, %zmm0
+ vfmadd213ps LOCAL_DATA(_sPC5)(%rip), %zmm5, %zmm4
+ vfmadd213ps LOCAL_DATA(_sPC4)(%rip), %zmm5, %zmm0
+ vfmadd213ps LOCAL_DATA(_sPC3)(%rip), %zmm5, %zmm4
+ vfmadd213ps LOCAL_DATA(_sPC2)(%rip), %zmm5, %zmm0
+ vfmadd213ps LOCAL_DATA(_sPC1)(%rip), %zmm5, %zmm4
+ vfmadd213ps %zmm4, %zmm1, %zmm0
+ vfmadd213ps %zmm2, %zmm1, %zmm0
+ vorps LOCAL_DATA(_sPIO2)(%rip), %zmm3, %zmm3{%k1}
+
+ /* Reconstruction. */
+ vfmadd213ps %zmm3, %zmm7, %zmm0
ret
END(_ZGVeN16v_atanf_skx)
- .section .rodata, "a"
+ .section .rodata.evex512, "a"
.align 64
-#ifdef __svml_satan_data_internal_avx512_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(64)) VUINT32 AbsMask[16][1];
- __declspec(align(64)) VUINT32 Shifter[16][1];
- __declspec(align(64)) VUINT32 MaxThreshold[16][1];
- __declspec(align(64)) VUINT32 MOne[16][1];
- __declspec(align(64)) VUINT32 One[16][1];
- __declspec(align(64)) VUINT32 LargeX[16][1];
- __declspec(align(64)) VUINT32 Zero[16][1];
- __declspec(align(64)) VUINT32 Tbl_H[32][1];
- __declspec(align(64)) VUINT32 Pi2[16][1];
- __declspec(align(64)) VUINT32 coeff[3][16][1];
-} __svml_satan_data_internal_avx512;
-#endif
-__svml_satan_data_internal_avx512:
- /* AbsMask */
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- /* Shifter */
- .align 64
- .long 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000, 0x4a000000
- /* MaxThreshold */
- .align 64
- .long 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000, 0x40F80000
- /* MOne */
- .align 64
- .long 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000
- /* One */
- .align 64
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* LargeX */
- .align 64
- .long 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000, 0x4f800000
- /* Zero */
- .align 64
- .long 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000
- /* Tbl_H */
- .align 64
- .long 0x00000000, 0x3e7adbb0
- .long 0x3eed6338, 0x3f24bc7d
- .long 0x3f490fdb, 0x3f6563e3
- .long 0x3f7b985f, 0x3f869c79
- .long 0x3f8db70d, 0x3f93877b
- .long 0x3f985b6c, 0x3f9c6b53
- .long 0x3f9fe0bb, 0x3fa2daa4
- .long 0x3fa57088, 0x3fa7b46f
- .long 0x3fa9b465, 0x3fab7b7a
- .long 0x3fad1283, 0x3fae809e
- .long 0x3fafcb99, 0x3fb0f836
- .long 0x3fb20a6a, 0x3fb30581
- .long 0x3fb3ec43, 0x3fb4c10a
- .long 0x3fb585d7, 0x3fb63c64
- .long 0x3fb6e62c, 0x3fb78478
- .long 0x3fb81868, 0x3fb8a2f5
- /* Pi2 */
- .align 64
- .long 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB
- /* coeff3 */
- .align 64
- .long 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de, 0xbe0fa8de
- .long 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2, 0x3e4cc8e2
- .long 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa, 0xbeaaaaaa
- .align 64
- .type __svml_satan_data_internal_avx512, @object
- .size __svml_satan_data_internal_avx512, .-__svml_satan_data_internal_avx512
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _sPC8, 0x3B322CC0)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC7, 0xBC7F2631)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC6, 0x3D2BC384)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC5, 0xBD987629)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC4, 0x3DD96474)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC3, 0xBE1161F8)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC2, 0x3E4CB79F)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC1, 0xBEAAAA49)
+ DATA_VEC (LOCAL_DATA_NAME, _sPIO2, 0x3FC90FDB)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 12/27] x86/fpu: Optimize svml_s_atanf4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (9 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 11/27] x86/fpu: Optimize svml_s_atanf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 13/27] x86/fpu: Optimize svml_s_atanf8_core_avx2.S Noah Goldstein via Libc-alpha
` (15 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
2. Remove unused rodata.
3. Use common data definitions where possible.
Code Size Change: -31 Bytes (173 - 204)
Input New Time / Old Time
0F (0x00000000) -> 0.9446
0F (0x0000ffff, Denorm) -> 0.9977
.1F (0x3dcccccd) -> 0.9380
5F (0x40a00000) -> 0.9542
2315255808F (0x4f0a0000) -> 1.0115
-NaN (0xffffffff) -> 0.9232
---
.../fpu/multiarch/svml_s_atanf4_core_sse4.S | 198 +++++++-----------
1 file changed, 75 insertions(+), 123 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf4_core_sse4.S
index 83cecb8ee5..2ab599f7a8 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf4_core_sse4.S
@@ -28,136 +28,88 @@
*
*/
-/* Offsets for data table __svml_satan_data_internal
- */
-#define _sSIGN_MASK 0
-#define _sABS_MASK 16
-#define _sONE 32
-#define _sPIO2 48
-#define _sPC8 64
-#define _sPC7 80
-#define _sPC6 96
-#define _sPC5 112
-#define _sPC4 128
-#define _sPC3 144
-#define _sPC2 160
-#define _sPC1 176
-#define _sPC0 192
+#define LOCAL_DATA_NAME __svml_satan_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+/* Offsets for data table __svml_satan_data_internal. */
+#define _SignMask 0
+#define _sPIO2 16
+#define _sPC7 32
+#define _sPC5 48
+#define _sPC3 64
+#define _sPC1 80
+#define _sPC8 96
+#define _sPC6 112
+#define _sPC4 128
+#define _sPC2 144
+#define _sPC0 160
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_atanf_sse4)
- /*
- * To use minps\maxps operations for argument reduction
- * uncomment _AT_USEMINMAX_ definition
- * Declarations
- * Variables
- * Constants
- */
- movups _sABS_MASK+__svml_satan_data_internal(%rip), %xmm2
-
- /*
- * 1) If x>1, then r=-1/x, PIO2=Pi/2
- * 2) If -1<=x<=1, then r=x, PIO2=0
- * 3) If x<-1, then r=-1/x, PIO2=-Pi/2
- */
- movups _sONE+__svml_satan_data_internal(%rip), %xmm1
- andps %xmm0, %xmm2
- movaps %xmm2, %xmm9
- movaps %xmm1, %xmm3
- cmpleps %xmm1, %xmm9
- maxps %xmm2, %xmm3
- minps %xmm2, %xmm1
- divps %xmm3, %xmm1
- movups __svml_satan_data_internal(%rip), %xmm4
- movaps %xmm9, %xmm10
- andps %xmm4, %xmm0
- andnps %xmm4, %xmm9
- pxor %xmm0, %xmm9
- pxor %xmm1, %xmm9
-
- /* Polynomial. */
- movaps %xmm9, %xmm8
- mulps %xmm9, %xmm8
- movaps %xmm8, %xmm7
- mulps %xmm8, %xmm7
- movups _sPC8+__svml_satan_data_internal(%rip), %xmm6
- mulps %xmm7, %xmm6
- movups _sPC7+__svml_satan_data_internal(%rip), %xmm5
- mulps %xmm7, %xmm5
- addps _sPC6+__svml_satan_data_internal(%rip), %xmm6
- mulps %xmm7, %xmm6
- addps _sPC5+__svml_satan_data_internal(%rip), %xmm5
- mulps %xmm7, %xmm5
- addps _sPC4+__svml_satan_data_internal(%rip), %xmm6
- mulps %xmm7, %xmm6
- addps _sPC3+__svml_satan_data_internal(%rip), %xmm5
- mulps %xmm5, %xmm7
- addps _sPC2+__svml_satan_data_internal(%rip), %xmm6
- mulps %xmm8, %xmm6
- addps _sPC1+__svml_satan_data_internal(%rip), %xmm7
- andnps _sPIO2+__svml_satan_data_internal(%rip), %xmm10
- addps %xmm6, %xmm7
- mulps %xmm7, %xmm8
- pxor %xmm0, %xmm10
- addps _sPC0+__svml_satan_data_internal(%rip), %xmm8
-
- /* Reconstruction. */
- mulps %xmm8, %xmm9
- addps %xmm9, %xmm10
- movaps %xmm10, %xmm0
+ /* 1) If x>1, then r=-1/x, PIO2=Pi/2
+ 2) If -1<=x<=1, then r=x, PIO2=0
+ 3) If x<-1, then r=-1/x, PIO2=-Pi/2. */
+ movups COMMON_DATA(_OneF)(%rip), %xmm1
+ /* use minud\maxud operations for argument reduction. */
+ movups LOCAL_DATA(_SignMask)(%rip), %xmm5
+ movaps %xmm5, %xmm6
+ andnps %xmm0, %xmm5
+ andps %xmm6, %xmm0
+ movaps %xmm5, %xmm7
+
+ movaps %xmmA, %xmm4
+ pminud %xmm5, %xmmA
+ pmaxud %xmm4, %xmm7
+ pcmpgtd %xmmA, %xmm5
+ divps %xmm7, %xmmA
+
+ andps %xmm5, %xmm6
+ pxor %xmm0, %xmm6
+ andps LOCAL_DATA(_sPIO2)(%rip), %xmm5
+ pxor %xmm0, %xmm5
+ pxor %xmmA, %xmm6
+ /* Polynomial. */
+ mulps %xmmA, %xmmA
+ movaps %xmmA, %xmm0
+ mulps %xmmA, %xmmA
+ movups LOCAL_DATA(_sPC7)(%rip), %xmm2
+ mulps %xmmA, %xmm2
+ addps LOCAL_DATA(_sPC5)(%rip), %xmm2
+ mulps %xmmA, %xmm2
+ addps LOCAL_DATA(_sPC3)(%rip), %xmm2
+ mulps %xmmA, %xmm2
+ addps LOCAL_DATA(_sPC1)(%rip), %xmm2
+ movups LOCAL_DATA(_sPC8)(%rip), %xmm3
+ mulps %xmmA, %xmm3
+ addps LOCAL_DATA(_sPC6)(%rip), %xmm3
+ mulps %xmmA, %xmm3
+ addps LOCAL_DATA(_sPC4)(%rip), %xmm3
+ mulps %xmmA, %xmm3
+ addps LOCAL_DATA(_sPC2)(%rip), %xmm3
+ mulps %xmm0, %xmm3
+ addps %xmm3, %xmm2
+ mulps %xmm2, %xmm0
+ addps %xmm4, %xmm0
+ /* Reconstruction. */
+ mulps %xmm6, %xmm0
+ addps %xmm5, %xmm0
ret
-
END(_ZGVbN4v_atanf_sse4)
- .section .rodata, "a"
+ .section .rodata.sse4, "a"
.align 16
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _SignMask, 0x80000000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPIO2, 0x3fc90fdb)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC7, 0xBC7F2631)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC5, 0xBD987629)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC3, 0xBE1161F8)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC1, 0xBEAAAA49)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC8, 0x3B322CC0)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC6, 0x3D2BC384)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC4, 0x3DD96474)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC2, 0x3E4CB79F)
-#ifdef __svml_satan_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(16)) VUINT32 _sSIGN_MASK[4][1];
- __declspec(align(16)) VUINT32 _sABS_MASK[4][1];
- __declspec(align(16)) VUINT32 _sONE[4][1];
- __declspec(align(16)) VUINT32 _sPIO2[4][1];
- __declspec(align(16)) VUINT32 _sPC8[4][1];
- __declspec(align(16)) VUINT32 _sPC7[4][1];
- __declspec(align(16)) VUINT32 _sPC6[4][1];
- __declspec(align(16)) VUINT32 _sPC5[4][1];
- __declspec(align(16)) VUINT32 _sPC4[4][1];
- __declspec(align(16)) VUINT32 _sPC3[4][1];
- __declspec(align(16)) VUINT32 _sPC2[4][1];
- __declspec(align(16)) VUINT32 _sPC1[4][1];
- __declspec(align(16)) VUINT32 _sPC0[4][1];
-} __svml_satan_data_internal;
-#endif
-__svml_satan_data_internal:
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000 // _sSIGN_MASK
- .align 16
- .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // _sABS_MASK
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // _sONE
- .align 16
- .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // _sPIO2
- .align 16
- .long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // _sPC8
- .align 16
- .long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // _sPC7
- .align 16
- .long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // _sPC6
- .align 16
- .long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // _sPC5
- .align 16
- .long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // _sPC4
- .align 16
- .long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // _sPC3
- .align 16
- .long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // _sPC2
- .align 16
- .long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // _sPC1
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // _sPC0
- .align 16
- .type __svml_satan_data_internal, @object
- .size __svml_satan_data_internal, .-__svml_satan_data_internal
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 13/27] x86/fpu: Optimize svml_s_atanf8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (10 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 12/27] x86/fpu: Optimize svml_s_atanf4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 14/27] x86/fpu: Add common rodata file for svml_s_tanf_*_{avx512, avx2, sse4}.S Noah Goldstein via Libc-alpha
` (14 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
2. Remove unused rodata.
3. Use common data definitions where possible.
Code Size Change: -12 Bytes (163 - 175)
Input New Time / Old Time
0F (0x00000000) -> 0.8484
0F (0x0000ffff, Denorm) -> 0.9993
.1F (0x3dcccccd) -> 0.9368
5F (0x40a00000) -> 0.9476
2315255808F (0x4f0a0000) -> 0.9454
-NaN (0xffffffff) -> 0.9193
---
.../fpu/multiarch/svml_s_atanf8_core_avx2.S | 162 +++++++-----------
1 file changed, 58 insertions(+), 104 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S
index ee49a3e10e..649277c682 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S
@@ -28,120 +28,74 @@
*
*/
-/* Offsets for data table __svml_satan_data_internal
- */
-#define _sSIGN_MASK 0
-#define _sABS_MASK 32
-#define _sONE 64
-#define _sPIO2 96
-#define _sPC8 128
-#define _sPC7 160
-#define _sPC6 192
-#define _sPC5 224
-#define _sPC4 256
-#define _sPC3 288
-#define _sPC2 320
-#define _sPC1 352
-#define _sPC0 384
+
+#define LOCAL_DATA_NAME __svml_satan_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+/* Offsets for data table __svml_satan_data_internal. */
+#define _sPC8 0
+#define _sPC7 32
+#define _sPC6 64
+#define _sPC5 96
+#define _sPC4 128
+#define _sPC3 160
+#define _sPC2 192
+#define _sPC1 224
+#define _sPC0 256
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_atanf_avx2)
- /*
- * 1) If x>1, then r=-1/x, PIO2=Pi/2
- * 2) If -1<=x<=1, then r=x, PIO2=0
- * 3) If x<-1, then r=-1/x, PIO2=-Pi/2
- */
- vmovups _sONE+__svml_satan_data_internal(%rip), %ymm2
- vmovups __svml_satan_data_internal(%rip), %ymm7
- vmovups _sPC7+__svml_satan_data_internal(%rip), %ymm13
+ /* 1) If x>1, then r=-1/x, PIO2=Pi/2
+ 2) If -1<=x<=1, then r=x, PIO2=0
+ 3) If x<-1, then r=-1/x, PIO2=-Pi/2. */
+ vmovups COMMON_DATA(_AbsMask)(%rip), %ymm7
+ vmovups COMMON_DATA(_OneF)(%rip), %ymm2
+
+ vandps %ymm0, %ymm7, %ymm3
+ /* Use minud\maxud operations for argument reduction. */
+ vpmaxud %ymm3, %ymm2, %ymm5
+ vpminud %ymm3, %ymm2, %ymm4
- /*
- * To use minps\maxps operations for argument reduction
- * uncomment _AT_USEMINMAX_ definition
- * Declarations
- * Variables
- * Constants
- */
- vandps _sABS_MASK+__svml_satan_data_internal(%rip), %ymm0, %ymm3
- vmaxps %ymm3, %ymm2, %ymm5
- vminps %ymm3, %ymm2, %ymm4
- vcmple_oqps %ymm2, %ymm3, %ymm6
- vdivps %ymm5, %ymm4, %ymm11
- vandps %ymm7, %ymm0, %ymm9
- vandnps %ymm7, %ymm6, %ymm8
- vxorps %ymm9, %ymm8, %ymm10
- vxorps %ymm11, %ymm10, %ymm15
+ vdivps %ymm5, %ymm4, %ymm4
- /* Polynomial. */
- vmulps %ymm15, %ymm15, %ymm14
- vmovups _sPC8+__svml_satan_data_internal(%rip), %ymm0
- vmulps %ymm14, %ymm14, %ymm12
- vfmadd213ps _sPC6+__svml_satan_data_internal(%rip), %ymm12, %ymm0
- vfmadd213ps _sPC5+__svml_satan_data_internal(%rip), %ymm12, %ymm13
- vfmadd213ps _sPC4+__svml_satan_data_internal(%rip), %ymm12, %ymm0
- vfmadd213ps _sPC3+__svml_satan_data_internal(%rip), %ymm12, %ymm13
- vfmadd213ps _sPC2+__svml_satan_data_internal(%rip), %ymm12, %ymm0
- vfmadd213ps _sPC1+__svml_satan_data_internal(%rip), %ymm12, %ymm13
- vfmadd213ps %ymm13, %ymm14, %ymm0
- vfmadd213ps _sPC0+__svml_satan_data_internal(%rip), %ymm14, %ymm0
- vandnps _sPIO2+__svml_satan_data_internal(%rip), %ymm6, %ymm1
- vxorps %ymm9, %ymm1, %ymm1
+ vpcmpgtd %ymm2, %ymm3, %ymm6
+ vandnps %ymm0, %ymm7, %ymm3
+ vandnps %ymm6, %ymm7, %ymm7
+ vxorps %ymm3, %ymm7, %ymm5
+ vxorps %ymm4, %ymm5, %ymm7
+ /* Polynomial. */
+ vmulps %ymm4, %ymm4, %ymm1
+ vmovups LOCAL_DATA(_sPC8)(%rip), %ymm0
+ vmovups LOCAL_DATA(_sPC7)(%rip), %ymm4
+ vmulps %ymm1, %ymm1, %ymm5
+ vfmadd213ps LOCAL_DATA(_sPC6)(%rip), %ymm5, %ymm0
+ vfmadd213ps LOCAL_DATA(_sPC5)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPC4)(%rip), %ymm5, %ymm0
+ vfmadd213ps LOCAL_DATA(_sPC3)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPC2)(%rip), %ymm5, %ymm0
+ vfmadd213ps LOCAL_DATA(_sPC1)(%rip), %ymm5, %ymm4
+ vfmadd213ps %ymm4, %ymm1, %ymm0
+ vfmadd213ps %ymm2, %ymm1, %ymm0
+ vandps COMMON_DATA(_TanSPI1_FMA)(%rip), %ymm6, %ymm1
+ vxorps %ymm3, %ymm1, %ymm1
- /* Reconstruction. */
- vfmadd213ps %ymm1, %ymm15, %ymm0
+ /* Reconstruction. */
+ vfmadd213ps %ymm1, %ymm7, %ymm0
ret
END(_ZGVdN8v_atanf_avx2)
- .section .rodata, "a"
- .align 32
-
-#ifdef __svml_satan_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(32)) VUINT32 _sSIGN_MASK[8][1];
- __declspec(align(32)) VUINT32 _sABS_MASK[8][1];
- __declspec(align(32)) VUINT32 _sONE[8][1];
- __declspec(align(32)) VUINT32 _sPIO2[8][1];
- __declspec(align(32)) VUINT32 _sPC8[8][1];
- __declspec(align(32)) VUINT32 _sPC7[8][1];
- __declspec(align(32)) VUINT32 _sPC6[8][1];
- __declspec(align(32)) VUINT32 _sPC5[8][1];
- __declspec(align(32)) VUINT32 _sPC4[8][1];
- __declspec(align(32)) VUINT32 _sPC3[8][1];
- __declspec(align(32)) VUINT32 _sPC2[8][1];
- __declspec(align(32)) VUINT32 _sPC1[8][1];
- __declspec(align(32)) VUINT32 _sPC0[8][1];
-} __svml_satan_data_internal;
-#endif
-__svml_satan_data_internal:
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 // _sSIGN_MASK
- .align 32
- .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // _sABS_MASK
- .align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // _sONE
- .align 32
- .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // _sPIO2
- .align 32
- .long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // _sPC8
- .align 32
- .long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // _sPC7
- .align 32
- .long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // _sPC6
- .align 32
- .long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // _sPC5
- .align 32
- .long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // _sPC4
- .align 32
- .long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // _sPC3
- .align 32
- .long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // _sPC2
- .align 32
- .long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // _sPC1
- .align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // _sPC0
+ .section .rodata.avx2, "a"
.align 32
- .type __svml_satan_data_internal, @object
- .size __svml_satan_data_internal, .-__svml_satan_data_internal
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _sPC8, 0x3B322CC0)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC7, 0xBC7F2631)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC6, 0x3D2BC384)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC5, 0xBD987629)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC4, 0x3DD96474)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC3, 0xBE1161F8)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC2, 0x3E4CB79F)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC1, 0xBEAAAA49)
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 14/27] x86/fpu: Add common rodata file for svml_s_tanf_*_{avx512, avx2, sse4}.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (11 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 13/27] x86/fpu: Optimize svml_s_atanf8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 15/27] x86/fpu: Optimize svml_s_tanf16_core_avx512.S Noah Goldstein via Libc-alpha
` (13 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
The avx2/sse4 implementation share many definitions including the
larger `_Coeffs` table. Sharing this data across avx2/sse4
implementations saves more than 5kb.
As well all three implementations use the `_Reduction` table. Sharing
this table across all three implementations saves more than 6kb.
---
.../fpu/multiarch/svml_s_tanf_rodata.h.S | 1641 +++++++++++++++++
1 file changed, 1641 insertions(+)
create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf_rodata.h.S
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf_rodata.h.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf_rodata.h.S
new file mode 100644
index 0000000000..d45125ff13
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf_rodata.h.S
@@ -0,0 +1,1641 @@
+/* Datatables for tanf_{avx512,avx2,sse4}
+ Copyright (C) 2022 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ https://www.gnu.org/licenses/. */
+
+#include "svml_common_data_macros.h.S"
+
+#if (defined AVX2_SHARED_OFFSETS) || (defined AVX2_SHARED_TABLE)
+
+/* Offsets are ordered by use in the function. On cold-starts this
+ might help the prefetcher. If the streaming prefetchers kick in it
+ will prefetch into the lookup table. */
+# define _sInvPi 0
+# define _sRShifter 32
+# define _sQ2 64
+# define _sP1 96
+# define _sQ1 128
+# define _sP0 160
+# define _sRangeReductionVal 192
+# define _Low16 224
+# define _SH_FLT_1 256
+# define _SH_FLT_2 288
+# define _Low18 320
+# define _Low9 352
+# define _SH_FLT_3 384
+# define _SH_FLT_4 416
+# define _Low7 448
+# define _Coeffs 480
+
+# define AVX2_SHARED_DATA(offset) ((offset) + (__svml_stan_common_data_avx2))
+
+# if (defined AVX2_SHARED_TABLE)
+ .section .rodata.avx2, "a"
+ .align 32
+ .globl __svml_stan_common_data_avx2
+__svml_stan_common_data_avx2:
+ float_vector32 (__svml_stan_common_data_avx2, _sInvPi, 0x3F22F983)
+ float_vector32 (__svml_stan_common_data_avx2, _sRShifter, 0x4B400000)
+ float_vector32 (__svml_stan_common_data_avx2, _sQ2, 0x3C1F336B)
+ float_vector32 (__svml_stan_common_data_avx2, _sP1, 0xBDC433B4)
+ float_vector32 (__svml_stan_common_data_avx2, _sQ1, 0xBEDBB7AB)
+ float_vector32 (__svml_stan_common_data_avx2, _sP0, 0x3F7FFFFC)
+ float_vector32 (__svml_stan_common_data_avx2, _sRangeReductionVal, 0x46010000)
+ float_vector32 (__svml_stan_common_data_avx2, _Low16, 0x0000ffff)
+ float_vector32 (__svml_stan_common_data_avx2, _SH_FLT_1, 0x47400000)
+ float_vector32 (__svml_stan_common_data_avx2, _SH_FLT_2, 0x28800000)
+ float_vector32 (__svml_stan_common_data_avx2, _Low18, 0x0003ffff)
+ float_vector32 (__svml_stan_common_data_avx2, _Low9, 0x000001ff)
+ float_vector32 (__svml_stan_common_data_avx2, _SH_FLT_3, 0x34000000)
+ float_vector32 (__svml_stan_common_data_avx2, _SH_FLT_4, 0x40c90fdb)
+ float_vector32 (__svml_stan_common_data_avx2, _Low7, 0x0000007f)
+
+ /* _Coeffs Breakpoint B = 0 * pi/128, function tan(B + x). */
+ float_block (__svml_stan_common_data_avx2, _Coeffs,
+ 0x3FC90FDB, /* B' = pi/2 - B (high single). */
+ 0xB33BBD2E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x00000000, /* c0 (high single). */
+ 0x00000000, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x00000000, /* c1 (low single). */
+ 0x00000000, /* c2. */
+ 0x3EAAACDD, /* c3. */
+ 0x00000000, /* c4. */
+ 0x3FC5EB9B, /* B' = pi/2 - B (high single). */
+ 0x32DE638C, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3CC91A31, /* c0 (high single). */
+ 0x2F8E8D1A, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3A1DFA00, /* c1 (low single). */
+ 0x3CC9392D, /* c2. */
+ 0x3EAB1889, /* c3. */
+ 0x3C885D3B, /* c4. */
+ 0x3FC2C75C, /* B' = pi/2 - B (high single). */
+ 0xB2CBBE8A, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3D49393C, /* c0 (high single). */
+ 0x30A39F5B, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3B1E2B00, /* c1 (low single). */
+ 0x3D49B5D4, /* c2. */
+ 0x3EAC4F10, /* c3. */
+ 0x3CFD9425, /* c4. */
+ 0x3FBFA31C, /* B' = pi/2 - B (high single). */
+ 0x33450FB0, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3D9711CE, /* c0 (high single). */
+ 0x314FEB28, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3BB24C00, /* c1 (low single). */
+ 0x3D97E43A, /* c2. */
+ 0x3EAE6A89, /* c3. */
+ 0x3D4D07E0, /* c4. */
+ 0x3FBC7EDD, /* B' = pi/2 - B (high single). */
+ 0xB1800ADD, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3DC9B5DC, /* c0 (high single). */
+ 0x3145AD86, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3C1EEF20, /* c1 (low single). */
+ 0x3DCBAAEA, /* c2. */
+ 0x3EB14E5E, /* c3. */
+ 0x3D858BB2, /* c4. */
+ 0x3FB95A9E, /* B' = pi/2 - B (high single). */
+ 0xB3651267, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3DFC98C2, /* c0 (high single). */
+ 0xB0AE525C, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3C793D20, /* c1 (low single). */
+ 0x3E003845, /* c2. */
+ 0x3EB5271F, /* c3. */
+ 0x3DAC669E, /* c4. */
+ 0x3FB6365E, /* B' = pi/2 - B (high single). */
+ 0x328BB91C, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E17E564, /* c0 (high single). */
+ 0xB1C5A2E4, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3CB440D0, /* c1 (low single). */
+ 0x3E1B3D00, /* c2. */
+ 0x3EB9F664, /* c3. */
+ 0x3DD647C0, /* c4. */
+ 0x3FB3121F, /* B' = pi/2 - B (high single). */
+ 0xB30F347D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E31AE4D, /* c0 (high single). */
+ 0xB1F32251, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3CF6A500, /* c1 (low single). */
+ 0x3E3707DA, /* c2. */
+ 0x3EBFA489, /* c3. */
+ 0x3DFBD9C7, /* c4. */
+ 0x3FAFEDDF, /* B' = pi/2 - B (high single). */
+ 0x331BBA77, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E4BAFAF, /* c0 (high single). */
+ 0x2F2A29E0, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D221018, /* c1 (low single). */
+ 0x3E53BED0, /* c2. */
+ 0x3EC67E26, /* c3. */
+ 0x3E1568E2, /* c4. */
+ 0x3FACC9A0, /* B' = pi/2 - B (high single). */
+ 0xB2655A50, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E65F267, /* c0 (high single). */
+ 0x31B4B1DF, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D4E8B90, /* c1 (low single). */
+ 0x3E718ACA, /* c2. */
+ 0x3ECE7164, /* c3. */
+ 0x3E2DC161, /* c4. */
+ 0x3FA9A560, /* B' = pi/2 - B (high single). */
+ 0x33719861, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E803FD4, /* c0 (high single). */
+ 0xB2279E66, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D807FC8, /* c1 (low single). */
+ 0x3E884BD4, /* c2. */
+ 0x3ED7812D, /* c3. */
+ 0x3E4636EB, /* c4. */
+ 0x3FA68121, /* B' = pi/2 - B (high single). */
+ 0x31E43AAC, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E8DB082, /* c0 (high single). */
+ 0xB132A234, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D9CD7D0, /* c1 (low single). */
+ 0x3E988A60, /* c2. */
+ 0x3EE203E3, /* c3. */
+ 0x3E63582C, /* c4. */
+ 0x3FA35CE2, /* B' = pi/2 - B (high single). */
+ 0xB33889B6, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3E9B5042, /* c0 (high single). */
+ 0xB22A3AEE, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3DBC7490, /* c1 (low single). */
+ 0x3EA99AF5, /* c2. */
+ 0x3EEDE107, /* c3. */
+ 0x3E80E9AA, /* c4. */
+ 0x3FA038A2, /* B' = pi/2 - B (high single). */
+ 0x32E4CA7E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3EA92457, /* c0 (high single). */
+ 0x30B80830, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3DDF8200, /* c1 (low single). */
+ 0x3EBB99E9, /* c2. */
+ 0x3EFB4AA8, /* c3. */
+ 0x3E9182BE, /* c4. */
+ 0x3F9D1463, /* B' = pi/2 - B (high single). */
+ 0xB2C55799, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3EB73250, /* c0 (high single). */
+ 0xB2028823, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E0318F8, /* c1 (low single). */
+ 0x3ECEA678, /* c2. */
+ 0x3F053C67, /* c3. */
+ 0x3EA41E53, /* c4. */
+ 0x3F99F023, /* B' = pi/2 - B (high single). */
+ 0x33484328, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3EC5800D, /* c0 (high single). */
+ 0xB214C3C1, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E185E54, /* c1 (low single). */
+ 0x3EE2E342, /* c2. */
+ 0x3F0DCA73, /* c3. */
+ 0x3EB8CC21, /* c4. */
+ 0x3F96CBE4, /* B' = pi/2 - B (high single). */
+ 0xB14CDE2E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3ED413CD, /* c0 (high single). */
+ 0xB1C06152, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E2FB0CC, /* c1 (low single). */
+ 0x3EF876CB, /* c2. */
+ 0x3F177807, /* c3. */
+ 0x3ED08437, /* c4. */
+ 0x3F93A7A5, /* B' = pi/2 - B (high single). */
+ 0xB361DEEE, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3EE2F439, /* c0 (high single). */
+ 0xB1F4399E, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E49341C, /* c1 (low single). */
+ 0x3F07C61A, /* c2. */
+ 0x3F22560F, /* c3. */
+ 0x3EEAA81E, /* c4. */
+ 0x3F908365, /* B' = pi/2 - B (high single). */
+ 0x3292200D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3EF22870, /* c0 (high single). */
+ 0x325271F4, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E65107A, /* c1 (low single). */
+ 0x3F1429F0, /* c2. */
+ 0x3F2E8AFC, /* c3. */
+ 0x3F040498, /* c4. */
+ 0x3F8D5F26, /* B' = pi/2 - B (high single). */
+ 0xB30C0105, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F00DC0D, /* c0 (high single). */
+ 0xB214AF72, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E81B994, /* c1 (low single). */
+ 0x3F218233, /* c2. */
+ 0x3F3C4531, /* c3. */
+ 0x3F149688, /* c4. */
+ 0x3F8A3AE6, /* B' = pi/2 - B (high single). */
+ 0x331EEDF0, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F08D5B9, /* c0 (high single). */
+ 0xB25EF98E, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E92478D, /* c1 (low single). */
+ 0x3F2FEDC9, /* c2. */
+ 0x3F4BCD58, /* c3. */
+ 0x3F27AE9E, /* c4. */
+ 0x3F8716A7, /* B' = pi/2 - B (high single). */
+ 0xB2588C6D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F1105AF, /* c0 (high single). */
+ 0x32F045B0, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EA44EE2, /* c1 (low single). */
+ 0x3F3F8FDB, /* c2. */
+ 0x3F5D3FD0, /* c3. */
+ 0x3F3D0A23, /* c4. */
+ 0x3F83F267, /* B' = pi/2 - B (high single). */
+ 0x3374CBD9, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F1970C4, /* c0 (high single). */
+ 0x32904848, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EB7EFF8, /* c1 (low single). */
+ 0x3F50907C, /* c2. */
+ 0x3F710FEA, /* c3. */
+ 0x3F561FED, /* c4. */
+ 0x3F80CE28, /* B' = pi/2 - B (high single). */
+ 0x31FDD672, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F221C37, /* c0 (high single). */
+ 0xB20C61DC, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3ECD4F71, /* c1 (low single). */
+ 0x3F631DAA, /* c2. */
+ 0x3F83B471, /* c3. */
+ 0x3F7281EA, /* c4. */
+ 0x3F7B53D1, /* B' = pi/2 - B (high single). */
+ 0x32955386, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F2B0DC1, /* c0 (high single). */
+ 0x32AB7EBA, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EE496C2, /* c1 (low single). */
+ 0x3F776C40, /* c2. */
+ 0x3F9065C1, /* c3. */
+ 0x3F89AFB6, /* c4. */
+ 0x3F750B52, /* B' = pi/2 - B (high single). */
+ 0x32EB316F, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F344BA9, /* c0 (high single). */
+ 0xB2B8B0EA, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EFDF4F7, /* c1 (low single). */
+ 0x3F86DCA8, /* c2. */
+ 0x3F9ED53B, /* c3. */
+ 0x3F9CBEDE, /* c4. */
+ 0x3F6EC2D4, /* B' = pi/2 - B (high single). */
+ 0xB2BEF0A7, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F3DDCCF, /* c0 (high single). */
+ 0x32D29606, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEE6606F, /* c1 (low single). */
+ 0x3F9325D6, /* c2. */
+ 0x3FAF4E69, /* c3. */
+ 0x3FB3080C, /* c4. */
+ 0x3F687A55, /* B' = pi/2 - B (high single). */
+ 0xB252257B, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F47C8CC, /* c0 (high single). */
+ 0xB200F51A, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEC82C6C, /* c1 (low single). */
+ 0x3FA0BAE9, /* c2. */
+ 0x3FC2252F, /* c3. */
+ 0x3FCD24C7, /* c4. */
+ 0x3F6231D6, /* B' = pi/2 - B (high single). */
+ 0xB119A6A2, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F521801, /* c0 (high single). */
+ 0x32AE4178, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEA72938, /* c1 (low single). */
+ 0x3FAFCC22, /* c2. */
+ 0x3FD7BD4A, /* c3. */
+ 0x3FEBB01B, /* c4. */
+ 0x3F5BE957, /* B' = pi/2 - B (high single). */
+ 0x3205522A, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F5CD3BE, /* c0 (high single). */
+ 0x31460308, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBE8306C5, /* c1 (low single). */
+ 0x3FC09232, /* c2. */
+ 0x3FF09632, /* c3. */
+ 0x4007DB00, /* c4. */
+ 0x3F55A0D8, /* B' = pi/2 - B (high single). */
+ 0x329886FF, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F68065E, /* c0 (high single). */
+ 0x32670D1A, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBE36D1D6, /* c1 (low single). */
+ 0x3FD35007, /* c2. */
+ 0x4006A861, /* c3. */
+ 0x401D4BDA, /* c4. */
+ 0x3F4F5859, /* B' = pi/2 - B (high single). */
+ 0x32EE64E8, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0x3F73BB75, /* c0 (high single). */
+ 0x32FC908D, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBDBF94B0, /* c1 (low single). */
+ 0x3FE8550F, /* c2. */
+ 0x40174F67, /* c3. */
+ 0x4036C608, /* c4. */
+ 0x3F490FDB, /* B' = pi/2 - B (high single). */
+ 0xB2BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE8BE60E, /* c0 (high single). */
+ 0x320D8D84, /* c0 (low single). */
+ 0x3F000000, /* c1 (high 1 bit). */
+ 0xBDF817B1, /* c1 (low single). */
+ 0xBD8345EB, /* c2. */
+ 0x3D1DFDAC, /* c3. */
+ 0xBC52CF6F, /* c4. */
+ 0x3F42C75C, /* B' = pi/2 - B (high single). */
+ 0xB24BBE8A, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE87283F, /* c0 (high single). */
+ 0xB268B966, /* c0 (low single). */
+ 0x3F000000, /* c1 (high 1 bit). */
+ 0xBDFE6529, /* c1 (low single). */
+ 0xBD7B1953, /* c2. */
+ 0x3D18E109, /* c3. */
+ 0xBC4570B0, /* c4. */
+ 0x3F3C7EDD, /* B' = pi/2 - B (high single). */
+ 0xB1000ADD, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE827420, /* c0 (high single). */
+ 0x320B8B4D, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DFB9428, /* c1 (low single). */
+ 0xBD7002B4, /* c2. */
+ 0x3D142A6C, /* c3. */
+ 0xBC3A47FF, /* c4. */
+ 0x3F36365E, /* B' = pi/2 - B (high single). */
+ 0x320BB91C, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE7B9282, /* c0 (high single). */
+ 0xB13383D2, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DF5D211, /* c1 (low single). */
+ 0xBD6542B3, /* c2. */
+ 0x3D0FE5E5, /* c3. */
+ 0xBC31FB14, /* c4. */
+ 0x3F2FEDDF, /* B' = pi/2 - B (high single). */
+ 0x329BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE724E73, /* c0 (high single). */
+ 0x3120C3E2, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DF05283, /* c1 (low single). */
+ 0xBD5AD45E, /* c2. */
+ 0x3D0BAFBF, /* c3. */
+ 0xBC27B8BB, /* c4. */
+ 0x3F29A560, /* B' = pi/2 - B (high single). */
+ 0x32F19861, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE691B44, /* c0 (high single). */
+ 0x31F18936, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DEB138B, /* c1 (low single). */
+ 0xBD50B2F7, /* c2. */
+ 0x3D07BE3A, /* c3. */
+ 0xBC1E46A7, /* c4. */
+ 0x3F235CE2, /* B' = pi/2 - B (high single). */
+ 0xB2B889B6, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE5FF82C, /* c0 (high single). */
+ 0xB170723A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DE61354, /* c1 (low single). */
+ 0xBD46DA06, /* c2. */
+ 0x3D0401F8, /* c3. */
+ 0xBC14E013, /* c4. */
+ 0x3F1D1463, /* B' = pi/2 - B (high single). */
+ 0xB2455799, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE56E46B, /* c0 (high single). */
+ 0x31E3F001, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DE15025, /* c1 (low single). */
+ 0xBD3D4550, /* c2. */
+ 0x3D00462D, /* c3. */
+ 0xBC092C98, /* c4. */
+ 0x3F16CBE4, /* B' = pi/2 - B (high single). */
+ 0xB0CCDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE4DDF41, /* c0 (high single). */
+ 0xB1AEA094, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DDCC85C, /* c1 (low single). */
+ 0xBD33F0BE, /* c2. */
+ 0x3CFA23B0, /* c3. */
+ 0xBC01FCF7, /* c4. */
+ 0x3F108365, /* B' = pi/2 - B (high single). */
+ 0x3212200D, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE44E7F8, /* c0 (high single). */
+ 0xB1CAA3CB, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD87A74, /* c1 (low single). */
+ 0xBD2AD885, /* c2. */
+ 0x3CF3C785, /* c3. */
+ 0xBBF1E348, /* c4. */
+ 0x3F0A3AE6, /* B' = pi/2 - B (high single). */
+ 0x329EEDF0, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE3BFDDC, /* c0 (high single). */
+ 0xB132521A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD464FC, /* c1 (low single). */
+ 0xBD21F8F1, /* c2. */
+ 0x3CEE3076, /* c3. */
+ 0xBBE6D263, /* c4. */
+ 0x3F03F267, /* B' = pi/2 - B (high single). */
+ 0x32F4CBD9, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE33203E, /* c0 (high single). */
+ 0x31FEF5BE, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD0869C, /* c1 (low single). */
+ 0xBD194E8C, /* c2. */
+ 0x3CE8DCA9, /* c3. */
+ 0xBBDADA55, /* c4. */
+ 0x3EFB53D1, /* B' = pi/2 - B (high single). */
+ 0x32155386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE2A4E71, /* c0 (high single). */
+ 0xB19CFCEC, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DCCDE11, /* c1 (low single). */
+ 0xBD10D605, /* c2. */
+ 0x3CE382A7, /* c3. */
+ 0xBBC8BD97, /* c4. */
+ 0x3EEEC2D4, /* B' = pi/2 - B (high single). */
+ 0xB23EF0A7, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE2187D0, /* c0 (high single). */
+ 0xB1B7C7F7, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC96A2B, /* c1 (low single). */
+ 0xBD088C22, /* c2. */
+ 0x3CDE950E, /* c3. */
+ 0xBBB89AD1, /* c4. */
+ 0x3EE231D6, /* B' = pi/2 - B (high single). */
+ 0xB099A6A2, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE18CBB7, /* c0 (high single). */
+ 0xAFE28430, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC629CE, /* c1 (low single). */
+ 0xBD006DCD, /* c2. */
+ 0x3CDA5A2C, /* c3. */
+ 0xBBB0B3D2, /* c4. */
+ 0x3ED5A0D8, /* B' = pi/2 - B (high single). */
+ 0x321886FF, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE101985, /* c0 (high single). */
+ 0xB02FB2B8, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC31BF3, /* c1 (low single). */
+ 0xBCF0F04D, /* c2. */
+ 0x3CD60BC7, /* c3. */
+ 0xBBA138BA, /* c4. */
+ 0x3EC90FDB, /* B' = pi/2 - B (high single). */
+ 0xB23BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBE07709D, /* c0 (high single). */
+ 0xB18A2A83, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC03FA2, /* c1 (low single). */
+ 0xBCE15096, /* c2. */
+ 0x3CD26472, /* c3. */
+ 0xBB9A1270, /* c4. */
+ 0x3EBC7EDD, /* B' = pi/2 - B (high single). */
+ 0xB0800ADD, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDFDA0CB, /* c0 (high single). */
+ 0x2F14FCA0, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DBD93F7, /* c1 (low single). */
+ 0xBCD1F71B, /* c2. */
+ 0x3CCEDD2B, /* c3. */
+ 0xBB905946, /* c4. */
+ 0x3EAFEDDF, /* B' = pi/2 - B (high single). */
+ 0x321BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDEC708C, /* c0 (high single). */
+ 0xB14895C4, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DBB181E, /* c1 (low single). */
+ 0xBCC2DEA6, /* c2. */
+ 0x3CCB5027, /* c3. */
+ 0xBB7F3969, /* c4. */
+ 0x3EA35CE2, /* B' = pi/2 - B (high single). */
+ 0xB23889B6, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDDB4F55, /* c0 (high single). */
+ 0x30F6437E, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB8CB52, /* c1 (low single). */
+ 0xBCB40210, /* c2. */
+ 0x3CC82D45, /* c3. */
+ 0xBB643075, /* c4. */
+ 0x3E96CBE4, /* B' = pi/2 - B (high single). */
+ 0xB04CDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDCA3BFF, /* c0 (high single). */
+ 0x311C95EA, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB6ACDE, /* c1 (low single). */
+ 0xBCA55C5B, /* c2. */
+ 0x3CC5BC04, /* c3. */
+ 0xBB63A969, /* c4. */
+ 0x3E8A3AE6, /* B' = pi/2 - B (high single). */
+ 0x321EEDF0, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDB93569, /* c0 (high single). */
+ 0xAFB9ED00, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB4BC1F, /* c1 (low single). */
+ 0xBC96E905, /* c2. */
+ 0x3CC2E6F5, /* c3. */
+ 0xBB3E10A6, /* c4. */
+ 0x3E7B53D1, /* B' = pi/2 - B (high single). */
+ 0x31955386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBDA83A77, /* c0 (high single). */
+ 0x316D967A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB2F87C, /* c1 (low single). */
+ 0xBC88A31F, /* c2. */
+ 0x3CC0E763, /* c3. */
+ 0xBB3F1666, /* c4. */
+ 0x3E6231D6, /* B' = pi/2 - B (high single). */
+ 0xB019A6A2, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD974A0D, /* c0 (high single). */
+ 0xB14F365B, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB1616F, /* c1 (low single). */
+ 0xBC750CD8, /* c2. */
+ 0x3CBEB595, /* c3. */
+ 0xBB22B883, /* c4. */
+ 0x3E490FDB, /* B' = pi/2 - B (high single). */
+ 0xB1BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD866317, /* c0 (high single). */
+ 0xAFF02140, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAFF67D, /* c1 (low single). */
+ 0xBC591CD0, /* c2. */
+ 0x3CBCBEAD, /* c3. */
+ 0xBB04BBEC, /* c4. */
+ 0x3E2FEDDF, /* B' = pi/2 - B (high single). */
+ 0x319BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD6B08FF, /* c0 (high single). */
+ 0xB0EED236, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAEB739, /* c1 (low single). */
+ 0xBC3D6D51, /* c2. */
+ 0x3CBB485D, /* c3. */
+ 0xBAFFF5BA, /* c4. */
+ 0x3E16CBE4, /* B' = pi/2 - B (high single). */
+ 0xAFCCDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD495A6C, /* c0 (high single). */
+ 0xB0A427BD, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DADA345, /* c1 (low single). */
+ 0xBC21F648, /* c2. */
+ 0x3CB9D1B4, /* c3. */
+ 0xBACB5567, /* c4. */
+ 0x3DFB53D1, /* B' = pi/2 - B (high single). */
+ 0x31155386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD27B856, /* c0 (high single). */
+ 0xB0F7EE91, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DACBA4E, /* c1 (low single). */
+ 0xBC06AEE3, /* c2. */
+ 0x3CB8E5DC, /* c3. */
+ 0xBAEC00EE, /* c4. */
+ 0x3DC90FDB, /* B' = pi/2 - B (high single). */
+ 0xB13BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBD0620A3, /* c0 (high single). */
+ 0xB0ECAB40, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DABFC11, /* c1 (low single). */
+ 0xBBD7200F, /* c2. */
+ 0x3CB79475, /* c3. */
+ 0xBA2B0ADC, /* c4. */
+ 0x3D96CBE4, /* B' = pi/2 - B (high single). */
+ 0xAF4CDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBCC92278, /* c0 (high single). */
+ 0x302F2E68, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAB6854, /* c1 (low single). */
+ 0xBBA1214F, /* c2. */
+ 0x3CB6C1E9, /* c3. */
+ 0x3843C2F3, /* c4. */
+ 0x3D490FDB, /* B' = pi/2 - B (high single). */
+ 0xB0BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBC861015, /* c0 (high single). */
+ 0xAFD68E2E, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAAFEEB, /* c1 (low single). */
+ 0xBB569F3F, /* c2. */
+ 0x3CB6A84E, /* c3. */
+ 0xBAC64194, /* c4. */
+ 0x3CC90FDB, /* B' = pi/2 - B (high single). */
+ 0xB03BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0xBC060BF3, /* c0 (high single). */
+ 0x2FE251AE, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAABFB9, /* c1 (low single). */
+ 0xBAD67C60, /* c2. */
+ 0x3CB64CA5, /* c3. */
+ 0xBACDE881, /* c4. */
+ 0x00000000, /* B' = pi/2 - B (high single). */
+ 0x00000000, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x00000000, /* c0 (high single). */
+ 0x00000000, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAAAAAB, /* c1 (low single). */
+ 0x00000000, /* c2. */
+ 0x3CB5E28B, /* c3. */
+ 0x00000000, /* c4. */
+ 0xBCC90FDB, /* B' = pi/2 - B (high single). */
+ 0x303BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3C060BF3, /* c0 (high single). */
+ 0xAFE251AE, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAABFB9, /* c1 (low single). */
+ 0x3AD67C60, /* c2. */
+ 0x3CB64CA5, /* c3. */
+ 0x3ACDE881, /* c4. */
+ 0xBD490FDB, /* B' = pi/2 - B (high single). */
+ 0x30BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3C861015, /* c0 (high single). */
+ 0x2FD68E2E, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAAFEEB, /* c1 (low single). */
+ 0x3B569F3F, /* c2. */
+ 0x3CB6A84E, /* c3. */
+ 0x3AC64194, /* c4. */
+ 0xBD96CBE4, /* B' = pi/2 - B (high single). */
+ 0x2F4CDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3CC92278, /* c0 (high single). */
+ 0xB02F2E68, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAB6854, /* c1 (low single). */
+ 0x3BA1214F, /* c2. */
+ 0x3CB6C1E9, /* c3. */
+ 0xB843C2F2, /* c4. */
+ 0xBDC90FDB, /* B' = pi/2 - B (high single). */
+ 0x313BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D0620A3, /* c0 (high single). */
+ 0x30ECAB40, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DABFC11, /* c1 (low single). */
+ 0x3BD7200F, /* c2. */
+ 0x3CB79475, /* c3. */
+ 0x3A2B0ADC, /* c4. */
+ 0xBDFB53D1, /* B' = pi/2 - B (high single). */
+ 0xB1155386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D27B856, /* c0 (high single). */
+ 0x30F7EE91, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DACBA4E, /* c1 (low single). */
+ 0x3C06AEE3, /* c2. */
+ 0x3CB8E5DC, /* c3. */
+ 0x3AEC00EE, /* c4. */
+ 0xBE16CBE4, /* B' = pi/2 - B (high single). */
+ 0x2FCCDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D495A6C, /* c0 (high single). */
+ 0x30A427BD, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DADA345, /* c1 (low single). */
+ 0x3C21F648, /* c2. */
+ 0x3CB9D1B4, /* c3. */
+ 0x3ACB5567, /* c4. */
+ 0xBE2FEDDF, /* B' = pi/2 - B (high single). */
+ 0xB19BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D6B08FF, /* c0 (high single). */
+ 0x30EED236, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAEB739, /* c1 (low single). */
+ 0x3C3D6D51, /* c2. */
+ 0x3CBB485D, /* c3. */
+ 0x3AFFF5BA, /* c4. */
+ 0xBE490FDB, /* B' = pi/2 - B (high single). */
+ 0x31BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D866317, /* c0 (high single). */
+ 0x2FF02140, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DAFF67D, /* c1 (low single). */
+ 0x3C591CD0, /* c2. */
+ 0x3CBCBEAD, /* c3. */
+ 0x3B04BBEC, /* c4. */
+ 0xBE6231D6, /* B' = pi/2 - B (high single). */
+ 0x3019A6A2, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3D974A0D, /* c0 (high single). */
+ 0x314F365B, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB1616F, /* c1 (low single). */
+ 0x3C750CD8, /* c2. */
+ 0x3CBEB595, /* c3. */
+ 0x3B22B883, /* c4. */
+ 0xBE7B53D1, /* B' = pi/2 - B (high single). */
+ 0xB1955386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DA83A77, /* c0 (high single). */
+ 0xB16D967A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB2F87C, /* c1 (low single). */
+ 0x3C88A31F, /* c2. */
+ 0x3CC0E763, /* c3. */
+ 0x3B3F1666, /* c4. */
+ 0xBE8A3AE6, /* B' = pi/2 - B (high single). */
+ 0xB21EEDF0, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DB93569, /* c0 (high single). */
+ 0x2FB9ED00, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB4BC1F, /* c1 (low single). */
+ 0x3C96E905, /* c2. */
+ 0x3CC2E6F5, /* c3. */
+ 0x3B3E10A6, /* c4. */
+ 0xBE96CBE4, /* B' = pi/2 - B (high single). */
+ 0x304CDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DCA3BFF, /* c0 (high single). */
+ 0xB11C95EA, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB6ACDE, /* c1 (low single). */
+ 0x3CA55C5B, /* c2. */
+ 0x3CC5BC04, /* c3. */
+ 0x3B63A969, /* c4. */
+ 0xBEA35CE2, /* B' = pi/2 - B (high single). */
+ 0x323889B6, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DDB4F55, /* c0 (high single). */
+ 0xB0F6437E, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DB8CB52, /* c1 (low single). */
+ 0x3CB40210, /* c2. */
+ 0x3CC82D45, /* c3. */
+ 0x3B643075, /* c4. */
+ 0xBEAFEDDF, /* B' = pi/2 - B (high single). */
+ 0xB21BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DEC708C, /* c0 (high single). */
+ 0x314895C4, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DBB181E, /* c1 (low single). */
+ 0x3CC2DEA6, /* c2. */
+ 0x3CCB5027, /* c3. */
+ 0x3B7F3969, /* c4. */
+ 0xBEBC7EDD, /* B' = pi/2 - B (high single). */
+ 0x30800ADD, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3DFDA0CB, /* c0 (high single). */
+ 0xAF14FCA0, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DBD93F7, /* c1 (low single). */
+ 0x3CD1F71B, /* c2. */
+ 0x3CCEDD2B, /* c3. */
+ 0x3B905946, /* c4. */
+ 0xBEC90FDB, /* B' = pi/2 - B (high single). */
+ 0x323BBD2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E07709D, /* c0 (high single). */
+ 0x318A2A83, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC03FA2, /* c1 (low single). */
+ 0x3CE15096, /* c2. */
+ 0x3CD26472, /* c3. */
+ 0x3B9A1270, /* c4. */
+ 0xBED5A0D8, /* B' = pi/2 - B (high single). */
+ 0xB21886FF, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E101985, /* c0 (high single). */
+ 0x302FB2B8, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC31BF3, /* c1 (low single). */
+ 0x3CF0F04D, /* c2. */
+ 0x3CD60BC7, /* c3. */
+ 0x3BA138BA, /* c4. */
+ 0xBEE231D6, /* B' = pi/2 - B (high single). */
+ 0x3099A6A2, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E18CBB7, /* c0 (high single). */
+ 0x2FE28430, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC629CE, /* c1 (low single). */
+ 0x3D006DCD, /* c2. */
+ 0x3CDA5A2C, /* c3. */
+ 0x3BB0B3D2, /* c4. */
+ 0xBEEEC2D4, /* B' = pi/2 - B (high single). */
+ 0x323EF0A7, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E2187D0, /* c0 (high single). */
+ 0x31B7C7F7, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DC96A2B, /* c1 (low single). */
+ 0x3D088C22, /* c2. */
+ 0x3CDE950E, /* c3. */
+ 0x3BB89AD1, /* c4. */
+ 0xBEFB53D1, /* B' = pi/2 - B (high single). */
+ 0xB2155386, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E2A4E71, /* c0 (high single). */
+ 0x319CFCEC, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DCCDE11, /* c1 (low single). */
+ 0x3D10D605, /* c2. */
+ 0x3CE382A7, /* c3. */
+ 0x3BC8BD97, /* c4. */
+ 0xBF03F267, /* B' = pi/2 - B (high single). */
+ 0xB2F4CBD9, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E33203E, /* c0 (high single). */
+ 0xB1FEF5BE, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD0869C, /* c1 (low single). */
+ 0x3D194E8C, /* c2. */
+ 0x3CE8DCA9, /* c3. */
+ 0x3BDADA55, /* c4. */
+ 0xBF0A3AE6, /* B' = pi/2 - B (high single). */
+ 0xB29EEDF0, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E3BFDDC, /* c0 (high single). */
+ 0x3132521A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD464FC, /* c1 (low single). */
+ 0x3D21F8F1, /* c2. */
+ 0x3CEE3076, /* c3. */
+ 0x3BE6D263, /* c4. */
+ 0xBF108365, /* B' = pi/2 - B (high single). */
+ 0xB212200D, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E44E7F8, /* c0 (high single). */
+ 0x31CAA3CB, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DD87A74, /* c1 (low single). */
+ 0x3D2AD885, /* c2. */
+ 0x3CF3C785, /* c3. */
+ 0x3BF1E348, /* c4. */
+ 0xBF16CBE4, /* B' = pi/2 - B (high single). */
+ 0x30CCDE2E, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E4DDF41, /* c0 (high single). */
+ 0x31AEA094, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DDCC85C, /* c1 (low single). */
+ 0x3D33F0BE, /* c2. */
+ 0x3CFA23B0, /* c3. */
+ 0x3C01FCF7, /* c4. */
+ 0xBF1D1463, /* B' = pi/2 - B (high single). */
+ 0x32455799, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E56E46B, /* c0 (high single). */
+ 0xB1E3F001, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DE15025, /* c1 (low single). */
+ 0x3D3D4550, /* c2. */
+ 0x3D00462D, /* c3. */
+ 0x3C092C98, /* c4. */
+ 0xBF235CE2, /* B' = pi/2 - B (high single). */
+ 0x32B889B6, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E5FF82C, /* c0 (high single). */
+ 0x3170723A, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DE61354, /* c1 (low single). */
+ 0x3D46DA06, /* c2. */
+ 0x3D0401F8, /* c3. */
+ 0x3C14E013, /* c4. */
+ 0xBF29A560, /* B' = pi/2 - B (high single). */
+ 0xB2F19861, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E691B44, /* c0 (high single). */
+ 0xB1F18936, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DEB138B, /* c1 (low single). */
+ 0x3D50B2F7, /* c2. */
+ 0x3D07BE3A, /* c3. */
+ 0x3C1E46A7, /* c4. */
+ 0xBF2FEDDF, /* B' = pi/2 - B (high single). */
+ 0xB29BBA77, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E724E73, /* c0 (high single). */
+ 0xB120C3E2, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DF05283, /* c1 (low single). */
+ 0x3D5AD45E, /* c2. */
+ 0x3D0BAFBF, /* c3. */
+ 0x3C27B8BB, /* c4. */
+ 0xBF36365E, /* B' = pi/2 - B (high single). */
+ 0xB20BB91C, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E7B9282, /* c0 (high single). */
+ 0x313383D2, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DF5D211, /* c1 (low single). */
+ 0x3D6542B3, /* c2. */
+ 0x3D0FE5E5, /* c3. */
+ 0x3C31FB14, /* c4. */
+ 0xBF3C7EDD, /* B' = pi/2 - B (high single). */
+ 0x31000ADD, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E827420, /* c0 (high single). */
+ 0xB20B8B4D, /* c0 (low single). */
+ 0x3E800000, /* c1 (high 1 bit). */
+ 0x3DFB9428, /* c1 (low single). */
+ 0x3D7002B4, /* c2. */
+ 0x3D142A6C, /* c3. */
+ 0x3C3A47FF, /* c4. */
+ 0xBF42C75C, /* B' = pi/2 - B (high single). */
+ 0x324BBE8A, /* B' = pi/2 - B (low single). */
+ 0x3F800000, /* tau (1 for cot path). */
+ 0x3E87283F, /* c0 (high single). */
+ 0x3268B966, /* c0 (low single). */
+ 0x3F000000, /* c1 (high 1 bit). */
+ 0xBDFE6529, /* c1 (low single). */
+ 0x3D7B1953, /* c2. */
+ 0x3D18E109, /* c3. */
+ 0x3C4570B0, /* c4. */
+ 0xBF490FDB, /* B' = pi/2 - B (high single). */
+ 0x32BBBD2E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF800000, /* c0 (high single). */
+ 0x2B410000, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xB3000000, /* c1 (low single). */
+ 0xC0000000, /* c2. */
+ 0x402AB7C8, /* c3. */
+ 0xC05561DB, /* c4. */
+ 0xBF4F5859, /* B' = pi/2 - B (high single). */
+ 0xB2EE64E8, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF73BB75, /* c0 (high single). */
+ 0xB2FC908D, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBDBF94B0, /* c1 (low single). */
+ 0xBFE8550F, /* c2. */
+ 0x40174F67, /* c3. */
+ 0xC036C608, /* c4. */
+ 0xBF55A0D8, /* B' = pi/2 - B (high single). */
+ 0xB29886FF, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF68065E, /* c0 (high single). */
+ 0xB2670D1A, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBE36D1D6, /* c1 (low single). */
+ 0xBFD35007, /* c2. */
+ 0x4006A861, /* c3. */
+ 0xC01D4BDA, /* c4. */
+ 0xBF5BE957, /* B' = pi/2 - B (high single). */
+ 0xB205522A, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF5CD3BE, /* c0 (high single). */
+ 0xB1460308, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBE8306C5, /* c1 (low single). */
+ 0xBFC09232, /* c2. */
+ 0x3FF09632, /* c3. */
+ 0xC007DB00, /* c4. */
+ 0xBF6231D6, /* B' = pi/2 - B (high single). */
+ 0x3119A6A2, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF521801, /* c0 (high single). */
+ 0xB2AE4178, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEA72938, /* c1 (low single). */
+ 0xBFAFCC22, /* c2. */
+ 0x3FD7BD4A, /* c3. */
+ 0xBFEBB01B, /* c4. */
+ 0xBF687A55, /* B' = pi/2 - B (high single). */
+ 0x3252257B, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF47C8CC, /* c0 (high single). */
+ 0x3200F51A, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEC82C6C, /* c1 (low single). */
+ 0xBFA0BAE9, /* c2. */
+ 0x3FC2252F, /* c3. */
+ 0xBFCD24C7, /* c4. */
+ 0xBF6EC2D4, /* B' = pi/2 - B (high single). */
+ 0x32BEF0A7, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF3DDCCF, /* c0 (high single). */
+ 0xB2D29606, /* c0 (low single). */
+ 0x40000000, /* c1 (high 1 bit). */
+ 0xBEE6606F, /* c1 (low single). */
+ 0xBF9325D6, /* c2. */
+ 0x3FAF4E69, /* c3. */
+ 0xBFB3080C, /* c4. */
+ 0xBF750B52, /* B' = pi/2 - B (high single). */
+ 0xB2EB316F, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF344BA9, /* c0 (high single). */
+ 0x32B8B0EA, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EFDF4F7, /* c1 (low single). */
+ 0xBF86DCA8, /* c2. */
+ 0x3F9ED53B, /* c3. */
+ 0xBF9CBEDE, /* c4. */
+ 0xBF7B53D1, /* B' = pi/2 - B (high single). */
+ 0xB2955386, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF2B0DC1, /* c0 (high single). */
+ 0xB2AB7EBA, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EE496C2, /* c1 (low single). */
+ 0xBF776C40, /* c2. */
+ 0x3F9065C1, /* c3. */
+ 0xBF89AFB6, /* c4. */
+ 0xBF80CE28, /* B' = pi/2 - B (high single). */
+ 0xB1FDD672, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF221C37, /* c0 (high single). */
+ 0x320C61DC, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3ECD4F71, /* c1 (low single). */
+ 0xBF631DAA, /* c2. */
+ 0x3F83B471, /* c3. */
+ 0xBF7281EA, /* c4. */
+ 0xBF83F267, /* B' = pi/2 - B (high single). */
+ 0xB374CBD9, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF1970C4, /* c0 (high single). */
+ 0xB2904848, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EB7EFF8, /* c1 (low single). */
+ 0xBF50907C, /* c2. */
+ 0x3F710FEA, /* c3. */
+ 0xBF561FED, /* c4. */
+ 0xBF8716A7, /* B' = pi/2 - B (high single). */
+ 0x32588C6D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF1105AF, /* c0 (high single). */
+ 0xB2F045B0, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3EA44EE2, /* c1 (low single). */
+ 0xBF3F8FDB, /* c2. */
+ 0x3F5D3FD0, /* c3. */
+ 0xBF3D0A23, /* c4. */
+ 0xBF8A3AE6, /* B' = pi/2 - B (high single). */
+ 0xB31EEDF0, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF08D5B9, /* c0 (high single). */
+ 0x325EF98E, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E92478D, /* c1 (low single). */
+ 0xBF2FEDC9, /* c2. */
+ 0x3F4BCD58, /* c3. */
+ 0xBF27AE9E, /* c4. */
+ 0xBF8D5F26, /* B' = pi/2 - B (high single). */
+ 0x330C0105, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBF00DC0D, /* c0 (high single). */
+ 0x3214AF72, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E81B994, /* c1 (low single). */
+ 0xBF218233, /* c2. */
+ 0x3F3C4531, /* c3. */
+ 0xBF149688, /* c4. */
+ 0xBF908365, /* B' = pi/2 - B (high single). */
+ 0xB292200D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBEF22870, /* c0 (high single). */
+ 0xB25271F4, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E65107A, /* c1 (low single). */
+ 0xBF1429F0, /* c2. */
+ 0x3F2E8AFC, /* c3. */
+ 0xBF040498, /* c4. */
+ 0xBF93A7A5, /* B' = pi/2 - B (high single). */
+ 0x3361DEEE, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBEE2F439, /* c0 (high single). */
+ 0x31F4399E, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E49341C, /* c1 (low single). */
+ 0xBF07C61A, /* c2. */
+ 0x3F22560F, /* c3. */
+ 0xBEEAA81E, /* c4. */
+ 0xBF96CBE4, /* B' = pi/2 - B (high single). */
+ 0x314CDE2E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBED413CD, /* c0 (high single). */
+ 0x31C06152, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E2FB0CC, /* c1 (low single). */
+ 0xBEF876CB, /* c2. */
+ 0x3F177807, /* c3. */
+ 0xBED08437, /* c4. */
+ 0xBF99F023, /* B' = pi/2 - B (high single). */
+ 0xB3484328, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBEC5800D, /* c0 (high single). */
+ 0x3214C3C1, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E185E54, /* c1 (low single). */
+ 0xBEE2E342, /* c2. */
+ 0x3F0DCA73, /* c3. */
+ 0xBEB8CC21, /* c4. */
+ 0xBF9D1463, /* B' = pi/2 - B (high single). */
+ 0x32C55799, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBEB73250, /* c0 (high single). */
+ 0x32028823, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3E0318F8, /* c1 (low single). */
+ 0xBECEA678, /* c2. */
+ 0x3F053C67, /* c3. */
+ 0xBEA41E53, /* c4. */
+ 0xBFA038A2, /* B' = pi/2 - B (high single). */
+ 0xB2E4CA7E, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBEA92457, /* c0 (high single). */
+ 0xB0B80830, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3DDF8200, /* c1 (low single). */
+ 0xBEBB99E9, /* c2. */
+ 0x3EFB4AA8, /* c3. */
+ 0xBE9182BE, /* c4. */
+ 0xBFA35CE2, /* B' = pi/2 - B (high single). */
+ 0x333889B6, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE9B5042, /* c0 (high single). */
+ 0x322A3AEE, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3DBC7490, /* c1 (low single). */
+ 0xBEA99AF5, /* c2. */
+ 0x3EEDE107, /* c3. */
+ 0xBE80E9AA, /* c4. */
+ 0xBFA68121, /* B' = pi/2 - B (high single). */
+ 0xB1E43AAC, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE8DB082, /* c0 (high single). */
+ 0x3132A234, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D9CD7D0, /* c1 (low single). */
+ 0xBE988A60, /* c2. */
+ 0x3EE203E3, /* c3. */
+ 0xBE63582C, /* c4. */
+ 0xBFA9A560, /* B' = pi/2 - B (high single). */
+ 0xB3719861, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE803FD4, /* c0 (high single). */
+ 0x32279E66, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D807FC8, /* c1 (low single). */
+ 0xBE884BD4, /* c2. */
+ 0x3ED7812D, /* c3. */
+ 0xBE4636EB, /* c4. */
+ 0xBFACC9A0, /* B' = pi/2 - B (high single). */
+ 0x32655A50, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE65F267, /* c0 (high single). */
+ 0xB1B4B1DF, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D4E8B90, /* c1 (low single). */
+ 0xBE718ACA, /* c2. */
+ 0x3ECE7164, /* c3. */
+ 0xBE2DC161, /* c4. */
+ 0xBFAFEDDF, /* B' = pi/2 - B (high single). */
+ 0xB31BBA77, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE4BAFAF, /* c0 (high single). */
+ 0xAF2A29E0, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3D221018, /* c1 (low single). */
+ 0xBE53BED0, /* c2. */
+ 0x3EC67E26, /* c3. */
+ 0xBE1568E2, /* c4. */
+ 0xBFB3121F, /* B' = pi/2 - B (high single). */
+ 0x330F347D, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE31AE4D, /* c0 (high single). */
+ 0x31F32251, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3CF6A500, /* c1 (low single). */
+ 0xBE3707DA, /* c2. */
+ 0x3EBFA489, /* c3. */
+ 0xBDFBD9C7, /* c4. */
+ 0xBFB6365E, /* B' = pi/2 - B (high single). */
+ 0xB28BB91C, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBE17E564, /* c0 (high single). */
+ 0x31C5A2E4, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3CB440D0, /* c1 (low single). */
+ 0xBE1B3D00, /* c2. */
+ 0x3EB9F664, /* c3. */
+ 0xBDD647C0, /* c4. */
+ 0xBFB95A9E, /* B' = pi/2 - B (high single). */
+ 0x33651267, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBDFC98C2, /* c0 (high single). */
+ 0x30AE525C, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3C793D20, /* c1 (low single). */
+ 0xBE003845, /* c2. */
+ 0x3EB5271F, /* c3. */
+ 0xBDAC669E, /* c4. */
+ 0xBFBC7EDD, /* B' = pi/2 - B (high single). */
+ 0x31800ADD, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBDC9B5DC, /* c0 (high single). */
+ 0xB145AD86, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3C1EEF20, /* c1 (low single). */
+ 0xBDCBAAEA, /* c2. */
+ 0x3EB14E5E, /* c3. */
+ 0xBD858BB2, /* c4. */
+ 0xBFBFA31C, /* B' = pi/2 - B (high single). */
+ 0xB3450FB0, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBD9711CE, /* c0 (high single). */
+ 0xB14FEB28, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3BB24C00, /* c1 (low single). */
+ 0xBD97E43A, /* c2. */
+ 0x3EAE6A89, /* c3. */
+ 0xBD4D07E0, /* c4. */
+ 0xBFC2C75C, /* B' = pi/2 - B (high single). */
+ 0x32CBBE8A, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBD49393C, /* c0 (high single). */
+ 0xB0A39F5B, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3B1E2B00, /* c1 (low single). */
+ 0xBD49B5D4, /* c2. */
+ 0x3EAC4F10, /* c3. */
+ 0xBCFD9425, /* c4. */
+ 0xBFC5EB9B, /* B' = pi/2 - B (high single). */
+ 0xB2DE638C, /* B' = pi/2 - B (low single). */
+ 0x00000000, /* tau (1 for cot path). */
+ 0xBCC91A31, /* c0 (high single). */
+ 0xAF8E8D1A, /* c0 (low single). */
+ 0x3F800000, /* c1 (high 1 bit). */
+ 0x3A1DFA00, /* c1 (low single). */
+ 0xBCC9392D, /* c2. */
+ 0x3EAB1889, /* c3. */
+ 0xBC885D3B, /* c4. */
+ /* So its save to read 32 bytes past the end. */
+ 0x00000000,
+ 0x00000000,
+ 0x00000000,
+ 0x00000000,
+ 0x00000000,
+ 0x00000000,
+ 0x00000000,
+ 0x00000000)
+ .type __svml_stan_common_data_avx2, @object
+ .size __svml_stan_common_data_avx2, .-__svml_stan_common_data_avx2
+
+# endif
+#endif
+
+#if (defined AVX512_SHARED_OFFSETS) || (defined AVX512_SHARED_TABLE)
+
+# define _Reduction 0
+# define AVX512_SHARED_DATA(offset) \
+ ((offset) + (__svml_stan_common_data_avx512))
+
+# if (defined AVX512_SHARED_TABLE)
+
+ .section .rodata.evex512, "a"
+ .align 64
+ .globl __svml_stan_common_data_avx512
+__svml_stan_common_data_avx512:
+ float_block (__svml_stan_common_data_avx512, _Reduction,
+ /* P_hi P_med P_lo. */
+ 0x00000000, 0x00000000, 0x00000000, /* 0 */
+ 0x00000000, 0x00000000, 0x00000000, /* 1 */
+ 0x00000000, 0x00000000, 0x00000000, /* 2 */
+ 0x00000000, 0x00000000, 0x00000000, /* 3 */
+ 0x00000000, 0x00000000, 0x00000000, /* 4 */
+ 0x00000000, 0x00000000, 0x00000000, /* 5 */
+ 0x00000000, 0x00000000, 0x00000000, /* 6 */
+ 0x00000000, 0x00000000, 0x00000000, /* 7 */
+ 0x00000000, 0x00000000, 0x00000000, /* 8 */
+ 0x00000000, 0x00000000, 0x00000000, /* 9 */
+ 0x00000000, 0x00000000, 0x00000000, /* 10 */
+ 0x00000000, 0x00000000, 0x00000000, /* 11 */
+ 0x00000000, 0x00000000, 0x00000000, /* 12 */
+ 0x00000000, 0x00000000, 0x00000000, /* 13 */
+ 0x00000000, 0x00000000, 0x00000000, /* 14 */
+ 0x00000000, 0x00000000, 0x00000000, /* 15 */
+ 0x00000000, 0x00000000, 0x00000000, /* 16 */
+ 0x00000000, 0x00000000, 0x00000000, /* 17 */
+ 0x00000000, 0x00000000, 0x00000000, /* 18 */
+ 0x00000000, 0x00000000, 0x00000000, /* 19 */
+ 0x00000000, 0x00000000, 0x00000000, /* 20 */
+ 0x00000000, 0x00000000, 0x00000000, /* 21 */
+ 0x00000000, 0x00000000, 0x00000000, /* 22 */
+ 0x00000000, 0x00000000, 0x00000000, /* 23 */
+ 0x00000000, 0x00000000, 0x00000000, /* 24 */
+ 0x00000000, 0x00000000, 0x00000000, /* 25 */
+ 0x00000000, 0x00000000, 0x00000000, /* 26 */
+ 0x00000000, 0x00000000, 0x00000000, /* 27 */
+ 0x00000000, 0x00000000, 0x00000000, /* 28 */
+ 0x00000000, 0x00000000, 0x00000000, /* 29 */
+ 0x00000000, 0x00000000, 0x00000000, /* 30 */
+ 0x00000000, 0x00000000, 0x00000000, /* 31 */
+ 0x00000000, 0x00000000, 0x00000000, /* 32 */
+ 0x00000000, 0x00000000, 0x00000000, /* 33 */
+ 0x00000000, 0x00000000, 0x00000000, /* 34 */
+ 0x00000000, 0x00000000, 0x00000000, /* 35 */
+ 0x00000000, 0x00000000, 0x00000000, /* 36 */
+ 0x00000000, 0x00000000, 0x00000000, /* 37 */
+ 0x00000000, 0x00000000, 0x00000000, /* 38 */
+ 0x00000000, 0x00000000, 0x00000000, /* 39 */
+ 0x00000000, 0x00000000, 0x00000000, /* 40 */
+ 0x00000000, 0x00000000, 0x00000000, /* 41 */
+ 0x00000000, 0x00000000, 0x00000000, /* 42 */
+ 0x00000000, 0x00000000, 0x00000000, /* 43 */
+ 0x00000000, 0x00000000, 0x00000000, /* 44 */
+ 0x00000000, 0x00000000, 0x00000000, /* 45 */
+ 0x00000000, 0x00000000, 0x00000000, /* 46 */
+ 0x00000000, 0x00000000, 0x00000000, /* 47 */
+ 0x00000000, 0x00000000, 0x00000000, /* 48 */
+ 0x00000000, 0x00000000, 0x00000000, /* 49 */
+ 0x00000000, 0x00000000, 0x00000000, /* 50 */
+ 0x00000000, 0x00000000, 0x00000000, /* 51 */
+ 0x00000000, 0x00000000, 0x00000000, /* 52 */
+ 0x00000000, 0x00000000, 0x00000000, /* 53 */
+ 0x00000000, 0x00000000, 0x00000000, /* 54 */
+ 0x00000000, 0x00000000, 0x00000000, /* 55 */
+ 0x00000000, 0x00000000, 0x00000000, /* 56 */
+ 0x00000000, 0x00000000, 0x00000001, /* 57 */
+ 0x00000000, 0x00000000, 0x00000002, /* 58 */
+ 0x00000000, 0x00000000, 0x00000005, /* 59 */
+ 0x00000000, 0x00000000, 0x0000000A, /* 60 */
+ 0x00000000, 0x00000000, 0x00000014, /* 61 */
+ 0x00000000, 0x00000000, 0x00000028, /* 62 */
+ 0x00000000, 0x00000000, 0x00000051, /* 63 */
+ 0x00000000, 0x00000000, 0x000000A2, /* 64 */
+ 0x00000000, 0x00000000, 0x00000145, /* 65 */
+ 0x00000000, 0x00000000, 0x0000028B, /* 66 */
+ 0x00000000, 0x00000000, 0x00000517, /* 67 */
+ 0x00000000, 0x00000000, 0x00000A2F, /* 68 */
+ 0x00000000, 0x00000000, 0x0000145F, /* 69 */
+ 0x00000000, 0x00000000, 0x000028BE, /* 70 */
+ 0x00000000, 0x00000000, 0x0000517C, /* 71 */
+ 0x00000000, 0x00000000, 0x0000A2F9, /* 72 */
+ 0x00000000, 0x00000000, 0x000145F3, /* 73 */
+ 0x00000000, 0x00000000, 0x00028BE6, /* 74 */
+ 0x00000000, 0x00000000, 0x000517CC, /* 75 */
+ 0x00000000, 0x00000000, 0x000A2F98, /* 76 */
+ 0x00000000, 0x00000000, 0x00145F30, /* 77 */
+ 0x00000000, 0x00000000, 0x0028BE60, /* 78 */
+ 0x00000000, 0x00000000, 0x00517CC1, /* 79 */
+ 0x00000000, 0x00000000, 0x00A2F983, /* 80 */
+ 0x00000000, 0x00000000, 0x0145F306, /* 81 */
+ 0x00000000, 0x00000000, 0x028BE60D, /* 82 */
+ 0x00000000, 0x00000000, 0x0517CC1B, /* 83 */
+ 0x00000000, 0x00000000, 0x0A2F9836, /* 84 */
+ 0x00000000, 0x00000000, 0x145F306D, /* 85 */
+ 0x00000000, 0x00000000, 0x28BE60DB, /* 86 */
+ 0x00000000, 0x00000000, 0x517CC1B7, /* 87 */
+ 0x00000000, 0x00000000, 0xA2F9836E, /* 88 */
+ 0x00000000, 0x00000001, 0x45F306DC, /* 89 */
+ 0x00000000, 0x00000002, 0x8BE60DB9, /* 90 */
+ 0x00000000, 0x00000005, 0x17CC1B72, /* 91 */
+ 0x00000000, 0x0000000A, 0x2F9836E4, /* 92 */
+ 0x00000000, 0x00000014, 0x5F306DC9, /* 93 */
+ 0x00000000, 0x00000028, 0xBE60DB93, /* 94 */
+ 0x00000000, 0x00000051, 0x7CC1B727, /* 95 */
+ 0x00000000, 0x000000A2, 0xF9836E4E, /* 96 */
+ 0x00000000, 0x00000145, 0xF306DC9C, /* 97 */
+ 0x00000000, 0x0000028B, 0xE60DB939, /* 98 */
+ 0x00000000, 0x00000517, 0xCC1B7272, /* 99 */
+ 0x00000000, 0x00000A2F, 0x9836E4E4, /* 100 */
+ 0x00000000, 0x0000145F, 0x306DC9C8, /* 101 */
+ 0x00000000, 0x000028BE, 0x60DB9391, /* 102 */
+ 0x00000000, 0x0000517C, 0xC1B72722, /* 103 */
+ 0x00000000, 0x0000A2F9, 0x836E4E44, /* 104 */
+ 0x00000000, 0x000145F3, 0x06DC9C88, /* 105 */
+ 0x00000000, 0x00028BE6, 0x0DB93910, /* 106 */
+ 0x00000000, 0x000517CC, 0x1B727220, /* 107 */
+ 0x00000000, 0x000A2F98, 0x36E4E441, /* 108 */
+ 0x00000000, 0x00145F30, 0x6DC9C882, /* 109 */
+ 0x00000000, 0x0028BE60, 0xDB939105, /* 110 */
+ 0x00000000, 0x00517CC1, 0xB727220A, /* 111 */
+ 0x00000000, 0x00A2F983, 0x6E4E4415, /* 112 */
+ 0x00000000, 0x0145F306, 0xDC9C882A, /* 113 */
+ 0x00000000, 0x028BE60D, 0xB9391054, /* 114 */
+ 0x00000000, 0x0517CC1B, 0x727220A9, /* 115 */
+ 0x00000000, 0x0A2F9836, 0xE4E44152, /* 116 */
+ 0x00000000, 0x145F306D, 0xC9C882A5, /* 117 */
+ 0x00000000, 0x28BE60DB, 0x9391054A, /* 118 */
+ 0x00000000, 0x517CC1B7, 0x27220A94, /* 119 */
+ 0x00000000, 0xA2F9836E, 0x4E441529, /* 120 */
+ 0x00000001, 0x45F306DC, 0x9C882A53, /* 121 */
+ 0x00000002, 0x8BE60DB9, 0x391054A7, /* 122 */
+ 0x00000005, 0x17CC1B72, 0x7220A94F, /* 123 */
+ 0x0000000A, 0x2F9836E4, 0xE441529F, /* 124 */
+ 0x00000014, 0x5F306DC9, 0xC882A53F, /* 125 */
+ 0x00000028, 0xBE60DB93, 0x91054A7F, /* 126 */
+ 0x00000051, 0x7CC1B727, 0x220A94FE, /* 127 */
+ 0x000000A2, 0xF9836E4E, 0x441529FC, /* 128 */
+ 0x00000145, 0xF306DC9C, 0x882A53F8, /* 129 */
+ 0x0000028B, 0xE60DB939, 0x1054A7F0, /* 130 */
+ 0x00000517, 0xCC1B7272, 0x20A94FE1, /* 131 */
+ 0x00000A2F, 0x9836E4E4, 0x41529FC2, /* 132 */
+ 0x0000145F, 0x306DC9C8, 0x82A53F84, /* 133 */
+ 0x000028BE, 0x60DB9391, 0x054A7F09, /* 134 */
+ 0x0000517C, 0xC1B72722, 0x0A94FE13, /* 135 */
+ 0x0000A2F9, 0x836E4E44, 0x1529FC27, /* 136 */
+ 0x000145F3, 0x06DC9C88, 0x2A53F84E, /* 137 */
+ 0x00028BE6, 0x0DB93910, 0x54A7F09D, /* 138 */
+ 0x000517CC, 0x1B727220, 0xA94FE13A, /* 139 */
+ 0x000A2F98, 0x36E4E441, 0x529FC275, /* 140 */
+ 0x00145F30, 0x6DC9C882, 0xA53F84EA, /* 141 */
+ 0x0028BE60, 0xDB939105, 0x4A7F09D5, /* 142 */
+ 0x00517CC1, 0xB727220A, 0x94FE13AB, /* 143 */
+ 0x00A2F983, 0x6E4E4415, 0x29FC2757, /* 144 */
+ 0x0145F306, 0xDC9C882A, 0x53F84EAF, /* 145 */
+ 0x028BE60D, 0xB9391054, 0xA7F09D5F, /* 146 */
+ 0x0517CC1B, 0x727220A9, 0x4FE13ABE, /* 147 */
+ 0x0A2F9836, 0xE4E44152, 0x9FC2757D, /* 148 */
+ 0x145F306D, 0xC9C882A5, 0x3F84EAFA, /* 149 */
+ 0x28BE60DB, 0x9391054A, 0x7F09D5F4, /* 150 */
+ 0x517CC1B7, 0x27220A94, 0xFE13ABE8, /* 151 */
+ 0xA2F9836E, 0x4E441529, 0xFC2757D1, /* 152 */
+ 0x45F306DC, 0x9C882A53, 0xF84EAFA3, /* 153 */
+ 0x8BE60DB9, 0x391054A7, 0xF09D5F47, /* 154 */
+ 0x17CC1B72, 0x7220A94F, 0xE13ABE8F, /* 155 */
+ 0x2F9836E4, 0xE441529F, 0xC2757D1F, /* 156 */
+ 0x5F306DC9, 0xC882A53F, 0x84EAFA3E, /* 157 */
+ 0xBE60DB93, 0x91054A7F, 0x09D5F47D, /* 158 */
+ 0x7CC1B727, 0x220A94FE, 0x13ABE8FA, /* 159 */
+ 0xF9836E4E, 0x441529FC, 0x2757D1F5, /* 160 */
+ 0xF306DC9C, 0x882A53F8, 0x4EAFA3EA, /* 161 */
+ 0xE60DB939, 0x1054A7F0, 0x9D5F47D4, /* 162 */
+ 0xCC1B7272, 0x20A94FE1, 0x3ABE8FA9, /* 163 */
+ 0x9836E4E4, 0x41529FC2, 0x757D1F53, /* 164 */
+ 0x306DC9C8, 0x82A53F84, 0xEAFA3EA6, /* 165 */
+ 0x60DB9391, 0x054A7F09, 0xD5F47D4D, /* 166 */
+ 0xC1B72722, 0x0A94FE13, 0xABE8FA9A, /* 167 */
+ 0x836E4E44, 0x1529FC27, 0x57D1F534, /* 168 */
+ 0x06DC9C88, 0x2A53F84E, 0xAFA3EA69, /* 169 */
+ 0x0DB93910, 0x54A7F09D, 0x5F47D4D3, /* 170 */
+ 0x1B727220, 0xA94FE13A, 0xBE8FA9A6, /* 171 */
+ 0x36E4E441, 0x529FC275, 0x7D1F534D, /* 172 */
+ 0x6DC9C882, 0xA53F84EA, 0xFA3EA69B, /* 173 */
+ 0xDB939105, 0x4A7F09D5, 0xF47D4D37, /* 174 */
+ 0xB727220A, 0x94FE13AB, 0xE8FA9A6E, /* 175 */
+ 0x6E4E4415, 0x29FC2757, 0xD1F534DD, /* 176 */
+ 0xDC9C882A, 0x53F84EAF, 0xA3EA69BB, /* 177 */
+ 0xB9391054, 0xA7F09D5F, 0x47D4D377, /* 178 */
+ 0x727220A9, 0x4FE13ABE, 0x8FA9A6EE, /* 179 */
+ 0xE4E44152, 0x9FC2757D, 0x1F534DDC, /* 180 */
+ 0xC9C882A5, 0x3F84EAFA, 0x3EA69BB8, /* 181 */
+ 0x9391054A, 0x7F09D5F4, 0x7D4D3770, /* 182 */
+ 0x27220A94, 0xFE13ABE8, 0xFA9A6EE0, /* 183 */
+ 0x4E441529, 0xFC2757D1, 0xF534DDC0, /* 184 */
+ 0x9C882A53, 0xF84EAFA3, 0xEA69BB81, /* 185 */
+ 0x391054A7, 0xF09D5F47, 0xD4D37703, /* 186 */
+ 0x7220A94F, 0xE13ABE8F, 0xA9A6EE06, /* 187 */
+ 0xE441529F, 0xC2757D1F, 0x534DDC0D, /* 188 */
+ 0xC882A53F, 0x84EAFA3E, 0xA69BB81B, /* 189 */
+ 0x91054A7F, 0x09D5F47D, 0x4D377036, /* 190 */
+ 0x220A94FE, 0x13ABE8FA, 0x9A6EE06D, /* 191 */
+ 0x441529FC, 0x2757D1F5, 0x34DDC0DB, /* 192 */
+ 0x882A53F8, 0x4EAFA3EA, 0x69BB81B6, /* 193 */
+ 0x1054A7F0, 0x9D5F47D4, 0xD377036D, /* 194 */
+ 0x20A94FE1, 0x3ABE8FA9, 0xA6EE06DB, /* 195 */
+ 0x41529FC2, 0x757D1F53, 0x4DDC0DB6, /* 196 */
+ 0x82A53F84, 0xEAFA3EA6, 0x9BB81B6C, /* 197 */
+ 0x054A7F09, 0xD5F47D4D, 0x377036D8, /* 198 */
+ 0x0A94FE13, 0xABE8FA9A, 0x6EE06DB1, /* 199 */
+ 0x1529FC27, 0x57D1F534, 0xDDC0DB62, /* 200 */
+ 0x2A53F84E, 0xAFA3EA69, 0xBB81B6C5, /* 201 */
+ 0x54A7F09D, 0x5F47D4D3, 0x77036D8A, /* 202 */
+ 0xA94FE13A, 0xBE8FA9A6, 0xEE06DB14, /* 203 */
+ 0x529FC275, 0x7D1F534D, 0xDC0DB629, /* 204 */
+ 0xA53F84EA, 0xFA3EA69B, 0xB81B6C52, /* 205 */
+ 0x4A7F09D5, 0xF47D4D37, 0x7036D8A5, /* 206 */
+ 0x94FE13AB, 0xE8FA9A6E, 0xE06DB14A, /* 207 */
+ 0x29FC2757, 0xD1F534DD, 0xC0DB6295, /* 208 */
+ 0x53F84EAF, 0xA3EA69BB, 0x81B6C52B, /* 209 */
+ 0xA7F09D5F, 0x47D4D377, 0x036D8A56, /* 210 */
+ 0x4FE13ABE, 0x8FA9A6EE, 0x06DB14AC, /* 211 */
+ 0x9FC2757D, 0x1F534DDC, 0x0DB62959, /* 212 */
+ 0x3F84EAFA, 0x3EA69BB8, 0x1B6C52B3, /* 213 */
+ 0x7F09D5F4, 0x7D4D3770, 0x36D8A566, /* 214 */
+ 0xFE13ABE8, 0xFA9A6EE0, 0x6DB14ACC, /* 215 */
+ 0xFC2757D1, 0xF534DDC0, 0xDB629599, /* 216 */
+ 0xF84EAFA3, 0xEA69BB81, 0xB6C52B32, /* 217 */
+ 0xF09D5F47, 0xD4D37703, 0x6D8A5664, /* 218 */
+ 0xE13ABE8F, 0xA9A6EE06, 0xDB14ACC9, /* 219 */
+ 0xC2757D1F, 0x534DDC0D, 0xB6295993, /* 220 */
+ 0x84EAFA3E, 0xA69BB81B, 0x6C52B327, /* 221 */
+ 0x09D5F47D, 0x4D377036, 0xD8A5664F, /* 222 */
+ 0x13ABE8FA, 0x9A6EE06D, 0xB14ACC9E, /* 223 */
+ 0x2757D1F5, 0x34DDC0DB, 0x6295993C, /* 224 */
+ 0x4EAFA3EA, 0x69BB81B6, 0xC52B3278, /* 225 */
+ 0x9D5F47D4, 0xD377036D, 0x8A5664F1, /* 226 */
+ 0x3ABE8FA9, 0xA6EE06DB, 0x14ACC9E2, /* 227 */
+ 0x757D1F53, 0x4DDC0DB6, 0x295993C4, /* 228 */
+ 0xEAFA3EA6, 0x9BB81B6C, 0x52B32788, /* 229 */
+ 0xD5F47D4D, 0x377036D8, 0xA5664F10, /* 230 */
+ 0xABE8FA9A, 0x6EE06DB1, 0x4ACC9E21, /* 231 */
+ 0x57D1F534, 0xDDC0DB62, 0x95993C43, /* 232 */
+ 0xAFA3EA69, 0xBB81B6C5, 0x2B327887, /* 233 */
+ 0x5F47D4D3, 0x77036D8A, 0x5664F10E, /* 234 */
+ 0xBE8FA9A6, 0xEE06DB14, 0xACC9E21C, /* 235 */
+ 0x7D1F534D, 0xDC0DB629, 0x5993C439, /* 236 */
+ 0xFA3EA69B, 0xB81B6C52, 0xB3278872, /* 237 */
+ 0xF47D4D37, 0x7036D8A5, 0x664F10E4, /* 238 */
+ 0xE8FA9A6E, 0xE06DB14A, 0xCC9E21C8, /* 239 */
+ 0xD1F534DD, 0xC0DB6295, 0x993C4390, /* 240 */
+ 0xA3EA69BB, 0x81B6C52B, 0x32788720, /* 241 */
+ 0x47D4D377, 0x036D8A56, 0x64F10E41, /* 242 */
+ 0x8FA9A6EE, 0x06DB14AC, 0xC9E21C82, /* 243 */
+ 0x1F534DDC, 0x0DB62959, 0x93C43904, /* 244 */
+ 0x3EA69BB8, 0x1B6C52B3, 0x27887208, /* 245 */
+ 0x7D4D3770, 0x36D8A566, 0x4F10E410, /* 246 */
+ 0xFA9A6EE0, 0x6DB14ACC, 0x9E21C820, /* 247 */
+ 0xF534DDC0, 0xDB629599, 0x3C439041, /* 248 */
+ 0xEA69BB81, 0xB6C52B32, 0x78872083, /* 249 */
+ 0xD4D37703, 0x6D8A5664, 0xF10E4107, /* 250 */
+ 0xA9A6EE06, 0xDB14ACC9, 0xE21C820F, /* 251 */
+ 0x534DDC0D, 0xB6295993, 0xC439041F, /* 252 */
+ 0xA69BB81B, 0x6C52B327, 0x8872083F, /* 253 */
+ 0x4D377036, 0xD8A5664F, 0x10E4107F, /* 254 */
+ 0x9A6EE06D, 0xB14ACC9E, 0x21C820FF, /* 255 */
+ /* Exists so that its save to read 32-bytes past
+ the end. */
+ 0x00000000, 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000)
+ .type __svml_stan_common_data_avx512, @object
+ .size __svml_stan_common_data_avx512, .-__svml_stan_common_data_avx512
+# endif
+#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 15/27] x86/fpu: Optimize svml_s_tanf16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (12 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 14/27] x86/fpu: Add common rodata file for svml_s_tanf_*_{avx512, avx2, sse4}.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 16/27] x86/fpu: Optimize svml_s_tanf4_core_sse4.S Noah Goldstein via Libc-alpha
` (12 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Add option to sacrifice some precision to save instructions.
- Three precision levels that can be set by defining `PRECISION`.
- Lower setting gets better perf but higher average ULP error.
- All settings stay in 4ulp bound.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
ULP Error results for the three `PRECISION` values:
PRECISION == 0:
ulp:
0 : 3374033104 (0.7856)
1 : 893707604 (0.2081)
2 : 26831634 (0.0062)
3 : 393466 (0.0001)
4 : 1488 (0.0000)
PRECISION == 1:
ulp:
0 : 3677094430 (0.8561)
1 : 609296734 (0.1419)
2 : 8347192 (0.0019)
3 : 228138 (0.0001)
4 : 802 (0.0000)
PRECISION == 2 (Same dist as current impl):
ulp:
error breakdown:
0 : 3722920128 (0.8668)
1 : 566817724 (0.1320)
2 : 5022802 (0.0012)
3 : 205902 (0.0000)
4 : 740 (0.0000)
Currently leaving `PRECISION` set at zero as the function stays in the
4 ulp limit and it gets the best performance.
Code Size Change: -176 Bytes (1130 - 1306)
Input New Time / Old Time
0F (0x00000000) -> 0.6867
0F (0x0000ffff, Denorm) -> 0.5873
.1F (0x3dcccccd) -> 0.6561
5F (0x40a00000) -> 0.6486
2315255808F (0x4f0a0000) -> 0.7996
-NaN (0xffffffff) -> 0.8154
---
.../fpu/multiarch/svml_s_tanf16_core_avx512.S | 1352 +++++++----------
1 file changed, 522 insertions(+), 830 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core_avx512.S
index da3477f16e..26362a673d 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core_avx512.S
@@ -32,893 +32,585 @@
*
*/
+#define LOCAL_DATA_NAME __svml_stan_data_internal
+#define LOCAL_DATA_NAME_UNALIGNED __svml_stan_data_internal_unaligned
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+#define AVX512_SHARED_TABLE
+#include "svml_s_tanf_rodata.h.S"
+
+/* Offsets for data table __svml_stan_data_internal_unaligned
+ */
+#define _FLT_1_1to16 0
+#define _FLT_2_1to16 4
+#define _FLT_3_1to16 8
+
+
/* Offsets for data table __svml_stan_data_internal
*/
-#define _sInvPI_uisa 0
-#define _sPI1_uisa 64
-#define _sPI2_uisa 128
-#define _sPI3_uisa 192
-#define Th_tbl_uisa 256
-#define _sPC3_uisa 384
-#define _sPC5_uisa 448
-#define _sRangeReductionVal_uisa 512
-#define _sAbsMask 576
-#define _sRangeVal 640
-#define _sRShifter 704
-#define _sOne 768
-#define _sRangeReductionVal 832
-#define _sPI1 896
-#define _sPI2 960
-#define _sPI3 1024
+#define _sInvPI_uisa 0
+#define _sRShifter 64
+#define _sPI1_uisa 128
+#define _sPI2_uisa 192
+#define _sPI3_uisa 256
+#define _sRangeReductionVal_uisa 320
+#define _sPC5_uisa 384
+#define _sPC3_uisa 448
+#define _Th_tbl_uisa_lo 512
+#define _Th_tbl_uisa_hi 576
+#define _sRangeVal 640
+#define _FLT_1 704
+#define _FLT_2 768
+#define _FLT_3 832
+#define _FLT_4 896
+#define _FLT_5 960
+#define _FLT_6 1024
+#define _FLT_7 1088
+
+#define PRECISION 0
+/* 0, 1, or 2. The following values get the following
+ ULP breakdowns:
+ PRECISION == 0:
+ ulp:
+ 0 : 3374033104 (0.7856)
+ 1 : 893707604 (0.2081)
+ 2 : 26831634 (0.0062)
+ 3 : 393466 (0.0001)
+ 4 : 1488 (0.0000)
+ Avg: 0.2209
+
+ PRECISION == 1:
+ ulp:
+ 0 : 3677094430 (0.8561)
+ 1 : 609296734 (0.1419)
+ 2 : 8347192 (0.0019)
+ 3 : 228138 (0.0001)
+ 4 : 802 (0.0000)
+ Avg: 0.1459
+
+ PRECISION == 2:
+ ulp:
+ error breakdown:
+ 0 : 3722920128 (0.8668)
+ 1 : 566817724 (0.1320)
+ 2 : 5022802 (0.0012)
+ 3 : 205902 (0.0000)
+ 4 : 740 (0.0000)
+ Avg: 0.1345 */
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_tanf_skx)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-64, %rsp
- subq $192, %rsp
- xorl %edx, %edx
-
- /* Large values check */
- vmovups _sRangeReductionVal_uisa+__svml_stan_data_internal(%rip), %zmm10
-
- /*
- *
- * Main path
- *
- * start arg. reduction
- */
- vmovups _sRShifter+__svml_stan_data_internal(%rip), %zmm1
- vmovups _sPI1_uisa+__svml_stan_data_internal(%rip), %zmm4
- vmovups _sPI2_uisa+__svml_stan_data_internal(%rip), %zmm2
- vmovups _sPI3_uisa+__svml_stan_data_internal(%rip), %zmm3
- vmovaps %zmm0, %zmm11
- vandps _sAbsMask+__svml_stan_data_internal(%rip), %zmm11, %zmm0
- vcmpps $22, {sae}, %zmm10, %zmm0, %k6
- vmovups __svml_stan_data_internal(%rip), %zmm10
-
- /*
- *
- * End of main path
- */
-
- kortestw %k6, %k6
- vfmadd213ps {rn-sae}, %zmm1, %zmm11, %zmm10
+ /* Main path start arg. reduction. */
+ vmovups LOCAL_DATA(_sInvPI_uisa)(%rip), %zmm10
+ vmovups LOCAL_DATA(_sRShifter)(%rip), %zmm1
+ vfmadd213ps {rn-sae}, %zmm1, %zmm0, %zmm10
vsubps {rn-sae}, %zmm1, %zmm10, %zmm5
- vfnmadd213ps {rn-sae}, %zmm11, %zmm5, %zmm4
+ vmovups LOCAL_DATA(_sPI1_uisa)(%rip), %zmm4
+ vfnmadd213ps {rn-sae}, %zmm0, %zmm5, %zmm4
+ vmovups LOCAL_DATA(_sPI2_uisa)(%rip), %zmm2
vfnmadd231ps {rn-sae}, %zmm5, %zmm2, %zmm4
+ vmovups LOCAL_DATA(_sPI3_uisa)(%rip), %zmm3
vfnmadd213ps {rn-sae}, %zmm4, %zmm3, %zmm5
- /* Go to auxilary branch */
+
+ /* Reused throughout in large case. */
+ vmovaps COMMON_DATA(_AbsMask)(%rip), %zmm7
+
+ /* Large values check. */
+ vmovups LOCAL_DATA(_sRangeReductionVal_uisa)(%rip), %zmm6
+ vandps %zmm7, %zmm0, %zmm11
+ vcmpps $22, {sae}, %zmm6, %zmm11, %k6
+
+ ktestd %k6, %k6
+ /* Go to auxilary branch. */
jne L(AUX_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx zmm0 zmm5 zmm10 zmm11 k6
- /* Return from auxilary branch
- * for out of main path inputs
- */
-L(AUX_BRANCH_RETURN):
- /* Table lookup */
- vmovups Th_tbl_uisa+__svml_stan_data_internal(%rip), %zmm3
- vmovups _sPC3_uisa+__svml_stan_data_internal(%rip), %zmm0
+ /* Table lookup. */
vmulps {rn-sae}, %zmm5, %zmm5, %zmm1
- vpermt2ps Th_tbl_uisa+64+__svml_stan_data_internal(%rip), %zmm10, %zmm3
- vmovups _sPC5_uisa+__svml_stan_data_internal(%rip), %zmm10
- vfmadd231ps {rn-sae}, %zmm1, %zmm10, %zmm0
- vmulps {rn-sae}, %zmm5, %zmm0, %zmm4
- vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm4
+ vmovups LOCAL_DATA(_sPC5_uisa)(%rip), %zmm4
+ vmovups LOCAL_DATA(_sPC3_uisa)(%rip), %zmm11
+ vfmadd231ps {rn-sae}, %zmm1, %zmm4, %zmm11
+ vmulps {rn-sae}, %zmm5, %zmm1, %zmm2
+ vmovups LOCAL_DATA(_Th_tbl_uisa_lo)(%rip), %zmm3
+ vpermt2ps LOCAL_DATA(_Th_tbl_uisa_hi)(%rip), %zmm10, %zmm3
+ vfmadd213ps {rn-sae}, %zmm5, %zmm2, %zmm11
- /*
- * Computer Denominator:
- * sDenominator - sDlow ~= 1-(sTh+sTl)*(sP+sPlow)
- */
- vmovups _sOne+__svml_stan_data_internal(%rip), %zmm5
- vmulps {rn-sae}, %zmm4, %zmm3, %zmm7
- /*
- * Compute Numerator:
- * sNumerator + sNlow ~= sTh+sTl+sP+sPlow
- */
- vaddps {rn-sae}, %zmm3, %zmm4, %zmm8
+ /* Computer Denominator:
+ sDenominator - sDlow ~= 1-(sTh+sTl) * (sP+sPlow). */
+ vmulps {rn-sae}, %zmm11, %zmm3, %zmm7
+
+
+ vmovups COMMON_DATA(_OneF)(%rip), %zmm5
+
+ /* Compute Numerator:
+ sNumerator + sNlow ~= sTh+sTl+sP+sPlow. */
+ vaddps {rn-sae}, %zmm3, %zmm11, %zmm8
vsubps {rn-sae}, %zmm7, %zmm5, %zmm9
- vsubps {rn-sae}, %zmm3, %zmm8, %zmm2
- /*
- * Now computes (sNumerator + sNlow)/(sDenominator - sDlow)
- * Choose NR iteration instead of hardware division
- */
+#if PRECISION >= 2
+ /* High Precision Version. */
vrcp14ps %zmm9, %zmm14
+ vsubps {rn-sae}, %zmm3, %zmm8, %zmm2
+
vsubps {rn-sae}, %zmm5, %zmm9, %zmm6
- vsubps {rn-sae}, %zmm2, %zmm4, %zmm13
vmulps {rn-sae}, %zmm8, %zmm14, %zmm15
- vaddps {rn-sae}, %zmm7, %zmm6, %zmm12
- /* One NR iteration to refine sQuotient */
+ /* One NR iteration to refine sQuotient. */
vfmsub213ps {rn-sae}, %zmm8, %zmm15, %zmm9
+ vaddps {rn-sae}, %zmm7, %zmm6, %zmm12
vfnmadd213ps {rn-sae}, %zmm9, %zmm15, %zmm12
+ vsubps {rn-sae}, %zmm2, %zmm11, %zmm13
vsubps {rn-sae}, %zmm13, %zmm12, %zmm0
- vfnmadd213ps {rn-sae}, %zmm15, %zmm14, %zmm0
- testl %edx, %edx
-
- /* Go to special inputs processing branch */
- jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx zmm0 zmm11
-
- /* Restore registers
- * and exit the function
- */
-L(EXIT):
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
+ vfnmadd213ps {rn-sae}, %zmm15, %zmm14, %zmm0
+#else
+ /* Low Precision Version. */
+ vdivps {rn-sae}, %zmm9, %zmm8, %zmm0
+#endif
ret
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
-
- /* Branch to process
- * special inputs
- */
-
-L(SPECIAL_VALUES_BRANCH):
- vmovups %zmm11, 64(%rsp)
- vmovups %zmm0, 128(%rsp)
- # LOE rbx r12 r13 r14 r15 edx zmm0
-
- xorl %eax, %eax
- # LOE rbx r12 r13 r14 r15 eax edx
-
- vzeroupper
- movq %r12, 16(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- movl %edx, %r13d
- movq %r14, (%rsp)
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
-
-L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $16, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- vmovups 128(%rsp), %zmm0
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r12 r13 r14 r15 zmm0
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- vmovss 64(%rsp, %r14, 4), %xmm0
- call tanf@PLT
- # LOE rbx r14 r15 r12d r13d xmm0
-
- vmovss %xmm0, 128(%rsp, %r14, 4)
-
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- cfi_restore(12)
- cfi_restore(13)
- cfi_restore(14)
- # LOE rbx r15 r12d r13d
-
- /* Auxilary branch
- * for out of main path inputs
- */
+ .p2align 4
L(AUX_BRANCH):
- vmovups _sRangeVal+__svml_stan_data_internal(%rip), %zmm6
-
- /*
- * Get the (2^a / 2pi) mod 1 values from the table.
- * Because doesn't have I-type gather, we need a trivial cast
- */
- lea __svml_stan_reduction_data_internal(%rip), %rax
- vmovups %zmm5, (%rsp)
- vandps %zmm0, %zmm6, %zmm14
- vcmpps $0, {sae}, %zmm6, %zmm14, %k0
-
- /*
- * Break the P_xxx and m into 16-bit chunks ready for
- * the long multiplication via 16x16->32 multiplications
- */
- vmovups .FLT_15(%rip), %zmm6
- kxnorw %k0, %k0, %k1
+ /* Hoping k0 doesn't have some long dependency chain attached to
+ it. NB: We really don't need all 1s, we only need the `k6`
+ mask. Currently `vpgatherdps` does not optimize out any
+ loads at zero-bits for the mask. */
kxnorw %k0, %k0, %k2
- kxnorw %k0, %k0, %k3
- kmovw %k0, %edx
- vpandd .FLT_12(%rip), %zmm11, %zmm5
- vpsrld $23, %zmm5, %zmm7
- vpslld $1, %zmm7, %zmm8
- vpaddd %zmm7, %zmm8, %zmm9
- vpslld $2, %zmm9, %zmm4
- vpxord %zmm3, %zmm3, %zmm3
- vpxord %zmm15, %zmm15, %zmm15
- vpxord %zmm2, %zmm2, %zmm2
- vgatherdps (%rax, %zmm4), %zmm3{%k1}
- vgatherdps 4(%rax, %zmm4), %zmm15{%k2}
- vgatherdps 8(%rax, %zmm4), %zmm2{%k3}
- vpsrld $16, %zmm3, %zmm5
- vpsrld $16, %zmm2, %zmm13
- /*
- * Also get the significand as an integer
- * NB: adding in the integer bit is wrong for denorms!
- * To make this work for denorms we should do something slightly different
- */
- vpandd .FLT_13(%rip), %zmm11, %zmm0
- vpaddd .FLT_14(%rip), %zmm0, %zmm1
- vpsrld $16, %zmm15, %zmm0
- vpsrld $16, %zmm1, %zmm8
- vpandd %zmm6, %zmm3, %zmm9
- vpandd %zmm6, %zmm15, %zmm12
- vpandd %zmm6, %zmm2, %zmm7
- vpandd %zmm6, %zmm1, %zmm14
-
- /* Now do the big multiplication and carry propagation */
- vpmulld %zmm9, %zmm8, %zmm4
- vpmulld %zmm0, %zmm8, %zmm3
- vpmulld %zmm12, %zmm8, %zmm2
- vpmulld %zmm13, %zmm8, %zmm1
- vpmulld %zmm7, %zmm8, %zmm8
- vpmulld %zmm5, %zmm14, %zmm7
- vpmulld %zmm9, %zmm14, %zmm5
- vpmulld %zmm0, %zmm14, %zmm9
- vpmulld %zmm12, %zmm14, %zmm0
- vpmulld %zmm13, %zmm14, %zmm12
- vpsrld $16, %zmm12, %zmm14
- vpsrld $16, %zmm0, %zmm13
- vpsrld $16, %zmm9, %zmm15
- vpsrld $16, %zmm5, %zmm12
- vpsrld $16, %zmm8, %zmm8
- vpaddd %zmm14, %zmm1, %zmm1
- vpaddd %zmm13, %zmm2, %zmm2
- vpaddd %zmm15, %zmm3, %zmm15
- vpaddd %zmm12, %zmm4, %zmm3
- vpandd %zmm6, %zmm0, %zmm13
- vpaddd %zmm1, %zmm13, %zmm4
- vpaddd %zmm4, %zmm8, %zmm14
- vpsrld $16, %zmm14, %zmm0
- vpandd %zmm6, %zmm9, %zmm9
- vpaddd %zmm2, %zmm9, %zmm1
- vpaddd %zmm1, %zmm0, %zmm8
+ /* Multiply indexes by 12. Note we could rearrange the data and
+ then just shift down by 23 saving 2x instructions. This will
+ probably look slightly better on microbenchmarks but as it
+ is now we get some constructive cache interference between
+ the gathers. As well this minimizes the total lines brought
+ in. Its a judgement call but intuitively this will be better
+ for applications. If someone has the time/inclination
+ benchmarking this on some real applications may be worth it. */
+ vpsrld $23, %zmm11, %zmm8
+ vpaddd %zmm8, %zmm8, %zmm1
+ vpaddd %zmm1, %zmm8, %zmm14
+
+ /* Get the (2^a / 2pi) mod 1 values from the table.
+ Because
+ doesn't have I-type gather, we need a trivial cast. */
+ lea AVX512_SHARED_DATA(_Reduction)(%rip), %rax
+
+ /* Offset 4 gather has the most work based on it so we want it
+ to be finished first to keep the backend busy. */
+
+ /* NB: The dependency break is VERY important. */
+ vpxor %ymm4, %ymm4, %ymm4
+ vgatherdps 4(%rax, %zmm14, 4), %zmm4{%k2}
+
+
+ /* If the magnitude of the input is <= 2^-20, then
+ just pass
+ through the input, since no reduction will be needed and
+ the main path will only work accurately if the reduced
+ argument is
+ about >= 2^-40 (which it is for all large pi
+ multiples). */
+ vmovups LOCAL_DATA(_sRangeVal)(%rip), %zmm9
+ /* `zmm11` already has sign bit cast off. We are checking if the
+ exp was 0xff so we can just use unsigned comparison. */
+ vpcmpd $5, %zmm9, %zmm11, %k1
+
+ /* Also get the significand as an integer
+ NB: adding in the
+ integer bit is wrong for denorms!
+ To make this work for
+ denorms we should do something slightly different. */
+
+ /* zmm9 = zmm9 & (~zmm11) | _FLT_1_1to16(%rip). */
+ vpternlogd $0xae, LOCAL_DATA_UNALIGNED(_FLT_1_1to16)(%rip){1to16}, %zmm11, %zmm9
+
+ /* Break the P_xxx and m into 16-bit chunks ready for
+ the
+ long multiplication via 16x16->32 multiplications. */
+ movl $0x55555555, %ecx
+ kmovd %ecx, %k2
+
+ vpsrld $16, %zmm9, %zmm8
+ vmovdqu16 %zmm11, %zmm9{%k2}{z}
+
+ vpsrld $16, %zmm4, %zmm15
+ vmovdqu16 %zmm4, %zmm1{%k2}{z}
+
+ /* Now do the big multiplication and carry propagation. */
+ vpmulld %zmm15, %zmm9, %zmm2
+ vpmulld %zmm1, %zmm9, %zmm12
+
+ vpmulld %zmm15, %zmm8, %zmm15
+ vpmulld %zmm1, %zmm8, %zmm1
+
+ vpsrld $16, %zmm2, %zmm4
+
+ vpaddd %zmm4, %zmm15, %zmm4
+ vmovdqu16 %zmm2, %zmm15{%k2}{z}
- /*
- * Now round at the 2^-8 bit position for reduction mod pi/2^7
- * instead of the original 2pi (but still with the same 2pi scaling).
- * Use a shifter of 2^15 + 2^14.
- * The N we get is our final version; it has an offset of
- * 2^8 because of the implicit integer bit, and anyway for negative
- * starting value it's a 2s complement thing. But we need to mask
- * off the exponent part anyway so it's fine.
- */
- vmovups .FLT_18(%rip), %zmm1
- vpandd %zmm6, %zmm7, %zmm7
- vpaddd %zmm3, %zmm7, %zmm13
- vpsrld $16, %zmm8, %zmm3
- vpandd %zmm6, %zmm5, %zmm5
- vpaddd %zmm15, %zmm5, %zmm2
- vpaddd %zmm2, %zmm3, %zmm15
- vpsrld $16, %zmm15, %zmm12
- vpaddd %zmm13, %zmm12, %zmm5
-
- /* Assemble reduced argument from the pieces */
- vpandd %zmm6, %zmm14, %zmm9
- vpandd %zmm6, %zmm15, %zmm7
- vpslld $16, %zmm5, %zmm6
- vpslld $16, %zmm8, %zmm5
- vpaddd %zmm7, %zmm6, %zmm4
- vpaddd %zmm9, %zmm5, %zmm9
- vpsrld $9, %zmm4, %zmm6
- /*
- * We want to incorporate the original sign now too.
- * Do it here for convenience in getting the right N value,
- * though we could wait right to the end if we were prepared
- * to modify the sign of N later too.
- * So get the appropriate sign mask now (or sooner).
- */
- vpandd .FLT_16(%rip), %zmm11, %zmm0
- vpandd .FLT_21(%rip), %zmm9, %zmm13
- vpslld $5, %zmm13, %zmm14
+ kxnorw %k0, %k0, %k3
+ vpxor %ymm3, %ymm3, %ymm3
+ vgatherdps (%rax, %zmm14, 4), %zmm3{%k3}
+ vpsrld $16, %zmm3, %zmm6
+ vmovdqu16 %zmm3, %zmm3{%k2}{z}
- /*
- * Create floating-point high part, implicitly adding integer bit 1
- * Incorporate overall sign at this stage too.
- */
- vpxord .FLT_17(%rip), %zmm0, %zmm8
- vpord %zmm8, %zmm6, %zmm2
- vaddps {rn-sae}, %zmm2, %zmm1, %zmm12
- vsubps {rn-sae}, %zmm1, %zmm12, %zmm3
- vsubps {rn-sae}, %zmm3, %zmm2, %zmm7
- /*
- * Create floating-point low and medium parts, respectively
- * lo_17, ... lo_0, 0, ..., 0
- * hi_8, ... hi_0, lo_31, ..., lo_18
- * then subtract off the implicitly added integer bits,
- * 2^-46 and 2^-23, respectively.
- * Put the original sign into all of them at this stage.
- */
- vpxord .FLT_20(%rip), %zmm0, %zmm6
- vpord %zmm6, %zmm14, %zmm15
- vpandd .FLT_23(%rip), %zmm4, %zmm4
- vsubps {rn-sae}, %zmm6, %zmm15, %zmm8
- vandps .FLT_26(%rip), %zmm11, %zmm15
- vpsrld $18, %zmm9, %zmm6
+ /* Do this comparison while `zmm11` still contains abs(input). */
+ vmovups LOCAL_DATA(_FLT_1)(%rip), %zmm2
+ vcmpps $22, {sae}, %zmm2, %zmm11, %k5
- /*
- * If the magnitude of the input is <= 2^-20, then
- * just pass through the input, since no reduction will be needed and
- * the main path will only work accurately if the reduced argument is
- * about >= 2^-40 (which it is for all large pi multiples)
- */
- vmovups .FLT_27(%rip), %zmm14
- vcmpps $26, {sae}, %zmm14, %zmm15, %k4
- vcmpps $22, {sae}, %zmm14, %zmm15, %k5
- vpxord .FLT_22(%rip), %zmm0, %zmm1
- vpslld $14, %zmm4, %zmm0
- vpord %zmm6, %zmm0, %zmm0
- vpord %zmm1, %zmm0, %zmm4
- vsubps {rn-sae}, %zmm1, %zmm4, %zmm2
- vpternlogd $255, %zmm6, %zmm6, %zmm6
-
- /* Now add them up into 2 reasonably aligned pieces */
- vaddps {rn-sae}, %zmm2, %zmm7, %zmm13
- vsubps {rn-sae}, %zmm13, %zmm7, %zmm7
- vaddps {rn-sae}, %zmm7, %zmm2, %zmm3
+ vpmulld %zmm3, %zmm9, %zmm11
+ vpmulld %zmm3, %zmm8, %zmm3
- /*
- * The output is _VRES_R (high) + _VRES_E (low), and the integer part is _VRES_IND
- * Set sRp2 = _VRES_R^2 and then resume the original code.
- */
- vmovups .FLT_28(%rip), %zmm2
- vaddps {rn-sae}, %zmm8, %zmm3, %zmm1
- vmovups .FLT_25(%rip), %zmm8
+ kxnorw %k0, %k0, %k4
+ vpxor %ymm2, %ymm2, %ymm2
+ vgatherdps 8(%rax, %zmm14, 4), %zmm2{%k4}
+ vpsrld $16, %zmm2, %zmm14
+ vpmulld %zmm14, %zmm9, %zmm13
+ vpmulld %zmm14, %zmm8, %zmm14
- /* Grab our final N value as an integer, appropriately masked mod 2^8 */
- vpandd .FLT_19(%rip), %zmm12, %zmm5
+ vmovdqu16 %zmm2, %zmm2{%k2}{z}
+ vpmulld %zmm2, %zmm8, %zmm8
+ /* We never take the upperhalf of zmm2. */
+ vpmullw %zmm6, %zmm9, %zmm2{%k2}{z}
- /*
- * Now multiply those numbers all by 2 pi, reasonably accurately.
- * (RHi + RLo) * (pi_lead + pi_trail) ~=
- * RHi * pi_lead + (RHi * pi_trail + RLo * pi_lead)
- */
- vmovups .FLT_24(%rip), %zmm12
- vmulps {rn-sae}, %zmm12, %zmm13, %zmm0
- vmovaps %zmm12, %zmm9
- vfmsub213ps {rn-sae}, %zmm0, %zmm13, %zmm9
- vfmadd213ps {rn-sae}, %zmm9, %zmm8, %zmm13
- vmovaps %zmm6, %zmm8
- vfmadd213ps {rn-sae}, %zmm13, %zmm12, %zmm1
- vpandnd %zmm15, %zmm15, %zmm8{%k4}
- vpandnd %zmm15, %zmm15, %zmm6{%k5}
- vandps %zmm11, %zmm6, %zmm14
- vandps %zmm0, %zmm8, %zmm15
- vandps %zmm1, %zmm8, %zmm12
- vorps %zmm15, %zmm14, %zmm6
- vpsrld $31, %zmm6, %zmm3
- vpsubd %zmm3, %zmm2, %zmm4
- vpaddd %zmm4, %zmm5, %zmm7
- vpsrld $2, %zmm7, %zmm13
- vpslld $2, %zmm13, %zmm9
+ vpsrld $16, %zmm12, %zmm9
+ vpsrld $16, %zmm11, %zmm6
+ vpsrld $16, %zmm13, %zmm13
- /*
- *
- * End of large arguments path
- *
- * Merge results from main and large paths:
- */
- vblendmps %zmm13, %zmm10, %zmm10{%k6}
- vpsubd %zmm9, %zmm5, %zmm5
- vmovups .FLT_29(%rip), %zmm9
- vcvtdq2ps {rn-sae}, %zmm5, %zmm0
- vmovups .FLT_30(%rip), %zmm5
- vfmadd231ps {rn-sae}, %zmm0, %zmm5, %zmm12
- vmovups (%rsp), %zmm5
- vaddps {rn-sae}, %zmm6, %zmm12, %zmm6
- vfmadd213ps {rn-sae}, %zmm6, %zmm9, %zmm0
- vblendmps %zmm0, %zmm5, %zmm5{%k6}
-
- /* Return to main vector processing path */
- jmp L(AUX_BRANCH_RETURN)
- # LOE rbx r12 r13 r14 r15 edx zmm5 zmm10 zmm11
-END(_ZGVeN16v_tanf_skx)
+ vpaddd %zmm9, %zmm1, %zmm9
+ vpaddd %zmm6, %zmm3, %zmm6
+ vpaddd %zmm13, %zmm14, %zmm14
- .section .rodata, "a"
- .align 64
+ vpsrld $16, %zmm8, %zmm8
-.FLT_12:
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000
- .type .FLT_12, @object
- .size .FLT_12, 64
- .align 64
+ vmovdqu16 %zmm12, %zmm13{%k2}{z}
+ vpaddd %zmm14, %zmm13, %zmm3
+
+ vpaddd %zmm9, %zmm15, %zmm14
+ vpaddd %zmm3, %zmm8, %zmm9
+ vpsrld $16, %zmm9, %zmm12
+
+ vpaddd %zmm14, %zmm12, %zmm8
+
+ /* Now round at the 2^-8 bit position for reduction mod pi/2^7
+ instead of the original 2pi (but still with the same 2pi
+ scaling).
+ Use a shifter of 2^15 + 2^14.
+ The N we get is
+ our final version; it has an offset of
+ 2^8 because of the
+ implicit integer bit, and anyway for negative
+ starting
+ value it's a 2s complement thing. But we need to mask
+ off
+ the exponent part anyway so it's fine. */
+
+ /* We already truncated zmm2. */
+ vpaddd %zmm6, %zmm2, %zmm13
+
+ vpsrld $16, %zmm8, %zmm15
+ vmovdqu16 %zmm11, %zmm11{%k2}{z}
+ vpaddd %zmm4, %zmm11, %zmm1
+
+
+ vpaddd %zmm1, %zmm15, %zmm4
+ vpsrld $16, %zmm4, %zmm12
+ vpaddd %zmm13, %zmm12, %zmm11
+
+ /* Assemble reduced argument from the pieces. */
+ vpslldq $2, %zmm11, %zmm1
+ vpslldq $2, %zmm8, %zmm11
+ vpblendmw %zmm4, %zmm1, %zmm3{%k2}
+ vmovdqu16 %zmm9, %zmm11{%k2}
+ vmovaps COMMON_DATA(_OneF)(%rip), %zmm9
+ vmovups LOCAL_DATA(_FLT_2)(%rip), %zmm14
+ vpsrld $9, %zmm3, %zmm2
+
+
+ /* We want to incorporate the original sign now too.
+ Do it
+ here for convenience in getting the right N value,
+ though
+ we could wait right to the end if we were prepared
+ to
+ modify the sign of N later too.
+ So get the appropriate
+ sign mask now (or sooner). */
+ vpandnd %zmm0, %zmm7, %zmm1
+ vpslld $5, %zmm11, %zmm13
+
+ /* Create floating-point high part, implicitly adding integer
+ bit 1
+ Incorporate overall sign at this stage too. */
+ vpternlogd $0xfe, %zmm9, %zmm1, %zmm2
+ vaddps {rn-sae}, %zmm2, %zmm14, %zmm12
+ vsubps {rn-sae}, %zmm14, %zmm12, %zmm15
+ vsubps {rn-sae}, %zmm15, %zmm2, %zmm2
+
+ /* Create floating-point low and medium parts, respectively
+ lo_17, ... lo_0, 0, ..., 0
+ hi_8, ... hi_0, lo_31, ...,
+ lo_18
+ then subtract off the implicitly added integer bits,
+ 2^-46 and 2^-23, respectively.
+ Put the original sign into
+ all of them at this stage. */
+
+ /* Save code size by microfusing vpord _FLT_2_1to16, %zmm1. This
+ increase the dependency chain on computing `zmm13` (we could
+ use vptern). */
+ vpord LOCAL_DATA_UNALIGNED(_FLT_2_1to16)(%rip){1to16}, %zmm1, %zmm15
+ /* Don't need to full addition result. */
+ vmovaps LOCAL_DATA(_FLT_3)(%rip), %zmm6
+ vpandd %zmm6, %zmm4, %zmm3
+ /* zmm13 = (zmm13 & ~_NotIOffExpoMask) | zmm15. */
+ vpternlogd $0xdc, COMMON_DATA(_NotiOffExpoMask)(%rip){1to16}, %zmm15, %zmm13
+
+ vsubps {rn-sae}, %zmm15, %zmm13, %zmm8
+ vpsrld $18, %zmm11, %zmm15
+
+ vpxord LOCAL_DATA_UNALIGNED(_FLT_3_1to16)(%rip){1to16}, %zmm1, %zmm14
+ vpslld $14, %zmm3, %zmm1
+
+ vpternlogd $0xfe, %zmm15, %zmm14, %zmm1
+ vsubps {rn-sae}, %zmm14, %zmm1, %zmm11
+
+
+ /* Now add them up into 2 reasonably aligned pieces. */
+ vaddps {rn-sae}, %zmm11, %zmm2, %zmm13
+ vsubps {rn-sae}, %zmm13, %zmm2, %zmm2
+ /* `zmm15` is generally zero. Possibly place for optimization
+ later on. */
+ vaddps {rn-sae}, %zmm2, %zmm11, %zmm15
-.FLT_13:
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- .type .FLT_13, @object
- .size .FLT_13, 64
- .align 64
-
-.FLT_14:
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000
- .type .FLT_14, @object
- .size .FLT_14, 64
- .align 64
-
-.FLT_15:
- .long 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff
- .type .FLT_15, @object
- .size .FLT_15, 64
- .align 64
+ /*
-.FLT_16:
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
- .type .FLT_16, @object
- .size .FLT_16, 64
- .align 64
+ The output is _VRES_R (high) + _VRES_E (low), and the
+ integer part is _VRES_IND
+ Set sRp2 = _VRES_R^2 and then
+ resume the original code. */
+ vaddps {rn-sae}, %zmm8, %zmm15, %zmm15
+ vmovups LOCAL_DATA(_FLT_4)(%rip), %zmm8
+
+ /* Grab our final N value as an integer, appropriately masked
+ mod 2^8. */
+ vpandd %zmm6, %zmm12, %zmm6
+
+ /* Now multiply those numbers all by 2 pi, reasonably
+ accurately.
+ (RHi + RLo)
+ (pi_lead + pi_trail) ~=
+ RHi
+ pi_lead + (RHi
+ pi_trail + RLo
+ pi_lead). */
+ vmovups LOCAL_DATA(_FLT_5)(%rip), %zmm12
+ vmulps {rn-sae}, %zmm12, %zmm13, %zmm1
+ vblendmps %zmm1, %zmm0, %zmm14{%k5}
+ vfmsub231ps {rn-sae}, %zmm12, %zmm13, %zmm1
+ vfmadd213ps {rn-sae}, %zmm1, %zmm8, %zmm13
+ vfmadd213ps {rn-sae}, %zmm13, %zmm15, %zmm12{%k5}{z}
+
+
+ vpsrld $31, %zmm14, %zmm15
+
+ vpsubd %zmm7, %zmm6, %zmm2
+ vpaddd %zmm7, %zmm15, %zmm3
+ vpsubd %zmm3, %zmm2, %zmm2
+
+ vpsrld $2, %zmm2, %zmm10{%k6}
+ vpslld $2, %zmm10, %zmm11
+
+ /* End of large arguments path
+ Merge results from main and
+ large paths:. */
+ vpsubd %zmm11, %zmm6, %zmm6
+ vmovups LOCAL_DATA(_FLT_6)(%rip), %zmm11
+ vcvtdq2ps {rn-sae}, %zmm6, %zmm1
+ vmovups LOCAL_DATA(_FLT_7)(%rip), %zmm6
+ vfmadd231ps {rn-sae}, %zmm1, %zmm6, %zmm12
+ vaddps {rn-sae}, %zmm14, %zmm12, %zmm5{%k6}
+ vfmadd231ps {rn-sae}, %zmm1, %zmm11, %zmm5{%k6}
+
+
+ /* Table lookup. */
+ vmovups LOCAL_DATA(_Th_tbl_uisa_lo)(%rip), %zmm3
+ vmovups LOCAL_DATA(_sPC3_uisa)(%rip), %zmm4
+ vmulps {rn-sae}, %zmm5, %zmm5, %zmm1
+ vpermt2ps LOCAL_DATA(_Th_tbl_uisa_hi)(%rip), %zmm10, %zmm3
+ vmovups LOCAL_DATA(_sPC5_uisa)(%rip), %zmm10
+ vfmadd231ps {rn-sae}, %zmm1, %zmm10, %zmm4
+ vmulps {rn-sae}, %zmm5, %zmm4, %zmm15
+ vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm15
+
+ /* Computer Denominator:
+ sDenominator - sDlow ~= 1-(sTh+sTl) * (sP+sPlow). */
+ vmulps {rn-sae}, %zmm15, %zmm3, %zmm7
+
+ /* Compute Numerator:
+ sNumerator + sNlow ~= sTh+sTl+sP+sPlow. */
+ vaddps {rn-sae}, %zmm3, %zmm15, %zmm8
+ vsubps {rn-sae}, %zmm7, %zmm9, %zmm11
+
+#if PRECISION >= 1
+ /* High Precision Version. */
+ vrcp14ps %zmm11, %zmm14
+ vsubps {rn-sae}, %zmm3, %zmm8, %zmm2
+ vsubps {rn-sae}, %zmm9, %zmm11, %zmm6
+ vsubps {rn-sae}, %zmm2, %zmm15, %zmm13
+ vmulps {rn-sae}, %zmm8, %zmm14, %zmm4
-.FLT_17:
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .type .FLT_17, @object
- .size .FLT_17, 64
- .align 64
+ vaddps {rn-sae}, %zmm7, %zmm6, %zmm12
+ /* One NR iteration to refine sQuotient. */
+ vfmsub213ps {rn-sae}, %zmm8, %zmm4, %zmm11
+ vfnmadd213ps {rn-sae}, %zmm11, %zmm4, %zmm12
+ kmovw %k1, %edx
+ testl %edx, %edx
+ /* Go to special inputs processing branch. */
+ jne L(SPECIAL_VALUES_BRANCH)
-.FLT_18:
- .long 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000
- .type .FLT_18, @object
- .size .FLT_18, 64
- .align 64
+ vsubps {rn-sae}, %zmm13, %zmm12, %zmm0
+ vfnmadd213ps {rn-sae}, %zmm4, %zmm14, %zmm0
+#else
+ /* Low Precision Version. */
+ kmovw %k1, %edx
+ testl %edx, %edx
+ /* Go to special inputs processing branch. */
+ jne L(SPECIAL_VALUES_BRANCH)
+ vdivps %zmm11, %zmm8, %zmm0
+#endif
+ /* Restore registers
+ and exit the function. */
+ ret
-.FLT_19:
- .long 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff
- .type .FLT_19, @object
- .size .FLT_19, 64
- .align 64
-.FLT_20:
- .long 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000
- .type .FLT_20, @object
- .size .FLT_20, 64
- .align 64
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanf call. Optimize for code size
+ moreso than speed here. */
+L(SPECIAL_VALUES_BRANCH):
-.FLT_21:
- .long 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff
- .type .FLT_21, @object
- .size .FLT_21, 64
- .align 64
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_def_cfa (rsp, 16)
+ /* Need to callee save registers to preserve state across tanf
+ calls. */
+ pushq %rbx
+ cfi_def_cfa (rsp, 24)
+ pushq %rbp
+ cfi_def_cfa (rsp, 32)
+ movq %rsp, %r13
+ cfi_def_cfa (r13, 32)
+#if PRECISION >= 1
+ vsubps {rn-sae}, %zmm13, %zmm12, %zmm1
+ vfnmadd213ps {rn-sae}, %zmm4, %zmm1, %zmm14
+#else
+ vdivps %zmm11, %zmm8, %zmm14
+#endif
+ /* Align stack and make room for 2x zmm vectors. */
+ andq $-64, %rsp
+ addq $-128, %rsp
-.FLT_22:
- .long 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000
- .type .FLT_22, @object
- .size .FLT_22, 64
- .align 64
-.FLT_23:
- .long 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff
- .type .FLT_23, @object
- .size .FLT_23, 64
- .align 64
-.FLT_24:
- .long 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb
- .type .FLT_24, @object
- .size .FLT_24, 64
- .align 64
+ /* Save origional input. */
+ vmovaps %zmm0, 64(%rsp)
+ /* Save all already computed inputs. */
+ vmovaps %zmm14, (%rsp)
-.FLT_25:
- .long 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e
- .type .FLT_25, @object
- .size .FLT_25, 64
- .align 64
-
-.FLT_26:
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- .type .FLT_26, @object
- .size .FLT_26, 64
- .align 64
+ vzeroupper
-.FLT_27:
- .long 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000
- .type .FLT_27, @object
- .size .FLT_27, 64
- .align 64
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ movl %edx, %ebx
+L(SPECIAL_VALUES_LOOP):
-.FLT_28:
- .long 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002, 0x00000002
- .type .FLT_28, @object
- .size .FLT_28, 64
- .align 64
+ /* use rbp as index for special value that is saved across calls
+ to tanf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 64(%rsp, %rbp, 4), %xmm0
+ call tanf@PLT
-.FLT_29:
- .long 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb, 0x3cc90fdb
- .type .FLT_29, @object
- .size .FLT_29, 64
- .align 64
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, (%rsp, %rbp, 4)
-.FLT_30:
- .long 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e, 0xb03bbd2e
- .type .FLT_30, @object
- .size .FLT_30, 64
- .align 64
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
-#ifdef __svml_stan_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(64)) VUINT32 _sInvPI_uisa[16][1];
- __declspec(align(64)) VUINT32 _sPI1_uisa[16][1];
- __declspec(align(64)) VUINT32 _sPI2_uisa[16][1];
- __declspec(align(64)) VUINT32 _sPI3_uisa[16][1];
- __declspec(align(64)) VUINT32 Th_tbl_uisa[32][1];
- __declspec(align(64)) VUINT32 _sPC3_uisa[16][1];
- __declspec(align(64)) VUINT32 _sPC5_uisa[16][1];
- __declspec(align(64)) VUINT32 _sRangeReductionVal_uisa[16][1];
- __declspec(align(64)) VUINT32 _sAbsMask[16][1];
- __declspec(align(64)) VUINT32 _sRangeVal[16][1];
- __declspec(align(64)) VUINT32 _sRShifter[16][1];
- __declspec(align(64)) VUINT32 _sOne[16][1];
- __declspec(align(64)) VUINT32 _sRangeReductionVal[16][1];
- __declspec(align(64)) VUINT32 _sPI1[16][1];
- __declspec(align(64)) VUINT32 _sPI2[16][1];
- __declspec(align(64)) VUINT32 _sPI3[16][1];
-} __svml_stan_data_internal;
-#endif
-__svml_stan_data_internal:
- /* UISA */
- .long 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983 /* _sInvPI_uisa */
- .align 64
- .long 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda /* _sPI1_uisa */
- .align 64
- .long 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168 /* _sPI2_uisa */
- .align 64
- .long 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5 /* _sPI3_uisa */
- /* Th_tbl_uisa for i from 0 to 31 do printsingle(tan(i*Pi/32)); */
- .align 64
- .long 0x80000000, 0x3dc9b5dc, 0x3e4bafaf, 0x3e9b5042
- .long 0x3ed413cd, 0x3f08d5b9, 0x3f2b0dc1, 0x3f521801
- .long 0x3f800000, 0x3f9bf7ec, 0x3fbf90c7, 0x3fef789e
- .long 0x401a827a, 0x4052facf, 0x40a0dff7, 0x41227363
- .long 0xff7fffff, 0xc1227363, 0xc0a0dff7, 0xc052facf
- .long 0xc01a827a, 0xbfef789e, 0xbfbf90c7, 0xbf9bf7ec
- .long 0xbf800000, 0xbf521801, 0xbf2b0dc1, 0xbf08d5b9
- .long 0xbed413cd, 0xbe9b5042, 0xbe4bafaf, 0xbdc9b5dc
- .align 64
- .long 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6 /* _sPC3_uisa */
- .align 64
- .long 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888 /* _sPC5_uisa */
- .align 64
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeReductionVal_uisa */
- .align 64
- .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF /* _sAbsMask */
- .align 64
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000 /* _sRangeVal */
- .align 64
- .long 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000 /* _sRShifter */
- .align 64
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 /* _sOne */
- .align 64
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeVal */
- .align 64
- .long 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000 /* _sPI1 */
- .align 64
- .long 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000 /* _sPI2 */
- .align 64
- .long 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000 /* _sPI3 */
- .align 64
- .type __svml_stan_data_internal, @object
- .size __svml_stan_data_internal, .-__svml_stan_data_internal
- .align 64
+ /* All results have been written to 64(%rsp). */
+ vmovaps (%rsp), %zmm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa (rsp, 32)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_def_cfa (rsp, 24)
+ popq %rbx
+ cfi_def_cfa (rsp, 16)
+ popq %r13
+ ret
+END(_ZGVeN16v_tanf_skx)
-#ifdef __svml_stan_reduction_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(64)) VUINT32 _sPtable[256][3][1];
-} __svml_stan_reduction_data_internal;
-#endif
-__svml_stan_reduction_data_internal:
- /* P_hi P_med P_lo */
- .long 0x00000000, 0x00000000, 0x00000000 /* 0 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 1 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 2 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 3 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 4 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 5 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 6 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 7 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 8 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 9 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 10 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 11 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 12 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 13 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 14 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 15 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 16 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 17 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 18 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 19 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 20 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 21 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 22 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 23 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 24 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 25 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 26 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 27 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 28 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 29 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 30 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 31 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 32 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 33 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 34 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 35 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 36 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 37 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 38 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 39 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 40 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 41 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 42 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 43 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 44 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 45 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 46 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 47 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 48 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 49 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 50 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 51 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 52 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 53 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 54 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 55 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 56 */
- .long 0x00000000, 0x00000000, 0x00000001 /* 57 */
- .long 0x00000000, 0x00000000, 0x00000002 /* 58 */
- .long 0x00000000, 0x00000000, 0x00000005 /* 59 */
- .long 0x00000000, 0x00000000, 0x0000000A /* 60 */
- .long 0x00000000, 0x00000000, 0x00000014 /* 61 */
- .long 0x00000000, 0x00000000, 0x00000028 /* 62 */
- .long 0x00000000, 0x00000000, 0x00000051 /* 63 */
- .long 0x00000000, 0x00000000, 0x000000A2 /* 64 */
- .long 0x00000000, 0x00000000, 0x00000145 /* 65 */
- .long 0x00000000, 0x00000000, 0x0000028B /* 66 */
- .long 0x00000000, 0x00000000, 0x00000517 /* 67 */
- .long 0x00000000, 0x00000000, 0x00000A2F /* 68 */
- .long 0x00000000, 0x00000000, 0x0000145F /* 69 */
- .long 0x00000000, 0x00000000, 0x000028BE /* 70 */
- .long 0x00000000, 0x00000000, 0x0000517C /* 71 */
- .long 0x00000000, 0x00000000, 0x0000A2F9 /* 72 */
- .long 0x00000000, 0x00000000, 0x000145F3 /* 73 */
- .long 0x00000000, 0x00000000, 0x00028BE6 /* 74 */
- .long 0x00000000, 0x00000000, 0x000517CC /* 75 */
- .long 0x00000000, 0x00000000, 0x000A2F98 /* 76 */
- .long 0x00000000, 0x00000000, 0x00145F30 /* 77 */
- .long 0x00000000, 0x00000000, 0x0028BE60 /* 78 */
- .long 0x00000000, 0x00000000, 0x00517CC1 /* 79 */
- .long 0x00000000, 0x00000000, 0x00A2F983 /* 80 */
- .long 0x00000000, 0x00000000, 0x0145F306 /* 81 */
- .long 0x00000000, 0x00000000, 0x028BE60D /* 82 */
- .long 0x00000000, 0x00000000, 0x0517CC1B /* 83 */
- .long 0x00000000, 0x00000000, 0x0A2F9836 /* 84 */
- .long 0x00000000, 0x00000000, 0x145F306D /* 85 */
- .long 0x00000000, 0x00000000, 0x28BE60DB /* 86 */
- .long 0x00000000, 0x00000000, 0x517CC1B7 /* 87 */
- .long 0x00000000, 0x00000000, 0xA2F9836E /* 88 */
- .long 0x00000000, 0x00000001, 0x45F306DC /* 89 */
- .long 0x00000000, 0x00000002, 0x8BE60DB9 /* 90 */
- .long 0x00000000, 0x00000005, 0x17CC1B72 /* 91 */
- .long 0x00000000, 0x0000000A, 0x2F9836E4 /* 92 */
- .long 0x00000000, 0x00000014, 0x5F306DC9 /* 93 */
- .long 0x00000000, 0x00000028, 0xBE60DB93 /* 94 */
- .long 0x00000000, 0x00000051, 0x7CC1B727 /* 95 */
- .long 0x00000000, 0x000000A2, 0xF9836E4E /* 96 */
- .long 0x00000000, 0x00000145, 0xF306DC9C /* 97 */
- .long 0x00000000, 0x0000028B, 0xE60DB939 /* 98 */
- .long 0x00000000, 0x00000517, 0xCC1B7272 /* 99 */
- .long 0x00000000, 0x00000A2F, 0x9836E4E4 /* 100 */
- .long 0x00000000, 0x0000145F, 0x306DC9C8 /* 101 */
- .long 0x00000000, 0x000028BE, 0x60DB9391 /* 102 */
- .long 0x00000000, 0x0000517C, 0xC1B72722 /* 103 */
- .long 0x00000000, 0x0000A2F9, 0x836E4E44 /* 104 */
- .long 0x00000000, 0x000145F3, 0x06DC9C88 /* 105 */
- .long 0x00000000, 0x00028BE6, 0x0DB93910 /* 106 */
- .long 0x00000000, 0x000517CC, 0x1B727220 /* 107 */
- .long 0x00000000, 0x000A2F98, 0x36E4E441 /* 108 */
- .long 0x00000000, 0x00145F30, 0x6DC9C882 /* 109 */
- .long 0x00000000, 0x0028BE60, 0xDB939105 /* 110 */
- .long 0x00000000, 0x00517CC1, 0xB727220A /* 111 */
- .long 0x00000000, 0x00A2F983, 0x6E4E4415 /* 112 */
- .long 0x00000000, 0x0145F306, 0xDC9C882A /* 113 */
- .long 0x00000000, 0x028BE60D, 0xB9391054 /* 114 */
- .long 0x00000000, 0x0517CC1B, 0x727220A9 /* 115 */
- .long 0x00000000, 0x0A2F9836, 0xE4E44152 /* 116 */
- .long 0x00000000, 0x145F306D, 0xC9C882A5 /* 117 */
- .long 0x00000000, 0x28BE60DB, 0x9391054A /* 118 */
- .long 0x00000000, 0x517CC1B7, 0x27220A94 /* 119 */
- .long 0x00000000, 0xA2F9836E, 0x4E441529 /* 120 */
- .long 0x00000001, 0x45F306DC, 0x9C882A53 /* 121 */
- .long 0x00000002, 0x8BE60DB9, 0x391054A7 /* 122 */
- .long 0x00000005, 0x17CC1B72, 0x7220A94F /* 123 */
- .long 0x0000000A, 0x2F9836E4, 0xE441529F /* 124 */
- .long 0x00000014, 0x5F306DC9, 0xC882A53F /* 125 */
- .long 0x00000028, 0xBE60DB93, 0x91054A7F /* 126 */
- .long 0x00000051, 0x7CC1B727, 0x220A94FE /* 127 */
- .long 0x000000A2, 0xF9836E4E, 0x441529FC /* 128 */
- .long 0x00000145, 0xF306DC9C, 0x882A53F8 /* 129 */
- .long 0x0000028B, 0xE60DB939, 0x1054A7F0 /* 130 */
- .long 0x00000517, 0xCC1B7272, 0x20A94FE1 /* 131 */
- .long 0x00000A2F, 0x9836E4E4, 0x41529FC2 /* 132 */
- .long 0x0000145F, 0x306DC9C8, 0x82A53F84 /* 133 */
- .long 0x000028BE, 0x60DB9391, 0x054A7F09 /* 134 */
- .long 0x0000517C, 0xC1B72722, 0x0A94FE13 /* 135 */
- .long 0x0000A2F9, 0x836E4E44, 0x1529FC27 /* 136 */
- .long 0x000145F3, 0x06DC9C88, 0x2A53F84E /* 137 */
- .long 0x00028BE6, 0x0DB93910, 0x54A7F09D /* 138 */
- .long 0x000517CC, 0x1B727220, 0xA94FE13A /* 139 */
- .long 0x000A2F98, 0x36E4E441, 0x529FC275 /* 140 */
- .long 0x00145F30, 0x6DC9C882, 0xA53F84EA /* 141 */
- .long 0x0028BE60, 0xDB939105, 0x4A7F09D5 /* 142 */
- .long 0x00517CC1, 0xB727220A, 0x94FE13AB /* 143 */
- .long 0x00A2F983, 0x6E4E4415, 0x29FC2757 /* 144 */
- .long 0x0145F306, 0xDC9C882A, 0x53F84EAF /* 145 */
- .long 0x028BE60D, 0xB9391054, 0xA7F09D5F /* 146 */
- .long 0x0517CC1B, 0x727220A9, 0x4FE13ABE /* 147 */
- .long 0x0A2F9836, 0xE4E44152, 0x9FC2757D /* 148 */
- .long 0x145F306D, 0xC9C882A5, 0x3F84EAFA /* 149 */
- .long 0x28BE60DB, 0x9391054A, 0x7F09D5F4 /* 150 */
- .long 0x517CC1B7, 0x27220A94, 0xFE13ABE8 /* 151 */
- .long 0xA2F9836E, 0x4E441529, 0xFC2757D1 /* 152 */
- .long 0x45F306DC, 0x9C882A53, 0xF84EAFA3 /* 153 */
- .long 0x8BE60DB9, 0x391054A7, 0xF09D5F47 /* 154 */
- .long 0x17CC1B72, 0x7220A94F, 0xE13ABE8F /* 155 */
- .long 0x2F9836E4, 0xE441529F, 0xC2757D1F /* 156 */
- .long 0x5F306DC9, 0xC882A53F, 0x84EAFA3E /* 157 */
- .long 0xBE60DB93, 0x91054A7F, 0x09D5F47D /* 158 */
- .long 0x7CC1B727, 0x220A94FE, 0x13ABE8FA /* 159 */
- .long 0xF9836E4E, 0x441529FC, 0x2757D1F5 /* 160 */
- .long 0xF306DC9C, 0x882A53F8, 0x4EAFA3EA /* 161 */
- .long 0xE60DB939, 0x1054A7F0, 0x9D5F47D4 /* 162 */
- .long 0xCC1B7272, 0x20A94FE1, 0x3ABE8FA9 /* 163 */
- .long 0x9836E4E4, 0x41529FC2, 0x757D1F53 /* 164 */
- .long 0x306DC9C8, 0x82A53F84, 0xEAFA3EA6 /* 165 */
- .long 0x60DB9391, 0x054A7F09, 0xD5F47D4D /* 166 */
- .long 0xC1B72722, 0x0A94FE13, 0xABE8FA9A /* 167 */
- .long 0x836E4E44, 0x1529FC27, 0x57D1F534 /* 168 */
- .long 0x06DC9C88, 0x2A53F84E, 0xAFA3EA69 /* 169 */
- .long 0x0DB93910, 0x54A7F09D, 0x5F47D4D3 /* 170 */
- .long 0x1B727220, 0xA94FE13A, 0xBE8FA9A6 /* 171 */
- .long 0x36E4E441, 0x529FC275, 0x7D1F534D /* 172 */
- .long 0x6DC9C882, 0xA53F84EA, 0xFA3EA69B /* 173 */
- .long 0xDB939105, 0x4A7F09D5, 0xF47D4D37 /* 174 */
- .long 0xB727220A, 0x94FE13AB, 0xE8FA9A6E /* 175 */
- .long 0x6E4E4415, 0x29FC2757, 0xD1F534DD /* 176 */
- .long 0xDC9C882A, 0x53F84EAF, 0xA3EA69BB /* 177 */
- .long 0xB9391054, 0xA7F09D5F, 0x47D4D377 /* 178 */
- .long 0x727220A9, 0x4FE13ABE, 0x8FA9A6EE /* 179 */
- .long 0xE4E44152, 0x9FC2757D, 0x1F534DDC /* 180 */
- .long 0xC9C882A5, 0x3F84EAFA, 0x3EA69BB8 /* 181 */
- .long 0x9391054A, 0x7F09D5F4, 0x7D4D3770 /* 182 */
- .long 0x27220A94, 0xFE13ABE8, 0xFA9A6EE0 /* 183 */
- .long 0x4E441529, 0xFC2757D1, 0xF534DDC0 /* 184 */
- .long 0x9C882A53, 0xF84EAFA3, 0xEA69BB81 /* 185 */
- .long 0x391054A7, 0xF09D5F47, 0xD4D37703 /* 186 */
- .long 0x7220A94F, 0xE13ABE8F, 0xA9A6EE06 /* 187 */
- .long 0xE441529F, 0xC2757D1F, 0x534DDC0D /* 188 */
- .long 0xC882A53F, 0x84EAFA3E, 0xA69BB81B /* 189 */
- .long 0x91054A7F, 0x09D5F47D, 0x4D377036 /* 190 */
- .long 0x220A94FE, 0x13ABE8FA, 0x9A6EE06D /* 191 */
- .long 0x441529FC, 0x2757D1F5, 0x34DDC0DB /* 192 */
- .long 0x882A53F8, 0x4EAFA3EA, 0x69BB81B6 /* 193 */
- .long 0x1054A7F0, 0x9D5F47D4, 0xD377036D /* 194 */
- .long 0x20A94FE1, 0x3ABE8FA9, 0xA6EE06DB /* 195 */
- .long 0x41529FC2, 0x757D1F53, 0x4DDC0DB6 /* 196 */
- .long 0x82A53F84, 0xEAFA3EA6, 0x9BB81B6C /* 197 */
- .long 0x054A7F09, 0xD5F47D4D, 0x377036D8 /* 198 */
- .long 0x0A94FE13, 0xABE8FA9A, 0x6EE06DB1 /* 199 */
- .long 0x1529FC27, 0x57D1F534, 0xDDC0DB62 /* 200 */
- .long 0x2A53F84E, 0xAFA3EA69, 0xBB81B6C5 /* 201 */
- .long 0x54A7F09D, 0x5F47D4D3, 0x77036D8A /* 202 */
- .long 0xA94FE13A, 0xBE8FA9A6, 0xEE06DB14 /* 203 */
- .long 0x529FC275, 0x7D1F534D, 0xDC0DB629 /* 204 */
- .long 0xA53F84EA, 0xFA3EA69B, 0xB81B6C52 /* 205 */
- .long 0x4A7F09D5, 0xF47D4D37, 0x7036D8A5 /* 206 */
- .long 0x94FE13AB, 0xE8FA9A6E, 0xE06DB14A /* 207 */
- .long 0x29FC2757, 0xD1F534DD, 0xC0DB6295 /* 208 */
- .long 0x53F84EAF, 0xA3EA69BB, 0x81B6C52B /* 209 */
- .long 0xA7F09D5F, 0x47D4D377, 0x036D8A56 /* 210 */
- .long 0x4FE13ABE, 0x8FA9A6EE, 0x06DB14AC /* 211 */
- .long 0x9FC2757D, 0x1F534DDC, 0x0DB62959 /* 212 */
- .long 0x3F84EAFA, 0x3EA69BB8, 0x1B6C52B3 /* 213 */
- .long 0x7F09D5F4, 0x7D4D3770, 0x36D8A566 /* 214 */
- .long 0xFE13ABE8, 0xFA9A6EE0, 0x6DB14ACC /* 215 */
- .long 0xFC2757D1, 0xF534DDC0, 0xDB629599 /* 216 */
- .long 0xF84EAFA3, 0xEA69BB81, 0xB6C52B32 /* 217 */
- .long 0xF09D5F47, 0xD4D37703, 0x6D8A5664 /* 218 */
- .long 0xE13ABE8F, 0xA9A6EE06, 0xDB14ACC9 /* 219 */
- .long 0xC2757D1F, 0x534DDC0D, 0xB6295993 /* 220 */
- .long 0x84EAFA3E, 0xA69BB81B, 0x6C52B327 /* 221 */
- .long 0x09D5F47D, 0x4D377036, 0xD8A5664F /* 222 */
- .long 0x13ABE8FA, 0x9A6EE06D, 0xB14ACC9E /* 223 */
- .long 0x2757D1F5, 0x34DDC0DB, 0x6295993C /* 224 */
- .long 0x4EAFA3EA, 0x69BB81B6, 0xC52B3278 /* 225 */
- .long 0x9D5F47D4, 0xD377036D, 0x8A5664F1 /* 226 */
- .long 0x3ABE8FA9, 0xA6EE06DB, 0x14ACC9E2 /* 227 */
- .long 0x757D1F53, 0x4DDC0DB6, 0x295993C4 /* 228 */
- .long 0xEAFA3EA6, 0x9BB81B6C, 0x52B32788 /* 229 */
- .long 0xD5F47D4D, 0x377036D8, 0xA5664F10 /* 230 */
- .long 0xABE8FA9A, 0x6EE06DB1, 0x4ACC9E21 /* 231 */
- .long 0x57D1F534, 0xDDC0DB62, 0x95993C43 /* 232 */
- .long 0xAFA3EA69, 0xBB81B6C5, 0x2B327887 /* 233 */
- .long 0x5F47D4D3, 0x77036D8A, 0x5664F10E /* 234 */
- .long 0xBE8FA9A6, 0xEE06DB14, 0xACC9E21C /* 235 */
- .long 0x7D1F534D, 0xDC0DB629, 0x5993C439 /* 236 */
- .long 0xFA3EA69B, 0xB81B6C52, 0xB3278872 /* 237 */
- .long 0xF47D4D37, 0x7036D8A5, 0x664F10E4 /* 238 */
- .long 0xE8FA9A6E, 0xE06DB14A, 0xCC9E21C8 /* 239 */
- .long 0xD1F534DD, 0xC0DB6295, 0x993C4390 /* 240 */
- .long 0xA3EA69BB, 0x81B6C52B, 0x32788720 /* 241 */
- .long 0x47D4D377, 0x036D8A56, 0x64F10E41 /* 242 */
- .long 0x8FA9A6EE, 0x06DB14AC, 0xC9E21C82 /* 243 */
- .long 0x1F534DDC, 0x0DB62959, 0x93C43904 /* 244 */
- .long 0x3EA69BB8, 0x1B6C52B3, 0x27887208 /* 245 */
- .long 0x7D4D3770, 0x36D8A566, 0x4F10E410 /* 246 */
- .long 0xFA9A6EE0, 0x6DB14ACC, 0x9E21C820 /* 247 */
- .long 0xF534DDC0, 0xDB629599, 0x3C439041 /* 248 */
- .long 0xEA69BB81, 0xB6C52B32, 0x78872083 /* 249 */
- .long 0xD4D37703, 0x6D8A5664, 0xF10E4107 /* 250 */
- .long 0xA9A6EE06, 0xDB14ACC9, 0xE21C820F /* 251 */
- .long 0x534DDC0D, 0xB6295993, 0xC439041F /* 252 */
- .long 0xA69BB81B, 0x6C52B327, 0x8872083F /* 253 */
- .long 0x4D377036, 0xD8A5664F, 0x10E4107F /* 254 */
- .long 0x9A6EE06D, 0xB14ACC9E, 0x21C820FF /* 255 */
- .align 64
- .type __svml_stan_reduction_data_internal, @object
- .size __svml_stan_reduction_data_internal, .-__svml_stan_reduction_data_internal
+ .section .rodata.evex512, "a"
+
+ /* Place the minimally aligned pieces at the begining so there
+ is a chance they fit in aligning bytes. */
+ .align 16
+LOCAL_DATA_NAME_UNALIGNED:
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _FLT_1_1to16, 0x00800000)
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _FLT_2_1to16, 0x28800000)
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _FLT_3_1to16, 0x34000000)
+
+ .type LOCAL_DATA_NAME_UNALIGNED, @object
+ .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
+
+
+ .align 64
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _sInvPI_uisa, 0x4122f983)
+ DATA_VEC (LOCAL_DATA_NAME, _sRShifter, 0x4B400000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI1_uisa, 0x3dc90fda)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI2_uisa, 0x31a22168)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI3_uisa, 0x25c234c5)
+ DATA_VEC (LOCAL_DATA_NAME, _sRangeReductionVal_uisa, 0x46010000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC5_uisa, 0x3e08b888)
+ DATA_VEC (LOCAL_DATA_NAME, _sPC3_uisa, 0x3eaaaaa6)
+
+ float_block (LOCAL_DATA_NAME, _Th_tbl_uisa_lo,
+ 0x80000000, 0x3dc9b5dc, 0x3e4bafaf, 0x3e9b5042,
+ 0x3ed413cd, 0x3f08d5b9, 0x3f2b0dc1, 0x3f521801,
+ 0x3f800000, 0x3f9bf7ec, 0x3fbf90c7, 0x3fef789e,
+ 0x401a827a, 0x4052facf, 0x40a0dff7, 0x41227363)
+
+ float_block (LOCAL_DATA_NAME, _Th_tbl_uisa_hi,
+ 0xff7fffff, 0xc1227363, 0xc0a0dff7, 0xc052facf,
+ 0xc01a827a, 0xbfef789e, 0xbfbf90c7, 0xbf9bf7ec,
+ 0xbf800000, 0xbf521801, 0xbf2b0dc1, 0xbf08d5b9,
+ 0xbed413cd, 0xbe9b5042, 0xbe4bafaf, 0xbdc9b5dc)
+
+ DATA_VEC (LOCAL_DATA_NAME, _sRangeVal, 0x7f800000)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_1, 0x35800000)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_2, 0x47400000)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_3, 0x000001ff)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_4, 0xb43bbd2e)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_5, 0x40c90fdb)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_6, 0x3cc90fdb)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_7, 0xb03bbd2e)
+
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 16/27] x86/fpu: Optimize svml_s_tanf4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (13 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 15/27] x86/fpu: Optimize svml_s_tanf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 17/27] x86/fpu: Optimize svml_s_tanf8_core_avx2.S Noah Goldstein via Libc-alpha
` (11 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Remove many unnecissary spills.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -980 Bytes (1619 - 2599)
Input New Time / Old Time
0F (0x00000000) -> 0.8527
0F (0x0000ffff, Denorm) -> 0.9879
.1F (0x3dcccccd) -> 0.8542
5F (0x40a00000) -> 0.8633
2315255808F (0x4f0a0000) -> 0.7640
-NaN (0xffffffff) -> 0.7966
---
.../fpu/multiarch/svml_s_tanf4_core_sse4.S | 3031 +++--------------
1 file changed, 531 insertions(+), 2500 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core_sse4.S
index 3dc82cae68..f3f0c867ef 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core_sse4.S
@@ -45,2553 +45,584 @@
*
*/
-/* Offsets for data table __svml_stan_data_internal
- */
-#define _sInvPI_uisa 0
-#define _sPI1_uisa 16
-#define _sPI2_uisa 32
-#define _sPI3_uisa 48
-#define _sPI2_ha_uisa 64
-#define _sPI3_ha_uisa 80
-#define Th_tbl_uisa 96
-#define Tl_tbl_uisa 224
-#define _sPC3_uisa 352
-#define _sPC5_uisa 368
-#define _sRangeReductionVal_uisa 384
-#define _sInvPi 400
-#define _sSignMask 416
-#define _sAbsMask 432
-#define _sRangeVal 448
-#define _sRShifter 464
-#define _sOne 480
-#define _sRangeReductionVal 496
-#define _sPI1 512
-#define _sPI2 528
-#define _sPI3 544
-#define _sPI4 560
-#define _sPI1_FMA 576
-#define _sPI2_FMA 592
-#define _sPI3_FMA 608
-#define _sP0 624
-#define _sP1 640
-#define _sQ0 656
-#define _sQ1 672
-#define _sQ2 688
-#define _sTwo 704
-#define _sCoeffs 720
+#define LOCAL_DATA_NAME __svml_stan_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+
+#define AVX2_SHARED_OFFSETS
+#define AVX512_SHARED_OFFSETS
+#include "svml_s_tanf_rodata.h.S"
+
+/* Offsets for data table __svml_stan_data_internal. */
+#define _sPI1 0
+#define _sPI2 16
+#define _sPI3 32
+#define _sPI4 48
+#define _sRangeVal 64
+#define _FLT_0 80
+#define _FLT_1 96
+
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_tanf_sse4)
- subq $232, %rsp
- cfi_def_cfa_offset(240)
- movaps %xmm0, %xmm13
- movups _sAbsMask+__svml_stan_data_internal(%rip), %xmm12
-
- /*
- * Legacy Code
- * Here HW FMA can be unavailable
- */
- xorl %eax, %eax
- movaps %xmm12, %xmm4
- pxor %xmm10, %xmm10
- movups _sInvPi+__svml_stan_data_internal(%rip), %xmm2
- andps %xmm13, %xmm4
- mulps %xmm4, %xmm2
-
- /* Range reduction */
- movaps %xmm4, %xmm1
-
- /*
- *
- * Main path (_LA_ and _EP_)
- *
- * Octant calculation
- */
- movups _sRShifter+__svml_stan_data_internal(%rip), %xmm3
-
- /* Large values check */
- movaps %xmm4, %xmm11
- movups _sPI1+__svml_stan_data_internal(%rip), %xmm5
- andnps %xmm13, %xmm12
- movups _sPI2+__svml_stan_data_internal(%rip), %xmm6
- addps %xmm3, %xmm2
- cmpnleps _sRangeReductionVal+__svml_stan_data_internal(%rip), %xmm11
- movaps %xmm2, %xmm8
- movups _sPI3+__svml_stan_data_internal(%rip), %xmm7
- subps %xmm3, %xmm8
- movmskps %xmm11, %edx
- movups _sPI4+__svml_stan_data_internal(%rip), %xmm9
- mulps %xmm8, %xmm5
- mulps %xmm8, %xmm6
- mulps %xmm8, %xmm7
- subps %xmm5, %xmm1
- mulps %xmm8, %xmm9
- subps %xmm6, %xmm1
- movups _sQ2+__svml_stan_data_internal(%rip), %xmm15
+ movaps %xmm0, %xmm15
+ movups COMMON_DATA(_AbsMask)(%rip), %xmm4
- /* Inversion mask and sign calculation */
- movaps %xmm2, %xmm5
+ andps %xmm0, %xmm4
- /* Rational approximation */
- movups _sP1+__svml_stan_data_internal(%rip), %xmm14
- pslld $30, %xmm2
- cmpneqps %xmm10, %xmm2
- subps %xmm7, %xmm1
+ movups AVX2_SHARED_DATA(_sInvPi)(%rip), %xmm0
+ mulps %xmm4, %xmm0
- /* Exchanged numerator and denominator if necessary */
- movaps %xmm2, %xmm0
- movaps %xmm2, %xmm10
- pslld $31, %xmm5
- subps %xmm9, %xmm1
- movaps %xmm1, %xmm3
- pxor %xmm12, %xmm5
- mulps %xmm1, %xmm3
- mulps %xmm3, %xmm15
- mulps %xmm3, %xmm14
- addps _sQ1+__svml_stan_data_internal(%rip), %xmm15
- addps _sP0+__svml_stan_data_internal(%rip), %xmm14
- mulps %xmm15, %xmm3
- mulps %xmm14, %xmm1
- addps _sQ0+__svml_stan_data_internal(%rip), %xmm3
- andnps %xmm1, %xmm0
- andps %xmm3, %xmm10
- andps %xmm2, %xmm1
- andnps %xmm3, %xmm2
- orps %xmm10, %xmm0
- orps %xmm2, %xmm1
-
- /* Division */
- divps %xmm1, %xmm0
-
- /* Sign setting */
- pxor %xmm5, %xmm0
+ /* Range reduction. */
+ movaps %xmm4, %xmm1
/*
- *
- * End of main path (_LA_ and _EP_)
- */
+ Main path (_LA_ and _EP_)
- testl %edx, %edx
+ Octant calculation. */
+ movups AVX2_SHARED_DATA(_sRShifter)(%rip), %xmm3
- /* Go to auxilary branch */
- jne L(AUX_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm4 xmm11 xmm12 xmm13
-
- /* Return from auxilary branch
- * for out of main path inputs
- */
+ /* Large values check. */
+ movups LOCAL_DATA(_sPI1)(%rip), %xmm5
+ movups LOCAL_DATA(_sPI2)(%rip), %xmm6
+ addps %xmm3, %xmm0
+ movaps %xmm0, %xmm2
+ movups LOCAL_DATA(_sPI3)(%rip), %xmm7
+ subps %xmm3, %xmm2
-L(AUX_BRANCH_RETURN):
- testl %eax, %eax
+ mulps %xmm2, %xmm5
+ mulps %xmm2, %xmm6
+ mulps %xmm2, %xmm7
- /* Go to special inputs processing branch */
- jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm13
+ subps %xmm5, %xmm1
+ mulps LOCAL_DATA(_sPI4)(%rip), %xmm2
+ subps %xmm6, %xmm1
+ movups AVX2_SHARED_DATA(_sQ2)(%rip), %xmm6
- /* Restore registers
- * and exit the function
- */
-L(EXIT):
- addq $232, %rsp
- cfi_def_cfa_offset(8)
- ret
- cfi_def_cfa_offset(240)
+ /* Rational approximation. */
+ movups AVX2_SHARED_DATA(_sP1)(%rip), %xmm5
- /* Branch to process
- * special inputs
- */
+ /* Inversion mask and sign calculation. */
+ pslld $31, %xmm0
+ subps %xmm7, %xmm1
-L(SPECIAL_VALUES_BRANCH):
- movups %xmm13, 32(%rsp)
- movups %xmm0, 48(%rsp)
- # LOE rbx rbp r12 r13 r14 r15 eax xmm0
-
- xorl %edx, %edx
- movq %r12, 16(%rsp)
- cfi_offset(12, -224)
- movl %edx, %r12d
- movq %r13, 8(%rsp)
- cfi_offset(13, -232)
- movl %eax, %r13d
- movq %r14, (%rsp)
- cfi_offset(14, -240)
- # LOE rbx rbp r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx rbp r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
+ /* Exchanged numerator and denominator if necessary. */
+ subps %xmm2, %xmm1
+ movaps %xmm1, %xmm3
+ mulps %xmm1, %xmm1
+ mulps %xmm1, %xmm6
+ mulps %xmm1, %xmm5
+ addps AVX2_SHARED_DATA(_sQ1)(%rip), %xmm6
+ movups AVX2_SHARED_DATA(_sP0)(%rip), %xmm2
+ addps %xmm2, %xmm5
+ mulps %xmm6, %xmm1
+ mulps %xmm5, %xmm3
+ addps %xmm2, %xmm1
-L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $4, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx rbp r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- movups 48(%rsp), %xmm0
-
- /* Go to exit */
- jmp L(EXIT)
- cfi_offset(12, -224)
- cfi_offset(13, -232)
- cfi_offset(14, -240)
- # LOE rbx rbp r12 r13 r14 r15 xmm0
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- movss 32(%rsp, %r14, 4), %xmm0
- call tanf@PLT
- # LOE rbx rbp r14 r15 r12d r13d xmm0
+ movaps %xmm3, %xmm2
+ blendvps %xmm0, %xmm1, %xmm3
+ blendvps %xmm0, %xmm2, %xmm1
- movss %xmm0, 48(%rsp, %r14, 4)
+ /* Division. */
+ divps %xmm1, %xmm3
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- cfi_restore(12)
- cfi_restore(13)
- cfi_restore(14)
- # LOE rbx rbp r15 r12d r13d
+ /* Sign setting. */
+ pxor %xmm3, %xmm0
- /* Auxilary branch
- * for out of main path inputs
- */
+ movaps %xmm4, %xmm3
+ pcmpgtd AVX2_SHARED_DATA(_sRangeReductionVal)(%rip), %xmm3
+ pmovmskb %xmm3, %edx
-L(AUX_BRANCH):
- movl $2139095040, %eax
+ /* End of main path (_LA_ and _EP_). */
+ testl %edx, %edx
+ /* Go to auxilary branch. */
+ jne L(AUX_BRANCH)
- /*
- * Get the (2^a / 2pi) mod 1 values from the table.
- * Because doesn't have I-type gather, we need a trivial cast
- */
- lea __svml_stan_reduction_data_internal(%rip), %r8
- movups %xmm13, 64(%rsp)
+ /* Set sign. */
+ andnps %xmm15, %xmm4
+ pxor %xmm4, %xmm0
+ ret
- /*
- * Also get the significand as an integer
- * NB: adding in the integer bit is wrong for denorms!
- * To make this work for denorms we should do something slightly different
- */
- movl $8388607, %r9d
- movups %xmm12, 80(%rsp)
- movl $8388608, %r10d
- movups %xmm11, 96(%rsp)
+L(AUX_BRANCH):
+ movaps %xmm3, %xmm14
+ andnps %xmm0, %xmm3
- /*
- * Break the P_xxx and m into 16-bit chunks ready for
- * the long multiplication via 16x16->32 multiplications
- */
- movl $65535, %r11d
- movd %eax, %xmm3
- pshufd $0, %xmm3, %xmm2
- andps %xmm2, %xmm13
- cmpeqps %xmm2, %xmm13
- pand %xmm4, %xmm2
- psrld $23, %xmm2
- movdqa %xmm2, %xmm12
- pslld $1, %xmm12
- paddd %xmm2, %xmm12
- pslld $2, %xmm12
- pshufd $1, %xmm12, %xmm10
- pshufd $2, %xmm12, %xmm11
- pshufd $3, %xmm12, %xmm14
- movd %xmm12, %edx
- movd %xmm10, %ecx
- movd %xmm11, %esi
- movd %r9d, %xmm11
- movd %xmm14, %edi
- movd 4(%rdx, %r8), %xmm6
- movd 4(%rcx, %r8), %xmm7
- movd 4(%rsi, %r8), %xmm3
- movl $872415232, %r9d
- movd 4(%rdi, %r8), %xmm5
- punpckldq %xmm7, %xmm6
- punpckldq %xmm5, %xmm3
- movd 8(%rdi, %r8), %xmm10
- movmskps %xmm13, %eax
- punpcklqdq %xmm3, %xmm6
- movd 8(%rdx, %r8), %xmm3
- movd 8(%rcx, %r8), %xmm2
- movd 8(%rsi, %r8), %xmm13
- punpckldq %xmm2, %xmm3
- punpckldq %xmm10, %xmm13
- punpcklqdq %xmm13, %xmm3
- pshufd $0, %xmm11, %xmm13
- movdqa %xmm3, %xmm2
- movups %xmm4, 48(%rsp)
- pand %xmm4, %xmm13
- movd %r10d, %xmm4
- psrld $16, %xmm2
- movd (%rdx, %r8), %xmm9
+ /* Get the (2^a / 2pi) mod 1 values from the table. */
+ movaps %xmm4, %xmm1
+ psrld $0x17, %xmm4
+ /* Compute indices in xmm5 (need 4x scale). */
+ movaps %xmm4, %xmm5
+ paddd %xmm4, %xmm4
+ paddd %xmm4, %xmm5
+
+ pextrq $0x1, %xmm5, %rcx
+ movq %xmm5, %rdx
+
+
+ /* Move indices into GPRs. */
+ movl %edx, %esi
+ movl %ecx, %edi
+ shrq $0x20, %rdx
+ shrq $0x20, %rcx
+
+ lea AVX512_SHARED_DATA(_Reduction)(%rip), %rax
+ movq 0(%rax, %rcx, 4), %xmm4
+ movq 0(%rax, %rdi, 4), %xmm5
+ punpckldq %xmm4, %xmm5
+ movq 0(%rax, %rsi, 4), %xmm4
+ movq 0(%rax, %rdx, 4), %xmm2
+ movaps AVX2_SHARED_DATA(_Low16)(%rip), %xmm9
+ punpckldq %xmm2, %xmm4
+ movaps %xmm4, %xmm2
+ punpcklqdq %xmm5, %xmm4
+ punpckhqdq %xmm5, %xmm2
+
+ /* Break the P_xxx and m into 16-bit chunks ready for
+ the long multiplication via 16x16->32 multiplications. */
+ movaps %xmm4, %xmm5
+ pand %xmm9, %xmm4
+ psrld $0x10, %xmm5
+ movaps %xmm4, %xmm6
+ psrlq $0x20, %xmm4
+ movaps COMMON_DATA(_NotiOffExpoMask)(%rip), %xmm8
+ pandn %xmm1, %xmm8
+ /* Also get the significand as an integer
+ NB: adding in the integer bit is wrong for denorms!
+ To make this work for denorms we should do something
+ slightly different. */
+ movaps LOCAL_DATA(_sRangeVal)(%rip), %xmm7
+ paddd %xmm7, %xmm1
+ movmskps %xmm1, %r8d
- /*
- * We want to incorporate the original sign now too.
- * Do it here for convenience in getting the right N value,
- * though we could wait right to the end if we were prepared
- * to modify the sign of N later too.
- * So get the appropriate sign mask now (or sooner).
- */
- movl $-2147483648, %edx
- movd (%rcx, %r8), %xmm8
+ por %xmm8, %xmm7
- /*
- * Create floating-point high part, implicitly adding integer bit 1
- * Incorporate overall sign at this stage too.
- */
- movl $1065353216, %ecx
- movd (%rsi, %r8), %xmm15
+ pand %xmm9, %xmm8
+ movaps %xmm8, %xmm1
- /*
- * Now round at the 2^-8 bit position for reduction mod pi/2^7
- * instead of the original 2pi (but still with the same 2pi scaling).
- * Use a shifter of 2^15 + 2^14.
- * The N we get is our final version; it has an offset of
- * 2^8 because of the implicit integer bit, and anyway for negative
- * starting value it's a 2s complement thing. But we need to mask
- * off the exponent part anyway so it's fine.
- */
- movl $1195376640, %esi
- movd (%rdi, %r8), %xmm1
- movl $511, %r10d
- movups %xmm0, 112(%rsp)
- movd %r11d, %xmm0
- pshufd $0, %xmm4, %xmm12
- movdqa %xmm2, %xmm4
- punpckldq %xmm8, %xmm9
- paddd %xmm12, %xmm13
- punpckldq %xmm1, %xmm15
- movdqa %xmm13, %xmm12
- pshufd $0, %xmm0, %xmm8
- movdqa %xmm6, %xmm0
- punpcklqdq %xmm15, %xmm9
- pand %xmm8, %xmm13
- movdqa %xmm9, %xmm14
- pand %xmm8, %xmm9
- movdqa %xmm13, %xmm10
- psrld $16, %xmm14
- movdqu %xmm14, 128(%rsp)
-
- /* Now do the big multiplication and carry propagation */
- movdqa %xmm9, %xmm14
- psrlq $32, %xmm10
- psrlq $32, %xmm14
- movdqa %xmm13, %xmm15
- movdqa %xmm10, %xmm7
- pmuludq %xmm9, %xmm15
- psrld $16, %xmm0
- pmuludq %xmm14, %xmm7
- movdqu %xmm9, 144(%rsp)
- psllq $32, %xmm7
- movdqu .FLT_16(%rip), %xmm9
- pand %xmm8, %xmm6
- pand %xmm9, %xmm15
- psrld $16, %xmm12
- movdqa %xmm0, %xmm1
- por %xmm7, %xmm15
- movdqa %xmm13, %xmm7
- pand %xmm8, %xmm3
- movdqu %xmm0, 160(%rsp)
- movdqa %xmm12, %xmm11
- movdqu %xmm15, 208(%rsp)
- psrlq $32, %xmm1
- pmuludq %xmm0, %xmm7
- movdqa %xmm6, %xmm5
- movdqa %xmm10, %xmm15
- movdqa %xmm12, %xmm0
- movdqu %xmm14, 176(%rsp)
- psrlq $32, %xmm11
- movdqu %xmm1, 192(%rsp)
- psrlq $32, %xmm5
- pmuludq %xmm1, %xmm15
- movdqa %xmm13, %xmm1
- pmuludq %xmm3, %xmm0
+ psrlq $0x20, %xmm8
+ movaps %xmm8, %xmm10
+ pmuludq %xmm4, %xmm8
+ psllq $0x20, %xmm8
+ movaps %xmm1, %xmm11
pmuludq %xmm6, %xmm1
- pmuludq %xmm12, %xmm6
- movdqa %xmm10, %xmm14
- psrlq $32, %xmm3
- pmuludq %xmm5, %xmm14
- pand %xmm9, %xmm1
- pmuludq %xmm11, %xmm3
- pmuludq %xmm11, %xmm5
- psllq $32, %xmm14
- pand %xmm9, %xmm0
- psllq $32, %xmm3
- psrlq $32, %xmm4
- por %xmm14, %xmm1
- por %xmm3, %xmm0
- movdqa %xmm12, %xmm14
- movdqa %xmm11, %xmm3
- pmuludq %xmm2, %xmm14
- pand %xmm9, %xmm7
- pmuludq %xmm4, %xmm3
- pmuludq %xmm13, %xmm2
- pmuludq %xmm10, %xmm4
- pand %xmm9, %xmm2
- psllq $32, %xmm4
- psllq $32, %xmm15
- pand %xmm9, %xmm14
- psllq $32, %xmm3
- por %xmm4, %xmm2
- por %xmm15, %xmm7
- por %xmm3, %xmm14
- psrld $16, %xmm2
- pand %xmm9, %xmm6
- psllq $32, %xmm5
- movdqa %xmm1, %xmm15
- paddd %xmm2, %xmm14
- movdqa %xmm7, %xmm2
- por %xmm5, %xmm6
- psrld $16, %xmm1
- pand %xmm8, %xmm2
+ blendps $0xaa, %xmm8, %xmm1
+ movaps %xmm1, %xmm8
+ psrld $0x10, %xmm1
+ pand %xmm9, %xmm8
+ movaps %xmm7, %xmm13
+ psrld $0x10, %xmm7
+ psrlq $0x30, %xmm13
+ pmuludq %xmm7, %xmm6
+ pmuludq %xmm13, %xmm4
+ psllq $0x20, %xmm4
+ blendps $0xaa, %xmm4, %xmm6
paddd %xmm1, %xmm6
- movdqu 160(%rsp), %xmm1
- paddd %xmm6, %xmm2
- movdqu 192(%rsp), %xmm6
- psrld $16, %xmm7
- pmuludq %xmm12, %xmm1
- pand %xmm8, %xmm15
- pmuludq %xmm11, %xmm6
- pmuludq 144(%rsp), %xmm12
- pmuludq 176(%rsp), %xmm11
+ movaps %xmm5, %xmm4
+ psrlq $0x20, %xmm5
+ pmuludq %xmm11, %xmm4
+ pmuludq %xmm10, %xmm5
+ psllq $0x20, %xmm5
+ blendps $0xaa, %xmm5, %xmm4
+ pand %xmm9, %xmm4
+ paddd %xmm6, %xmm4
+ movaps %xmm2, %xmm5
+ psrld $0x10, %xmm2
+ movaps %xmm11, %xmm6
+ pmuludq %xmm2, %xmm11
+ pmuludq %xmm7, %xmm2
+ movaps %xmm5, %xmm1
+ psrlq $0x30, %xmm5
pand %xmm9, %xmm1
- psllq $32, %xmm6
- por %xmm6, %xmm1
- psrld $16, %xmm0
- paddd %xmm7, %xmm1
- paddd %xmm14, %xmm15
- movdqu 128(%rsp), %xmm7
- paddd %xmm15, %xmm0
- pmuludq %xmm7, %xmm13
- psrlq $32, %xmm7
- pmuludq %xmm7, %xmm10
- movdqa %xmm0, %xmm14
- pand %xmm9, %xmm13
- movdqu 208(%rsp), %xmm5
- psrld $16, %xmm14
- paddd %xmm2, %xmm14
- movdqa %xmm5, %xmm15
- movdqa %xmm14, %xmm3
- pand %xmm8, %xmm15
- psrld $16, %xmm3
- paddd %xmm1, %xmm15
- psllq $32, %xmm10
- pand %xmm9, %xmm12
- psllq $32, %xmm11
- paddd %xmm15, %xmm3
- por %xmm10, %xmm13
- por %xmm11, %xmm12
- psrld $16, %xmm5
- movdqa %xmm3, %xmm4
- pand %xmm8, %xmm13
+ movaps %xmm10, %xmm12
+ pmuludq %xmm5, %xmm10
+ psllq $0x20, %xmm10
+ blendps $0xaa, %xmm10, %xmm11
+ pmuludq %xmm13, %xmm5
+ psllq $0x20, %xmm5
+ blendps $0xaa, %xmm5, %xmm2
+ movaps %xmm11, %xmm5
+ pand %xmm9, %xmm11
+ psrld $0x10, %xmm5
+ paddd %xmm5, %xmm2
+ paddd %xmm2, %xmm8
+ movaps %xmm6, %xmm5
+ pmuludq %xmm1, %xmm6
+ movaps %xmm1, %xmm2
+ psrlq $0x20, %xmm1
+ pmuludq %xmm7, %xmm2
+ movaps %xmm12, %xmm10
+ pmuludq %xmm1, %xmm12
+ psllq $0x20, %xmm12
+ pmuludq %xmm13, %xmm1
+ psllq $0x20, %xmm1
+ blendps $0xaa, %xmm1, %xmm2
+ blendps $0xaa, %xmm12, %xmm6
+ movaps %xmm6, %xmm1
+ psrld $0x10, %xmm6
+ pand %xmm9, %xmm1
+ paddd %xmm6, %xmm2
+ paddd %xmm2, %xmm11
+ movd 8(%rax, %rcx, 4), %xmm2
+ movd 8(%rax, %rdi, 4), %xmm6
+ punpckldq %xmm2, %xmm6
+ movd 8(%rax, %rdx, 4), %xmm2
+ movd 8(%rax, %rsi, 4), %xmm12
+ punpckldq %xmm2, %xmm12
+ punpcklqdq %xmm6, %xmm12
+ movaps %xmm12, %xmm2
+ psrld $0x10, %xmm12
+ pmuludq %xmm12, %xmm5
+ pmuludq %xmm7, %xmm12
+ movaps %xmm2, %xmm6
+ psrlq $0x30, %xmm2
+ pand %xmm9, %xmm6
+ pmuludq %xmm6, %xmm7
+ psrlq $0x20, %xmm6
+ pmuludq %xmm13, %xmm6
+ psllq $0x20, %xmm6
+ blendps $0xaa, %xmm6, %xmm7
+ psrld $0x10, %xmm7
+ pmuludq %xmm2, %xmm13
+ pmuludq %xmm10, %xmm2
+ psllq $0x20, %xmm2
+ psllq $0x20, %xmm13
+ blendps $0xaa, %xmm2, %xmm5
+ psrld $0x10, %xmm5
+ blendps $0xaa, %xmm13, %xmm12
paddd %xmm5, %xmm12
- psrld $16, %xmm4
- paddd %xmm12, %xmm13
- paddd %xmm13, %xmm4
- pand %xmm8, %xmm3
- pslld $16, %xmm4
- movd %edx, %xmm9
- movups 48(%rsp), %xmm15
- paddd %xmm3, %xmm4
- pshufd $0, %xmm9, %xmm7
-
- /* Assemble reduced argument from the pieces */
- pand %xmm8, %xmm0
- movd %ecx, %xmm8
- pand %xmm15, %xmm7
- pshufd $0, %xmm8, %xmm1
- movdqa %xmm4, %xmm5
- psrld $9, %xmm5
- pxor %xmm7, %xmm1
- por %xmm1, %xmm5
- movd %esi, %xmm6
- pshufd $0, %xmm6, %xmm3
- movdqa %xmm5, %xmm6
- movl $262143, %r8d
-
- /*
- * Create floating-point low and medium parts, respectively
- * lo_17, ... lo_0, 0, ..., 0
- * hi_8, ... hi_0, lo_31, ..., lo_18
- * then subtract off the implicitly added integer bits,
- * 2^-46 and 2^-23, respectively.
- * Put the original sign into all of them at this stage.
- */
- movl $679477248, %edi
- movd %r10d, %xmm13
- pslld $16, %xmm14
- pshufd $0, %xmm13, %xmm1
- paddd %xmm0, %xmm14
- movd %r9d, %xmm11
- pand %xmm4, %xmm1
- movd %r8d, %xmm9
- movd %edi, %xmm10
- pshufd $0, %xmm9, %xmm8
- pslld $14, %xmm1
- pshufd $0, %xmm10, %xmm0
- pand %xmm14, %xmm8
- pshufd $0, %xmm11, %xmm12
- psrld $18, %xmm14
- pxor %xmm7, %xmm0
- pxor %xmm12, %xmm7
- por %xmm14, %xmm1
- pslld $5, %xmm8
- por %xmm7, %xmm1
-
- /*
- * Now multiply those numbers all by 2 pi, reasonably accurately.
- * The top part uses 2pi = s2pi_lead + s2pi_trail, where
- * s2pi_lead has 12 significant bits.
- */
- movl $1086918619, %r11d
-
- /* Split RHi into 12-bit leading and trailing parts. */
- movl $-4096, %esi
- por %xmm0, %xmm8
- movl $1086918656, %edx
- movl $-1214941318, %ecx
-
- /*
- * If the magnitude of the input is <= 2^-20, then
- * just pass through the input, since no reduction will be needed and
- * the main path will only work accurately if the reduced argument is
- * about >= 2^-40 (which it is for all large pi multiples)
- */
- movl $2147483647, %edi
- addps %xmm3, %xmm6
- subps %xmm7, %xmm1
- subps %xmm0, %xmm8
- movaps %xmm6, %xmm2
- movd %r11d, %xmm14
- movd %esi, %xmm4
- movd %edx, %xmm7
- movl $897581056, %r8d
- subps %xmm3, %xmm2
-
- /* Grab our final N value as an integer, appropriately masked mod 2^8 */
- movl $255, %r9d
- subps %xmm2, %xmm5
-
- /* Now add them up into 2 reasonably aligned pieces */
- movaps %xmm5, %xmm3
-
- /*
- * The output is _VRES_R (high) + _VRES_E (low), and the integer part is _VRES_IND
- * Set sRp2 = _VRES_R^2 and then resume the original code.
- * Argument reduction is now finished: x = n * pi/128 + r
- * where n = iIndex and r = sR (high) + sE (low).
- * But we have n modulo 256, needed for sin/cos with period 2pi
- * but we want it modulo 128 since tan has period pi.
- */
- movl $127, %r10d
- pshufd $0, %xmm14, %xmm2
- addps %xmm1, %xmm3
- pshufd $0, %xmm4, %xmm14
- movd %r8d, %xmm4
- pshufd $0, %xmm4, %xmm9
- subps %xmm3, %xmm5
- movdqa %xmm9, %xmm11
- addps %xmm5, %xmm1
- movd %ecx, %xmm5
- addps %xmm1, %xmm8
- pshufd $0, %xmm7, %xmm1
- movdqa %xmm14, %xmm7
- andps %xmm3, %xmm7
+ paddd %xmm12, %xmm1
+ paddd %xmm1, %xmm7
+ movaps %xmm7, %xmm5
+ psrld $0x10, %xmm7
+ pand %xmm9, %xmm5
+ paddd %xmm11, %xmm7
+ movaps %xmm7, %xmm2
+ psrld $0x10, %xmm7
+ paddd %xmm8, %xmm7
+ pslld $0x10, %xmm2
+ paddd %xmm5, %xmm2
+ pand %xmm7, %xmm9
+ psrld $0x10, %xmm7
+ paddd %xmm4, %xmm7
+ pslld $0x10, %xmm7
+ paddd %xmm9, %xmm7
+ movaps %xmm7, %xmm4
+ /* Assemble reduced argument from the pieces. */
+ psrld $0x9, %xmm7
+ /* Create floating-point high part, implicitly adding integer
+ bit 1
+ Incorporate overall sign at this stage too. */
+ por COMMON_DATA(_OneF)(%rip), %xmm7
+ movaps AVX2_SHARED_DATA(_SH_FLT_1)(%rip), %xmm9
+ movaps %xmm7, %xmm5
+ addps %xmm9, %xmm7
+ movaps %xmm7, %xmm6
+ subps %xmm9, %xmm7
+ /* Grab our final N value as an integer, appropriately masked
+ mod 2^8. */
+ subps %xmm7, %xmm5
+
+ movaps %xmm2, %xmm9
+ psrld $0x12, %xmm2
+ movaps AVX2_SHARED_DATA(_Low9)(%rip), %xmm7
+ pand %xmm4, %xmm7
+ pslld $0xe, %xmm7
+ por %xmm2, %xmm7
+ movaps AVX2_SHARED_DATA(_SH_FLT_3)(%rip), %xmm4
+ por %xmm4, %xmm7
+ subps %xmm4, %xmm7
+ movaps %xmm5, %xmm4
+ addps %xmm7, %xmm5
- /*
- * Do the multiplication as exact top part and "naive" low part.
- * This still maintains a similar level of offset and doesn't drop
- * the accuracy much below what we already have.
- */
- movdqa %xmm1, %xmm10
- pshufd $0, %xmm5, %xmm5
- subps %xmm7, %xmm3
- mulps %xmm7, %xmm10
+ /* Split RHi into 12-bit leading and trailing parts. */
+ movaps COMMON_DATA(_Neg4096)(%rip), %xmm0
+ subps %xmm5, %xmm4
+ addps %xmm4, %xmm7
+ movaps %xmm0, %xmm4
+ andps %xmm5, %xmm0
+ subps %xmm0, %xmm5
+ /* Do the multiplication as exact top part and "naive" low. */
+ movaps LOCAL_DATA(_FLT_0)(%rip), %xmm2
+ movaps %xmm2, %xmm8
+ mulps %xmm5, %xmm2
+ movaps AVX2_SHARED_DATA(_Low18)(%rip), %xmm10
+
+ mulps %xmm0, %xmm8
+
+
+ pand %xmm9, %xmm10
+ pslld $0x5, %xmm10
+ movaps AVX2_SHARED_DATA(_SH_FLT_2)(%rip), %xmm1
+
+ /* If the magnitude of the input is <= 2^-20, then
+ just pass through the input, since no reduction will be needed and
+ the main path will only work accurately if the reduced argument is
+ about >= 2^-40 (which it is for all large pi multiples). */
+
+ por %xmm1, %xmm10
+ subps %xmm1, %xmm10
+ addps %xmm7, %xmm10
+
+ /* Now multiply those numbers all by 2 pi, reasonably accurately.
+ The top part uses 2pi = s2pi_lead + s2pi_trail, where
+ s2pi_lead has 12 significant bits. */
+ movaps AVX2_SHARED_DATA(_SH_FLT_4)(%rip), %xmm9
+ mulps %xmm10, %xmm9
+ addps %xmm2, %xmm9
+ /* Now add them up into 2 reasonably aligned pieces. */
+ movaps LOCAL_DATA(_FLT_1)(%rip), %xmm7
+ mulps %xmm7, %xmm0
mulps %xmm5, %xmm7
- mulps %xmm3, %xmm1
- mulps %xmm8, %xmm2
- mulps %xmm3, %xmm5
- addps %xmm7, %xmm1
- addps %xmm5, %xmm2
- movd %edi, %xmm8
- addps %xmm2, %xmm1
-
- /*
- * Do another stage of compensated summation to get full offset
- * between the pieces sRedHi + sRedLo.
- * Depending on the later algorithm, we might avoid this stage.
- */
+ addps %xmm8, %xmm7
+ addps %xmm9, %xmm7
+ addps %xmm7, %xmm0
+ lea AVX2_SHARED_DATA(_Coeffs)(%rip), %rax
+
+ /* The output is _VRES_R (high) + _VRES_E (low), and the integer
+ part is _VRES_IND Set sRp2 = _VRES_R^2 and then resume the
+ original code. Argument reduction is now finished: x = n *
+ pi/128 + r where n = iIndex and r = sR (high) + sE (low).
+ But we have n modulo 256, needed for sin/cos with period 2pi
+ but we want it modulo 128 since tan has period pi. */
+ pand AVX2_SHARED_DATA(_Low7)(%rip), %xmm6
+ movaps %xmm6, %xmm9
+ /* Simply combine the two parts of the reduced argument
+ since we can afford a few ulps in this case. */
+ pslld $0x2, %xmm6
+ paddd %xmm9, %xmm6
+ movq %xmm6, %rcx
+ movl %ecx, %edx
+ shrq $0x20, %rcx
+ pextrq $0x1, %xmm6, %rsi
+ movl %esi, %edi
+ shrq $0x20, %rsi
+ movups 16(%rax, %rcx, 8), %xmm9
+ movups 16(%rax, %rdx, 8), %xmm7
+ movaps %xmm7, %xmm5
+ punpckhdq %xmm9, %xmm7
+ punpckldq %xmm9, %xmm5
+ movups 16(%rax, %rsi, 8), %xmm9
+ movups 16(%rax, %rdi, 8), %xmm2
+ movaps %xmm2, %xmm6
+ punpckhdq %xmm9, %xmm2
+ punpckldq %xmm9, %xmm6
+ movaps %xmm7, %xmm9
+ punpckhqdq %xmm2, %xmm7
+ punpcklqdq %xmm2, %xmm9
+
+ /* Higher polynomial terms
+ Stage 1 (with unlimited parallelism)
+ P3 = C1_lo + C2 * Z. */
+ mulps %xmm0, %xmm7
+ addps %xmm7, %xmm9
+ movq 32(%rax, %rsi, 8), %xmm7
+ movq 32(%rax, %rdi, 8), %xmm2
+ punpckldq %xmm7, %xmm2
+ movq 32(%rax, %rcx, 8), %xmm7
+ movq 32(%rax, %rdx, 8), %xmm8
+ punpckldq %xmm7, %xmm8
+ movaps %xmm8, %xmm7
+ punpckhqdq %xmm2, %xmm8
+ punpcklqdq %xmm2, %xmm7
+ mulps %xmm0, %xmm8
+ addps %xmm8, %xmm7
+ movaps %xmm0, %xmm2
+ mulps %xmm0, %xmm0
+
+ mulps %xmm0, %xmm7
+ addps %xmm7, %xmm9
+ /* Final accumulation of low part. */
+ mulps %xmm2, %xmm9
+ movups 0(%rax, %rsi, 8), %xmm0
+ movups 0(%rax, %rdi, 8), %xmm7
+ movaps %xmm7, %xmm8
+ punpckldq %xmm0, %xmm7
+ punpckhdq %xmm0, %xmm8
+ movups 0(%rax, %rcx, 8), %xmm0
+ movups 0(%rax, %rdx, 8), %xmm1
+ movaps %xmm1, %xmm10
+ punpckldq %xmm0, %xmm1
+ punpckhdq %xmm0, %xmm10
movaps %xmm1, %xmm0
-
- /* Load constants (not all needed at once) */
- lea _sCoeffs+36+__svml_stan_data_internal(%rip), %rdi
- pshufd $0, %xmm8, %xmm8
- addps %xmm10, %xmm0
- andps %xmm15, %xmm8
- subps %xmm0, %xmm10
- cmpltps %xmm8, %xmm11
- cmpleps %xmm9, %xmm8
- addps %xmm10, %xmm1
- andps %xmm15, %xmm8
- movd %r9d, %xmm15
- andps %xmm11, %xmm0
- andps %xmm1, %xmm11
- pshufd $0, %xmm15, %xmm1
- movd %r10d, %xmm15
- pshufd $0, %xmm15, %xmm7
- pand %xmm1, %xmm6
- pand %xmm7, %xmm6
- orps %xmm0, %xmm8
+ punpcklqdq %xmm7, %xmm1
+ punpckhqdq %xmm7, %xmm0
+
+ /* Compute 2-part reciprocal component Construct a separate
+ reduced argument modulo pi near pi/2 multiples. i.e. (pi/2 -
+ x) mod pi, simply by subtracting the reduced argument from
+ an accurate B_hi + B_lo = (128 - n) pi/128. Force the upper
+ part of this reduced argument to half-length to simplify
+ accurate reciprocation later on. */
+ subps %xmm2, %xmm1
+ movaps %xmm4, %xmm7
+ andps %xmm1, %xmm4
+ subps %xmm4, %xmm1
+ addps %xmm1, %xmm0
+
+ /* Now compute an approximate reciprocal to mix into the computation
+ To avoid any danger of nonportability, force it to 12 bits,
+ though I suspect it always is anyway on current platforms. */
+ rcpps %xmm4, %xmm1
+ andps %xmm7, %xmm1
+ mulps %xmm1, %xmm4
+ movaps %xmm10, %xmm7
+ punpcklqdq %xmm8, %xmm10
+ punpckhqdq %xmm8, %xmm7
+ movaps %xmm1, %xmm8
+ /* Finally, multiplex both parts so they are only used in
+ cotangent path. */
+ mulps %xmm10, %xmm1
+ movaps %xmm5, %xmm11
+ punpckhqdq %xmm6, %xmm5
+ punpcklqdq %xmm6, %xmm11
+
+ /* Compensated sum of dominant component(s) Compute C0_hi +
+ C1_hi * Z + Recip_hi + Recip_lo = H4 (hi) + H9 (lo) H1 =
+ C1_hi * Z (exact since C1_hi is 1 bit). */
+ mulps %xmm2, %xmm5
+ movaps %xmm7, %xmm2
+ /* H2 = high(C0_hi + C1_hi * Z). */
+ addps %xmm5, %xmm7
+ /* H4 = high(H2 + Recip_hi). */
+
+ subps %xmm7, %xmm2
+ /* H5 = low(C0_hi + C1_hi * Z). */
+ addps %xmm2, %xmm5
+ movaps %xmm7, %xmm2
+ addps %xmm1, %xmm7
+
+ /* intermediate in compensated sum. */
+ subps %xmm7, %xmm1
+ /* H8 = low(H2 + Recip_hi). */
+ addps %xmm1, %xmm2
+
+ /* Get a better approximation to 1/sR_hi (not far short of an ulp)
+ using a third-order polynomial approximation. */
+ movups COMMON_DATA(_OneF)(%rip), %xmm6
+ movaps %xmm6, %xmm1
+ subps %xmm4, %xmm6
movaps %xmm6, %xmm4
-
- /*
- * Simply combine the two parts of the reduced argument
- * since we can afford a few ulps in this case.
- */
- addps %xmm11, %xmm8
- pslld $2, %xmm4
- paddd %xmm6, %xmm4
- pslld $3, %xmm4
- pshufd $1, %xmm4, %xmm6
- pshufd $2, %xmm4, %xmm5
- pshufd $3, %xmm4, %xmm3
- movd %xmm4, %r11d
- movd %xmm6, %edx
- movd %xmm5, %ecx
- movd %xmm3, %esi
- movd -32(%r11, %rdi), %xmm15
- movd -32(%rdx, %rdi), %xmm12
- movd -32(%rcx, %rdi), %xmm7
- movd -32(%rsi, %rdi), %xmm13
- punpckldq %xmm12, %xmm15
- punpckldq %xmm13, %xmm7
- movd -28(%rsi, %rdi), %xmm5
- punpcklqdq %xmm7, %xmm15
- movd -28(%r11, %rdi), %xmm7
- movd -28(%rdx, %rdi), %xmm6
- movd -28(%rcx, %rdi), %xmm4
- movd -36(%rcx, %rdi), %xmm9
- movd -36(%r11, %rdi), %xmm1
- movd -36(%rdx, %rdi), %xmm2
- movd -24(%rdx, %rdi), %xmm3
- movd -36(%rsi, %rdi), %xmm10
- punpckldq %xmm6, %xmm7
- punpckldq %xmm5, %xmm4
- movd -24(%r11, %rdi), %xmm6
- punpckldq %xmm2, %xmm1
- punpckldq %xmm10, %xmm9
- punpcklqdq %xmm4, %xmm7
- movd -16(%r11, %rdi), %xmm4
- punpckldq %xmm3, %xmm6
- movd -24(%rcx, %rdi), %xmm10
- movd -16(%rcx, %rdi), %xmm3
- movd -24(%rsi, %rdi), %xmm2
- movd -16(%rsi, %rdi), %xmm13
- movd -16(%rdx, %rdi), %xmm12
- punpcklqdq %xmm9, %xmm1
- movd -20(%rdx, %rdi), %xmm9
- punpckldq %xmm2, %xmm10
- movd -20(%r11, %rdi), %xmm5
- movd -20(%rcx, %rdi), %xmm11
- movd -20(%rsi, %rdi), %xmm0
- punpckldq %xmm12, %xmm4
- punpckldq %xmm13, %xmm3
- punpcklqdq %xmm10, %xmm6
- movd -12(%rsi, %rdi), %xmm10
- punpckldq %xmm9, %xmm5
- punpckldq %xmm0, %xmm11
- punpcklqdq %xmm3, %xmm4
- movd -12(%r11, %rdi), %xmm3
- movd -12(%rdx, %rdi), %xmm2
- movd -12(%rcx, %rdi), %xmm9
- punpcklqdq %xmm11, %xmm5
- punpckldq %xmm2, %xmm3
- punpckldq %xmm10, %xmm9
- movd -8(%rcx, %rdi), %xmm10
- movd -8(%r11, %rdi), %xmm2
- movd -8(%rdx, %rdi), %xmm0
- movd -8(%rsi, %rdi), %xmm11
- punpckldq %xmm0, %xmm2
- punpckldq %xmm11, %xmm10
- movd -4(%rsi, %rdi), %xmm13
- punpcklqdq %xmm9, %xmm3
- punpcklqdq %xmm10, %xmm2
- movd -4(%r11, %rdi), %xmm10
- movd -4(%rdx, %rdi), %xmm12
- movd -4(%rcx, %rdi), %xmm9
- punpckldq %xmm12, %xmm10
- punpckldq %xmm13, %xmm9
- punpcklqdq %xmm9, %xmm10
-
- /*
- * Compute 2-part reciprocal component
- * Construct a separate reduced argument modulo pi near pi/2 multiples.
- * i.e. (pi/2 - x) mod pi, simply by subtracting the reduced argument
- * from an accurate B_hi + B_lo = (128 - n) pi/128. Force the upper part
- * of this reduced argument to half-length to simplify accurate
- * reciprocation later on.
- */
- movdqa %xmm1, %xmm9
- movd (%r11, %rdi), %xmm13
- subps %xmm8, %xmm9
- movd (%rdx, %rdi), %xmm0
- subps %xmm9, %xmm1
- punpckldq %xmm0, %xmm13
- movdqa %xmm14, %xmm0
- andps %xmm9, %xmm0
- subps %xmm8, %xmm1
- subps %xmm0, %xmm9
- movd (%rcx, %rdi), %xmm12
- addps %xmm9, %xmm15
-
- /*
- * Now compute an approximate reciprocal to mix into the computation
- * To avoid any danger of nonportability, force it to 12 bits,
- * though I suspect it always is anyway on current platforms.
- */
- rcpps %xmm0, %xmm9
- addps %xmm15, %xmm1
- andps %xmm14, %xmm9
- mulps %xmm9, %xmm0
-
- /*
- * Get a better approximation to 1/sR_hi (not far short of an ulp)
- * using a third-order polynomial approximation
- */
- movaps %xmm9, %xmm14
- movd (%rsi, %rdi), %xmm11
-
- /*
- * Now compute the error sEr where sRecip_hi = (1/R_hi) * (1 - sEr)
- * so that we can compensate for it.
- */
- movups _sOne+__svml_stan_data_internal(%rip), %xmm15
- punpckldq %xmm11, %xmm12
- movaps %xmm15, %xmm11
- punpcklqdq %xmm12, %xmm13
- subps %xmm0, %xmm11
- mulps %xmm11, %xmm14
- movups %xmm11, (%rsp)
- addps %xmm9, %xmm14
- mulps %xmm11, %xmm11
- movups %xmm13, 32(%rsp)
- movups %xmm11, 16(%rsp)
- movups 112(%rsp), %xmm0
- movups 96(%rsp), %xmm11
- movups 80(%rsp), %xmm12
- movups 64(%rsp), %xmm13
- # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm1 xmm2 xmm3 xmm4 xmm5 xmm6 xmm7 xmm8 xmm9 xmm10 xmm11 xmm12 xmm13 xmm14 xmm15
-
- /*
- * Compensated sum of dominant component(s)
- * Compute C0_hi + C1_hi * Z + Recip_hi + Recip_lo = H4 (hi) + H9 (lo)
- * H1 = C1_hi * Z (exact since C1_hi is 1 bit)
- */
- mulps %xmm8, %xmm4
- addps 16(%rsp), %xmm15
-
- /* Finally, multiplex both parts so they are only used in cotangent path */
- mulps %xmm7, %xmm9
-
- /*
- * Higher polynomial terms
- * Stage 1 (with unlimited parallelism)
- * P3 = C1_lo + C2 * Z
- */
- mulps %xmm8, %xmm2
- mulps %xmm15, %xmm14
- addps %xmm2, %xmm3
-
- /*
- * Multiply by sRecip_ok to make sR_lo relative to sR_hi
- * Since sR_lo is shifted off by about 12 bits, this is accurate enough.
- */
- mulps %xmm14, %xmm1
-
- /*
- * Now create a low reciprocal using
- * (Recip_hi + Er * Recip_ok) * (1 + sR_lo^2 - sR_lo)
- * =~= Recip_hi + Recip_ok * (Er + sR_lo^2 - sR_lo)
- */
- movaps %xmm1, %xmm15
- mulps %xmm1, %xmm1
- subps (%rsp), %xmm15
-
- /* P4 = C3 + C4 * Z */
- movups 32(%rsp), %xmm2
- subps %xmm15, %xmm1
- mulps %xmm8, %xmm2
- mulps %xmm1, %xmm14
+ mulps %xmm6, %xmm6
+ addps %xmm6, %xmm1
+ movaps %xmm8, %xmm6
+ mulps %xmm4, %xmm8
+ addps %xmm6, %xmm8
+ mulps %xmm1, %xmm8
+
+ /* Multiply by sRecip_ok to make sR_lo relative to sR_hi Since
+ sR_lo is shifted off by about 12 bits, this is accurate
+ enough. */
+ mulps %xmm8, %xmm0
+ movaps %xmm0, %xmm6
+ subps %xmm4, %xmm0
+
+ /* Now create a low reciprocal using
+ (Recip_hi + Er * Recip_ok) * (1 + sR_lo^2 - sR_lo)
+ =~= Recip_hi + Recip_ok * (Er + sR_lo^2 - sR_lo). */
+ mulps %xmm6, %xmm6
+ /* P4 = C3 + C4 * Z. */
+ subps %xmm0, %xmm6
+ mulps %xmm6, %xmm8
+ mulps %xmm8, %xmm10
+ /* H7 = low(C0_hi + C1_hi * Z) + Recip_lo. */
+ addps %xmm5, %xmm10
+ /* Z2 = Z^2. */
+
+ /* Now H4 + H9 should be that part. */
addps %xmm2, %xmm10
- mulps %xmm14, %xmm7
-
- /* H2 = high(C0_hi + C1_hi * Z) */
- movdqa %xmm6, %xmm14
- addps %xmm4, %xmm14
-
- /* H4 = high(H2 + Recip_hi) */
- movaps %xmm14, %xmm1
-
- /* intermediate in compensated sum */
- subps %xmm14, %xmm6
- addps %xmm9, %xmm1
-
- /* H5 = low(C0_hi + C1_hi * Z) */
- addps %xmm6, %xmm4
-
- /* intermediate in compensated sum */
- subps %xmm1, %xmm9
-
- /* H7 = low(C0_hi + C1_hi * Z) + Recip_lo */
- addps %xmm4, %xmm7
-
- /* H8 = low(H2 + Recip_hi) */
- addps %xmm9, %xmm14
-
- /* Z2 = Z^2 */
- movaps %xmm8, %xmm4
+ /* P9 = trail(dominant part) + C0_lo. */
+ addps %xmm10, %xmm11
+ /* Merge results from main and large paths:. */
+ addps %xmm9, %xmm11
+ addps %xmm7, %xmm11
+ /* And now the very final summation. */
+ andps %xmm14, %xmm11
+
+ /* The end of implementation (LA with huge args reduction)
+ End of large arguments path (_HA_, _LA_ and _EP_). */
+ orps %xmm3, %xmm11
+ movups COMMON_DATA(_AbsMask)(%rip), %xmm3
+ andnps %xmm15, %xmm3
+
+ /* Incorperate original sign. */
+ xorps %xmm3, %xmm11
+ /* Return to main vector processing path. */
+ testl %r8d, %r8d
+ /* Go to special inputs processing branch. */
+ jne L(SPECIAL_VALUES_BRANCH)
+ movaps %xmm11, %xmm0
+ ret
- /* Now H4 + H9 should be that part */
- addps %xmm14, %xmm7
- mulps %xmm8, %xmm4
- /* P9 = trail(dominant part) + C0_lo */
- addps %xmm7, %xmm5
-
- /*
- * Stage 2 (with unlimited parallelism)
- * P6 = C1_lo + C2 * Z + C3 * Z^2 + C4 * Z^3
- */
- mulps %xmm4, %xmm10
- addps %xmm10, %xmm3
-
- /* Final accumulation of low part */
- mulps %xmm3, %xmm8
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanhf call. Optimize for code size
+ more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
- /* Merge results from main and large paths: */
- movaps %xmm11, %xmm3
- andnps %xmm0, %xmm3
- addps %xmm8, %xmm5
- movaps %xmm3, %xmm0
+ /* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
+ call entry will be 16-byte aligned. */
+ subq $56, %rsp
+ cfi_def_cfa_offset (64)
+ movups %xmm11, 24(%rsp)
+ movups %xmm15, 40(%rsp)
+
+ /* Use rbx/rbp for callee save registers as they get short
+ encoding for many instructions (as compared with r12/r13). */
+ movq %rbx, (%rsp)
+ cfi_offset (rbx, -64)
+ movq %rbp, 8(%rsp)
+ cfi_offset (rbp, -56)
+ /* r8d has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ movl %r8d, %ebx
+L(SPECIAL_VALUES_LOOP):
- /* And now the very final summation */
- addps %xmm5, %xmm1
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
+ xorl %ebp, %ebp
+ bsfl %ebx, %ebp
- /*
- * The end of implementation (LA with huge args reduction)
- * End of large arguments path (_HA_, _LA_ and _EP_)
- */
+ /* Scalar math fucntion call to process special input. */
+ movss 40(%rsp, %rbp, 4), %xmm0
+ call tanf@PLT
- pxor %xmm12, %xmm1
- andps %xmm11, %xmm1
- orps %xmm1, %xmm0
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, 24(%rsp, %rbp, 4)
+
+ leal -1(%rbx), %eax
+ andl %eax, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+ /* All results have been written to 24(%rsp). */
+ movups 24(%rsp), %xmm0
+ movq (%rsp), %rbx
+ cfi_restore (rbx)
+ movq 8(%rsp), %rbp
+ cfi_restore (rbp)
+ addq $56, %rsp
+ cfi_def_cfa_offset (8)
+ ret
- /* Return to main vector processing path */
- jmp L(AUX_BRANCH_RETURN)
- # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm13
END(_ZGVbN4v_tanf_sse4)
- .section .rodata, "a"
+ .section .rodata.sse4, "a"
.align 16
-#ifdef __svml_stan_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(16)) VUINT32 _sInvPI_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPI1_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPI2_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPI3_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPI2_ha_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPI3_ha_uisa[4][1];
- __declspec(align(16)) VUINT32 Th_tbl_uisa[32][1];
- __declspec(align(16)) VUINT32 Tl_tbl_uisa[32][1];
- __declspec(align(16)) VUINT32 _sPC3_uisa[4][1];
- __declspec(align(16)) VUINT32 _sPC5_uisa[4][1];
- __declspec(align(16)) VUINT32 _sRangeReductionVal_uisa[4][1];
- __declspec(align(16)) VUINT32 _sInvPi[4][1];
- __declspec(align(16)) VUINT32 _sSignMask[4][1];
- __declspec(align(16)) VUINT32 _sAbsMask[4][1];
- __declspec(align(16)) VUINT32 _sRangeVal[4][1];
- __declspec(align(16)) VUINT32 _sRShifter[4][1];
- __declspec(align(16)) VUINT32 _sOne[4][1];
- __declspec(align(16)) VUINT32 _sRangeReductionVal[4][1];
- __declspec(align(16)) VUINT32 _sPI1[4][1];
- __declspec(align(16)) VUINT32 _sPI2[4][1];
- __declspec(align(16)) VUINT32 _sPI3[4][1];
- __declspec(align(16)) VUINT32 _sPI4[4][1];
- __declspec(align(16)) VUINT32 _sPI1_FMA[4][1];
- __declspec(align(16)) VUINT32 _sPI2_FMA[4][1];
- __declspec(align(16)) VUINT32 _sPI3_FMA[4][1];
- __declspec(align(16)) VUINT32 _sP0[4][1];
- __declspec(align(16)) VUINT32 _sP1[4][1];
- __declspec(align(16)) VUINT32 _sQ0[4][1];
- __declspec(align(16)) VUINT32 _sQ1[4][1];
- __declspec(align(16)) VUINT32 _sQ2[4][1];
- __declspec(align(16)) VUINT32 _sTwo[4][1];
- __declspec(align(16)) VUINT32 _sCoeffs[128][10][1];
-} __svml_stan_data_internal;
-#endif
-__svml_stan_data_internal:
- /* UISA */
- .long 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983 /* _sInvPI_uisa */
- .align 16
- .long 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda /* _sPI1_uisa */
- .align 16
- .long 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168 /* _sPI2_uisa */
- .align 16
- .long 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5 /* _sPI3_uisa */
- .align 16
- .long 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000 /* _sPI2_ha_uisa */
- .align 16
- .long 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a /* _sPI3_ha_uisa */
- /* Th_tbl_uisa for i from 0 to 31 do printsingle(tan(i*Pi/32)); */
- .align 16
- .long 0x80000000, 0x3dc9b5dc, 0x3e4bafaf, 0x3e9b5042
- .long 0x3ed413cd, 0x3f08d5b9, 0x3f2b0dc1, 0x3f521801
- .long 0x3f800000, 0x3f9bf7ec, 0x3fbf90c7, 0x3fef789e
- .long 0x401a827a, 0x4052facf, 0x40a0dff7, 0x41227363
- .long 0xff7fffff, 0xc1227363, 0xc0a0dff7, 0xc052facf
- .long 0xc01a827a, 0xbfef789e, 0xbfbf90c7, 0xbf9bf7ec
- .long 0xbf800000, 0xbf521801, 0xbf2b0dc1, 0xbf08d5b9
- .long 0xbed413cd, 0xbe9b5042, 0xbe4bafaf, 0xbdc9b5dc
- /* Tl_tbl_uisa for i from 0 to 31 do printsingle(tan(i*Pi/32)-round(tan(i*Pi/32), SG, RN)); */
- .align 16
- .long 0x80000000, 0x3145b2da, 0x2f2a62b0, 0xb22a39c2
- .long 0xb1c0621a, 0xb25ef963, 0x32ab7f99, 0x32ae4285
- .long 0x00000000, 0x33587608, 0x32169d18, 0xb30c3ec0
- .long 0xb3cc0622, 0x3390600e, 0x331091dc, 0xb454a046
- .long 0xf3800000, 0x3454a046, 0xb31091dc, 0xb390600e
- .long 0x33cc0622, 0x330c3ec0, 0xb2169d18, 0xb3587608
- .long 0x00000000, 0xb2ae4285, 0xb2ab7f99, 0x325ef963
- .long 0x31c0621a, 0x322a39c2, 0xaf2a62b0, 0xb145b2da
- .align 16
- .long 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6 /* _sPC3_uisa */
- .align 16
- .long 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888 /* _sPC5_uisa */
- .align 16
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeReductionVal_uisa */
- .align 16
- .long 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983 /* _sInvPi */
- .align 16
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000 /* _sSignMask */
- .align 16
- .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF /* _sAbsMask */
- .align 16
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000 /* _sRangeVal */
- .align 16
- .long 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000 /* _sRShifter */
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 /* _sOne */
- .align 16
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeVal */
- .align 16
- .long 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000 /* _sPI1 */
- .align 16
- .long 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000 /* _sPI2 */
- .align 16
- .long 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000 /* _sPI3 */
- .align 16
- .long 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A /* _sPI4 */
- // PI1, PI2, and PI3 when FMA is available
- .align 16
- .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB /* _sPI1_FMA */
- .align 16
- .long 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E /* _sPI2_FMA */
- .align 16
- .long 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED /* _sPI3_FMA */
- .align 16
- .long 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC /* _sP0 */
- .align 16
- .long 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4 /* _sP1 */
- .align 16
- .long 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC /* _sQ0 */
- .align 16
- .long 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB /* _sQ1 */
- .align 16
- .long 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B /* _sQ2 */
- .align 16
- .long 0x40000000, 0x40000000, 0x40000000, 0x40000000 /* _sTwo */
- // _sCoeffs Breakpoint B = 0 * pi/128, function tan(B + x)
- .align 16
- .long 0x3FC90FDB // B' = pi/2 - B (high single)
- .long 0xB33BBD2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x00000000 // c0 (high single)
- .long 0x00000000 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x00000000 // c1 (low single)
- .long 0x00000000 // c2
- .long 0x3EAAACDD // c3
- .long 0x00000000 // c4
- .long 0x3FC5EB9B // B' = pi/2 - B (high single)
- .long 0x32DE638C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3CC91A31 // c0 (high single)
- .long 0x2F8E8D1A // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3A1DFA00 // c1 (low single)
- .long 0x3CC9392D // c2
- .long 0x3EAB1889 // c3
- .long 0x3C885D3B // c4
- .long 0x3FC2C75C // B' = pi/2 - B (high single)
- .long 0xB2CBBE8A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3D49393C // c0 (high single)
- .long 0x30A39F5B // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3B1E2B00 // c1 (low single)
- .long 0x3D49B5D4 // c2
- .long 0x3EAC4F10 // c3
- .long 0x3CFD9425 // c4
- .long 0x3FBFA31C // B' = pi/2 - B (high single)
- .long 0x33450FB0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3D9711CE // c0 (high single)
- .long 0x314FEB28 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3BB24C00 // c1 (low single)
- .long 0x3D97E43A // c2
- .long 0x3EAE6A89 // c3
- .long 0x3D4D07E0 // c4
- .long 0x3FBC7EDD // B' = pi/2 - B (high single)
- .long 0xB1800ADD // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3DC9B5DC // c0 (high single)
- .long 0x3145AD86 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C1EEF20 // c1 (low single)
- .long 0x3DCBAAEA // c2
- .long 0x3EB14E5E // c3
- .long 0x3D858BB2 // c4
- .long 0x3FB95A9E // B' = pi/2 - B (high single)
- .long 0xB3651267 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3DFC98C2 // c0 (high single)
- .long 0xB0AE525C // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C793D20 // c1 (low single)
- .long 0x3E003845 // c2
- .long 0x3EB5271F // c3
- .long 0x3DAC669E // c4
- .long 0x3FB6365E // B' = pi/2 - B (high single)
- .long 0x328BB91C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E17E564 // c0 (high single)
- .long 0xB1C5A2E4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CB440D0 // c1 (low single)
- .long 0x3E1B3D00 // c2
- .long 0x3EB9F664 // c3
- .long 0x3DD647C0 // c4
- .long 0x3FB3121F // B' = pi/2 - B (high single)
- .long 0xB30F347D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E31AE4D // c0 (high single)
- .long 0xB1F32251 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CF6A500 // c1 (low single)
- .long 0x3E3707DA // c2
- .long 0x3EBFA489 // c3
- .long 0x3DFBD9C7 // c4
- .long 0x3FAFEDDF // B' = pi/2 - B (high single)
- .long 0x331BBA77 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E4BAFAF // c0 (high single)
- .long 0x2F2A29E0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D221018 // c1 (low single)
- .long 0x3E53BED0 // c2
- .long 0x3EC67E26 // c3
- .long 0x3E1568E2 // c4
- .long 0x3FACC9A0 // B' = pi/2 - B (high single)
- .long 0xB2655A50 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E65F267 // c0 (high single)
- .long 0x31B4B1DF // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D4E8B90 // c1 (low single)
- .long 0x3E718ACA // c2
- .long 0x3ECE7164 // c3
- .long 0x3E2DC161 // c4
- .long 0x3FA9A560 // B' = pi/2 - B (high single)
- .long 0x33719861 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E803FD4 // c0 (high single)
- .long 0xB2279E66 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D807FC8 // c1 (low single)
- .long 0x3E884BD4 // c2
- .long 0x3ED7812D // c3
- .long 0x3E4636EB // c4
- .long 0x3FA68121 // B' = pi/2 - B (high single)
- .long 0x31E43AAC // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E8DB082 // c0 (high single)
- .long 0xB132A234 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D9CD7D0 // c1 (low single)
- .long 0x3E988A60 // c2
- .long 0x3EE203E3 // c3
- .long 0x3E63582C // c4
- .long 0x3FA35CE2 // B' = pi/2 - B (high single)
- .long 0xB33889B6 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E9B5042 // c0 (high single)
- .long 0xB22A3AEE // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DBC7490 // c1 (low single)
- .long 0x3EA99AF5 // c2
- .long 0x3EEDE107 // c3
- .long 0x3E80E9AA // c4
- .long 0x3FA038A2 // B' = pi/2 - B (high single)
- .long 0x32E4CA7E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EA92457 // c0 (high single)
- .long 0x30B80830 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DDF8200 // c1 (low single)
- .long 0x3EBB99E9 // c2
- .long 0x3EFB4AA8 // c3
- .long 0x3E9182BE // c4
- .long 0x3F9D1463 // B' = pi/2 - B (high single)
- .long 0xB2C55799 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EB73250 // c0 (high single)
- .long 0xB2028823 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E0318F8 // c1 (low single)
- .long 0x3ECEA678 // c2
- .long 0x3F053C67 // c3
- .long 0x3EA41E53 // c4
- .long 0x3F99F023 // B' = pi/2 - B (high single)
- .long 0x33484328 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EC5800D // c0 (high single)
- .long 0xB214C3C1 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E185E54 // c1 (low single)
- .long 0x3EE2E342 // c2
- .long 0x3F0DCA73 // c3
- .long 0x3EB8CC21 // c4
- .long 0x3F96CBE4 // B' = pi/2 - B (high single)
- .long 0xB14CDE2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3ED413CD // c0 (high single)
- .long 0xB1C06152 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E2FB0CC // c1 (low single)
- .long 0x3EF876CB // c2
- .long 0x3F177807 // c3
- .long 0x3ED08437 // c4
- .long 0x3F93A7A5 // B' = pi/2 - B (high single)
- .long 0xB361DEEE // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EE2F439 // c0 (high single)
- .long 0xB1F4399E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E49341C // c1 (low single)
- .long 0x3F07C61A // c2
- .long 0x3F22560F // c3
- .long 0x3EEAA81E // c4
- .long 0x3F908365 // B' = pi/2 - B (high single)
- .long 0x3292200D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EF22870 // c0 (high single)
- .long 0x325271F4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E65107A // c1 (low single)
- .long 0x3F1429F0 // c2
- .long 0x3F2E8AFC // c3
- .long 0x3F040498 // c4
- .long 0x3F8D5F26 // B' = pi/2 - B (high single)
- .long 0xB30C0105 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F00DC0D // c0 (high single)
- .long 0xB214AF72 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E81B994 // c1 (low single)
- .long 0x3F218233 // c2
- .long 0x3F3C4531 // c3
- .long 0x3F149688 // c4
- .long 0x3F8A3AE6 // B' = pi/2 - B (high single)
- .long 0x331EEDF0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F08D5B9 // c0 (high single)
- .long 0xB25EF98E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E92478D // c1 (low single)
- .long 0x3F2FEDC9 // c2
- .long 0x3F4BCD58 // c3
- .long 0x3F27AE9E // c4
- .long 0x3F8716A7 // B' = pi/2 - B (high single)
- .long 0xB2588C6D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F1105AF // c0 (high single)
- .long 0x32F045B0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EA44EE2 // c1 (low single)
- .long 0x3F3F8FDB // c2
- .long 0x3F5D3FD0 // c3
- .long 0x3F3D0A23 // c4
- .long 0x3F83F267 // B' = pi/2 - B (high single)
- .long 0x3374CBD9 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F1970C4 // c0 (high single)
- .long 0x32904848 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EB7EFF8 // c1 (low single)
- .long 0x3F50907C // c2
- .long 0x3F710FEA // c3
- .long 0x3F561FED // c4
- .long 0x3F80CE28 // B' = pi/2 - B (high single)
- .long 0x31FDD672 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F221C37 // c0 (high single)
- .long 0xB20C61DC // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3ECD4F71 // c1 (low single)
- .long 0x3F631DAA // c2
- .long 0x3F83B471 // c3
- .long 0x3F7281EA // c4
- .long 0x3F7B53D1 // B' = pi/2 - B (high single)
- .long 0x32955386 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F2B0DC1 // c0 (high single)
- .long 0x32AB7EBA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EE496C2 // c1 (low single)
- .long 0x3F776C40 // c2
- .long 0x3F9065C1 // c3
- .long 0x3F89AFB6 // c4
- .long 0x3F750B52 // B' = pi/2 - B (high single)
- .long 0x32EB316F // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F344BA9 // c0 (high single)
- .long 0xB2B8B0EA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EFDF4F7 // c1 (low single)
- .long 0x3F86DCA8 // c2
- .long 0x3F9ED53B // c3
- .long 0x3F9CBEDE // c4
- .long 0x3F6EC2D4 // B' = pi/2 - B (high single)
- .long 0xB2BEF0A7 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F3DDCCF // c0 (high single)
- .long 0x32D29606 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEE6606F // c1 (low single)
- .long 0x3F9325D6 // c2
- .long 0x3FAF4E69 // c3
- .long 0x3FB3080C // c4
- .long 0x3F687A55 // B' = pi/2 - B (high single)
- .long 0xB252257B // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F47C8CC // c0 (high single)
- .long 0xB200F51A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEC82C6C // c1 (low single)
- .long 0x3FA0BAE9 // c2
- .long 0x3FC2252F // c3
- .long 0x3FCD24C7 // c4
- .long 0x3F6231D6 // B' = pi/2 - B (high single)
- .long 0xB119A6A2 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F521801 // c0 (high single)
- .long 0x32AE4178 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEA72938 // c1 (low single)
- .long 0x3FAFCC22 // c2
- .long 0x3FD7BD4A // c3
- .long 0x3FEBB01B // c4
- .long 0x3F5BE957 // B' = pi/2 - B (high single)
- .long 0x3205522A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F5CD3BE // c0 (high single)
- .long 0x31460308 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE8306C5 // c1 (low single)
- .long 0x3FC09232 // c2
- .long 0x3FF09632 // c3
- .long 0x4007DB00 // c4
- .long 0x3F55A0D8 // B' = pi/2 - B (high single)
- .long 0x329886FF // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F68065E // c0 (high single)
- .long 0x32670D1A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE36D1D6 // c1 (low single)
- .long 0x3FD35007 // c2
- .long 0x4006A861 // c3
- .long 0x401D4BDA // c4
- .long 0x3F4F5859 // B' = pi/2 - B (high single)
- .long 0x32EE64E8 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F73BB75 // c0 (high single)
- .long 0x32FC908D // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBDBF94B0 // c1 (low single)
- .long 0x3FE8550F // c2
- .long 0x40174F67 // c3
- .long 0x4036C608 // c4
- .long 0x3F490FDB // B' = pi/2 - B (high single)
- .long 0xB2BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE8BE60E // c0 (high single)
- .long 0x320D8D84 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDF817B1 // c1 (low single)
- .long 0xBD8345EB // c2
- .long 0x3D1DFDAC // c3
- .long 0xBC52CF6F // c4
- .long 0x3F42C75C // B' = pi/2 - B (high single)
- .long 0xB24BBE8A // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE87283F // c0 (high single)
- .long 0xB268B966 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDFE6529 // c1 (low single)
- .long 0xBD7B1953 // c2
- .long 0x3D18E109 // c3
- .long 0xBC4570B0 // c4
- .long 0x3F3C7EDD // B' = pi/2 - B (high single)
- .long 0xB1000ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE827420 // c0 (high single)
- .long 0x320B8B4D // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DFB9428 // c1 (low single)
- .long 0xBD7002B4 // c2
- .long 0x3D142A6C // c3
- .long 0xBC3A47FF // c4
- .long 0x3F36365E // B' = pi/2 - B (high single)
- .long 0x320BB91C // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE7B9282 // c0 (high single)
- .long 0xB13383D2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF5D211 // c1 (low single)
- .long 0xBD6542B3 // c2
- .long 0x3D0FE5E5 // c3
- .long 0xBC31FB14 // c4
- .long 0x3F2FEDDF // B' = pi/2 - B (high single)
- .long 0x329BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE724E73 // c0 (high single)
- .long 0x3120C3E2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF05283 // c1 (low single)
- .long 0xBD5AD45E // c2
- .long 0x3D0BAFBF // c3
- .long 0xBC27B8BB // c4
- .long 0x3F29A560 // B' = pi/2 - B (high single)
- .long 0x32F19861 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE691B44 // c0 (high single)
- .long 0x31F18936 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DEB138B // c1 (low single)
- .long 0xBD50B2F7 // c2
- .long 0x3D07BE3A // c3
- .long 0xBC1E46A7 // c4
- .long 0x3F235CE2 // B' = pi/2 - B (high single)
- .long 0xB2B889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE5FF82C // c0 (high single)
- .long 0xB170723A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE61354 // c1 (low single)
- .long 0xBD46DA06 // c2
- .long 0x3D0401F8 // c3
- .long 0xBC14E013 // c4
- .long 0x3F1D1463 // B' = pi/2 - B (high single)
- .long 0xB2455799 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE56E46B // c0 (high single)
- .long 0x31E3F001 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE15025 // c1 (low single)
- .long 0xBD3D4550 // c2
- .long 0x3D00462D // c3
- .long 0xBC092C98 // c4
- .long 0x3F16CBE4 // B' = pi/2 - B (high single)
- .long 0xB0CCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE4DDF41 // c0 (high single)
- .long 0xB1AEA094 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DDCC85C // c1 (low single)
- .long 0xBD33F0BE // c2
- .long 0x3CFA23B0 // c3
- .long 0xBC01FCF7 // c4
- .long 0x3F108365 // B' = pi/2 - B (high single)
- .long 0x3212200D // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE44E7F8 // c0 (high single)
- .long 0xB1CAA3CB // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD87A74 // c1 (low single)
- .long 0xBD2AD885 // c2
- .long 0x3CF3C785 // c3
- .long 0xBBF1E348 // c4
- .long 0x3F0A3AE6 // B' = pi/2 - B (high single)
- .long 0x329EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE3BFDDC // c0 (high single)
- .long 0xB132521A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD464FC // c1 (low single)
- .long 0xBD21F8F1 // c2
- .long 0x3CEE3076 // c3
- .long 0xBBE6D263 // c4
- .long 0x3F03F267 // B' = pi/2 - B (high single)
- .long 0x32F4CBD9 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE33203E // c0 (high single)
- .long 0x31FEF5BE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD0869C // c1 (low single)
- .long 0xBD194E8C // c2
- .long 0x3CE8DCA9 // c3
- .long 0xBBDADA55 // c4
- .long 0x3EFB53D1 // B' = pi/2 - B (high single)
- .long 0x32155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE2A4E71 // c0 (high single)
- .long 0xB19CFCEC // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DCCDE11 // c1 (low single)
- .long 0xBD10D605 // c2
- .long 0x3CE382A7 // c3
- .long 0xBBC8BD97 // c4
- .long 0x3EEEC2D4 // B' = pi/2 - B (high single)
- .long 0xB23EF0A7 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE2187D0 // c0 (high single)
- .long 0xB1B7C7F7 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC96A2B // c1 (low single)
- .long 0xBD088C22 // c2
- .long 0x3CDE950E // c3
- .long 0xBBB89AD1 // c4
- .long 0x3EE231D6 // B' = pi/2 - B (high single)
- .long 0xB099A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE18CBB7 // c0 (high single)
- .long 0xAFE28430 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC629CE // c1 (low single)
- .long 0xBD006DCD // c2
- .long 0x3CDA5A2C // c3
- .long 0xBBB0B3D2 // c4
- .long 0x3ED5A0D8 // B' = pi/2 - B (high single)
- .long 0x321886FF // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE101985 // c0 (high single)
- .long 0xB02FB2B8 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC31BF3 // c1 (low single)
- .long 0xBCF0F04D // c2
- .long 0x3CD60BC7 // c3
- .long 0xBBA138BA // c4
- .long 0x3EC90FDB // B' = pi/2 - B (high single)
- .long 0xB23BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE07709D // c0 (high single)
- .long 0xB18A2A83 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC03FA2 // c1 (low single)
- .long 0xBCE15096 // c2
- .long 0x3CD26472 // c3
- .long 0xBB9A1270 // c4
- .long 0x3EBC7EDD // B' = pi/2 - B (high single)
- .long 0xB0800ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDFDA0CB // c0 (high single)
- .long 0x2F14FCA0 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBD93F7 // c1 (low single)
- .long 0xBCD1F71B // c2
- .long 0x3CCEDD2B // c3
- .long 0xBB905946 // c4
- .long 0x3EAFEDDF // B' = pi/2 - B (high single)
- .long 0x321BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDEC708C // c0 (high single)
- .long 0xB14895C4 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBB181E // c1 (low single)
- .long 0xBCC2DEA6 // c2
- .long 0x3CCB5027 // c3
- .long 0xBB7F3969 // c4
- .long 0x3EA35CE2 // B' = pi/2 - B (high single)
- .long 0xB23889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDDB4F55 // c0 (high single)
- .long 0x30F6437E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB8CB52 // c1 (low single)
- .long 0xBCB40210 // c2
- .long 0x3CC82D45 // c3
- .long 0xBB643075 // c4
- .long 0x3E96CBE4 // B' = pi/2 - B (high single)
- .long 0xB04CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDCA3BFF // c0 (high single)
- .long 0x311C95EA // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB6ACDE // c1 (low single)
- .long 0xBCA55C5B // c2
- .long 0x3CC5BC04 // c3
- .long 0xBB63A969 // c4
- .long 0x3E8A3AE6 // B' = pi/2 - B (high single)
- .long 0x321EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDB93569 // c0 (high single)
- .long 0xAFB9ED00 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB4BC1F // c1 (low single)
- .long 0xBC96E905 // c2
- .long 0x3CC2E6F5 // c3
- .long 0xBB3E10A6 // c4
- .long 0x3E7B53D1 // B' = pi/2 - B (high single)
- .long 0x31955386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDA83A77 // c0 (high single)
- .long 0x316D967A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB2F87C // c1 (low single)
- .long 0xBC88A31F // c2
- .long 0x3CC0E763 // c3
- .long 0xBB3F1666 // c4
- .long 0x3E6231D6 // B' = pi/2 - B (high single)
- .long 0xB019A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD974A0D // c0 (high single)
- .long 0xB14F365B // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB1616F // c1 (low single)
- .long 0xBC750CD8 // c2
- .long 0x3CBEB595 // c3
- .long 0xBB22B883 // c4
- .long 0x3E490FDB // B' = pi/2 - B (high single)
- .long 0xB1BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD866317 // c0 (high single)
- .long 0xAFF02140 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAFF67D // c1 (low single)
- .long 0xBC591CD0 // c2
- .long 0x3CBCBEAD // c3
- .long 0xBB04BBEC // c4
- .long 0x3E2FEDDF // B' = pi/2 - B (high single)
- .long 0x319BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD6B08FF // c0 (high single)
- .long 0xB0EED236 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAEB739 // c1 (low single)
- .long 0xBC3D6D51 // c2
- .long 0x3CBB485D // c3
- .long 0xBAFFF5BA // c4
- .long 0x3E16CBE4 // B' = pi/2 - B (high single)
- .long 0xAFCCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD495A6C // c0 (high single)
- .long 0xB0A427BD // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DADA345 // c1 (low single)
- .long 0xBC21F648 // c2
- .long 0x3CB9D1B4 // c3
- .long 0xBACB5567 // c4
- .long 0x3DFB53D1 // B' = pi/2 - B (high single)
- .long 0x31155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD27B856 // c0 (high single)
- .long 0xB0F7EE91 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DACBA4E // c1 (low single)
- .long 0xBC06AEE3 // c2
- .long 0x3CB8E5DC // c3
- .long 0xBAEC00EE // c4
- .long 0x3DC90FDB // B' = pi/2 - B (high single)
- .long 0xB13BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD0620A3 // c0 (high single)
- .long 0xB0ECAB40 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DABFC11 // c1 (low single)
- .long 0xBBD7200F // c2
- .long 0x3CB79475 // c3
- .long 0xBA2B0ADC // c4
- .long 0x3D96CBE4 // B' = pi/2 - B (high single)
- .long 0xAF4CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBCC92278 // c0 (high single)
- .long 0x302F2E68 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAB6854 // c1 (low single)
- .long 0xBBA1214F // c2
- .long 0x3CB6C1E9 // c3
- .long 0x3843C2F3 // c4
- .long 0x3D490FDB // B' = pi/2 - B (high single)
- .long 0xB0BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBC861015 // c0 (high single)
- .long 0xAFD68E2E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAFEEB // c1 (low single)
- .long 0xBB569F3F // c2
- .long 0x3CB6A84E // c3
- .long 0xBAC64194 // c4
- .long 0x3CC90FDB // B' = pi/2 - B (high single)
- .long 0xB03BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBC060BF3 // c0 (high single)
- .long 0x2FE251AE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAABFB9 // c1 (low single)
- .long 0xBAD67C60 // c2
- .long 0x3CB64CA5 // c3
- .long 0xBACDE881 // c4
- .long 0x00000000 // B' = pi/2 - B (high single)
- .long 0x00000000 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x00000000 // c0 (high single)
- .long 0x00000000 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAAAAB // c1 (low single)
- .long 0x00000000 // c2
- .long 0x3CB5E28B // c3
- .long 0x00000000 // c4
- .long 0xBCC90FDB // B' = pi/2 - B (high single)
- .long 0x303BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3C060BF3 // c0 (high single)
- .long 0xAFE251AE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAABFB9 // c1 (low single)
- .long 0x3AD67C60 // c2
- .long 0x3CB64CA5 // c3
- .long 0x3ACDE881 // c4
- .long 0xBD490FDB // B' = pi/2 - B (high single)
- .long 0x30BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3C861015 // c0 (high single)
- .long 0x2FD68E2E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAFEEB // c1 (low single)
- .long 0x3B569F3F // c2
- .long 0x3CB6A84E // c3
- .long 0x3AC64194 // c4
- .long 0xBD96CBE4 // B' = pi/2 - B (high single)
- .long 0x2F4CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3CC92278 // c0 (high single)
- .long 0xB02F2E68 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAB6854 // c1 (low single)
- .long 0x3BA1214F // c2
- .long 0x3CB6C1E9 // c3
- .long 0xB843C2F2 // c4
- .long 0xBDC90FDB // B' = pi/2 - B (high single)
- .long 0x313BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D0620A3 // c0 (high single)
- .long 0x30ECAB40 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DABFC11 // c1 (low single)
- .long 0x3BD7200F // c2
- .long 0x3CB79475 // c3
- .long 0x3A2B0ADC // c4
- .long 0xBDFB53D1 // B' = pi/2 - B (high single)
- .long 0xB1155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D27B856 // c0 (high single)
- .long 0x30F7EE91 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DACBA4E // c1 (low single)
- .long 0x3C06AEE3 // c2
- .long 0x3CB8E5DC // c3
- .long 0x3AEC00EE // c4
- .long 0xBE16CBE4 // B' = pi/2 - B (high single)
- .long 0x2FCCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D495A6C // c0 (high single)
- .long 0x30A427BD // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DADA345 // c1 (low single)
- .long 0x3C21F648 // c2
- .long 0x3CB9D1B4 // c3
- .long 0x3ACB5567 // c4
- .long 0xBE2FEDDF // B' = pi/2 - B (high single)
- .long 0xB19BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D6B08FF // c0 (high single)
- .long 0x30EED236 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAEB739 // c1 (low single)
- .long 0x3C3D6D51 // c2
- .long 0x3CBB485D // c3
- .long 0x3AFFF5BA // c4
- .long 0xBE490FDB // B' = pi/2 - B (high single)
- .long 0x31BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D866317 // c0 (high single)
- .long 0x2FF02140 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAFF67D // c1 (low single)
- .long 0x3C591CD0 // c2
- .long 0x3CBCBEAD // c3
- .long 0x3B04BBEC // c4
- .long 0xBE6231D6 // B' = pi/2 - B (high single)
- .long 0x3019A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D974A0D // c0 (high single)
- .long 0x314F365B // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB1616F // c1 (low single)
- .long 0x3C750CD8 // c2
- .long 0x3CBEB595 // c3
- .long 0x3B22B883 // c4
- .long 0xBE7B53D1 // B' = pi/2 - B (high single)
- .long 0xB1955386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DA83A77 // c0 (high single)
- .long 0xB16D967A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB2F87C // c1 (low single)
- .long 0x3C88A31F // c2
- .long 0x3CC0E763 // c3
- .long 0x3B3F1666 // c4
- .long 0xBE8A3AE6 // B' = pi/2 - B (high single)
- .long 0xB21EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DB93569 // c0 (high single)
- .long 0x2FB9ED00 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB4BC1F // c1 (low single)
- .long 0x3C96E905 // c2
- .long 0x3CC2E6F5 // c3
- .long 0x3B3E10A6 // c4
- .long 0xBE96CBE4 // B' = pi/2 - B (high single)
- .long 0x304CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DCA3BFF // c0 (high single)
- .long 0xB11C95EA // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB6ACDE // c1 (low single)
- .long 0x3CA55C5B // c2
- .long 0x3CC5BC04 // c3
- .long 0x3B63A969 // c4
- .long 0xBEA35CE2 // B' = pi/2 - B (high single)
- .long 0x323889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DDB4F55 // c0 (high single)
- .long 0xB0F6437E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB8CB52 // c1 (low single)
- .long 0x3CB40210 // c2
- .long 0x3CC82D45 // c3
- .long 0x3B643075 // c4
- .long 0xBEAFEDDF // B' = pi/2 - B (high single)
- .long 0xB21BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DEC708C // c0 (high single)
- .long 0x314895C4 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBB181E // c1 (low single)
- .long 0x3CC2DEA6 // c2
- .long 0x3CCB5027 // c3
- .long 0x3B7F3969 // c4
- .long 0xBEBC7EDD // B' = pi/2 - B (high single)
- .long 0x30800ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DFDA0CB // c0 (high single)
- .long 0xAF14FCA0 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBD93F7 // c1 (low single)
- .long 0x3CD1F71B // c2
- .long 0x3CCEDD2B // c3
- .long 0x3B905946 // c4
- .long 0xBEC90FDB // B' = pi/2 - B (high single)
- .long 0x323BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E07709D // c0 (high single)
- .long 0x318A2A83 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC03FA2 // c1 (low single)
- .long 0x3CE15096 // c2
- .long 0x3CD26472 // c3
- .long 0x3B9A1270 // c4
- .long 0xBED5A0D8 // B' = pi/2 - B (high single)
- .long 0xB21886FF // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E101985 // c0 (high single)
- .long 0x302FB2B8 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC31BF3 // c1 (low single)
- .long 0x3CF0F04D // c2
- .long 0x3CD60BC7 // c3
- .long 0x3BA138BA // c4
- .long 0xBEE231D6 // B' = pi/2 - B (high single)
- .long 0x3099A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E18CBB7 // c0 (high single)
- .long 0x2FE28430 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC629CE // c1 (low single)
- .long 0x3D006DCD // c2
- .long 0x3CDA5A2C // c3
- .long 0x3BB0B3D2 // c4
- .long 0xBEEEC2D4 // B' = pi/2 - B (high single)
- .long 0x323EF0A7 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E2187D0 // c0 (high single)
- .long 0x31B7C7F7 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC96A2B // c1 (low single)
- .long 0x3D088C22 // c2
- .long 0x3CDE950E // c3
- .long 0x3BB89AD1 // c4
- .long 0xBEFB53D1 // B' = pi/2 - B (high single)
- .long 0xB2155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E2A4E71 // c0 (high single)
- .long 0x319CFCEC // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DCCDE11 // c1 (low single)
- .long 0x3D10D605 // c2
- .long 0x3CE382A7 // c3
- .long 0x3BC8BD97 // c4
- .long 0xBF03F267 // B' = pi/2 - B (high single)
- .long 0xB2F4CBD9 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E33203E // c0 (high single)
- .long 0xB1FEF5BE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD0869C // c1 (low single)
- .long 0x3D194E8C // c2
- .long 0x3CE8DCA9 // c3
- .long 0x3BDADA55 // c4
- .long 0xBF0A3AE6 // B' = pi/2 - B (high single)
- .long 0xB29EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E3BFDDC // c0 (high single)
- .long 0x3132521A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD464FC // c1 (low single)
- .long 0x3D21F8F1 // c2
- .long 0x3CEE3076 // c3
- .long 0x3BE6D263 // c4
- .long 0xBF108365 // B' = pi/2 - B (high single)
- .long 0xB212200D // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E44E7F8 // c0 (high single)
- .long 0x31CAA3CB // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD87A74 // c1 (low single)
- .long 0x3D2AD885 // c2
- .long 0x3CF3C785 // c3
- .long 0x3BF1E348 // c4
- .long 0xBF16CBE4 // B' = pi/2 - B (high single)
- .long 0x30CCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E4DDF41 // c0 (high single)
- .long 0x31AEA094 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DDCC85C // c1 (low single)
- .long 0x3D33F0BE // c2
- .long 0x3CFA23B0 // c3
- .long 0x3C01FCF7 // c4
- .long 0xBF1D1463 // B' = pi/2 - B (high single)
- .long 0x32455799 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E56E46B // c0 (high single)
- .long 0xB1E3F001 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE15025 // c1 (low single)
- .long 0x3D3D4550 // c2
- .long 0x3D00462D // c3
- .long 0x3C092C98 // c4
- .long 0xBF235CE2 // B' = pi/2 - B (high single)
- .long 0x32B889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E5FF82C // c0 (high single)
- .long 0x3170723A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE61354 // c1 (low single)
- .long 0x3D46DA06 // c2
- .long 0x3D0401F8 // c3
- .long 0x3C14E013 // c4
- .long 0xBF29A560 // B' = pi/2 - B (high single)
- .long 0xB2F19861 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E691B44 // c0 (high single)
- .long 0xB1F18936 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DEB138B // c1 (low single)
- .long 0x3D50B2F7 // c2
- .long 0x3D07BE3A // c3
- .long 0x3C1E46A7 // c4
- .long 0xBF2FEDDF // B' = pi/2 - B (high single)
- .long 0xB29BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E724E73 // c0 (high single)
- .long 0xB120C3E2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF05283 // c1 (low single)
- .long 0x3D5AD45E // c2
- .long 0x3D0BAFBF // c3
- .long 0x3C27B8BB // c4
- .long 0xBF36365E // B' = pi/2 - B (high single)
- .long 0xB20BB91C // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E7B9282 // c0 (high single)
- .long 0x313383D2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF5D211 // c1 (low single)
- .long 0x3D6542B3 // c2
- .long 0x3D0FE5E5 // c3
- .long 0x3C31FB14 // c4
- .long 0xBF3C7EDD // B' = pi/2 - B (high single)
- .long 0x31000ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E827420 // c0 (high single)
- .long 0xB20B8B4D // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DFB9428 // c1 (low single)
- .long 0x3D7002B4 // c2
- .long 0x3D142A6C // c3
- .long 0x3C3A47FF // c4
- .long 0xBF42C75C // B' = pi/2 - B (high single)
- .long 0x324BBE8A // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E87283F // c0 (high single)
- .long 0x3268B966 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDFE6529 // c1 (low single)
- .long 0x3D7B1953 // c2
- .long 0x3D18E109 // c3
- .long 0x3C4570B0 // c4
- .long 0xBF490FDB // B' = pi/2 - B (high single)
- .long 0x32BBBD2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF800000 // c0 (high single)
- .long 0x2B410000 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xB3000000 // c1 (low single)
- .long 0xC0000000 // c2
- .long 0x402AB7C8 // c3
- .long 0xC05561DB // c4
- .long 0xBF4F5859 // B' = pi/2 - B (high single)
- .long 0xB2EE64E8 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF73BB75 // c0 (high single)
- .long 0xB2FC908D // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBDBF94B0 // c1 (low single)
- .long 0xBFE8550F // c2
- .long 0x40174F67 // c3
- .long 0xC036C608 // c4
- .long 0xBF55A0D8 // B' = pi/2 - B (high single)
- .long 0xB29886FF // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF68065E // c0 (high single)
- .long 0xB2670D1A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE36D1D6 // c1 (low single)
- .long 0xBFD35007 // c2
- .long 0x4006A861 // c3
- .long 0xC01D4BDA // c4
- .long 0xBF5BE957 // B' = pi/2 - B (high single)
- .long 0xB205522A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF5CD3BE // c0 (high single)
- .long 0xB1460308 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE8306C5 // c1 (low single)
- .long 0xBFC09232 // c2
- .long 0x3FF09632 // c3
- .long 0xC007DB00 // c4
- .long 0xBF6231D6 // B' = pi/2 - B (high single)
- .long 0x3119A6A2 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF521801 // c0 (high single)
- .long 0xB2AE4178 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEA72938 // c1 (low single)
- .long 0xBFAFCC22 // c2
- .long 0x3FD7BD4A // c3
- .long 0xBFEBB01B // c4
- .long 0xBF687A55 // B' = pi/2 - B (high single)
- .long 0x3252257B // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF47C8CC // c0 (high single)
- .long 0x3200F51A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEC82C6C // c1 (low single)
- .long 0xBFA0BAE9 // c2
- .long 0x3FC2252F // c3
- .long 0xBFCD24C7 // c4
- .long 0xBF6EC2D4 // B' = pi/2 - B (high single)
- .long 0x32BEF0A7 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF3DDCCF // c0 (high single)
- .long 0xB2D29606 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEE6606F // c1 (low single)
- .long 0xBF9325D6 // c2
- .long 0x3FAF4E69 // c3
- .long 0xBFB3080C // c4
- .long 0xBF750B52 // B' = pi/2 - B (high single)
- .long 0xB2EB316F // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF344BA9 // c0 (high single)
- .long 0x32B8B0EA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EFDF4F7 // c1 (low single)
- .long 0xBF86DCA8 // c2
- .long 0x3F9ED53B // c3
- .long 0xBF9CBEDE // c4
- .long 0xBF7B53D1 // B' = pi/2 - B (high single)
- .long 0xB2955386 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF2B0DC1 // c0 (high single)
- .long 0xB2AB7EBA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EE496C2 // c1 (low single)
- .long 0xBF776C40 // c2
- .long 0x3F9065C1 // c3
- .long 0xBF89AFB6 // c4
- .long 0xBF80CE28 // B' = pi/2 - B (high single)
- .long 0xB1FDD672 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF221C37 // c0 (high single)
- .long 0x320C61DC // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3ECD4F71 // c1 (low single)
- .long 0xBF631DAA // c2
- .long 0x3F83B471 // c3
- .long 0xBF7281EA // c4
- .long 0xBF83F267 // B' = pi/2 - B (high single)
- .long 0xB374CBD9 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF1970C4 // c0 (high single)
- .long 0xB2904848 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EB7EFF8 // c1 (low single)
- .long 0xBF50907C // c2
- .long 0x3F710FEA // c3
- .long 0xBF561FED // c4
- .long 0xBF8716A7 // B' = pi/2 - B (high single)
- .long 0x32588C6D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF1105AF // c0 (high single)
- .long 0xB2F045B0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EA44EE2 // c1 (low single)
- .long 0xBF3F8FDB // c2
- .long 0x3F5D3FD0 // c3
- .long 0xBF3D0A23 // c4
- .long 0xBF8A3AE6 // B' = pi/2 - B (high single)
- .long 0xB31EEDF0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF08D5B9 // c0 (high single)
- .long 0x325EF98E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E92478D // c1 (low single)
- .long 0xBF2FEDC9 // c2
- .long 0x3F4BCD58 // c3
- .long 0xBF27AE9E // c4
- .long 0xBF8D5F26 // B' = pi/2 - B (high single)
- .long 0x330C0105 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF00DC0D // c0 (high single)
- .long 0x3214AF72 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E81B994 // c1 (low single)
- .long 0xBF218233 // c2
- .long 0x3F3C4531 // c3
- .long 0xBF149688 // c4
- .long 0xBF908365 // B' = pi/2 - B (high single)
- .long 0xB292200D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEF22870 // c0 (high single)
- .long 0xB25271F4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E65107A // c1 (low single)
- .long 0xBF1429F0 // c2
- .long 0x3F2E8AFC // c3
- .long 0xBF040498 // c4
- .long 0xBF93A7A5 // B' = pi/2 - B (high single)
- .long 0x3361DEEE // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEE2F439 // c0 (high single)
- .long 0x31F4399E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E49341C // c1 (low single)
- .long 0xBF07C61A // c2
- .long 0x3F22560F // c3
- .long 0xBEEAA81E // c4
- .long 0xBF96CBE4 // B' = pi/2 - B (high single)
- .long 0x314CDE2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBED413CD // c0 (high single)
- .long 0x31C06152 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E2FB0CC // c1 (low single)
- .long 0xBEF876CB // c2
- .long 0x3F177807 // c3
- .long 0xBED08437 // c4
- .long 0xBF99F023 // B' = pi/2 - B (high single)
- .long 0xB3484328 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEC5800D // c0 (high single)
- .long 0x3214C3C1 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E185E54 // c1 (low single)
- .long 0xBEE2E342 // c2
- .long 0x3F0DCA73 // c3
- .long 0xBEB8CC21 // c4
- .long 0xBF9D1463 // B' = pi/2 - B (high single)
- .long 0x32C55799 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEB73250 // c0 (high single)
- .long 0x32028823 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E0318F8 // c1 (low single)
- .long 0xBECEA678 // c2
- .long 0x3F053C67 // c3
- .long 0xBEA41E53 // c4
- .long 0xBFA038A2 // B' = pi/2 - B (high single)
- .long 0xB2E4CA7E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEA92457 // c0 (high single)
- .long 0xB0B80830 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DDF8200 // c1 (low single)
- .long 0xBEBB99E9 // c2
- .long 0x3EFB4AA8 // c3
- .long 0xBE9182BE // c4
- .long 0xBFA35CE2 // B' = pi/2 - B (high single)
- .long 0x333889B6 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE9B5042 // c0 (high single)
- .long 0x322A3AEE // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DBC7490 // c1 (low single)
- .long 0xBEA99AF5 // c2
- .long 0x3EEDE107 // c3
- .long 0xBE80E9AA // c4
- .long 0xBFA68121 // B' = pi/2 - B (high single)
- .long 0xB1E43AAC // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE8DB082 // c0 (high single)
- .long 0x3132A234 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D9CD7D0 // c1 (low single)
- .long 0xBE988A60 // c2
- .long 0x3EE203E3 // c3
- .long 0xBE63582C // c4
- .long 0xBFA9A560 // B' = pi/2 - B (high single)
- .long 0xB3719861 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE803FD4 // c0 (high single)
- .long 0x32279E66 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D807FC8 // c1 (low single)
- .long 0xBE884BD4 // c2
- .long 0x3ED7812D // c3
- .long 0xBE4636EB // c4
- .long 0xBFACC9A0 // B' = pi/2 - B (high single)
- .long 0x32655A50 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE65F267 // c0 (high single)
- .long 0xB1B4B1DF // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D4E8B90 // c1 (low single)
- .long 0xBE718ACA // c2
- .long 0x3ECE7164 // c3
- .long 0xBE2DC161 // c4
- .long 0xBFAFEDDF // B' = pi/2 - B (high single)
- .long 0xB31BBA77 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE4BAFAF // c0 (high single)
- .long 0xAF2A29E0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D221018 // c1 (low single)
- .long 0xBE53BED0 // c2
- .long 0x3EC67E26 // c3
- .long 0xBE1568E2 // c4
- .long 0xBFB3121F // B' = pi/2 - B (high single)
- .long 0x330F347D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE31AE4D // c0 (high single)
- .long 0x31F32251 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CF6A500 // c1 (low single)
- .long 0xBE3707DA // c2
- .long 0x3EBFA489 // c3
- .long 0xBDFBD9C7 // c4
- .long 0xBFB6365E // B' = pi/2 - B (high single)
- .long 0xB28BB91C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE17E564 // c0 (high single)
- .long 0x31C5A2E4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CB440D0 // c1 (low single)
- .long 0xBE1B3D00 // c2
- .long 0x3EB9F664 // c3
- .long 0xBDD647C0 // c4
- .long 0xBFB95A9E // B' = pi/2 - B (high single)
- .long 0x33651267 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBDFC98C2 // c0 (high single)
- .long 0x30AE525C // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C793D20 // c1 (low single)
- .long 0xBE003845 // c2
- .long 0x3EB5271F // c3
- .long 0xBDAC669E // c4
- .long 0xBFBC7EDD // B' = pi/2 - B (high single)
- .long 0x31800ADD // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBDC9B5DC // c0 (high single)
- .long 0xB145AD86 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C1EEF20 // c1 (low single)
- .long 0xBDCBAAEA // c2
- .long 0x3EB14E5E // c3
- .long 0xBD858BB2 // c4
- .long 0xBFBFA31C // B' = pi/2 - B (high single)
- .long 0xB3450FB0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBD9711CE // c0 (high single)
- .long 0xB14FEB28 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3BB24C00 // c1 (low single)
- .long 0xBD97E43A // c2
- .long 0x3EAE6A89 // c3
- .long 0xBD4D07E0 // c4
- .long 0xBFC2C75C // B' = pi/2 - B (high single)
- .long 0x32CBBE8A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBD49393C // c0 (high single)
- .long 0xB0A39F5B // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3B1E2B00 // c1 (low single)
- .long 0xBD49B5D4 // c2
- .long 0x3EAC4F10 // c3
- .long 0xBCFD9425 // c4
- .long 0xBFC5EB9B // B' = pi/2 - B (high single)
- .long 0xB2DE638C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBCC91A31 // c0 (high single)
- .long 0xAF8E8D1A // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3A1DFA00 // c1 (low single)
- .long 0xBCC9392D // c2
- .long 0x3EAB1889 // c3
- .long 0xBC885D3B // c4
- .align 16
- .type __svml_stan_data_internal, @object
- .size __svml_stan_data_internal, .-__svml_stan_data_internal
- .space 16, 0x00
- .align 16
-
-#ifdef __svml_stan_reduction_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(16)) VUINT32 _sPtable[256][3][1];
-} __svml_stan_reduction_data_internal;
-#endif
-__svml_stan_reduction_data_internal:
- /* P_hi P_med P_lo */
- .long 0x00000000, 0x00000000, 0x00000000 /* 0 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 1 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 2 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 3 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 4 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 5 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 6 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 7 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 8 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 9 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 10 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 11 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 12 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 13 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 14 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 15 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 16 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 17 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 18 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 19 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 20 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 21 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 22 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 23 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 24 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 25 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 26 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 27 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 28 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 29 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 30 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 31 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 32 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 33 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 34 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 35 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 36 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 37 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 38 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 39 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 40 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 41 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 42 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 43 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 44 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 45 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 46 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 47 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 48 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 49 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 50 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 51 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 52 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 53 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 54 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 55 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 56 */
- .long 0x00000000, 0x00000000, 0x00000001 /* 57 */
- .long 0x00000000, 0x00000000, 0x00000002 /* 58 */
- .long 0x00000000, 0x00000000, 0x00000005 /* 59 */
- .long 0x00000000, 0x00000000, 0x0000000A /* 60 */
- .long 0x00000000, 0x00000000, 0x00000014 /* 61 */
- .long 0x00000000, 0x00000000, 0x00000028 /* 62 */
- .long 0x00000000, 0x00000000, 0x00000051 /* 63 */
- .long 0x00000000, 0x00000000, 0x000000A2 /* 64 */
- .long 0x00000000, 0x00000000, 0x00000145 /* 65 */
- .long 0x00000000, 0x00000000, 0x0000028B /* 66 */
- .long 0x00000000, 0x00000000, 0x00000517 /* 67 */
- .long 0x00000000, 0x00000000, 0x00000A2F /* 68 */
- .long 0x00000000, 0x00000000, 0x0000145F /* 69 */
- .long 0x00000000, 0x00000000, 0x000028BE /* 70 */
- .long 0x00000000, 0x00000000, 0x0000517C /* 71 */
- .long 0x00000000, 0x00000000, 0x0000A2F9 /* 72 */
- .long 0x00000000, 0x00000000, 0x000145F3 /* 73 */
- .long 0x00000000, 0x00000000, 0x00028BE6 /* 74 */
- .long 0x00000000, 0x00000000, 0x000517CC /* 75 */
- .long 0x00000000, 0x00000000, 0x000A2F98 /* 76 */
- .long 0x00000000, 0x00000000, 0x00145F30 /* 77 */
- .long 0x00000000, 0x00000000, 0x0028BE60 /* 78 */
- .long 0x00000000, 0x00000000, 0x00517CC1 /* 79 */
- .long 0x00000000, 0x00000000, 0x00A2F983 /* 80 */
- .long 0x00000000, 0x00000000, 0x0145F306 /* 81 */
- .long 0x00000000, 0x00000000, 0x028BE60D /* 82 */
- .long 0x00000000, 0x00000000, 0x0517CC1B /* 83 */
- .long 0x00000000, 0x00000000, 0x0A2F9836 /* 84 */
- .long 0x00000000, 0x00000000, 0x145F306D /* 85 */
- .long 0x00000000, 0x00000000, 0x28BE60DB /* 86 */
- .long 0x00000000, 0x00000000, 0x517CC1B7 /* 87 */
- .long 0x00000000, 0x00000000, 0xA2F9836E /* 88 */
- .long 0x00000000, 0x00000001, 0x45F306DC /* 89 */
- .long 0x00000000, 0x00000002, 0x8BE60DB9 /* 90 */
- .long 0x00000000, 0x00000005, 0x17CC1B72 /* 91 */
- .long 0x00000000, 0x0000000A, 0x2F9836E4 /* 92 */
- .long 0x00000000, 0x00000014, 0x5F306DC9 /* 93 */
- .long 0x00000000, 0x00000028, 0xBE60DB93 /* 94 */
- .long 0x00000000, 0x00000051, 0x7CC1B727 /* 95 */
- .long 0x00000000, 0x000000A2, 0xF9836E4E /* 96 */
- .long 0x00000000, 0x00000145, 0xF306DC9C /* 97 */
- .long 0x00000000, 0x0000028B, 0xE60DB939 /* 98 */
- .long 0x00000000, 0x00000517, 0xCC1B7272 /* 99 */
- .long 0x00000000, 0x00000A2F, 0x9836E4E4 /* 100 */
- .long 0x00000000, 0x0000145F, 0x306DC9C8 /* 101 */
- .long 0x00000000, 0x000028BE, 0x60DB9391 /* 102 */
- .long 0x00000000, 0x0000517C, 0xC1B72722 /* 103 */
- .long 0x00000000, 0x0000A2F9, 0x836E4E44 /* 104 */
- .long 0x00000000, 0x000145F3, 0x06DC9C88 /* 105 */
- .long 0x00000000, 0x00028BE6, 0x0DB93910 /* 106 */
- .long 0x00000000, 0x000517CC, 0x1B727220 /* 107 */
- .long 0x00000000, 0x000A2F98, 0x36E4E441 /* 108 */
- .long 0x00000000, 0x00145F30, 0x6DC9C882 /* 109 */
- .long 0x00000000, 0x0028BE60, 0xDB939105 /* 110 */
- .long 0x00000000, 0x00517CC1, 0xB727220A /* 111 */
- .long 0x00000000, 0x00A2F983, 0x6E4E4415 /* 112 */
- .long 0x00000000, 0x0145F306, 0xDC9C882A /* 113 */
- .long 0x00000000, 0x028BE60D, 0xB9391054 /* 114 */
- .long 0x00000000, 0x0517CC1B, 0x727220A9 /* 115 */
- .long 0x00000000, 0x0A2F9836, 0xE4E44152 /* 116 */
- .long 0x00000000, 0x145F306D, 0xC9C882A5 /* 117 */
- .long 0x00000000, 0x28BE60DB, 0x9391054A /* 118 */
- .long 0x00000000, 0x517CC1B7, 0x27220A94 /* 119 */
- .long 0x00000000, 0xA2F9836E, 0x4E441529 /* 120 */
- .long 0x00000001, 0x45F306DC, 0x9C882A53 /* 121 */
- .long 0x00000002, 0x8BE60DB9, 0x391054A7 /* 122 */
- .long 0x00000005, 0x17CC1B72, 0x7220A94F /* 123 */
- .long 0x0000000A, 0x2F9836E4, 0xE441529F /* 124 */
- .long 0x00000014, 0x5F306DC9, 0xC882A53F /* 125 */
- .long 0x00000028, 0xBE60DB93, 0x91054A7F /* 126 */
- .long 0x00000051, 0x7CC1B727, 0x220A94FE /* 127 */
- .long 0x000000A2, 0xF9836E4E, 0x441529FC /* 128 */
- .long 0x00000145, 0xF306DC9C, 0x882A53F8 /* 129 */
- .long 0x0000028B, 0xE60DB939, 0x1054A7F0 /* 130 */
- .long 0x00000517, 0xCC1B7272, 0x20A94FE1 /* 131 */
- .long 0x00000A2F, 0x9836E4E4, 0x41529FC2 /* 132 */
- .long 0x0000145F, 0x306DC9C8, 0x82A53F84 /* 133 */
- .long 0x000028BE, 0x60DB9391, 0x054A7F09 /* 134 */
- .long 0x0000517C, 0xC1B72722, 0x0A94FE13 /* 135 */
- .long 0x0000A2F9, 0x836E4E44, 0x1529FC27 /* 136 */
- .long 0x000145F3, 0x06DC9C88, 0x2A53F84E /* 137 */
- .long 0x00028BE6, 0x0DB93910, 0x54A7F09D /* 138 */
- .long 0x000517CC, 0x1B727220, 0xA94FE13A /* 139 */
- .long 0x000A2F98, 0x36E4E441, 0x529FC275 /* 140 */
- .long 0x00145F30, 0x6DC9C882, 0xA53F84EA /* 141 */
- .long 0x0028BE60, 0xDB939105, 0x4A7F09D5 /* 142 */
- .long 0x00517CC1, 0xB727220A, 0x94FE13AB /* 143 */
- .long 0x00A2F983, 0x6E4E4415, 0x29FC2757 /* 144 */
- .long 0x0145F306, 0xDC9C882A, 0x53F84EAF /* 145 */
- .long 0x028BE60D, 0xB9391054, 0xA7F09D5F /* 146 */
- .long 0x0517CC1B, 0x727220A9, 0x4FE13ABE /* 147 */
- .long 0x0A2F9836, 0xE4E44152, 0x9FC2757D /* 148 */
- .long 0x145F306D, 0xC9C882A5, 0x3F84EAFA /* 149 */
- .long 0x28BE60DB, 0x9391054A, 0x7F09D5F4 /* 150 */
- .long 0x517CC1B7, 0x27220A94, 0xFE13ABE8 /* 151 */
- .long 0xA2F9836E, 0x4E441529, 0xFC2757D1 /* 152 */
- .long 0x45F306DC, 0x9C882A53, 0xF84EAFA3 /* 153 */
- .long 0x8BE60DB9, 0x391054A7, 0xF09D5F47 /* 154 */
- .long 0x17CC1B72, 0x7220A94F, 0xE13ABE8F /* 155 */
- .long 0x2F9836E4, 0xE441529F, 0xC2757D1F /* 156 */
- .long 0x5F306DC9, 0xC882A53F, 0x84EAFA3E /* 157 */
- .long 0xBE60DB93, 0x91054A7F, 0x09D5F47D /* 158 */
- .long 0x7CC1B727, 0x220A94FE, 0x13ABE8FA /* 159 */
- .long 0xF9836E4E, 0x441529FC, 0x2757D1F5 /* 160 */
- .long 0xF306DC9C, 0x882A53F8, 0x4EAFA3EA /* 161 */
- .long 0xE60DB939, 0x1054A7F0, 0x9D5F47D4 /* 162 */
- .long 0xCC1B7272, 0x20A94FE1, 0x3ABE8FA9 /* 163 */
- .long 0x9836E4E4, 0x41529FC2, 0x757D1F53 /* 164 */
- .long 0x306DC9C8, 0x82A53F84, 0xEAFA3EA6 /* 165 */
- .long 0x60DB9391, 0x054A7F09, 0xD5F47D4D /* 166 */
- .long 0xC1B72722, 0x0A94FE13, 0xABE8FA9A /* 167 */
- .long 0x836E4E44, 0x1529FC27, 0x57D1F534 /* 168 */
- .long 0x06DC9C88, 0x2A53F84E, 0xAFA3EA69 /* 169 */
- .long 0x0DB93910, 0x54A7F09D, 0x5F47D4D3 /* 170 */
- .long 0x1B727220, 0xA94FE13A, 0xBE8FA9A6 /* 171 */
- .long 0x36E4E441, 0x529FC275, 0x7D1F534D /* 172 */
- .long 0x6DC9C882, 0xA53F84EA, 0xFA3EA69B /* 173 */
- .long 0xDB939105, 0x4A7F09D5, 0xF47D4D37 /* 174 */
- .long 0xB727220A, 0x94FE13AB, 0xE8FA9A6E /* 175 */
- .long 0x6E4E4415, 0x29FC2757, 0xD1F534DD /* 176 */
- .long 0xDC9C882A, 0x53F84EAF, 0xA3EA69BB /* 177 */
- .long 0xB9391054, 0xA7F09D5F, 0x47D4D377 /* 178 */
- .long 0x727220A9, 0x4FE13ABE, 0x8FA9A6EE /* 179 */
- .long 0xE4E44152, 0x9FC2757D, 0x1F534DDC /* 180 */
- .long 0xC9C882A5, 0x3F84EAFA, 0x3EA69BB8 /* 181 */
- .long 0x9391054A, 0x7F09D5F4, 0x7D4D3770 /* 182 */
- .long 0x27220A94, 0xFE13ABE8, 0xFA9A6EE0 /* 183 */
- .long 0x4E441529, 0xFC2757D1, 0xF534DDC0 /* 184 */
- .long 0x9C882A53, 0xF84EAFA3, 0xEA69BB81 /* 185 */
- .long 0x391054A7, 0xF09D5F47, 0xD4D37703 /* 186 */
- .long 0x7220A94F, 0xE13ABE8F, 0xA9A6EE06 /* 187 */
- .long 0xE441529F, 0xC2757D1F, 0x534DDC0D /* 188 */
- .long 0xC882A53F, 0x84EAFA3E, 0xA69BB81B /* 189 */
- .long 0x91054A7F, 0x09D5F47D, 0x4D377036 /* 190 */
- .long 0x220A94FE, 0x13ABE8FA, 0x9A6EE06D /* 191 */
- .long 0x441529FC, 0x2757D1F5, 0x34DDC0DB /* 192 */
- .long 0x882A53F8, 0x4EAFA3EA, 0x69BB81B6 /* 193 */
- .long 0x1054A7F0, 0x9D5F47D4, 0xD377036D /* 194 */
- .long 0x20A94FE1, 0x3ABE8FA9, 0xA6EE06DB /* 195 */
- .long 0x41529FC2, 0x757D1F53, 0x4DDC0DB6 /* 196 */
- .long 0x82A53F84, 0xEAFA3EA6, 0x9BB81B6C /* 197 */
- .long 0x054A7F09, 0xD5F47D4D, 0x377036D8 /* 198 */
- .long 0x0A94FE13, 0xABE8FA9A, 0x6EE06DB1 /* 199 */
- .long 0x1529FC27, 0x57D1F534, 0xDDC0DB62 /* 200 */
- .long 0x2A53F84E, 0xAFA3EA69, 0xBB81B6C5 /* 201 */
- .long 0x54A7F09D, 0x5F47D4D3, 0x77036D8A /* 202 */
- .long 0xA94FE13A, 0xBE8FA9A6, 0xEE06DB14 /* 203 */
- .long 0x529FC275, 0x7D1F534D, 0xDC0DB629 /* 204 */
- .long 0xA53F84EA, 0xFA3EA69B, 0xB81B6C52 /* 205 */
- .long 0x4A7F09D5, 0xF47D4D37, 0x7036D8A5 /* 206 */
- .long 0x94FE13AB, 0xE8FA9A6E, 0xE06DB14A /* 207 */
- .long 0x29FC2757, 0xD1F534DD, 0xC0DB6295 /* 208 */
- .long 0x53F84EAF, 0xA3EA69BB, 0x81B6C52B /* 209 */
- .long 0xA7F09D5F, 0x47D4D377, 0x036D8A56 /* 210 */
- .long 0x4FE13ABE, 0x8FA9A6EE, 0x06DB14AC /* 211 */
- .long 0x9FC2757D, 0x1F534DDC, 0x0DB62959 /* 212 */
- .long 0x3F84EAFA, 0x3EA69BB8, 0x1B6C52B3 /* 213 */
- .long 0x7F09D5F4, 0x7D4D3770, 0x36D8A566 /* 214 */
- .long 0xFE13ABE8, 0xFA9A6EE0, 0x6DB14ACC /* 215 */
- .long 0xFC2757D1, 0xF534DDC0, 0xDB629599 /* 216 */
- .long 0xF84EAFA3, 0xEA69BB81, 0xB6C52B32 /* 217 */
- .long 0xF09D5F47, 0xD4D37703, 0x6D8A5664 /* 218 */
- .long 0xE13ABE8F, 0xA9A6EE06, 0xDB14ACC9 /* 219 */
- .long 0xC2757D1F, 0x534DDC0D, 0xB6295993 /* 220 */
- .long 0x84EAFA3E, 0xA69BB81B, 0x6C52B327 /* 221 */
- .long 0x09D5F47D, 0x4D377036, 0xD8A5664F /* 222 */
- .long 0x13ABE8FA, 0x9A6EE06D, 0xB14ACC9E /* 223 */
- .long 0x2757D1F5, 0x34DDC0DB, 0x6295993C /* 224 */
- .long 0x4EAFA3EA, 0x69BB81B6, 0xC52B3278 /* 225 */
- .long 0x9D5F47D4, 0xD377036D, 0x8A5664F1 /* 226 */
- .long 0x3ABE8FA9, 0xA6EE06DB, 0x14ACC9E2 /* 227 */
- .long 0x757D1F53, 0x4DDC0DB6, 0x295993C4 /* 228 */
- .long 0xEAFA3EA6, 0x9BB81B6C, 0x52B32788 /* 229 */
- .long 0xD5F47D4D, 0x377036D8, 0xA5664F10 /* 230 */
- .long 0xABE8FA9A, 0x6EE06DB1, 0x4ACC9E21 /* 231 */
- .long 0x57D1F534, 0xDDC0DB62, 0x95993C43 /* 232 */
- .long 0xAFA3EA69, 0xBB81B6C5, 0x2B327887 /* 233 */
- .long 0x5F47D4D3, 0x77036D8A, 0x5664F10E /* 234 */
- .long 0xBE8FA9A6, 0xEE06DB14, 0xACC9E21C /* 235 */
- .long 0x7D1F534D, 0xDC0DB629, 0x5993C439 /* 236 */
- .long 0xFA3EA69B, 0xB81B6C52, 0xB3278872 /* 237 */
- .long 0xF47D4D37, 0x7036D8A5, 0x664F10E4 /* 238 */
- .long 0xE8FA9A6E, 0xE06DB14A, 0xCC9E21C8 /* 239 */
- .long 0xD1F534DD, 0xC0DB6295, 0x993C4390 /* 240 */
- .long 0xA3EA69BB, 0x81B6C52B, 0x32788720 /* 241 */
- .long 0x47D4D377, 0x036D8A56, 0x64F10E41 /* 242 */
- .long 0x8FA9A6EE, 0x06DB14AC, 0xC9E21C82 /* 243 */
- .long 0x1F534DDC, 0x0DB62959, 0x93C43904 /* 244 */
- .long 0x3EA69BB8, 0x1B6C52B3, 0x27887208 /* 245 */
- .long 0x7D4D3770, 0x36D8A566, 0x4F10E410 /* 246 */
- .long 0xFA9A6EE0, 0x6DB14ACC, 0x9E21C820 /* 247 */
- .long 0xF534DDC0, 0xDB629599, 0x3C439041 /* 248 */
- .long 0xEA69BB81, 0xB6C52B32, 0x78872083 /* 249 */
- .long 0xD4D37703, 0x6D8A5664, 0xF10E4107 /* 250 */
- .long 0xA9A6EE06, 0xDB14ACC9, 0xE21C820F /* 251 */
- .long 0x534DDC0D, 0xB6295993, 0xC439041F /* 252 */
- .long 0xA69BB81B, 0x6C52B327, 0x8872083F /* 253 */
- .long 0x4D377036, 0xD8A5664F, 0x10E4107F /* 254 */
- .long 0x9A6EE06D, 0xB14ACC9E, 0x21C820FF /* 255 */
- .align 16
- .type __svml_stan_reduction_data_internal, @object
- .size __svml_stan_reduction_data_internal, .-__svml_stan_reduction_data_internal
- .align 16
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _sPI1, 0x3FC90000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI2, 0x39FDA000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI3, 0x33A22000)
+ DATA_VEC (LOCAL_DATA_NAME, _sPI4, 0x2C34611A)
+ DATA_VEC (LOCAL_DATA_NAME, _sRangeVal, 0x00800000)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_0, 0xb795777a)
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_1, 0x40c91000)
-.FLT_16:
- .long 0xffffffff, 0x00000000, 0xffffffff, 0x00000000
- .type .FLT_16, @object
- .size .FLT_16, 16
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 17/27] x86/fpu: Optimize svml_s_tanf8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (14 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 16/27] x86/fpu: Optimize svml_s_tanf4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 18/27] x86/fpu: Optimize svml_s_log10f16_core_avx512.S Noah Goldstein via Libc-alpha
` (10 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Remove many unnecissary spills.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: 935 Bytes (1438 - 2373)
Input New Time / Old Time
0F (0x00000000) -> 0.8508
0F (0x0000ffff, Denorm) -> 0.9556
.1F (0x3dcccccd) -> 0.8491
5F (0x40a00000) -> 0.7777
2315255808F (0x4f0a0000) -> 0.7410
-NaN (0xffffffff) -> 0.7444
---
.../fpu/multiarch/svml_s_tanf8_core_avx2.S | 2967 +++--------------
1 file changed, 503 insertions(+), 2464 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core_avx2.S
index d34e61ac41..de4c849c45 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core_avx2.S
@@ -45,2548 +45,587 @@
*
*/
-/* Offsets for data table __svml_stan_data_internal
- */
-#define _sInvPI_uisa 0
-#define _sPI1_uisa 32
-#define _sPI2_uisa 64
-#define _sPI3_uisa 96
-#define _sPI2_ha_uisa 128
-#define _sPI3_ha_uisa 160
-#define Th_tbl_uisa 192
-#define Tl_tbl_uisa 320
-#define _sPC3_uisa 448
-#define _sPC5_uisa 480
-#define _sRangeReductionVal_uisa 512
-#define _sInvPi 544
-#define _sSignMask 576
-#define _sAbsMask 608
-#define _sRangeVal 640
-#define _sRShifter 672
-#define _sOne 704
-#define _sRangeReductionVal 736
-#define _sPI1 768
-#define _sPI2 800
-#define _sPI3 832
-#define _sPI4 864
-#define _sPI1_FMA 896
-#define _sPI2_FMA 928
-#define _sPI3_FMA 960
-#define _sP0 992
-#define _sP1 1024
-#define _sQ0 1056
-#define _sQ1 1088
-#define _sQ2 1120
-#define _sTwo 1152
-#define _sCoeffs 1184
+#define LOCAL_DATA_NAME __svml_stan_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+
+#define AVX2_SHARED_TABLE
+#define AVX512_SHARED_OFFSETS
+#include "svml_s_tanf_rodata.h.S"
+
+/* Offsets for data table __svml_stan_data_internal. */
+#define _sPI2_FMA 0
+#define _sPI3_FMA 32
+#define _FLT_0 64
+#define _FLT_1 96
+#define _FLT_2 128
+#define _FLT_3 160
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_tanf_avx2)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-32, %rsp
- pushq %rbx
- subq $184, %rsp
-
- /*
- * Legacy Code
- * Here HW FMA can be unavailable
- */
- xorl %eax, %eax
- vmovups _sAbsMask+__svml_stan_data_internal(%rip), %ymm10
-
- /*
- *
- * Main path (_LA_ and _EP_)
- *
- * Octant calculation
- */
- vmovups _sInvPi+__svml_stan_data_internal(%rip), %ymm5
- vmovups _sRShifter+__svml_stan_data_internal(%rip), %ymm2
-
- /* Range reduction */
- vmovups _sPI1_FMA+__svml_stan_data_internal(%rip), %ymm3
-
- /* Rational approximation */
- vmovups _sP1+__svml_stan_data_internal(%rip), %ymm9
- vmovaps %ymm0, %ymm12
- vandps %ymm10, %ymm12, %ymm1
+ vmovups COMMON_DATA(_AbsMask)(%rip), %ymm6
+ /* Main path (_LA_ and _EP_)
+ Octant calculation. */
+ vmovups AVX2_SHARED_DATA(_sInvPi)(%rip), %ymm5
+ vmovups AVX2_SHARED_DATA(_sRShifter)(%rip), %ymm2
+
+
+ vandps %ymm6, %ymm0, %ymm1
+
vfmadd213ps %ymm2, %ymm1, %ymm5
- vsubps %ymm2, %ymm5, %ymm8
- vpslld $30, %ymm5, %ymm6
-
- /* Inversion mask and sign calculation */
- vpslld $31, %ymm5, %ymm4
- vfnmadd213ps %ymm1, %ymm8, %ymm3
- vfnmadd231ps _sPI2_FMA+__svml_stan_data_internal(%rip), %ymm8, %ymm3
- vfnmadd132ps _sPI3_FMA+__svml_stan_data_internal(%rip), %ymm3, %ymm8
- vmovups _sQ2+__svml_stan_data_internal(%rip), %ymm3
- vmulps %ymm8, %ymm8, %ymm13
- vfmadd213ps _sQ1+__svml_stan_data_internal(%rip), %ymm13, %ymm3
- vfmadd213ps _sP0+__svml_stan_data_internal(%rip), %ymm13, %ymm9
- vfmadd213ps _sQ0+__svml_stan_data_internal(%rip), %ymm13, %ymm3
- vmulps %ymm9, %ymm8, %ymm8
- vxorps %ymm7, %ymm7, %ymm7
- vcmpneqps %ymm7, %ymm6, %ymm2
- vandnps %ymm12, %ymm10, %ymm11
- vxorps %ymm11, %ymm4, %ymm0
-
- /* Exchanged numerator and denominator if necessary */
- vandnps %ymm8, %ymm2, %ymm14
- vandps %ymm3, %ymm2, %ymm15
- vandps %ymm8, %ymm2, %ymm4
- vandnps %ymm3, %ymm2, %ymm5
- vorps %ymm15, %ymm14, %ymm6
- vorps %ymm5, %ymm4, %ymm7
-
- /* Division */
- vdivps %ymm7, %ymm6, %ymm9
-
- /* Large values check */
- vcmpnle_uqps _sRangeReductionVal+__svml_stan_data_internal(%rip), %ymm1, %ymm10
- vmovmskps %ymm10, %edx
-
- /* Sign setting */
- vxorps %ymm0, %ymm9, %ymm0
-
- /*
- *
- * End of main path (_LA_ and _EP_)
- */
+ vsubps %ymm2, %ymm5, %ymm7
+
+ /* Range reduction. */
+ vmovups COMMON_DATA(_TanSPI1_FMA)(%rip), %ymm3
+ vfnmadd213ps %ymm1, %ymm7, %ymm3
+
+ vfnmadd231ps LOCAL_DATA(_sPI2_FMA)(%rip), %ymm7, %ymm3
+ vfnmadd132ps LOCAL_DATA(_sPI3_FMA)(%rip), %ymm3, %ymm7
+ vmovups AVX2_SHARED_DATA(_sQ2)(%rip), %ymm3
+ /* Rational approximation. */
+ vmovups AVX2_SHARED_DATA(_sP1)(%rip), %ymm4
+ vmulps %ymm7, %ymm7, %ymm2
+ vfmadd213ps AVX2_SHARED_DATA(_sQ1)(%rip), %ymm2, %ymm3
+ vmovups AVX2_SHARED_DATA(_sP0)(%rip), %ymm8
+ vfmadd213ps %ymm8, %ymm2, %ymm4
+ vfmadd213ps %ymm8, %ymm2, %ymm3
+ vmulps %ymm4, %ymm7, %ymm4
+ /* Inversion mask and sign calculation. */
+ vpslld $31, %ymm5, %ymm2
+
+
+ vandnps %ymm0, %ymm6, %ymm7
+
+ /* Exchanged numerator and denominator if necessary. */
+ vblendvps %ymm2, %ymm3, %ymm4, %ymm6
+ vblendvps %ymm2, %ymm4, %ymm3, %ymm3
+
+ /* Large values check. */
+ vpcmpgtd AVX2_SHARED_DATA(_sRangeReductionVal)(%rip), %ymm1, %ymm10
+ vpmovmskb %ymm10, %edx
+
+ /* Division. */
+ vdivps %ymm3, %ymm6, %ymm3
+
+ /* End of main path (_LA_ and _EP_). */
testl %edx, %edx
- /* Go to auxilary branch */
+ /* Go to auxilary branch. */
jne L(AUX_BRANCH)
- /* DW_CFA_expression: r3 (rbx) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -8; DW_OP_plus) */
- .cfi_escape 0x10, 0x03, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf8, 0xff, 0xff, 0xff, 0x22
- # LOE r12 r13 r14 r15 eax ymm0 ymm1 ymm10 ymm11 ymm12
- /* Return from auxilary branch
- * for out of main path inputs
- */
+ vxorps %ymm2, %ymm7, %ymm7
+ /* Sign setting. */
+ vxorps %ymm7, %ymm3, %ymm0
+ ret
-L(AUX_BRANCH_RETURN):
- testl %eax, %eax
+L(AUX_BRANCH):
+ /* Sign setting. NB for all special case values this is
+ equivilent to the input (ymm0). */
+ vpandn %ymm3, %ymm10, %ymm3
+ vpxor %ymm3, %ymm7, %ymm12
+ vmovaps %ymm0, %ymm11
- /* Go to special inputs processing branch */
- jne L(SPECIAL_VALUES_BRANCH)
- # LOE r12 r13 r14 r15 eax ymm0 ymm12
- /* Restore registers
- * and exit the function
- */
+ /* Get the (2^a / 2pi) mod 1 values from the table. */
+ lea AVX512_SHARED_DATA(_Reduction)(%rip), %rdx
-L(EXIT):
- addq $184, %rsp
- cfi_restore(3)
- popq %rbx
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
- ret
- cfi_def_cfa(6, 16)
- /* DW_CFA_expression: r3 (rbx) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -8; DW_OP_plus) */
- .cfi_escape 0x10, 0x03, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf8, 0xff, 0xff, 0xff, 0x22
- cfi_offset(6, -16)
+ vpsrld $23, %ymm1, %ymm6
+ vpaddd %ymm6, %ymm6, %ymm2
- /* Branch to process
- * special inputs
- */
+ vpaddd %ymm6, %ymm2, %ymm3
-L(SPECIAL_VALUES_BRANCH):
- vmovups %ymm12, 32(%rsp)
- vmovups %ymm0, 64(%rsp)
- # LOE r12 r13 r14 r15 eax ymm0
+ /* Collect indexes. */
+ vmovq %xmm3, %rax
+ movl %eax, %ecx
+ shrq $32, %rax
- xorl %ebx, %ebx
- # LOE r12 r13 r14 r15 eax ebx
+ vmovq (%rdx, %rcx, 4), %xmm4
+ vmovq (%rdx, %rax, 4), %xmm5
+ vpunpckldq %xmm5, %xmm4, %xmm4
- vzeroupper
- movq %r12, 8(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, (%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE r14 r15 ebx r12d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %ebx, %r12d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE r14 r15 ebx r12d
-
- /* Special inputs
- * processing loop
- */
+ vpextrq $1, %xmm3, %rdi
+ movl %edi, %esi
+ shrq $32, %rdi
-L(SPECIAL_VALUES_LOOP):
- incl %ebx
- cmpl $8, %ebx
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE r14 r15 ebx r12d
-
- movq 8(%rsp), %r12
- cfi_restore(12)
- movq (%rsp), %r13
- cfi_restore(13)
- vmovups 64(%rsp), %ymm0
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE r12 r13 r14 r15 ymm0
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %ebx, %r13d
- vmovss 32(%rsp, %r13, 4), %xmm0
- call tanf@PLT
- # LOE r13 r14 r15 ebx r12d xmm0
+ vmovq (%rdx, %rsi, 4), %xmm2
+ vmovq (%rdx, %rdi, 4), %xmm5
+ vpunpckldq %xmm5, %xmm2, %xmm2
- vmovss %xmm0, 64(%rsp, %r13, 4)
+ vextractf128 $1, %ymm3, %xmm7
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- cfi_restore(12)
- cfi_restore(13)
- # LOE r14 r15 ebx r12d
+ vmovq %xmm7, %r10
+ movl %r10d, %r8d
+ shrq $32, %r10
- /* Auxilary branch
- * for out of main path inputs
- */
+ vmovq (%rdx, %r8, 4), %xmm3
+ vmovq (%rdx, %r10, 4), %xmm5
+ vpunpckldq %xmm5, %xmm3, %xmm3
-L(AUX_BRANCH):
- vpand .FLT_16(%rip), %ymm1, %ymm5
-
- /*
- * Get the (2^a / 2pi) mod 1 values from the table.
- * Because doesn't have I-type gather, we need a trivial cast
- */
- lea __svml_stan_reduction_data_internal(%rip), %rdx
- vmovups %ymm11, 64(%rsp)
- vmovups .FLT_15(%rip), %ymm7
- vmovups %ymm10, 96(%rsp)
- vmovups %ymm0, 128(%rsp)
- vpsrld $23, %ymm5, %ymm6
- vpslld $1, %ymm6, %ymm11
- vpaddd %ymm6, %ymm11, %ymm13
- vpslld $2, %ymm13, %ymm15
- vandps %ymm7, %ymm12, %ymm14
- vcmpeqps %ymm7, %ymm14, %ymm10
- vmovmskps %ymm10, %eax
- vextractf128 $1, %ymm15, %xmm7
- vmovd %xmm15, %ecx
- vmovd %xmm7, %r8d
- vmovd (%rcx, %rdx), %xmm8
- vpextrd $1, %xmm15, %ebx
- vpextrd $2, %xmm15, %esi
- vpextrd $3, %xmm15, %edi
- vpextrd $1, %xmm7, %r10d
- vpextrd $2, %xmm7, %r9d
- vpextrd $3, %xmm7, %r11d
- vmovd (%rbx, %rdx), %xmm3
- vmovd (%rsi, %rdx), %xmm2
- vmovd (%rdi, %rdx), %xmm14
- vmovd (%r8, %rdx), %xmm10
- vmovd (%r10, %rdx), %xmm5
- vmovd (%r9, %rdx), %xmm11
- vmovd (%r11, %rdx), %xmm6
- vpunpckldq %xmm3, %xmm8, %xmm4
- vpunpckldq %xmm14, %xmm2, %xmm0
- vpunpckldq %xmm5, %xmm10, %xmm13
- vpunpckldq %xmm6, %xmm11, %xmm15
- vpunpcklqdq %xmm0, %xmm4, %xmm9
- vmovd 4(%rcx, %rdx), %xmm3
- vmovd 4(%rbx, %rdx), %xmm2
- vmovd 4(%rsi, %rdx), %xmm14
- vmovd 4(%rdi, %rdx), %xmm4
- vpunpcklqdq %xmm15, %xmm13, %xmm8
- vmovd 4(%r8, %rdx), %xmm5
- vmovd 4(%r10, %rdx), %xmm6
- vmovd 4(%r9, %rdx), %xmm13
- vmovd 4(%r11, %rdx), %xmm15
- vpunpckldq %xmm2, %xmm3, %xmm0
- vpunpckldq %xmm4, %xmm14, %xmm7
- vpunpckldq %xmm15, %xmm13, %xmm3
- vpunpcklqdq %xmm7, %xmm0, %xmm10
- vmovd 8(%rsi, %rdx), %xmm0
- vmovd 8(%rdi, %rdx), %xmm7
- vmovd 8(%rcx, %rdx), %xmm14
- vmovd 8(%rbx, %rdx), %xmm4
- vmovd 8(%r8, %rdx), %xmm15
- vinsertf128 $1, %xmm8, %ymm9, %ymm11
- vpunpckldq %xmm6, %xmm5, %xmm8
- vpunpcklqdq %xmm3, %xmm8, %xmm2
- vpunpckldq %xmm7, %xmm0, %xmm6
-
- /*
- * Also get the significand as an integer
- * NB: adding in the integer bit is wrong for denorms!
- * To make this work for denorms we should do something slightly different
- */
- vpand .FLT_17(%rip), %ymm1, %ymm7
- vmovd 8(%r10, %rdx), %xmm8
- vmovd 8(%r9, %rdx), %xmm3
- vpunpckldq %xmm4, %xmm14, %xmm5
- vpunpckldq %xmm8, %xmm15, %xmm14
-
- /* Load constants (not all needed at once) */
- lea _sCoeffs+36+__svml_stan_data_internal(%rip), %r9
- vpunpcklqdq %xmm6, %xmm5, %xmm13
- vpaddd .FLT_18(%rip), %ymm7, %ymm5
- vinsertf128 $1, %xmm2, %ymm10, %ymm9
- vmovd 8(%r11, %rdx), %xmm2
- vpunpckldq %xmm2, %xmm3, %xmm4
- vpunpcklqdq %xmm4, %xmm14, %xmm0
-
- /*
- * Break the P_xxx and m into 16-bit chunks ready for
- * the long multiplication via 16x16->32 multiplications
- */
- vmovdqu .FLT_19(%rip), %ymm14
- vpsrld $16, %ymm5, %ymm10
- vpand %ymm14, %ymm5, %ymm5
- vpand %ymm14, %ymm9, %ymm3
- vpand %ymm14, %ymm11, %ymm7
- vpsrld $16, %ymm11, %ymm11
- vpmulld %ymm3, %ymm5, %ymm8
- vpmulld %ymm3, %ymm10, %ymm3
+ vpextrq $1, %xmm7, %r11
+ movl %r11d, %r9d
+ shrq $32, %r11
+
+ vmovq (%rdx, %r9, 4), %xmm7
+ vmovq (%rdx, %r11, 4), %xmm5
+ vpunpckldq %xmm5, %xmm7, %xmm7
+
+ vinsertf128 $1, %xmm3, %ymm4, %ymm4
+ vinsertf128 $1, %xmm7, %ymm2, %ymm2
+
+ vmovdqa LOCAL_DATA(_FLT_0)(%rip), %ymm9
+
+
+ vpunpcklqdq %ymm2, %ymm4, %ymm7
+ vpunpckhqdq %ymm2, %ymm4, %ymm6
+
+ /* Break the P_xxx and m into 16-bit chunks ready for
+ the long multiplication via 16x16->32 multiplications. */
+ vpandn %ymm1, %ymm9, %ymm5
+ vpsrld $16, %ymm5, %ymm3
+
+ vpor LOCAL_DATA(_FLT_1)(%rip), %ymm3, %ymm4
+ vmovd 8(%rdx, %rcx, 4), %xmm5
+ vmovd 8(%rdx, %rax, 4), %xmm2
+ vpunpckldq %xmm2, %xmm5, %xmm3
+
+ vmovd 8(%rdx, %rsi, 4), %xmm2
+ vmovd 8(%rdx, %rdi, 4), %xmm5
+ vpunpckldq %xmm5, %xmm2, %xmm2
+
+ vpunpcklqdq %xmm2, %xmm3, %xmm13
+
+ vmovd 8(%rdx, %r8, 4), %xmm3
+ vmovd 8(%rdx, %r10, 4), %xmm5
+ vpunpckldq %xmm5, %xmm3, %xmm0
+ /* Also get the significand as an integer
+ NB: adding in the integer bit is wrong for denorms!
+ To make this work for denorms we should do something
+ slightly different. */
+ vmovd 8(%rdx, %r9, 4), %xmm2
+ vmovd 8(%rdx, %r11, 4), %xmm5
+ vpunpckldq %xmm5, %xmm2, %xmm2
+
+ /* Better to use `vpand` than `vpblendw`. */
+ vmovdqu AVX2_SHARED_DATA(_Low16)(%rip), %ymm3
+
+ vpunpcklqdq %xmm2, %xmm0, %xmm0
vinsertf128 $1, %xmm0, %ymm13, %ymm13
+
+ vpand %ymm3, %ymm1, %ymm5
+ vpand %ymm3, %ymm6, %ymm0
+ vpsrld $16, %ymm7, %ymm2
+ vpand %ymm3, %ymm7, %ymm7
+ vpmulld %ymm0, %ymm5, %ymm8
+ vpmulld %ymm0, %ymm4, %ymm14
+ vpsrld $16, %ymm6, %ymm0
+ vpmulld %ymm2, %ymm5, %ymm2
+ vpand %ymm3, %ymm2, %ymm15
vpsrld $16, %ymm13, %ymm6
- vpand %ymm14, %ymm13, %ymm15
- vpsrld $16, %ymm9, %ymm0
- vpmulld %ymm6, %ymm10, %ymm13
+ vpand %ymm3, %ymm13, %ymm2
+ vpmulld %ymm6, %ymm4, %ymm13
vpmulld %ymm6, %ymm5, %ymm6
vpsrld $16, %ymm6, %ymm6
- vpmulld %ymm15, %ymm10, %ymm4
- vpand %ymm14, %ymm8, %ymm15
+ vpmulld %ymm2, %ymm4, %ymm2
vpaddd %ymm6, %ymm13, %ymm13
- vpsrld $16, %ymm4, %ymm4
+ vpsrld $16, %ymm2, %ymm6
+ vpand %ymm3, %ymm8, %ymm2
vpsrld $16, %ymm8, %ymm8
- vpaddd %ymm13, %ymm15, %ymm15
+ vpaddd %ymm13, %ymm2, %ymm13
vpmulld %ymm0, %ymm5, %ymm2
- vpaddd %ymm15, %ymm4, %ymm13
- vpand %ymm14, %ymm2, %ymm4
- vpaddd %ymm8, %ymm3, %ymm15
+ vpaddd %ymm13, %ymm6, %ymm13
+ vpaddd %ymm8, %ymm14, %ymm14
+ vpand %ymm3, %ymm2, %ymm8
vpsrld $16, %ymm2, %ymm2
vpsrld $16, %ymm13, %ymm6
- /* Assemble reduced argument from the pieces */
- vpand %ymm14, %ymm13, %ymm13
- vpaddd %ymm15, %ymm4, %ymm8
- vpmulld %ymm7, %ymm5, %ymm9
- vpmulld %ymm0, %ymm10, %ymm0
- vpaddd %ymm8, %ymm6, %ymm4
- vpand %ymm14, %ymm9, %ymm6
- vpaddd %ymm2, %ymm0, %ymm8
- vpsrld $16, %ymm9, %ymm3
- vpsrld $16, %ymm4, %ymm15
- vpslld $16, %ymm4, %ymm4
- vpaddd %ymm8, %ymm6, %ymm6
- vpaddd %ymm6, %ymm15, %ymm0
- vpmulld %ymm11, %ymm5, %ymm6
-
- /* Now do the big multiplication and carry propagation */
- vpmulld %ymm7, %ymm10, %ymm8
- vpand %ymm14, %ymm6, %ymm2
- vpaddd %ymm3, %ymm8, %ymm5
- vpsrld $16, %ymm0, %ymm15
- vpand %ymm14, %ymm0, %ymm0
-
- /*
- * We want to incorporate the original sign now too.
- * Do it here for convenience in getting the right N value,
- * though we could wait right to the end if we were prepared
- * to modify the sign of N later too.
- * So get the appropriate sign mask now (or sooner).
- */
- vpand .FLT_20(%rip), %ymm1, %ymm3
- vpaddd %ymm5, %ymm2, %ymm7
- vpaddd %ymm13, %ymm4, %ymm8
-
- /*
- * Now round at the 2^-8 bit position for reduction mod pi/2^7
- * instead of the original 2pi (but still with the same 2pi scaling).
- * Use a shifter of 2^15 + 2^14.
- * The N we get is our final version; it has an offset of
- * 2^8 because of the implicit integer bit, and anyway for negative
- * starting value it's a 2s complement thing. But we need to mask
- * off the exponent part anyway so it's fine.
- */
- vmovups .FLT_22(%rip), %ymm14
- vpaddd %ymm7, %ymm15, %ymm15
-
- /*
- * Create floating-point high part, implicitly adding integer bit 1
- * Incorporate overall sign at this stage too.
- */
- vpxor .FLT_21(%rip), %ymm3, %ymm11
-
- /*
- * Create floating-point low and medium parts, respectively
- * lo_17, ... lo_0, 0, ..., 0
- * hi_8, ... hi_0, lo_31, ..., lo_18
- * then subtract off the implicitly added integer bits,
- * 2^-46 and 2^-23, respectively.
- * Put the original sign into all of them at this stage.
- */
- vpxor .FLT_23(%rip), %ymm3, %ymm7
- vpslld $16, %ymm15, %ymm9
- vpaddd %ymm0, %ymm9, %ymm2
- vpand .FLT_24(%rip), %ymm8, %ymm0
+ /* Assemble reduced argument from the pieces. */
+ vpand %ymm3, %ymm13, %ymm13
+ vpaddd %ymm14, %ymm8, %ymm8
+ vpmulld %ymm7, %ymm5, %ymm5
+ vpmulld %ymm0, %ymm4, %ymm0
+ vpaddd %ymm8, %ymm6, %ymm8
+ vpand %ymm3, %ymm5, %ymm6
+ vpaddd %ymm2, %ymm0, %ymm0
+ vpsrld $16, %ymm5, %ymm14
+ vpsrld $16, %ymm8, %ymm5
+ vpslld $16, %ymm8, %ymm8
+ vpaddd %ymm0, %ymm6, %ymm6
+ vpaddd %ymm6, %ymm5, %ymm0
+
+
+ /* Now do the big multiplication and carry propagation. */
+ vpmulld %ymm7, %ymm4, %ymm7
+ vpaddd %ymm14, %ymm7, %ymm5
+ vpsrld $16, %ymm0, %ymm2
+ vpand %ymm3, %ymm0, %ymm0
+
+ vpaddd %ymm5, %ymm15, %ymm7
+ vpaddd %ymm13, %ymm8, %ymm8
+
+ /* Now round at the 2^-8 bit position for reduction mod pi/2^7
+ instead of the original 2pi (but still with the same 2pi scaling).
+ Use a shifter of 2^15 + 2^14.
+ The N we get is our final version; it has an offset of
+ 2^8 because of the implicit integer bit, and anyway for negative
+ starting value it's a 2s complement thing. But we need to mask
+ off the exponent part anyway so it's fine. */
+ vpaddd %ymm7, %ymm2, %ymm2
+ vmovups AVX2_SHARED_DATA(_SH_FLT_1)(%rip), %ymm14
+
+ /* Create floating-point low and medium parts, respectively
+ lo_17, ... lo_0, 0, ..., 0
+ hi_8, ... hi_0, lo_31, ..., lo_18
+ then subtract off the implicitly added integer bits,
+ 2^-46 and 2^-23, respectively.
+ Put the original sign into all of them at this stage. */
+ vmovdqa AVX2_SHARED_DATA(_SH_FLT_2)(%rip), %ymm7
+
+ vpslld $16, %ymm2, %ymm2
+ vpaddd %ymm0, %ymm2, %ymm2
+ vpand AVX2_SHARED_DATA(_Low18)(%rip), %ymm8, %ymm0
vpsrld $18, %ymm8, %ymm8
- vpsrld $9, %ymm2, %ymm10
+ vpsrld $9, %ymm2, %ymm6
vpslld $5, %ymm0, %ymm4
- vpor %ymm11, %ymm10, %ymm6
- vpxor .FLT_25(%rip), %ymm3, %ymm11
- vpand .FLT_26(%rip), %ymm2, %ymm3
+ vmovdqa COMMON_DATA(_OneF)(%rip), %ymm15
+ vpor %ymm15, %ymm6, %ymm6
+
+
+ vpand AVX2_SHARED_DATA(_Low9)(%rip), %ymm2, %ymm3
vpor %ymm7, %ymm4, %ymm5
+ vmovdqa AVX2_SHARED_DATA(_SH_FLT_3)(%rip), %ymm4
- /*
- * If the magnitude of the input is <= 2^-20, then
- * just pass through the input, since no reduction will be needed and
- * the main path will only work accurately if the reduced argument is
- * about >= 2^-40 (which it is for all large pi multiples)
- */
- vmovups .FLT_30(%rip), %ymm4
+ /* If the magnitude of the input is <= 2^-20, then
+ just pass through the input, since no reduction will be needed
+ and the main path will only work accurately if the reduced
+ argument is about >= 2^-40 (which it is for all large pi
+ multiples). */
vpslld $14, %ymm3, %ymm2
- /*
- * Now multiply those numbers all by 2 pi, reasonably accurately.
- * (RHi + RLo) * (pi_lead + pi_trail) ~=
- * RHi * pi_lead + (RHi * pi_trail + RLo * pi_lead)
- */
- vmovups .FLT_27(%rip), %ymm3
+ /* Now multiply those numbers all by 2 pi, reasonably accurately.
+ (RHi + RLo) * (pi_lead + pi_trail) ~=
+ RHi * pi_lead + (RHi * pi_trail + RLo * pi_lead). */
+ vmovups AVX2_SHARED_DATA(_SH_FLT_4)(%rip), %ymm3
vaddps %ymm14, %ymm6, %ymm13
- vpor %ymm8, %ymm2, %ymm9
- vsubps %ymm14, %ymm13, %ymm15
-
- /* Grab our final N value as an integer, appropriately masked mod 2^8 */
- vpand .FLT_31(%rip), %ymm13, %ymm13
- vpor %ymm11, %ymm9, %ymm10
- vsubps %ymm15, %ymm6, %ymm6
- vsubps %ymm7, %ymm5, %ymm15
- vsubps %ymm11, %ymm10, %ymm14
-
- /* Now add them up into 2 reasonably aligned pieces */
+ vpor %ymm8, %ymm2, %ymm2
+ vsubps %ymm14, %ymm13, %ymm0
+
+ /* Grab our final N value as an integer, appropriately masked
+ mod 2^8. */
+ vpor %ymm4, %ymm2, %ymm2
+ vsubps %ymm0, %ymm6, %ymm6
+ vsubps %ymm7, %ymm5, %ymm0
+ vsubps %ymm4, %ymm2, %ymm14
+
+ vmovups LOCAL_DATA(_FLT_2)(%rip), %ymm4
+ /* Now add them up into 2 reasonably aligned pieces. */
vaddps %ymm14, %ymm6, %ymm2
vsubps %ymm2, %ymm6, %ymm6
vmulps %ymm2, %ymm3, %ymm7
vaddps %ymm6, %ymm14, %ymm8
- vaddps %ymm8, %ymm15, %ymm8
- vmovaps %ymm3, %ymm15
- vfmsub213ps %ymm7, %ymm2, %ymm15
- vandps .FLT_29(%rip), %ymm1, %ymm0
- vfmadd132ps .FLT_28(%rip), %ymm15, %ymm2
- vcmpgt_oqps %ymm4, %ymm0, %ymm9
- vcmple_oqps %ymm4, %ymm0, %ymm5
-
- /*
- * The output is _VRES_R (high) + _VRES_E (low), and the integer part is _VRES_IND
- * Set sRp2 = _VRES_R^2 and then resume the original code.
- * Argument reduction is now finished: x = n * pi/128 + r
- * where n = iIndex and r = sR (high) + sE (low).
- * But we have n modulo 256, needed for sin/cos with period 2pi
- * but we want it modulo 128 since tan has period pi.
- */
- vpand .FLT_32(%rip), %ymm13, %ymm0
+ vaddps %ymm8, %ymm0, %ymm8
+ vmovaps %ymm3, %ymm0
+ vfmsub213ps %ymm7, %ymm2, %ymm0
+
+
+ vfmadd132ps LOCAL_DATA(_FLT_3)(%rip), %ymm0, %ymm2
+ vpcmpgtd %ymm4, %ymm1, %ymm5
+
+ /* The output is _VRES_R (high) + _VRES_E (low), and the integer
+ part is _VRES_IND Set sRp2 = _VRES_R^2 and then resume the
+ original code. Argument reduction is now finished: x = n *
+ pi/128 + r where n = iIndex and r = sR (high) + sE (low).
+ But we have n modulo 256, needed for sin/cos with period 2pi
+ but we want it modulo 128 since tan has period pi. */
+ vpand AVX2_SHARED_DATA(_Low7)(%rip), %ymm13, %ymm0
vfmadd213ps %ymm2, %ymm3, %ymm8
+
+
+
vpslld $2, %ymm0, %ymm2
- vandps %ymm1, %ymm5, %ymm1
- vandps %ymm7, %ymm9, %ymm6
- vorps %ymm6, %ymm1, %ymm15
- vpaddd %ymm0, %ymm2, %ymm1
- vpslld $3, %ymm1, %ymm4
- vandps %ymm8, %ymm9, %ymm3
-
- /*
- * Simply combine the two parts of the reduced argument
- * since we can afford a few ulps in this case.
- */
- vaddps %ymm3, %ymm15, %ymm6
- vextractf128 $1, %ymm4, %xmm8
- vmovd %xmm4, %r10d
- vmovd %xmm8, %ebx
- vmovd -36(%r10, %r9), %xmm5
- vmovd -32(%r10, %r9), %xmm9
- vpextrd $1, %xmm4, %r8d
- vpextrd $2, %xmm4, %edi
- vpextrd $3, %xmm4, %esi
- vpextrd $1, %xmm8, %ecx
- vpextrd $2, %xmm8, %edx
- vpextrd $3, %xmm8, %r11d
- vmovd -36(%r8, %r9), %xmm7
- vmovd -36(%rdi, %r9), %xmm10
- vmovd -36(%rsi, %r9), %xmm11
- vmovd -36(%rbx, %r9), %xmm3
- vmovd -36(%rcx, %r9), %xmm2
- vmovd -36(%rdx, %r9), %xmm0
- vmovd -36(%r11, %r9), %xmm1
- vpunpckldq %xmm7, %xmm5, %xmm14
- vpunpckldq %xmm11, %xmm10, %xmm13
- vpunpckldq %xmm2, %xmm3, %xmm4
- vpunpckldq %xmm1, %xmm0, %xmm5
- vpunpcklqdq %xmm13, %xmm14, %xmm15
- vpunpcklqdq %xmm5, %xmm4, %xmm7
- vmovd -32(%r8, %r9), %xmm10
- vmovd -32(%rdi, %r9), %xmm11
- vmovd -32(%rsi, %r9), %xmm14
- vmovd -32(%rbx, %r9), %xmm2
- vmovd -32(%rcx, %r9), %xmm0
- vmovd -32(%rdx, %r9), %xmm1
- vmovd -32(%r11, %r9), %xmm4
- vpunpckldq %xmm14, %xmm11, %xmm8
- vpunpckldq %xmm0, %xmm2, %xmm5
- vmovd -28(%r8, %r9), %xmm11
- vmovd -28(%rdi, %r9), %xmm14
- vinsertf128 $1, %xmm7, %ymm15, %ymm13
- vpunpckldq %xmm10, %xmm9, %xmm15
- vpunpckldq %xmm4, %xmm1, %xmm7
- vpunpcklqdq %xmm8, %xmm15, %xmm3
- vpunpcklqdq %xmm7, %xmm5, %xmm9
- vmovd -28(%r10, %r9), %xmm10
- vmovd -28(%rsi, %r9), %xmm8
- vmovd -28(%rbx, %r9), %xmm1
- vmovd -28(%rcx, %r9), %xmm4
- vmovd -28(%rdx, %r9), %xmm5
- vmovd -28(%r11, %r9), %xmm7
- vpunpckldq %xmm8, %xmm14, %xmm2
- vmovd -24(%r10, %r9), %xmm14
- vinsertf128 $1, %xmm9, %ymm3, %ymm15
- vpunpckldq %xmm11, %xmm10, %xmm3
- vpunpckldq %xmm4, %xmm1, %xmm9
- vpunpckldq %xmm7, %xmm5, %xmm10
- vpunpcklqdq %xmm2, %xmm3, %xmm0
- vpunpcklqdq %xmm10, %xmm9, %xmm11
- vmovd -24(%r8, %r9), %xmm3
- vmovd -24(%rdi, %r9), %xmm2
- vmovd -24(%rbx, %r9), %xmm7
- vmovd -24(%rcx, %r9), %xmm9
- vmovd -24(%rdx, %r9), %xmm10
- vpunpckldq %xmm3, %xmm14, %xmm1
- vpunpckldq %xmm9, %xmm7, %xmm14
- vmovd -20(%rsi, %r9), %xmm7
- vinsertf128 $1, %xmm11, %ymm0, %ymm8
- vmovd -24(%rsi, %r9), %xmm0
- vmovd -24(%r11, %r9), %xmm11
- vpunpckldq %xmm0, %xmm2, %xmm4
- vpunpckldq %xmm11, %xmm10, %xmm3
- vpunpcklqdq %xmm4, %xmm1, %xmm5
- vpunpcklqdq %xmm3, %xmm14, %xmm2
- vmovd -20(%r10, %r9), %xmm0
- vmovd -20(%r8, %r9), %xmm1
- vmovd -20(%rbx, %r9), %xmm14
- vmovd -20(%rdi, %r9), %xmm4
- vpunpckldq %xmm1, %xmm0, %xmm9
- vmovd -20(%r11, %r9), %xmm0
- vpunpckldq %xmm7, %xmm4, %xmm10
- vpunpcklqdq %xmm10, %xmm9, %xmm11
- vmovd -16(%r10, %r9), %xmm9
- vmovd -16(%r8, %r9), %xmm10
- vinsertf128 $1, %xmm2, %ymm5, %ymm3
- vmovd -20(%rcx, %r9), %xmm2
- vpunpckldq %xmm2, %xmm14, %xmm1
- vmovd -20(%rdx, %r9), %xmm14
- vpunpckldq %xmm0, %xmm14, %xmm4
- vpunpcklqdq %xmm4, %xmm1, %xmm5
- vmovd -16(%rdi, %r9), %xmm2
- vmovd -16(%rsi, %r9), %xmm0
- vpunpckldq %xmm10, %xmm9, %xmm1
- vmovd -16(%rcx, %r9), %xmm9
- vmovd -16(%rdx, %r9), %xmm10
- vpunpckldq %xmm0, %xmm2, %xmm4
- vinsertf128 $1, %xmm5, %ymm11, %ymm7
- vmovups %ymm7, 32(%rsp)
- vmovd -16(%rbx, %r9), %xmm7
- vmovd -16(%r11, %r9), %xmm11
- vpunpckldq %xmm9, %xmm7, %xmm14
- vpunpckldq %xmm11, %xmm10, %xmm2
- vpunpcklqdq %xmm4, %xmm1, %xmm5
- vpunpcklqdq %xmm2, %xmm14, %xmm0
- vmovd -12(%r10, %r9), %xmm1
- vmovd -12(%r8, %r9), %xmm4
- vmovd -12(%rdi, %r9), %xmm7
- vmovd -12(%rsi, %r9), %xmm9
- vpunpckldq %xmm4, %xmm1, %xmm10
- vmovd -12(%rcx, %r9), %xmm1
- vmovd -12(%rdx, %r9), %xmm4
- vpunpckldq %xmm9, %xmm7, %xmm11
- vpunpcklqdq %xmm11, %xmm10, %xmm14
- vinsertf128 $1, %xmm0, %ymm5, %ymm2
- vmovd -12(%rbx, %r9), %xmm0
- vmovd -12(%r11, %r9), %xmm5
- vpunpckldq %xmm1, %xmm0, %xmm7
- vpunpckldq %xmm5, %xmm4, %xmm9
- vpunpcklqdq %xmm9, %xmm7, %xmm10
- vmovd -8(%r10, %r9), %xmm1
- vmovd -8(%r8, %r9), %xmm4
- vmovups 128(%rsp), %ymm0
- vinsertf128 $1, %xmm10, %ymm14, %ymm11
- vmovups %ymm11, (%rsp)
- vmovups 96(%rsp), %ymm10
- vmovups 64(%rsp), %ymm11
- # LOE rdx rcx rbx rsi rdi r8 r9 r10 r11 r12 r13 r14 r15 eax xmm1 xmm4 ymm0 ymm2 ymm3 ymm6 ymm8 ymm10 ymm11 ymm12 ymm13 ymm15
-
- vmovd -8(%rdi, %r9), %xmm7
- vmovd -8(%rsi, %r9), %xmm5
- vpunpckldq %xmm4, %xmm1, %xmm4
- vpunpckldq %xmm5, %xmm7, %xmm9
- vpunpcklqdq %xmm9, %xmm4, %xmm7
- vmovd -8(%rbx, %r9), %xmm1
- vmovd -8(%rcx, %r9), %xmm14
- vmovd -8(%rdx, %r9), %xmm5
- vmovd -8(%r11, %r9), %xmm4
- vpunpckldq %xmm14, %xmm1, %xmm9
- vpunpckldq %xmm4, %xmm5, %xmm1
- vpunpcklqdq %xmm1, %xmm9, %xmm14
- vmovd -4(%r10, %r9), %xmm5
- vmovd -4(%r8, %r9), %xmm4
- vmovd -4(%rdi, %r9), %xmm9
- vmovd -4(%rsi, %r9), %xmm1
- vinsertf128 $1, %xmm14, %ymm7, %ymm7
- vpunpckldq %xmm4, %xmm5, %xmm14
- vpunpckldq %xmm1, %xmm9, %xmm5
- vpunpcklqdq %xmm5, %xmm14, %xmm4
- vmovd -4(%rbx, %r9), %xmm9
- vmovd -4(%rcx, %r9), %xmm1
- vmovd -4(%rdx, %r9), %xmm14
- vmovd -4(%r11, %r9), %xmm5
- vpunpckldq %xmm1, %xmm9, %xmm9
- vpunpckldq %xmm5, %xmm14, %xmm1
- vpunpcklqdq %xmm1, %xmm9, %xmm14
- vmovd (%r10, %r9), %xmm5
- vmovd (%r8, %r9), %xmm9
- vmovd (%rdi, %r9), %xmm1
- vpunpckldq %xmm9, %xmm5, %xmm5
-
- /*
- * Higher polynomial terms
- * Stage 1 (with unlimited parallelism)
- * P3 = C1_lo + C2 * Z
- */
- vfmadd213ps (%rsp), %ymm6, %ymm7
- vinsertf128 $1, %xmm14, %ymm4, %ymm4
- vmovd (%rsi, %r9), %xmm14
- vpunpckldq %xmm14, %xmm1, %xmm9
- vmovd (%rbx, %r9), %xmm1
- vmovd (%rcx, %r9), %xmm14
- vpunpcklqdq %xmm9, %xmm5, %xmm9
- vpunpckldq %xmm14, %xmm1, %xmm5
- vmovd (%rdx, %r9), %xmm1
- vmovd (%r11, %r9), %xmm14
- vpunpckldq %xmm14, %xmm1, %xmm1
- vpunpcklqdq %xmm1, %xmm5, %xmm5
- vmovups .FLT_33(%rip), %ymm1
-
- /*
- * Compute 2-part reciprocal component
- * Construct a separate reduced argument modulo pi near pi/2 multiples.
- * i.e. (pi/2 - x) mod pi, simply by subtracting the reduced argument
- * from an accurate B_hi + B_lo = (128 - n) pi/128. Force the upper part
- * of this reduced argument to half-length to simplify accurate
- * reciprocation later on.
- */
- vsubps %ymm6, %ymm13, %ymm14
- vsubps %ymm14, %ymm13, %ymm13
+ vpaddd %ymm0, %ymm2, %ymm4
+
+ vpblendvb %ymm5, %ymm7, %ymm1, %ymm6
+
+ vandps %ymm8, %ymm5, %ymm3
+ vaddps %ymm3, %ymm6, %ymm6
+
+
+
+
+ /* Simply combine the two parts of the reduced argument
+ since we can afford a few ulps in this case. */
+
+ /* Load constants (not all needed at once). */
+ lea AVX2_SHARED_DATA(_Coeffs)(%rip), %rdx
+
+ vmovq %xmm4, %rcx
+ movl %ecx, %eax
+ shrq $32, %rcx
+
+ vmovdqu (%rdx, %rax, 8), %ymm5
+ vmovdqu (%rdx, %rcx, 8), %ymm7
+ vpunpckldq %ymm7, %ymm5, %ymm3
+ vpunpckhdq %ymm7, %ymm5, %ymm7
+
+ vpextrq $1, %xmm4, %rsi
+ movl %esi, %edi
+ shrq $32, %rsi
+
+ vmovdqu (%rdx, %rdi, 8), %ymm5
+ vmovdqu (%rdx, %rsi, 8), %ymm2
+ vpunpckldq %ymm2, %ymm5, %ymm0
+ vpunpckhdq %ymm2, %ymm5, %ymm2
+
+ vextractf128 $1, %ymm4, %xmm4
+
+ vmovq %xmm4, %r8
+ movl %r8d, %r10d
+ shrq $32, %r8
+
+ vmovdqu (%rdx, %r10, 8), %ymm8
+ vmovdqu (%rdx, %r8, 8), %ymm5
+ vpunpckldq %ymm5, %ymm8, %ymm14
+ vpunpckhdq %ymm5, %ymm8, %ymm8
+
+
+ vpextrq $1, %xmm4, %r11
+ movl %r11d, %r9d
+ shrq $32, %r11
+
+ vmovdqu (%rdx, %r9, 8), %ymm5
+ vmovdqu (%rdx, %r11, 8), %ymm4
+
+ vpunpckldq %ymm4, %ymm5, %ymm13
+ vpunpckhdq %ymm4, %ymm5, %ymm4
+
+ vpunpcklqdq %ymm0, %ymm3, %ymm5
+ vpunpckhqdq %ymm0, %ymm3, %ymm3
+
+ vpunpcklqdq %ymm13, %ymm14, %ymm0
+ vpunpckhqdq %ymm13, %ymm14, %ymm14
+
+ vinserti128 $0x1, %xmm0, %ymm5, %ymm13
+ vperm2i128 $0x31, %ymm0, %ymm5, %ymm5
+
+ vinserti128 $0x1, %xmm14, %ymm3, %ymm0
+ vperm2i128 $0x31, %ymm14, %ymm3, %ymm14
+
+ vpunpcklqdq %ymm2, %ymm7, %ymm3
+ vpunpckhqdq %ymm2, %ymm7, %ymm2
+
+ vpunpcklqdq %ymm4, %ymm8, %ymm7
+ vpunpckhqdq %ymm4, %ymm8, %ymm4
+
+ vinserti128 $0x1, %xmm7, %ymm3, %ymm8
+ vperm2i128 $0x31, %ymm7, %ymm3, %ymm3
+
+ vperm2i128 $0x31, %ymm4, %ymm2, %ymm7
+ vfmadd213ps %ymm3, %ymm6, %ymm7
+ vinserti128 $0x1, %xmm4, %ymm2, %ymm3
+
+ /* Compute 2-part reciprocal component Construct a separate
+ reduced argument modulo pi near pi/2 multiples. i.e. (pi/2 -
+ x) mod pi, simply by subtracting the reduced argument from
+ an accurate B_hi + B_lo = (128 - n) pi/128. Force the upper
+ part of this reduced argument to half-length to simplify
+ accurate reciprocation later on. */
+ vsubps %ymm6, %ymm13, %ymm2
+ vsubps %ymm2, %ymm13, %ymm13
vsubps %ymm6, %ymm13, %ymm13
- vinsertf128 $1, %xmm5, %ymm9, %ymm5
- vandps %ymm1, %ymm14, %ymm9
- vsubps %ymm9, %ymm14, %ymm14
-
- /* P4 = C3 + C4 * Z */
- vfmadd213ps %ymm4, %ymm6, %ymm5
- vaddps %ymm14, %ymm15, %ymm15
- vaddps %ymm15, %ymm13, %ymm15
-
- /*
- * Now compute an approximate reciprocal to mix into the computation
- * To avoid any danger of nonportability, force it to 12 bits,
- * though I suspect it always is anyway on current platforms.
- */
- vrcpps %ymm9, %ymm13
- vandps %ymm1, %ymm13, %ymm13
- /*
- * Now compute the error sEr where sRecip_hi = (1/R_hi) * (1 - sEr)
- * so that we can compensate for it.
- */
- vmovups _sOne+__svml_stan_data_internal(%rip), %ymm1
- vfnmadd213ps %ymm1, %ymm13, %ymm9
-
- /*
- * Get a better approximation to 1/sR_hi (not far short of an ulp)
- * using a third-order polynomial approximation
- */
- vmovaps %ymm13, %ymm14
- vfmadd213ps %ymm13, %ymm9, %ymm14
- vfmadd231ps %ymm9, %ymm9, %ymm1
- vmulps %ymm1, %ymm14, %ymm1
-
- /*
- * Multiply by sRecip_ok to make sR_lo relative to sR_hi
- * Since sR_lo is shifted off by about 12 bits, this is accurate enough.
- */
- vmulps %ymm1, %ymm15, %ymm14
-
- /*
- * Now create a low reciprocal using
- * (Recip_hi + Er * Recip_ok) * (1 + sR_lo^2 - sR_lo)
- * =~= Recip_hi + Recip_ok * (Er + sR_lo^2 - sR_lo)
- */
- vsubps %ymm9, %ymm14, %ymm9
- vfmsub213ps %ymm9, %ymm14, %ymm14
- vmulps %ymm14, %ymm1, %ymm9
- vmovaps %ymm2, %ymm1
- vfmadd213ps %ymm3, %ymm6, %ymm1
- vsubps %ymm1, %ymm3, %ymm15
- vmovaps %ymm8, %ymm3
- vfmadd213ps %ymm1, %ymm13, %ymm3
- vfmadd213ps %ymm15, %ymm6, %ymm2
- vfmsub213ps %ymm3, %ymm8, %ymm13
- vfmadd213ps %ymm2, %ymm8, %ymm9
- vaddps %ymm13, %ymm1, %ymm2
+ /* Higher polynomial terms
+ Stage 1 (with unlimited parallelism)
+ P3 = C1_lo + C2 * Z. */
+ vmovq 32(%rdx, %rax, 8), %xmm4
+ vpcmpgtd %ymm1, %ymm9, %ymm9
+ vmovmskps %ymm9, %eax
- /* Z2 = Z^2 */
- vmulps %ymm6, %ymm6, %ymm1
- vaddps %ymm2, %ymm9, %ymm8
+ vmovq 32(%rdx, %rcx, 8), %xmm1
- /*
- * Stage 2 (with unlimited parallelism)
- * P6 = C1_lo + C2 * Z + C3 * Z^2 + C4 * Z^3
- */
- vfmadd213ps %ymm7, %ymm5, %ymm1
+ vinsertf128 $1, 32(%rdx, %r10, 8), %ymm4, %ymm4
+ vinsertf128 $1, 32(%rdx, %r8, 8), %ymm1, %ymm1
+ vpunpckldq %ymm1, %ymm4, %ymm9
- /* P9 = trail(dominant part) + C0_lo */
- vaddps 32(%rsp), %ymm8, %ymm5
+ vmovq 32(%rdx, %rdi, 8), %xmm1
+ vmovq 32(%rdx, %rsi, 8), %xmm4
- /* Final accumulation of low part */
- vfmadd213ps %ymm5, %ymm6, %ymm1
+ vinsertf128 $1, 32(%rdx, %r9, 8), %ymm1, %ymm1
+ vinsertf128 $1, 32(%rdx, %r11, 8), %ymm4, %ymm4
+ vpunpckldq %ymm4, %ymm1, %ymm1
- /* And now the very final summation */
- vaddps %ymm1, %ymm3, %ymm6
+ vpunpckhqdq %ymm1, %ymm9, %ymm4
+ vpunpcklqdq %ymm1, %ymm9, %ymm9
- /*
- * The end of implementation (LA with huge args reduction)
- * End of large arguments path (_HA_, _LA_ and _EP_)
- */
- vxorps %ymm11, %ymm6, %ymm11
+ vmovups COMMON_DATA(_Neg4096)(%rip), %ymm1
- /* Merge results from main and large paths: */
- vblendvps %ymm10, %ymm11, %ymm0, %ymm0
+ vfmadd213ps %ymm9, %ymm6, %ymm4
- /* Return to main vector processing path */
- jmp L(AUX_BRANCH_RETURN)
- # LOE r12 r13 r14 r15 eax ymm0 ymm12
-END(_ZGVdN8v_tanf_avx2)
+ vandps %ymm1, %ymm2, %ymm9
+ vsubps %ymm9, %ymm2, %ymm2
- .section .rodata, "a"
- .align 32
+ /* P4 = C3 + C4 * Z. */
+ vaddps %ymm2, %ymm0, %ymm0
+ vaddps %ymm0, %ymm13, %ymm0
-.FLT_15:
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000
- .type .FLT_15, @object
- .size .FLT_15, 32
- .align 32
+ /* Now compute an approximate reciprocal to mix into the computation
+ To avoid any danger of nonportability, force it to 12 bits,
+ though I suspect it always is anyway on current platforms. */
+ vrcpps %ymm9, %ymm13
+ vandps %ymm1, %ymm13, %ymm13
-.FLT_16:
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000
- .type .FLT_16, @object
- .size .FLT_16, 32
- .align 32
+ /* Now compute the error sEr where sRecip_hi = (1/R_hi) * (1 - sEr)
+ so that we can compensate for it. */
+ vfnmadd213ps %ymm15, %ymm13, %ymm9
+
+ /* Get a better approximation to 1/sR_hi (not far short of an ulp)
+ using a third-order polynomial approximation. */
+ vmovaps %ymm13, %ymm2
+ vfmadd231ps %ymm9, %ymm9, %ymm15
+ vfmadd213ps %ymm13, %ymm9, %ymm2
+ vmulps %ymm15, %ymm2, %ymm1
+
+ /* Multiply by sRecip_ok to make sR_lo relative to sR_hi Since
+ sR_lo is shifted off by about 12 bits, this is accurate
+ enough. */
+ vmulps %ymm1, %ymm0, %ymm2
+
+ /* Now create a low reciprocal using
+ (Recip_hi + Er * Recip_ok) * (1 + sR_lo^2 - sR_lo)
+ =~= Recip_hi + Recip_ok * (Er + sR_lo^2 - sR_lo). */
+ vsubps %ymm9, %ymm2, %ymm9
+ vfmsub213ps %ymm9, %ymm2, %ymm2
+ vmulps %ymm2, %ymm1, %ymm9
+ vmovaps %ymm14, %ymm1
+ vfmadd213ps %ymm3, %ymm6, %ymm1
+ vsubps %ymm1, %ymm3, %ymm0
+ vmovaps %ymm8, %ymm3
+ vfmadd213ps %ymm1, %ymm13, %ymm3
+ vfmadd213ps %ymm0, %ymm6, %ymm14
+ vfmsub213ps %ymm3, %ymm8, %ymm13
+ vfmadd213ps %ymm14, %ymm8, %ymm9
+ vaddps %ymm13, %ymm1, %ymm2
-.FLT_17:
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- .type .FLT_17, @object
- .size .FLT_17, 32
- .align 32
+ /* Z2 = Z^2. */
+ vmulps %ymm6, %ymm6, %ymm1
+ vaddps %ymm2, %ymm9, %ymm2
-.FLT_18:
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000
- .type .FLT_18, @object
- .size .FLT_18, 32
- .align 32
+ /* Stage 2 (with unlimited parallelism)
+ P6 = C1_lo + C2 * Z + C3 * Z^2 + C4 * Z^3. */
+ vfmadd213ps %ymm7, %ymm4, %ymm1
-.FLT_19:
- .long 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff, 0x0000ffff
- .type .FLT_19, @object
- .size .FLT_19, 32
- .align 32
+ /* P9 = trail(dominant part) + C0_lo. */
+ vaddps %ymm5, %ymm2, %ymm4
-.FLT_20:
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
- .type .FLT_20, @object
- .size .FLT_20, 32
- .align 32
+ /* Final accumulation of low part. */
+ vfmadd213ps %ymm4, %ymm6, %ymm1
-.FLT_21:
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- .type .FLT_21, @object
- .size .FLT_21, 32
- .align 32
+ /* And now the very final summation. */
+ vaddps %ymm1, %ymm3, %ymm6
-.FLT_22:
- .long 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000, 0x47400000
- .type .FLT_22, @object
- .size .FLT_22, 32
- .align 32
+ /* The end of implementation (LA with huge args reduction)
+ End of large arguments path (_HA_, _LA_ and _EP_). */
+ vpand %ymm6, %ymm10, %ymm6
+ /* Merge results from main and large paths:. */
+ vpxor %ymm6, %ymm12, %ymm0
-.FLT_23:
- .long 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000, 0x28800000
- .type .FLT_23, @object
- .size .FLT_23, 32
- .align 32
-.FLT_24:
- .long 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff, 0x0003ffff
- .type .FLT_24, @object
- .size .FLT_24, 32
- .align 32
+ /* `al` has 0 at special values. If all 1s `incb al` will
+ overflow and set zero flag. */
+ incb %al
+ /* Go to special inputs processing branch. */
+ jne L(SPECIAL_VALUES_BRANCH)
+ ret
-.FLT_25:
- .long 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000, 0x34000000
- .type .FLT_25, @object
- .size .FLT_25, 32
- .align 32
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanhf call. Optimize for code size
+ more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
-.FLT_26:
- .long 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff
- .type .FLT_26, @object
- .size .FLT_26, 32
- .align 32
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
+ pushq %rbx
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
+ pushq %rbp
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
+ movq %rsp, %r13
+ cfi_def_cfa_register (r13)
-.FLT_27:
- .long 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb, 0x40c90fdb
- .type .FLT_27, @object
- .size .FLT_27, 32
- .align 32
+ /* Align stack and make room for 2x ymm vectors. */
+ andq $-32, %rsp
+ addq $-64, %rsp
-.FLT_28:
- .long 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e, 0xb43bbd2e
- .type .FLT_28, @object
- .size .FLT_28, 32
- .align 32
-.FLT_29:
- .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
- .type .FLT_29, @object
- .size .FLT_29, 32
- .align 32
+ /* Save original input (ymm0 unchanged up to this point). */
+ vmovaps %ymm11, 32(%rsp)
+ vmovaps %ymm0, (%rsp)
-.FLT_30:
- .long 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000, 0x35800000
- .type .FLT_30, @object
- .size .FLT_30, 32
- .align 32
+ vzeroupper
-.FLT_31:
- .long 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff, 0x000000ff
- .type .FLT_31, @object
- .size .FLT_31, 32
- .align 32
+ /* eax has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ negb %al
+ movzbl %al, %ebx
+L(SPECIAL_VALUES_LOOP):
-.FLT_32:
- .long 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f
- .type .FLT_32, @object
- .size .FLT_32, 32
- .align 32
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math function call to process special input. */
+ vmovss 32(%rsp, %rbp, 4), %xmm0
+ call tanf@PLT
-.FLT_33:
- .long 0xfffff000, 0xfffff000, 0xfffff000, 0xfffff000, 0xfffff000, 0xfffff000, 0xfffff000, 0xfffff000
- .type .FLT_33, @object
- .size .FLT_33, 32
- .align 32
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ vmovss %xmm0, (%rsp, %rbp, 4)
-#ifdef __svml_stan_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(32)) VUINT32 _sInvPI_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPI1_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPI2_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPI3_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPI2_ha_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPI3_ha_uisa[8][1];
- __declspec(align(32)) VUINT32 Th_tbl_uisa[32][1];
- __declspec(align(32)) VUINT32 Tl_tbl_uisa[32][1];
- __declspec(align(32)) VUINT32 _sPC3_uisa[8][1];
- __declspec(align(32)) VUINT32 _sPC5_uisa[8][1];
- __declspec(align(32)) VUINT32 _sRangeReductionVal_uisa[8][1];
- __declspec(align(32)) VUINT32 _sInvPi[8][1];
- __declspec(align(32)) VUINT32 _sSignMask[8][1];
- __declspec(align(32)) VUINT32 _sAbsMask[8][1];
- __declspec(align(32)) VUINT32 _sRangeVal[8][1];
- __declspec(align(32)) VUINT32 _sRShifter[8][1];
- __declspec(align(32)) VUINT32 _sOne[8][1];
- __declspec(align(32)) VUINT32 _sRangeReductionVal[8][1];
- __declspec(align(32)) VUINT32 _sPI1[8][1];
- __declspec(align(32)) VUINT32 _sPI2[8][1];
- __declspec(align(32)) VUINT32 _sPI3[8][1];
- __declspec(align(32)) VUINT32 _sPI4[8][1];
- __declspec(align(32)) VUINT32 _sPI1_FMA[8][1];
- __declspec(align(32)) VUINT32 _sPI2_FMA[8][1];
- __declspec(align(32)) VUINT32 _sPI3_FMA[8][1];
- __declspec(align(32)) VUINT32 _sP0[8][1];
- __declspec(align(32)) VUINT32 _sP1[8][1];
- __declspec(align(32)) VUINT32 _sQ0[8][1];
- __declspec(align(32)) VUINT32 _sQ1[8][1];
- __declspec(align(32)) VUINT32 _sQ2[8][1];
- __declspec(align(32)) VUINT32 _sTwo[8][1];
- __declspec(align(32)) VUINT32 _sCoeffs[128][10][1];
-} __svml_stan_data_internal;
-#endif
-__svml_stan_data_internal:
- /* UISA */
- .long 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983, 0x4122f983 /* _sInvPI_uisa */
- .align 32
- .long 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda, 0x3dc90fda /* _sPI1_uisa */
- .align 32
- .long 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168, 0x31a22168 /* _sPI2_uisa */
- .align 32
- .long 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5, 0x25c234c5 /* _sPI3_uisa */
- .align 32
- .long 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000, 0x31a22000 /* _sPI2_ha_uisa */
- .align 32
- .long 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a, 0x2a34611a /* _sPI3_ha_uisa */
- /* Th_tbl_uisa for i from 0 to 31 do printsingle(tan(i*Pi/32)); */
- .align 32
- .long 0x80000000, 0x3dc9b5dc, 0x3e4bafaf, 0x3e9b5042
- .long 0x3ed413cd, 0x3f08d5b9, 0x3f2b0dc1, 0x3f521801
- .long 0x3f800000, 0x3f9bf7ec, 0x3fbf90c7, 0x3fef789e
- .long 0x401a827a, 0x4052facf, 0x40a0dff7, 0x41227363
- .long 0xff7fffff, 0xc1227363, 0xc0a0dff7, 0xc052facf
- .long 0xc01a827a, 0xbfef789e, 0xbfbf90c7, 0xbf9bf7ec
- .long 0xbf800000, 0xbf521801, 0xbf2b0dc1, 0xbf08d5b9
- .long 0xbed413cd, 0xbe9b5042, 0xbe4bafaf, 0xbdc9b5dc
- /* Tl_tbl_uisa for i from 0 to 31 do printsingle(tan(i*Pi/32)-round(tan(i*Pi/32), SG, RN)); */
- .align 32
- .long 0x80000000, 0x3145b2da, 0x2f2a62b0, 0xb22a39c2
- .long 0xb1c0621a, 0xb25ef963, 0x32ab7f99, 0x32ae4285
- .long 0x00000000, 0x33587608, 0x32169d18, 0xb30c3ec0
- .long 0xb3cc0622, 0x3390600e, 0x331091dc, 0xb454a046
- .long 0xf3800000, 0x3454a046, 0xb31091dc, 0xb390600e
- .long 0x33cc0622, 0x330c3ec0, 0xb2169d18, 0xb3587608
- .long 0x00000000, 0xb2ae4285, 0xb2ab7f99, 0x325ef963
- .long 0x31c0621a, 0x322a39c2, 0xaf2a62b0, 0xb145b2da
- .align 32
- .long 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6, 0x3eaaaaa6 /* _sPC3_uisa */
- .align 32
- .long 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888, 0x3e08b888 /* _sPC5_uisa */
- .align 32
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeReductionVal_uisa */
- .align 32
- .long 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983, 0x3F22F983 /* _sInvPi */
- .align 32
- .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 /* _sSignMask */
- .align 32
- .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF /* _sAbsMask */
- .align 32
- .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000 /* _sRangeVal */
- .align 32
- .long 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000, 0x4B400000 /* _sRShifter */
- .align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 /* _sOne */
- .align 32
- .long 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000, 0x46010000 /* _sRangeVal */
- .align 32
- .long 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000, 0x3FC90000 /* _sPI1 */
- .align 32
- .long 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000, 0x39FDA000 /* _sPI2 */
- .align 32
- .long 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000, 0x33A22000 /* _sPI3 */
- .align 32
- .long 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A, 0x2C34611A /* _sPI4 */
- // PI1, PI2, and PI3 when FMA is available
- .align 32
- .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB /* _sPI1_FMA */
- .align 32
- .long 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E, 0xB33BBD2E /* _sPI2_FMA */
- .align 32
- .long 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED, 0xA6F72CED /* _sPI3_FMA */
- .align 32
- .long 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC /* _sP0 */
- .align 32
- .long 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4, 0xBDC433B4 /* _sP1 */
- .align 32
- .long 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC, 0x3F7FFFFC /* _sQ0 */
- .align 32
- .long 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB, 0xBEDBB7AB /* _sQ1 */
- .align 32
- .long 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B, 0x3C1F336B /* _sQ2 */
- .align 32
- .long 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000 /* _sTwo */
- // _sCoeffs Breakpoint B = 0 * pi/128, function tan(B + x)
- .align 32
- .long 0x3FC90FDB // B' = pi/2 - B (high single)
- .long 0xB33BBD2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x00000000 // c0 (high single)
- .long 0x00000000 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x00000000 // c1 (low single)
- .long 0x00000000 // c2
- .long 0x3EAAACDD // c3
- .long 0x00000000 // c4
- .long 0x3FC5EB9B // B' = pi/2 - B (high single)
- .long 0x32DE638C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3CC91A31 // c0 (high single)
- .long 0x2F8E8D1A // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3A1DFA00 // c1 (low single)
- .long 0x3CC9392D // c2
- .long 0x3EAB1889 // c3
- .long 0x3C885D3B // c4
- .long 0x3FC2C75C // B' = pi/2 - B (high single)
- .long 0xB2CBBE8A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3D49393C // c0 (high single)
- .long 0x30A39F5B // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3B1E2B00 // c1 (low single)
- .long 0x3D49B5D4 // c2
- .long 0x3EAC4F10 // c3
- .long 0x3CFD9425 // c4
- .long 0x3FBFA31C // B' = pi/2 - B (high single)
- .long 0x33450FB0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3D9711CE // c0 (high single)
- .long 0x314FEB28 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3BB24C00 // c1 (low single)
- .long 0x3D97E43A // c2
- .long 0x3EAE6A89 // c3
- .long 0x3D4D07E0 // c4
- .long 0x3FBC7EDD // B' = pi/2 - B (high single)
- .long 0xB1800ADD // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3DC9B5DC // c0 (high single)
- .long 0x3145AD86 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C1EEF20 // c1 (low single)
- .long 0x3DCBAAEA // c2
- .long 0x3EB14E5E // c3
- .long 0x3D858BB2 // c4
- .long 0x3FB95A9E // B' = pi/2 - B (high single)
- .long 0xB3651267 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3DFC98C2 // c0 (high single)
- .long 0xB0AE525C // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C793D20 // c1 (low single)
- .long 0x3E003845 // c2
- .long 0x3EB5271F // c3
- .long 0x3DAC669E // c4
- .long 0x3FB6365E // B' = pi/2 - B (high single)
- .long 0x328BB91C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E17E564 // c0 (high single)
- .long 0xB1C5A2E4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CB440D0 // c1 (low single)
- .long 0x3E1B3D00 // c2
- .long 0x3EB9F664 // c3
- .long 0x3DD647C0 // c4
- .long 0x3FB3121F // B' = pi/2 - B (high single)
- .long 0xB30F347D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E31AE4D // c0 (high single)
- .long 0xB1F32251 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CF6A500 // c1 (low single)
- .long 0x3E3707DA // c2
- .long 0x3EBFA489 // c3
- .long 0x3DFBD9C7 // c4
- .long 0x3FAFEDDF // B' = pi/2 - B (high single)
- .long 0x331BBA77 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E4BAFAF // c0 (high single)
- .long 0x2F2A29E0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D221018 // c1 (low single)
- .long 0x3E53BED0 // c2
- .long 0x3EC67E26 // c3
- .long 0x3E1568E2 // c4
- .long 0x3FACC9A0 // B' = pi/2 - B (high single)
- .long 0xB2655A50 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E65F267 // c0 (high single)
- .long 0x31B4B1DF // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D4E8B90 // c1 (low single)
- .long 0x3E718ACA // c2
- .long 0x3ECE7164 // c3
- .long 0x3E2DC161 // c4
- .long 0x3FA9A560 // B' = pi/2 - B (high single)
- .long 0x33719861 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E803FD4 // c0 (high single)
- .long 0xB2279E66 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D807FC8 // c1 (low single)
- .long 0x3E884BD4 // c2
- .long 0x3ED7812D // c3
- .long 0x3E4636EB // c4
- .long 0x3FA68121 // B' = pi/2 - B (high single)
- .long 0x31E43AAC // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E8DB082 // c0 (high single)
- .long 0xB132A234 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D9CD7D0 // c1 (low single)
- .long 0x3E988A60 // c2
- .long 0x3EE203E3 // c3
- .long 0x3E63582C // c4
- .long 0x3FA35CE2 // B' = pi/2 - B (high single)
- .long 0xB33889B6 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3E9B5042 // c0 (high single)
- .long 0xB22A3AEE // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DBC7490 // c1 (low single)
- .long 0x3EA99AF5 // c2
- .long 0x3EEDE107 // c3
- .long 0x3E80E9AA // c4
- .long 0x3FA038A2 // B' = pi/2 - B (high single)
- .long 0x32E4CA7E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EA92457 // c0 (high single)
- .long 0x30B80830 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DDF8200 // c1 (low single)
- .long 0x3EBB99E9 // c2
- .long 0x3EFB4AA8 // c3
- .long 0x3E9182BE // c4
- .long 0x3F9D1463 // B' = pi/2 - B (high single)
- .long 0xB2C55799 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EB73250 // c0 (high single)
- .long 0xB2028823 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E0318F8 // c1 (low single)
- .long 0x3ECEA678 // c2
- .long 0x3F053C67 // c3
- .long 0x3EA41E53 // c4
- .long 0x3F99F023 // B' = pi/2 - B (high single)
- .long 0x33484328 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EC5800D // c0 (high single)
- .long 0xB214C3C1 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E185E54 // c1 (low single)
- .long 0x3EE2E342 // c2
- .long 0x3F0DCA73 // c3
- .long 0x3EB8CC21 // c4
- .long 0x3F96CBE4 // B' = pi/2 - B (high single)
- .long 0xB14CDE2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3ED413CD // c0 (high single)
- .long 0xB1C06152 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E2FB0CC // c1 (low single)
- .long 0x3EF876CB // c2
- .long 0x3F177807 // c3
- .long 0x3ED08437 // c4
- .long 0x3F93A7A5 // B' = pi/2 - B (high single)
- .long 0xB361DEEE // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EE2F439 // c0 (high single)
- .long 0xB1F4399E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E49341C // c1 (low single)
- .long 0x3F07C61A // c2
- .long 0x3F22560F // c3
- .long 0x3EEAA81E // c4
- .long 0x3F908365 // B' = pi/2 - B (high single)
- .long 0x3292200D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3EF22870 // c0 (high single)
- .long 0x325271F4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E65107A // c1 (low single)
- .long 0x3F1429F0 // c2
- .long 0x3F2E8AFC // c3
- .long 0x3F040498 // c4
- .long 0x3F8D5F26 // B' = pi/2 - B (high single)
- .long 0xB30C0105 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F00DC0D // c0 (high single)
- .long 0xB214AF72 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E81B994 // c1 (low single)
- .long 0x3F218233 // c2
- .long 0x3F3C4531 // c3
- .long 0x3F149688 // c4
- .long 0x3F8A3AE6 // B' = pi/2 - B (high single)
- .long 0x331EEDF0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F08D5B9 // c0 (high single)
- .long 0xB25EF98E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E92478D // c1 (low single)
- .long 0x3F2FEDC9 // c2
- .long 0x3F4BCD58 // c3
- .long 0x3F27AE9E // c4
- .long 0x3F8716A7 // B' = pi/2 - B (high single)
- .long 0xB2588C6D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F1105AF // c0 (high single)
- .long 0x32F045B0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EA44EE2 // c1 (low single)
- .long 0x3F3F8FDB // c2
- .long 0x3F5D3FD0 // c3
- .long 0x3F3D0A23 // c4
- .long 0x3F83F267 // B' = pi/2 - B (high single)
- .long 0x3374CBD9 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F1970C4 // c0 (high single)
- .long 0x32904848 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EB7EFF8 // c1 (low single)
- .long 0x3F50907C // c2
- .long 0x3F710FEA // c3
- .long 0x3F561FED // c4
- .long 0x3F80CE28 // B' = pi/2 - B (high single)
- .long 0x31FDD672 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F221C37 // c0 (high single)
- .long 0xB20C61DC // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3ECD4F71 // c1 (low single)
- .long 0x3F631DAA // c2
- .long 0x3F83B471 // c3
- .long 0x3F7281EA // c4
- .long 0x3F7B53D1 // B' = pi/2 - B (high single)
- .long 0x32955386 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F2B0DC1 // c0 (high single)
- .long 0x32AB7EBA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EE496C2 // c1 (low single)
- .long 0x3F776C40 // c2
- .long 0x3F9065C1 // c3
- .long 0x3F89AFB6 // c4
- .long 0x3F750B52 // B' = pi/2 - B (high single)
- .long 0x32EB316F // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F344BA9 // c0 (high single)
- .long 0xB2B8B0EA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EFDF4F7 // c1 (low single)
- .long 0x3F86DCA8 // c2
- .long 0x3F9ED53B // c3
- .long 0x3F9CBEDE // c4
- .long 0x3F6EC2D4 // B' = pi/2 - B (high single)
- .long 0xB2BEF0A7 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F3DDCCF // c0 (high single)
- .long 0x32D29606 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEE6606F // c1 (low single)
- .long 0x3F9325D6 // c2
- .long 0x3FAF4E69 // c3
- .long 0x3FB3080C // c4
- .long 0x3F687A55 // B' = pi/2 - B (high single)
- .long 0xB252257B // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F47C8CC // c0 (high single)
- .long 0xB200F51A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEC82C6C // c1 (low single)
- .long 0x3FA0BAE9 // c2
- .long 0x3FC2252F // c3
- .long 0x3FCD24C7 // c4
- .long 0x3F6231D6 // B' = pi/2 - B (high single)
- .long 0xB119A6A2 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F521801 // c0 (high single)
- .long 0x32AE4178 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEA72938 // c1 (low single)
- .long 0x3FAFCC22 // c2
- .long 0x3FD7BD4A // c3
- .long 0x3FEBB01B // c4
- .long 0x3F5BE957 // B' = pi/2 - B (high single)
- .long 0x3205522A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F5CD3BE // c0 (high single)
- .long 0x31460308 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE8306C5 // c1 (low single)
- .long 0x3FC09232 // c2
- .long 0x3FF09632 // c3
- .long 0x4007DB00 // c4
- .long 0x3F55A0D8 // B' = pi/2 - B (high single)
- .long 0x329886FF // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F68065E // c0 (high single)
- .long 0x32670D1A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE36D1D6 // c1 (low single)
- .long 0x3FD35007 // c2
- .long 0x4006A861 // c3
- .long 0x401D4BDA // c4
- .long 0x3F4F5859 // B' = pi/2 - B (high single)
- .long 0x32EE64E8 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0x3F73BB75 // c0 (high single)
- .long 0x32FC908D // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBDBF94B0 // c1 (low single)
- .long 0x3FE8550F // c2
- .long 0x40174F67 // c3
- .long 0x4036C608 // c4
- .long 0x3F490FDB // B' = pi/2 - B (high single)
- .long 0xB2BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE8BE60E // c0 (high single)
- .long 0x320D8D84 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDF817B1 // c1 (low single)
- .long 0xBD8345EB // c2
- .long 0x3D1DFDAC // c3
- .long 0xBC52CF6F // c4
- .long 0x3F42C75C // B' = pi/2 - B (high single)
- .long 0xB24BBE8A // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE87283F // c0 (high single)
- .long 0xB268B966 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDFE6529 // c1 (low single)
- .long 0xBD7B1953 // c2
- .long 0x3D18E109 // c3
- .long 0xBC4570B0 // c4
- .long 0x3F3C7EDD // B' = pi/2 - B (high single)
- .long 0xB1000ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE827420 // c0 (high single)
- .long 0x320B8B4D // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DFB9428 // c1 (low single)
- .long 0xBD7002B4 // c2
- .long 0x3D142A6C // c3
- .long 0xBC3A47FF // c4
- .long 0x3F36365E // B' = pi/2 - B (high single)
- .long 0x320BB91C // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE7B9282 // c0 (high single)
- .long 0xB13383D2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF5D211 // c1 (low single)
- .long 0xBD6542B3 // c2
- .long 0x3D0FE5E5 // c3
- .long 0xBC31FB14 // c4
- .long 0x3F2FEDDF // B' = pi/2 - B (high single)
- .long 0x329BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE724E73 // c0 (high single)
- .long 0x3120C3E2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF05283 // c1 (low single)
- .long 0xBD5AD45E // c2
- .long 0x3D0BAFBF // c3
- .long 0xBC27B8BB // c4
- .long 0x3F29A560 // B' = pi/2 - B (high single)
- .long 0x32F19861 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE691B44 // c0 (high single)
- .long 0x31F18936 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DEB138B // c1 (low single)
- .long 0xBD50B2F7 // c2
- .long 0x3D07BE3A // c3
- .long 0xBC1E46A7 // c4
- .long 0x3F235CE2 // B' = pi/2 - B (high single)
- .long 0xB2B889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE5FF82C // c0 (high single)
- .long 0xB170723A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE61354 // c1 (low single)
- .long 0xBD46DA06 // c2
- .long 0x3D0401F8 // c3
- .long 0xBC14E013 // c4
- .long 0x3F1D1463 // B' = pi/2 - B (high single)
- .long 0xB2455799 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE56E46B // c0 (high single)
- .long 0x31E3F001 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE15025 // c1 (low single)
- .long 0xBD3D4550 // c2
- .long 0x3D00462D // c3
- .long 0xBC092C98 // c4
- .long 0x3F16CBE4 // B' = pi/2 - B (high single)
- .long 0xB0CCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE4DDF41 // c0 (high single)
- .long 0xB1AEA094 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DDCC85C // c1 (low single)
- .long 0xBD33F0BE // c2
- .long 0x3CFA23B0 // c3
- .long 0xBC01FCF7 // c4
- .long 0x3F108365 // B' = pi/2 - B (high single)
- .long 0x3212200D // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE44E7F8 // c0 (high single)
- .long 0xB1CAA3CB // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD87A74 // c1 (low single)
- .long 0xBD2AD885 // c2
- .long 0x3CF3C785 // c3
- .long 0xBBF1E348 // c4
- .long 0x3F0A3AE6 // B' = pi/2 - B (high single)
- .long 0x329EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE3BFDDC // c0 (high single)
- .long 0xB132521A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD464FC // c1 (low single)
- .long 0xBD21F8F1 // c2
- .long 0x3CEE3076 // c3
- .long 0xBBE6D263 // c4
- .long 0x3F03F267 // B' = pi/2 - B (high single)
- .long 0x32F4CBD9 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE33203E // c0 (high single)
- .long 0x31FEF5BE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD0869C // c1 (low single)
- .long 0xBD194E8C // c2
- .long 0x3CE8DCA9 // c3
- .long 0xBBDADA55 // c4
- .long 0x3EFB53D1 // B' = pi/2 - B (high single)
- .long 0x32155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE2A4E71 // c0 (high single)
- .long 0xB19CFCEC // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DCCDE11 // c1 (low single)
- .long 0xBD10D605 // c2
- .long 0x3CE382A7 // c3
- .long 0xBBC8BD97 // c4
- .long 0x3EEEC2D4 // B' = pi/2 - B (high single)
- .long 0xB23EF0A7 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE2187D0 // c0 (high single)
- .long 0xB1B7C7F7 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC96A2B // c1 (low single)
- .long 0xBD088C22 // c2
- .long 0x3CDE950E // c3
- .long 0xBBB89AD1 // c4
- .long 0x3EE231D6 // B' = pi/2 - B (high single)
- .long 0xB099A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE18CBB7 // c0 (high single)
- .long 0xAFE28430 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC629CE // c1 (low single)
- .long 0xBD006DCD // c2
- .long 0x3CDA5A2C // c3
- .long 0xBBB0B3D2 // c4
- .long 0x3ED5A0D8 // B' = pi/2 - B (high single)
- .long 0x321886FF // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE101985 // c0 (high single)
- .long 0xB02FB2B8 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC31BF3 // c1 (low single)
- .long 0xBCF0F04D // c2
- .long 0x3CD60BC7 // c3
- .long 0xBBA138BA // c4
- .long 0x3EC90FDB // B' = pi/2 - B (high single)
- .long 0xB23BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBE07709D // c0 (high single)
- .long 0xB18A2A83 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC03FA2 // c1 (low single)
- .long 0xBCE15096 // c2
- .long 0x3CD26472 // c3
- .long 0xBB9A1270 // c4
- .long 0x3EBC7EDD // B' = pi/2 - B (high single)
- .long 0xB0800ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDFDA0CB // c0 (high single)
- .long 0x2F14FCA0 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBD93F7 // c1 (low single)
- .long 0xBCD1F71B // c2
- .long 0x3CCEDD2B // c3
- .long 0xBB905946 // c4
- .long 0x3EAFEDDF // B' = pi/2 - B (high single)
- .long 0x321BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDEC708C // c0 (high single)
- .long 0xB14895C4 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBB181E // c1 (low single)
- .long 0xBCC2DEA6 // c2
- .long 0x3CCB5027 // c3
- .long 0xBB7F3969 // c4
- .long 0x3EA35CE2 // B' = pi/2 - B (high single)
- .long 0xB23889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDDB4F55 // c0 (high single)
- .long 0x30F6437E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB8CB52 // c1 (low single)
- .long 0xBCB40210 // c2
- .long 0x3CC82D45 // c3
- .long 0xBB643075 // c4
- .long 0x3E96CBE4 // B' = pi/2 - B (high single)
- .long 0xB04CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDCA3BFF // c0 (high single)
- .long 0x311C95EA // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB6ACDE // c1 (low single)
- .long 0xBCA55C5B // c2
- .long 0x3CC5BC04 // c3
- .long 0xBB63A969 // c4
- .long 0x3E8A3AE6 // B' = pi/2 - B (high single)
- .long 0x321EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDB93569 // c0 (high single)
- .long 0xAFB9ED00 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB4BC1F // c1 (low single)
- .long 0xBC96E905 // c2
- .long 0x3CC2E6F5 // c3
- .long 0xBB3E10A6 // c4
- .long 0x3E7B53D1 // B' = pi/2 - B (high single)
- .long 0x31955386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBDA83A77 // c0 (high single)
- .long 0x316D967A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB2F87C // c1 (low single)
- .long 0xBC88A31F // c2
- .long 0x3CC0E763 // c3
- .long 0xBB3F1666 // c4
- .long 0x3E6231D6 // B' = pi/2 - B (high single)
- .long 0xB019A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD974A0D // c0 (high single)
- .long 0xB14F365B // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB1616F // c1 (low single)
- .long 0xBC750CD8 // c2
- .long 0x3CBEB595 // c3
- .long 0xBB22B883 // c4
- .long 0x3E490FDB // B' = pi/2 - B (high single)
- .long 0xB1BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD866317 // c0 (high single)
- .long 0xAFF02140 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAFF67D // c1 (low single)
- .long 0xBC591CD0 // c2
- .long 0x3CBCBEAD // c3
- .long 0xBB04BBEC // c4
- .long 0x3E2FEDDF // B' = pi/2 - B (high single)
- .long 0x319BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD6B08FF // c0 (high single)
- .long 0xB0EED236 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAEB739 // c1 (low single)
- .long 0xBC3D6D51 // c2
- .long 0x3CBB485D // c3
- .long 0xBAFFF5BA // c4
- .long 0x3E16CBE4 // B' = pi/2 - B (high single)
- .long 0xAFCCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD495A6C // c0 (high single)
- .long 0xB0A427BD // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DADA345 // c1 (low single)
- .long 0xBC21F648 // c2
- .long 0x3CB9D1B4 // c3
- .long 0xBACB5567 // c4
- .long 0x3DFB53D1 // B' = pi/2 - B (high single)
- .long 0x31155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD27B856 // c0 (high single)
- .long 0xB0F7EE91 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DACBA4E // c1 (low single)
- .long 0xBC06AEE3 // c2
- .long 0x3CB8E5DC // c3
- .long 0xBAEC00EE // c4
- .long 0x3DC90FDB // B' = pi/2 - B (high single)
- .long 0xB13BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBD0620A3 // c0 (high single)
- .long 0xB0ECAB40 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DABFC11 // c1 (low single)
- .long 0xBBD7200F // c2
- .long 0x3CB79475 // c3
- .long 0xBA2B0ADC // c4
- .long 0x3D96CBE4 // B' = pi/2 - B (high single)
- .long 0xAF4CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBCC92278 // c0 (high single)
- .long 0x302F2E68 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAB6854 // c1 (low single)
- .long 0xBBA1214F // c2
- .long 0x3CB6C1E9 // c3
- .long 0x3843C2F3 // c4
- .long 0x3D490FDB // B' = pi/2 - B (high single)
- .long 0xB0BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBC861015 // c0 (high single)
- .long 0xAFD68E2E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAFEEB // c1 (low single)
- .long 0xBB569F3F // c2
- .long 0x3CB6A84E // c3
- .long 0xBAC64194 // c4
- .long 0x3CC90FDB // B' = pi/2 - B (high single)
- .long 0xB03BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0xBC060BF3 // c0 (high single)
- .long 0x2FE251AE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAABFB9 // c1 (low single)
- .long 0xBAD67C60 // c2
- .long 0x3CB64CA5 // c3
- .long 0xBACDE881 // c4
- .long 0x00000000 // B' = pi/2 - B (high single)
- .long 0x00000000 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x00000000 // c0 (high single)
- .long 0x00000000 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAAAAB // c1 (low single)
- .long 0x00000000 // c2
- .long 0x3CB5E28B // c3
- .long 0x00000000 // c4
- .long 0xBCC90FDB // B' = pi/2 - B (high single)
- .long 0x303BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3C060BF3 // c0 (high single)
- .long 0xAFE251AE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAABFB9 // c1 (low single)
- .long 0x3AD67C60 // c2
- .long 0x3CB64CA5 // c3
- .long 0x3ACDE881 // c4
- .long 0xBD490FDB // B' = pi/2 - B (high single)
- .long 0x30BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3C861015 // c0 (high single)
- .long 0x2FD68E2E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAAFEEB // c1 (low single)
- .long 0x3B569F3F // c2
- .long 0x3CB6A84E // c3
- .long 0x3AC64194 // c4
- .long 0xBD96CBE4 // B' = pi/2 - B (high single)
- .long 0x2F4CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3CC92278 // c0 (high single)
- .long 0xB02F2E68 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAB6854 // c1 (low single)
- .long 0x3BA1214F // c2
- .long 0x3CB6C1E9 // c3
- .long 0xB843C2F2 // c4
- .long 0xBDC90FDB // B' = pi/2 - B (high single)
- .long 0x313BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D0620A3 // c0 (high single)
- .long 0x30ECAB40 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DABFC11 // c1 (low single)
- .long 0x3BD7200F // c2
- .long 0x3CB79475 // c3
- .long 0x3A2B0ADC // c4
- .long 0xBDFB53D1 // B' = pi/2 - B (high single)
- .long 0xB1155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D27B856 // c0 (high single)
- .long 0x30F7EE91 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DACBA4E // c1 (low single)
- .long 0x3C06AEE3 // c2
- .long 0x3CB8E5DC // c3
- .long 0x3AEC00EE // c4
- .long 0xBE16CBE4 // B' = pi/2 - B (high single)
- .long 0x2FCCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D495A6C // c0 (high single)
- .long 0x30A427BD // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DADA345 // c1 (low single)
- .long 0x3C21F648 // c2
- .long 0x3CB9D1B4 // c3
- .long 0x3ACB5567 // c4
- .long 0xBE2FEDDF // B' = pi/2 - B (high single)
- .long 0xB19BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D6B08FF // c0 (high single)
- .long 0x30EED236 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAEB739 // c1 (low single)
- .long 0x3C3D6D51 // c2
- .long 0x3CBB485D // c3
- .long 0x3AFFF5BA // c4
- .long 0xBE490FDB // B' = pi/2 - B (high single)
- .long 0x31BBBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D866317 // c0 (high single)
- .long 0x2FF02140 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DAFF67D // c1 (low single)
- .long 0x3C591CD0 // c2
- .long 0x3CBCBEAD // c3
- .long 0x3B04BBEC // c4
- .long 0xBE6231D6 // B' = pi/2 - B (high single)
- .long 0x3019A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3D974A0D // c0 (high single)
- .long 0x314F365B // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB1616F // c1 (low single)
- .long 0x3C750CD8 // c2
- .long 0x3CBEB595 // c3
- .long 0x3B22B883 // c4
- .long 0xBE7B53D1 // B' = pi/2 - B (high single)
- .long 0xB1955386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DA83A77 // c0 (high single)
- .long 0xB16D967A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB2F87C // c1 (low single)
- .long 0x3C88A31F // c2
- .long 0x3CC0E763 // c3
- .long 0x3B3F1666 // c4
- .long 0xBE8A3AE6 // B' = pi/2 - B (high single)
- .long 0xB21EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DB93569 // c0 (high single)
- .long 0x2FB9ED00 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB4BC1F // c1 (low single)
- .long 0x3C96E905 // c2
- .long 0x3CC2E6F5 // c3
- .long 0x3B3E10A6 // c4
- .long 0xBE96CBE4 // B' = pi/2 - B (high single)
- .long 0x304CDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DCA3BFF // c0 (high single)
- .long 0xB11C95EA // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB6ACDE // c1 (low single)
- .long 0x3CA55C5B // c2
- .long 0x3CC5BC04 // c3
- .long 0x3B63A969 // c4
- .long 0xBEA35CE2 // B' = pi/2 - B (high single)
- .long 0x323889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DDB4F55 // c0 (high single)
- .long 0xB0F6437E // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DB8CB52 // c1 (low single)
- .long 0x3CB40210 // c2
- .long 0x3CC82D45 // c3
- .long 0x3B643075 // c4
- .long 0xBEAFEDDF // B' = pi/2 - B (high single)
- .long 0xB21BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DEC708C // c0 (high single)
- .long 0x314895C4 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBB181E // c1 (low single)
- .long 0x3CC2DEA6 // c2
- .long 0x3CCB5027 // c3
- .long 0x3B7F3969 // c4
- .long 0xBEBC7EDD // B' = pi/2 - B (high single)
- .long 0x30800ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3DFDA0CB // c0 (high single)
- .long 0xAF14FCA0 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DBD93F7 // c1 (low single)
- .long 0x3CD1F71B // c2
- .long 0x3CCEDD2B // c3
- .long 0x3B905946 // c4
- .long 0xBEC90FDB // B' = pi/2 - B (high single)
- .long 0x323BBD2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E07709D // c0 (high single)
- .long 0x318A2A83 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC03FA2 // c1 (low single)
- .long 0x3CE15096 // c2
- .long 0x3CD26472 // c3
- .long 0x3B9A1270 // c4
- .long 0xBED5A0D8 // B' = pi/2 - B (high single)
- .long 0xB21886FF // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E101985 // c0 (high single)
- .long 0x302FB2B8 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC31BF3 // c1 (low single)
- .long 0x3CF0F04D // c2
- .long 0x3CD60BC7 // c3
- .long 0x3BA138BA // c4
- .long 0xBEE231D6 // B' = pi/2 - B (high single)
- .long 0x3099A6A2 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E18CBB7 // c0 (high single)
- .long 0x2FE28430 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC629CE // c1 (low single)
- .long 0x3D006DCD // c2
- .long 0x3CDA5A2C // c3
- .long 0x3BB0B3D2 // c4
- .long 0xBEEEC2D4 // B' = pi/2 - B (high single)
- .long 0x323EF0A7 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E2187D0 // c0 (high single)
- .long 0x31B7C7F7 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DC96A2B // c1 (low single)
- .long 0x3D088C22 // c2
- .long 0x3CDE950E // c3
- .long 0x3BB89AD1 // c4
- .long 0xBEFB53D1 // B' = pi/2 - B (high single)
- .long 0xB2155386 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E2A4E71 // c0 (high single)
- .long 0x319CFCEC // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DCCDE11 // c1 (low single)
- .long 0x3D10D605 // c2
- .long 0x3CE382A7 // c3
- .long 0x3BC8BD97 // c4
- .long 0xBF03F267 // B' = pi/2 - B (high single)
- .long 0xB2F4CBD9 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E33203E // c0 (high single)
- .long 0xB1FEF5BE // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD0869C // c1 (low single)
- .long 0x3D194E8C // c2
- .long 0x3CE8DCA9 // c3
- .long 0x3BDADA55 // c4
- .long 0xBF0A3AE6 // B' = pi/2 - B (high single)
- .long 0xB29EEDF0 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E3BFDDC // c0 (high single)
- .long 0x3132521A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD464FC // c1 (low single)
- .long 0x3D21F8F1 // c2
- .long 0x3CEE3076 // c3
- .long 0x3BE6D263 // c4
- .long 0xBF108365 // B' = pi/2 - B (high single)
- .long 0xB212200D // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E44E7F8 // c0 (high single)
- .long 0x31CAA3CB // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DD87A74 // c1 (low single)
- .long 0x3D2AD885 // c2
- .long 0x3CF3C785 // c3
- .long 0x3BF1E348 // c4
- .long 0xBF16CBE4 // B' = pi/2 - B (high single)
- .long 0x30CCDE2E // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E4DDF41 // c0 (high single)
- .long 0x31AEA094 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DDCC85C // c1 (low single)
- .long 0x3D33F0BE // c2
- .long 0x3CFA23B0 // c3
- .long 0x3C01FCF7 // c4
- .long 0xBF1D1463 // B' = pi/2 - B (high single)
- .long 0x32455799 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E56E46B // c0 (high single)
- .long 0xB1E3F001 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE15025 // c1 (low single)
- .long 0x3D3D4550 // c2
- .long 0x3D00462D // c3
- .long 0x3C092C98 // c4
- .long 0xBF235CE2 // B' = pi/2 - B (high single)
- .long 0x32B889B6 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E5FF82C // c0 (high single)
- .long 0x3170723A // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DE61354 // c1 (low single)
- .long 0x3D46DA06 // c2
- .long 0x3D0401F8 // c3
- .long 0x3C14E013 // c4
- .long 0xBF29A560 // B' = pi/2 - B (high single)
- .long 0xB2F19861 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E691B44 // c0 (high single)
- .long 0xB1F18936 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DEB138B // c1 (low single)
- .long 0x3D50B2F7 // c2
- .long 0x3D07BE3A // c3
- .long 0x3C1E46A7 // c4
- .long 0xBF2FEDDF // B' = pi/2 - B (high single)
- .long 0xB29BBA77 // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E724E73 // c0 (high single)
- .long 0xB120C3E2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF05283 // c1 (low single)
- .long 0x3D5AD45E // c2
- .long 0x3D0BAFBF // c3
- .long 0x3C27B8BB // c4
- .long 0xBF36365E // B' = pi/2 - B (high single)
- .long 0xB20BB91C // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E7B9282 // c0 (high single)
- .long 0x313383D2 // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DF5D211 // c1 (low single)
- .long 0x3D6542B3 // c2
- .long 0x3D0FE5E5 // c3
- .long 0x3C31FB14 // c4
- .long 0xBF3C7EDD // B' = pi/2 - B (high single)
- .long 0x31000ADD // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E827420 // c0 (high single)
- .long 0xB20B8B4D // c0 (low single)
- .long 0x3E800000 // c1 (high 1 bit)
- .long 0x3DFB9428 // c1 (low single)
- .long 0x3D7002B4 // c2
- .long 0x3D142A6C // c3
- .long 0x3C3A47FF // c4
- .long 0xBF42C75C // B' = pi/2 - B (high single)
- .long 0x324BBE8A // B' = pi/2 - B (low single)
- .long 0x3F800000 // tau (1 for cot path)
- .long 0x3E87283F // c0 (high single)
- .long 0x3268B966 // c0 (low single)
- .long 0x3F000000 // c1 (high 1 bit)
- .long 0xBDFE6529 // c1 (low single)
- .long 0x3D7B1953 // c2
- .long 0x3D18E109 // c3
- .long 0x3C4570B0 // c4
- .long 0xBF490FDB // B' = pi/2 - B (high single)
- .long 0x32BBBD2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF800000 // c0 (high single)
- .long 0x2B410000 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xB3000000 // c1 (low single)
- .long 0xC0000000 // c2
- .long 0x402AB7C8 // c3
- .long 0xC05561DB // c4
- .long 0xBF4F5859 // B' = pi/2 - B (high single)
- .long 0xB2EE64E8 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF73BB75 // c0 (high single)
- .long 0xB2FC908D // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBDBF94B0 // c1 (low single)
- .long 0xBFE8550F // c2
- .long 0x40174F67 // c3
- .long 0xC036C608 // c4
- .long 0xBF55A0D8 // B' = pi/2 - B (high single)
- .long 0xB29886FF // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF68065E // c0 (high single)
- .long 0xB2670D1A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE36D1D6 // c1 (low single)
- .long 0xBFD35007 // c2
- .long 0x4006A861 // c3
- .long 0xC01D4BDA // c4
- .long 0xBF5BE957 // B' = pi/2 - B (high single)
- .long 0xB205522A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF5CD3BE // c0 (high single)
- .long 0xB1460308 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBE8306C5 // c1 (low single)
- .long 0xBFC09232 // c2
- .long 0x3FF09632 // c3
- .long 0xC007DB00 // c4
- .long 0xBF6231D6 // B' = pi/2 - B (high single)
- .long 0x3119A6A2 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF521801 // c0 (high single)
- .long 0xB2AE4178 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEA72938 // c1 (low single)
- .long 0xBFAFCC22 // c2
- .long 0x3FD7BD4A // c3
- .long 0xBFEBB01B // c4
- .long 0xBF687A55 // B' = pi/2 - B (high single)
- .long 0x3252257B // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF47C8CC // c0 (high single)
- .long 0x3200F51A // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEC82C6C // c1 (low single)
- .long 0xBFA0BAE9 // c2
- .long 0x3FC2252F // c3
- .long 0xBFCD24C7 // c4
- .long 0xBF6EC2D4 // B' = pi/2 - B (high single)
- .long 0x32BEF0A7 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF3DDCCF // c0 (high single)
- .long 0xB2D29606 // c0 (low single)
- .long 0x40000000 // c1 (high 1 bit)
- .long 0xBEE6606F // c1 (low single)
- .long 0xBF9325D6 // c2
- .long 0x3FAF4E69 // c3
- .long 0xBFB3080C // c4
- .long 0xBF750B52 // B' = pi/2 - B (high single)
- .long 0xB2EB316F // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF344BA9 // c0 (high single)
- .long 0x32B8B0EA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EFDF4F7 // c1 (low single)
- .long 0xBF86DCA8 // c2
- .long 0x3F9ED53B // c3
- .long 0xBF9CBEDE // c4
- .long 0xBF7B53D1 // B' = pi/2 - B (high single)
- .long 0xB2955386 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF2B0DC1 // c0 (high single)
- .long 0xB2AB7EBA // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EE496C2 // c1 (low single)
- .long 0xBF776C40 // c2
- .long 0x3F9065C1 // c3
- .long 0xBF89AFB6 // c4
- .long 0xBF80CE28 // B' = pi/2 - B (high single)
- .long 0xB1FDD672 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF221C37 // c0 (high single)
- .long 0x320C61DC // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3ECD4F71 // c1 (low single)
- .long 0xBF631DAA // c2
- .long 0x3F83B471 // c3
- .long 0xBF7281EA // c4
- .long 0xBF83F267 // B' = pi/2 - B (high single)
- .long 0xB374CBD9 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF1970C4 // c0 (high single)
- .long 0xB2904848 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EB7EFF8 // c1 (low single)
- .long 0xBF50907C // c2
- .long 0x3F710FEA // c3
- .long 0xBF561FED // c4
- .long 0xBF8716A7 // B' = pi/2 - B (high single)
- .long 0x32588C6D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF1105AF // c0 (high single)
- .long 0xB2F045B0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3EA44EE2 // c1 (low single)
- .long 0xBF3F8FDB // c2
- .long 0x3F5D3FD0 // c3
- .long 0xBF3D0A23 // c4
- .long 0xBF8A3AE6 // B' = pi/2 - B (high single)
- .long 0xB31EEDF0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF08D5B9 // c0 (high single)
- .long 0x325EF98E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E92478D // c1 (low single)
- .long 0xBF2FEDC9 // c2
- .long 0x3F4BCD58 // c3
- .long 0xBF27AE9E // c4
- .long 0xBF8D5F26 // B' = pi/2 - B (high single)
- .long 0x330C0105 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBF00DC0D // c0 (high single)
- .long 0x3214AF72 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E81B994 // c1 (low single)
- .long 0xBF218233 // c2
- .long 0x3F3C4531 // c3
- .long 0xBF149688 // c4
- .long 0xBF908365 // B' = pi/2 - B (high single)
- .long 0xB292200D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEF22870 // c0 (high single)
- .long 0xB25271F4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E65107A // c1 (low single)
- .long 0xBF1429F0 // c2
- .long 0x3F2E8AFC // c3
- .long 0xBF040498 // c4
- .long 0xBF93A7A5 // B' = pi/2 - B (high single)
- .long 0x3361DEEE // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEE2F439 // c0 (high single)
- .long 0x31F4399E // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E49341C // c1 (low single)
- .long 0xBF07C61A // c2
- .long 0x3F22560F // c3
- .long 0xBEEAA81E // c4
- .long 0xBF96CBE4 // B' = pi/2 - B (high single)
- .long 0x314CDE2E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBED413CD // c0 (high single)
- .long 0x31C06152 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E2FB0CC // c1 (low single)
- .long 0xBEF876CB // c2
- .long 0x3F177807 // c3
- .long 0xBED08437 // c4
- .long 0xBF99F023 // B' = pi/2 - B (high single)
- .long 0xB3484328 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEC5800D // c0 (high single)
- .long 0x3214C3C1 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E185E54 // c1 (low single)
- .long 0xBEE2E342 // c2
- .long 0x3F0DCA73 // c3
- .long 0xBEB8CC21 // c4
- .long 0xBF9D1463 // B' = pi/2 - B (high single)
- .long 0x32C55799 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEB73250 // c0 (high single)
- .long 0x32028823 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3E0318F8 // c1 (low single)
- .long 0xBECEA678 // c2
- .long 0x3F053C67 // c3
- .long 0xBEA41E53 // c4
- .long 0xBFA038A2 // B' = pi/2 - B (high single)
- .long 0xB2E4CA7E // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBEA92457 // c0 (high single)
- .long 0xB0B80830 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DDF8200 // c1 (low single)
- .long 0xBEBB99E9 // c2
- .long 0x3EFB4AA8 // c3
- .long 0xBE9182BE // c4
- .long 0xBFA35CE2 // B' = pi/2 - B (high single)
- .long 0x333889B6 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE9B5042 // c0 (high single)
- .long 0x322A3AEE // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3DBC7490 // c1 (low single)
- .long 0xBEA99AF5 // c2
- .long 0x3EEDE107 // c3
- .long 0xBE80E9AA // c4
- .long 0xBFA68121 // B' = pi/2 - B (high single)
- .long 0xB1E43AAC // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE8DB082 // c0 (high single)
- .long 0x3132A234 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D9CD7D0 // c1 (low single)
- .long 0xBE988A60 // c2
- .long 0x3EE203E3 // c3
- .long 0xBE63582C // c4
- .long 0xBFA9A560 // B' = pi/2 - B (high single)
- .long 0xB3719861 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE803FD4 // c0 (high single)
- .long 0x32279E66 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D807FC8 // c1 (low single)
- .long 0xBE884BD4 // c2
- .long 0x3ED7812D // c3
- .long 0xBE4636EB // c4
- .long 0xBFACC9A0 // B' = pi/2 - B (high single)
- .long 0x32655A50 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE65F267 // c0 (high single)
- .long 0xB1B4B1DF // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D4E8B90 // c1 (low single)
- .long 0xBE718ACA // c2
- .long 0x3ECE7164 // c3
- .long 0xBE2DC161 // c4
- .long 0xBFAFEDDF // B' = pi/2 - B (high single)
- .long 0xB31BBA77 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE4BAFAF // c0 (high single)
- .long 0xAF2A29E0 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3D221018 // c1 (low single)
- .long 0xBE53BED0 // c2
- .long 0x3EC67E26 // c3
- .long 0xBE1568E2 // c4
- .long 0xBFB3121F // B' = pi/2 - B (high single)
- .long 0x330F347D // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE31AE4D // c0 (high single)
- .long 0x31F32251 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CF6A500 // c1 (low single)
- .long 0xBE3707DA // c2
- .long 0x3EBFA489 // c3
- .long 0xBDFBD9C7 // c4
- .long 0xBFB6365E // B' = pi/2 - B (high single)
- .long 0xB28BB91C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBE17E564 // c0 (high single)
- .long 0x31C5A2E4 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3CB440D0 // c1 (low single)
- .long 0xBE1B3D00 // c2
- .long 0x3EB9F664 // c3
- .long 0xBDD647C0 // c4
- .long 0xBFB95A9E // B' = pi/2 - B (high single)
- .long 0x33651267 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBDFC98C2 // c0 (high single)
- .long 0x30AE525C // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C793D20 // c1 (low single)
- .long 0xBE003845 // c2
- .long 0x3EB5271F // c3
- .long 0xBDAC669E // c4
- .long 0xBFBC7EDD // B' = pi/2 - B (high single)
- .long 0x31800ADD // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBDC9B5DC // c0 (high single)
- .long 0xB145AD86 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3C1EEF20 // c1 (low single)
- .long 0xBDCBAAEA // c2
- .long 0x3EB14E5E // c3
- .long 0xBD858BB2 // c4
- .long 0xBFBFA31C // B' = pi/2 - B (high single)
- .long 0xB3450FB0 // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBD9711CE // c0 (high single)
- .long 0xB14FEB28 // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3BB24C00 // c1 (low single)
- .long 0xBD97E43A // c2
- .long 0x3EAE6A89 // c3
- .long 0xBD4D07E0 // c4
- .long 0xBFC2C75C // B' = pi/2 - B (high single)
- .long 0x32CBBE8A // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBD49393C // c0 (high single)
- .long 0xB0A39F5B // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3B1E2B00 // c1 (low single)
- .long 0xBD49B5D4 // c2
- .long 0x3EAC4F10 // c3
- .long 0xBCFD9425 // c4
- .long 0xBFC5EB9B // B' = pi/2 - B (high single)
- .long 0xB2DE638C // B' = pi/2 - B (low single)
- .long 0x00000000 // tau (1 for cot path)
- .long 0xBCC91A31 // c0 (high single)
- .long 0xAF8E8D1A // c0 (low single)
- .long 0x3F800000 // c1 (high 1 bit)
- .long 0x3A1DFA00 // c1 (low single)
- .long 0xBCC9392D // c2
- .long 0x3EAB1889 // c3
- .long 0xBC885D3B // c4
- .align 32
- .type __svml_stan_data_internal, @object
- .size __svml_stan_data_internal, .-__svml_stan_data_internal
- .align 32
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+ /* All results have been written to (%rsp). */
+ vmovups (%rsp), %ymm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa_register (rsp)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %rbx
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %r13
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
+ ret
+END(_ZGVdN8v_tanf_avx2)
-#ifdef __svml_stan_reduction_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(32)) VUINT32 _sPtable[256][3][1];
-} __svml_stan_reduction_data_internal;
-#endif
-__svml_stan_reduction_data_internal:
- /* P_hi P_med P_lo */
- .long 0x00000000, 0x00000000, 0x00000000 /* 0 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 1 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 2 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 3 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 4 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 5 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 6 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 7 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 8 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 9 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 10 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 11 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 12 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 13 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 14 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 15 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 16 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 17 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 18 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 19 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 20 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 21 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 22 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 23 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 24 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 25 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 26 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 27 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 28 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 29 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 30 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 31 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 32 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 33 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 34 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 35 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 36 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 37 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 38 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 39 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 40 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 41 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 42 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 43 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 44 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 45 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 46 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 47 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 48 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 49 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 50 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 51 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 52 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 53 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 54 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 55 */
- .long 0x00000000, 0x00000000, 0x00000000 /* 56 */
- .long 0x00000000, 0x00000000, 0x00000001 /* 57 */
- .long 0x00000000, 0x00000000, 0x00000002 /* 58 */
- .long 0x00000000, 0x00000000, 0x00000005 /* 59 */
- .long 0x00000000, 0x00000000, 0x0000000A /* 60 */
- .long 0x00000000, 0x00000000, 0x00000014 /* 61 */
- .long 0x00000000, 0x00000000, 0x00000028 /* 62 */
- .long 0x00000000, 0x00000000, 0x00000051 /* 63 */
- .long 0x00000000, 0x00000000, 0x000000A2 /* 64 */
- .long 0x00000000, 0x00000000, 0x00000145 /* 65 */
- .long 0x00000000, 0x00000000, 0x0000028B /* 66 */
- .long 0x00000000, 0x00000000, 0x00000517 /* 67 */
- .long 0x00000000, 0x00000000, 0x00000A2F /* 68 */
- .long 0x00000000, 0x00000000, 0x0000145F /* 69 */
- .long 0x00000000, 0x00000000, 0x000028BE /* 70 */
- .long 0x00000000, 0x00000000, 0x0000517C /* 71 */
- .long 0x00000000, 0x00000000, 0x0000A2F9 /* 72 */
- .long 0x00000000, 0x00000000, 0x000145F3 /* 73 */
- .long 0x00000000, 0x00000000, 0x00028BE6 /* 74 */
- .long 0x00000000, 0x00000000, 0x000517CC /* 75 */
- .long 0x00000000, 0x00000000, 0x000A2F98 /* 76 */
- .long 0x00000000, 0x00000000, 0x00145F30 /* 77 */
- .long 0x00000000, 0x00000000, 0x0028BE60 /* 78 */
- .long 0x00000000, 0x00000000, 0x00517CC1 /* 79 */
- .long 0x00000000, 0x00000000, 0x00A2F983 /* 80 */
- .long 0x00000000, 0x00000000, 0x0145F306 /* 81 */
- .long 0x00000000, 0x00000000, 0x028BE60D /* 82 */
- .long 0x00000000, 0x00000000, 0x0517CC1B /* 83 */
- .long 0x00000000, 0x00000000, 0x0A2F9836 /* 84 */
- .long 0x00000000, 0x00000000, 0x145F306D /* 85 */
- .long 0x00000000, 0x00000000, 0x28BE60DB /* 86 */
- .long 0x00000000, 0x00000000, 0x517CC1B7 /* 87 */
- .long 0x00000000, 0x00000000, 0xA2F9836E /* 88 */
- .long 0x00000000, 0x00000001, 0x45F306DC /* 89 */
- .long 0x00000000, 0x00000002, 0x8BE60DB9 /* 90 */
- .long 0x00000000, 0x00000005, 0x17CC1B72 /* 91 */
- .long 0x00000000, 0x0000000A, 0x2F9836E4 /* 92 */
- .long 0x00000000, 0x00000014, 0x5F306DC9 /* 93 */
- .long 0x00000000, 0x00000028, 0xBE60DB93 /* 94 */
- .long 0x00000000, 0x00000051, 0x7CC1B727 /* 95 */
- .long 0x00000000, 0x000000A2, 0xF9836E4E /* 96 */
- .long 0x00000000, 0x00000145, 0xF306DC9C /* 97 */
- .long 0x00000000, 0x0000028B, 0xE60DB939 /* 98 */
- .long 0x00000000, 0x00000517, 0xCC1B7272 /* 99 */
- .long 0x00000000, 0x00000A2F, 0x9836E4E4 /* 100 */
- .long 0x00000000, 0x0000145F, 0x306DC9C8 /* 101 */
- .long 0x00000000, 0x000028BE, 0x60DB9391 /* 102 */
- .long 0x00000000, 0x0000517C, 0xC1B72722 /* 103 */
- .long 0x00000000, 0x0000A2F9, 0x836E4E44 /* 104 */
- .long 0x00000000, 0x000145F3, 0x06DC9C88 /* 105 */
- .long 0x00000000, 0x00028BE6, 0x0DB93910 /* 106 */
- .long 0x00000000, 0x000517CC, 0x1B727220 /* 107 */
- .long 0x00000000, 0x000A2F98, 0x36E4E441 /* 108 */
- .long 0x00000000, 0x00145F30, 0x6DC9C882 /* 109 */
- .long 0x00000000, 0x0028BE60, 0xDB939105 /* 110 */
- .long 0x00000000, 0x00517CC1, 0xB727220A /* 111 */
- .long 0x00000000, 0x00A2F983, 0x6E4E4415 /* 112 */
- .long 0x00000000, 0x0145F306, 0xDC9C882A /* 113 */
- .long 0x00000000, 0x028BE60D, 0xB9391054 /* 114 */
- .long 0x00000000, 0x0517CC1B, 0x727220A9 /* 115 */
- .long 0x00000000, 0x0A2F9836, 0xE4E44152 /* 116 */
- .long 0x00000000, 0x145F306D, 0xC9C882A5 /* 117 */
- .long 0x00000000, 0x28BE60DB, 0x9391054A /* 118 */
- .long 0x00000000, 0x517CC1B7, 0x27220A94 /* 119 */
- .long 0x00000000, 0xA2F9836E, 0x4E441529 /* 120 */
- .long 0x00000001, 0x45F306DC, 0x9C882A53 /* 121 */
- .long 0x00000002, 0x8BE60DB9, 0x391054A7 /* 122 */
- .long 0x00000005, 0x17CC1B72, 0x7220A94F /* 123 */
- .long 0x0000000A, 0x2F9836E4, 0xE441529F /* 124 */
- .long 0x00000014, 0x5F306DC9, 0xC882A53F /* 125 */
- .long 0x00000028, 0xBE60DB93, 0x91054A7F /* 126 */
- .long 0x00000051, 0x7CC1B727, 0x220A94FE /* 127 */
- .long 0x000000A2, 0xF9836E4E, 0x441529FC /* 128 */
- .long 0x00000145, 0xF306DC9C, 0x882A53F8 /* 129 */
- .long 0x0000028B, 0xE60DB939, 0x1054A7F0 /* 130 */
- .long 0x00000517, 0xCC1B7272, 0x20A94FE1 /* 131 */
- .long 0x00000A2F, 0x9836E4E4, 0x41529FC2 /* 132 */
- .long 0x0000145F, 0x306DC9C8, 0x82A53F84 /* 133 */
- .long 0x000028BE, 0x60DB9391, 0x054A7F09 /* 134 */
- .long 0x0000517C, 0xC1B72722, 0x0A94FE13 /* 135 */
- .long 0x0000A2F9, 0x836E4E44, 0x1529FC27 /* 136 */
- .long 0x000145F3, 0x06DC9C88, 0x2A53F84E /* 137 */
- .long 0x00028BE6, 0x0DB93910, 0x54A7F09D /* 138 */
- .long 0x000517CC, 0x1B727220, 0xA94FE13A /* 139 */
- .long 0x000A2F98, 0x36E4E441, 0x529FC275 /* 140 */
- .long 0x00145F30, 0x6DC9C882, 0xA53F84EA /* 141 */
- .long 0x0028BE60, 0xDB939105, 0x4A7F09D5 /* 142 */
- .long 0x00517CC1, 0xB727220A, 0x94FE13AB /* 143 */
- .long 0x00A2F983, 0x6E4E4415, 0x29FC2757 /* 144 */
- .long 0x0145F306, 0xDC9C882A, 0x53F84EAF /* 145 */
- .long 0x028BE60D, 0xB9391054, 0xA7F09D5F /* 146 */
- .long 0x0517CC1B, 0x727220A9, 0x4FE13ABE /* 147 */
- .long 0x0A2F9836, 0xE4E44152, 0x9FC2757D /* 148 */
- .long 0x145F306D, 0xC9C882A5, 0x3F84EAFA /* 149 */
- .long 0x28BE60DB, 0x9391054A, 0x7F09D5F4 /* 150 */
- .long 0x517CC1B7, 0x27220A94, 0xFE13ABE8 /* 151 */
- .long 0xA2F9836E, 0x4E441529, 0xFC2757D1 /* 152 */
- .long 0x45F306DC, 0x9C882A53, 0xF84EAFA3 /* 153 */
- .long 0x8BE60DB9, 0x391054A7, 0xF09D5F47 /* 154 */
- .long 0x17CC1B72, 0x7220A94F, 0xE13ABE8F /* 155 */
- .long 0x2F9836E4, 0xE441529F, 0xC2757D1F /* 156 */
- .long 0x5F306DC9, 0xC882A53F, 0x84EAFA3E /* 157 */
- .long 0xBE60DB93, 0x91054A7F, 0x09D5F47D /* 158 */
- .long 0x7CC1B727, 0x220A94FE, 0x13ABE8FA /* 159 */
- .long 0xF9836E4E, 0x441529FC, 0x2757D1F5 /* 160 */
- .long 0xF306DC9C, 0x882A53F8, 0x4EAFA3EA /* 161 */
- .long 0xE60DB939, 0x1054A7F0, 0x9D5F47D4 /* 162 */
- .long 0xCC1B7272, 0x20A94FE1, 0x3ABE8FA9 /* 163 */
- .long 0x9836E4E4, 0x41529FC2, 0x757D1F53 /* 164 */
- .long 0x306DC9C8, 0x82A53F84, 0xEAFA3EA6 /* 165 */
- .long 0x60DB9391, 0x054A7F09, 0xD5F47D4D /* 166 */
- .long 0xC1B72722, 0x0A94FE13, 0xABE8FA9A /* 167 */
- .long 0x836E4E44, 0x1529FC27, 0x57D1F534 /* 168 */
- .long 0x06DC9C88, 0x2A53F84E, 0xAFA3EA69 /* 169 */
- .long 0x0DB93910, 0x54A7F09D, 0x5F47D4D3 /* 170 */
- .long 0x1B727220, 0xA94FE13A, 0xBE8FA9A6 /* 171 */
- .long 0x36E4E441, 0x529FC275, 0x7D1F534D /* 172 */
- .long 0x6DC9C882, 0xA53F84EA, 0xFA3EA69B /* 173 */
- .long 0xDB939105, 0x4A7F09D5, 0xF47D4D37 /* 174 */
- .long 0xB727220A, 0x94FE13AB, 0xE8FA9A6E /* 175 */
- .long 0x6E4E4415, 0x29FC2757, 0xD1F534DD /* 176 */
- .long 0xDC9C882A, 0x53F84EAF, 0xA3EA69BB /* 177 */
- .long 0xB9391054, 0xA7F09D5F, 0x47D4D377 /* 178 */
- .long 0x727220A9, 0x4FE13ABE, 0x8FA9A6EE /* 179 */
- .long 0xE4E44152, 0x9FC2757D, 0x1F534DDC /* 180 */
- .long 0xC9C882A5, 0x3F84EAFA, 0x3EA69BB8 /* 181 */
- .long 0x9391054A, 0x7F09D5F4, 0x7D4D3770 /* 182 */
- .long 0x27220A94, 0xFE13ABE8, 0xFA9A6EE0 /* 183 */
- .long 0x4E441529, 0xFC2757D1, 0xF534DDC0 /* 184 */
- .long 0x9C882A53, 0xF84EAFA3, 0xEA69BB81 /* 185 */
- .long 0x391054A7, 0xF09D5F47, 0xD4D37703 /* 186 */
- .long 0x7220A94F, 0xE13ABE8F, 0xA9A6EE06 /* 187 */
- .long 0xE441529F, 0xC2757D1F, 0x534DDC0D /* 188 */
- .long 0xC882A53F, 0x84EAFA3E, 0xA69BB81B /* 189 */
- .long 0x91054A7F, 0x09D5F47D, 0x4D377036 /* 190 */
- .long 0x220A94FE, 0x13ABE8FA, 0x9A6EE06D /* 191 */
- .long 0x441529FC, 0x2757D1F5, 0x34DDC0DB /* 192 */
- .long 0x882A53F8, 0x4EAFA3EA, 0x69BB81B6 /* 193 */
- .long 0x1054A7F0, 0x9D5F47D4, 0xD377036D /* 194 */
- .long 0x20A94FE1, 0x3ABE8FA9, 0xA6EE06DB /* 195 */
- .long 0x41529FC2, 0x757D1F53, 0x4DDC0DB6 /* 196 */
- .long 0x82A53F84, 0xEAFA3EA6, 0x9BB81B6C /* 197 */
- .long 0x054A7F09, 0xD5F47D4D, 0x377036D8 /* 198 */
- .long 0x0A94FE13, 0xABE8FA9A, 0x6EE06DB1 /* 199 */
- .long 0x1529FC27, 0x57D1F534, 0xDDC0DB62 /* 200 */
- .long 0x2A53F84E, 0xAFA3EA69, 0xBB81B6C5 /* 201 */
- .long 0x54A7F09D, 0x5F47D4D3, 0x77036D8A /* 202 */
- .long 0xA94FE13A, 0xBE8FA9A6, 0xEE06DB14 /* 203 */
- .long 0x529FC275, 0x7D1F534D, 0xDC0DB629 /* 204 */
- .long 0xA53F84EA, 0xFA3EA69B, 0xB81B6C52 /* 205 */
- .long 0x4A7F09D5, 0xF47D4D37, 0x7036D8A5 /* 206 */
- .long 0x94FE13AB, 0xE8FA9A6E, 0xE06DB14A /* 207 */
- .long 0x29FC2757, 0xD1F534DD, 0xC0DB6295 /* 208 */
- .long 0x53F84EAF, 0xA3EA69BB, 0x81B6C52B /* 209 */
- .long 0xA7F09D5F, 0x47D4D377, 0x036D8A56 /* 210 */
- .long 0x4FE13ABE, 0x8FA9A6EE, 0x06DB14AC /* 211 */
- .long 0x9FC2757D, 0x1F534DDC, 0x0DB62959 /* 212 */
- .long 0x3F84EAFA, 0x3EA69BB8, 0x1B6C52B3 /* 213 */
- .long 0x7F09D5F4, 0x7D4D3770, 0x36D8A566 /* 214 */
- .long 0xFE13ABE8, 0xFA9A6EE0, 0x6DB14ACC /* 215 */
- .long 0xFC2757D1, 0xF534DDC0, 0xDB629599 /* 216 */
- .long 0xF84EAFA3, 0xEA69BB81, 0xB6C52B32 /* 217 */
- .long 0xF09D5F47, 0xD4D37703, 0x6D8A5664 /* 218 */
- .long 0xE13ABE8F, 0xA9A6EE06, 0xDB14ACC9 /* 219 */
- .long 0xC2757D1F, 0x534DDC0D, 0xB6295993 /* 220 */
- .long 0x84EAFA3E, 0xA69BB81B, 0x6C52B327 /* 221 */
- .long 0x09D5F47D, 0x4D377036, 0xD8A5664F /* 222 */
- .long 0x13ABE8FA, 0x9A6EE06D, 0xB14ACC9E /* 223 */
- .long 0x2757D1F5, 0x34DDC0DB, 0x6295993C /* 224 */
- .long 0x4EAFA3EA, 0x69BB81B6, 0xC52B3278 /* 225 */
- .long 0x9D5F47D4, 0xD377036D, 0x8A5664F1 /* 226 */
- .long 0x3ABE8FA9, 0xA6EE06DB, 0x14ACC9E2 /* 227 */
- .long 0x757D1F53, 0x4DDC0DB6, 0x295993C4 /* 228 */
- .long 0xEAFA3EA6, 0x9BB81B6C, 0x52B32788 /* 229 */
- .long 0xD5F47D4D, 0x377036D8, 0xA5664F10 /* 230 */
- .long 0xABE8FA9A, 0x6EE06DB1, 0x4ACC9E21 /* 231 */
- .long 0x57D1F534, 0xDDC0DB62, 0x95993C43 /* 232 */
- .long 0xAFA3EA69, 0xBB81B6C5, 0x2B327887 /* 233 */
- .long 0x5F47D4D3, 0x77036D8A, 0x5664F10E /* 234 */
- .long 0xBE8FA9A6, 0xEE06DB14, 0xACC9E21C /* 235 */
- .long 0x7D1F534D, 0xDC0DB629, 0x5993C439 /* 236 */
- .long 0xFA3EA69B, 0xB81B6C52, 0xB3278872 /* 237 */
- .long 0xF47D4D37, 0x7036D8A5, 0x664F10E4 /* 238 */
- .long 0xE8FA9A6E, 0xE06DB14A, 0xCC9E21C8 /* 239 */
- .long 0xD1F534DD, 0xC0DB6295, 0x993C4390 /* 240 */
- .long 0xA3EA69BB, 0x81B6C52B, 0x32788720 /* 241 */
- .long 0x47D4D377, 0x036D8A56, 0x64F10E41 /* 242 */
- .long 0x8FA9A6EE, 0x06DB14AC, 0xC9E21C82 /* 243 */
- .long 0x1F534DDC, 0x0DB62959, 0x93C43904 /* 244 */
- .long 0x3EA69BB8, 0x1B6C52B3, 0x27887208 /* 245 */
- .long 0x7D4D3770, 0x36D8A566, 0x4F10E410 /* 246 */
- .long 0xFA9A6EE0, 0x6DB14ACC, 0x9E21C820 /* 247 */
- .long 0xF534DDC0, 0xDB629599, 0x3C439041 /* 248 */
- .long 0xEA69BB81, 0xB6C52B32, 0x78872083 /* 249 */
- .long 0xD4D37703, 0x6D8A5664, 0xF10E4107 /* 250 */
- .long 0xA9A6EE06, 0xDB14ACC9, 0xE21C820F /* 251 */
- .long 0x534DDC0D, 0xB6295993, 0xC439041F /* 252 */
- .long 0xA69BB81B, 0x6C52B327, 0x8872083F /* 253 */
- .long 0x4D377036, 0xD8A5664F, 0x10E4107F /* 254 */
- .long 0x9A6EE06D, 0xB14ACC9E, 0x21C820FF /* 255 */
+ .section .rodata.avx2, "a"
.align 32
- .type __svml_stan_reduction_data_internal, @object
- .size __svml_stan_reduction_data_internal, .-__svml_stan_reduction_data_internal
+LOCAL_DATA_NAME:
+
+ DATA_VEC (LOCAL_DATA_NAME, _sPI2_FMA, 0xB33BBD2E) // AVX2
+ DATA_VEC (LOCAL_DATA_NAME, _sPI3_FMA, 0xA6F72CED) // AVX2
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_0, 0x7f800000) // AVX512, AVX2
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_1, 0x00000080) // AVX2
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_2, 0x35800000) // AVX512, AVX2
+ DATA_VEC (LOCAL_DATA_NAME, _FLT_3, 0xb43bbd2e) // AVX512, AVX2
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 18/27] x86/fpu: Optimize svml_s_log10f16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (15 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 17/27] x86/fpu: Optimize svml_s_tanf8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 19/27] x86/fpu: Optimize svml_s_log10f4_core_sse4.S Noah Goldstein via Libc-alpha
` (9 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -52 Bytes (226 - 278)
Input New Time / Old Time
0F (0x00000000) -> 0.9484
0F (0x0000ffff, Denorm) -> 0.9668
.1F (0x3dcccccd) -> 0.9934
5F (0x40a00000) -> 0.9859
2315255808F (0x4f0a0000) -> 0.9926
-NaN (0xffffffff) -> 0.9808
---
.../multiarch/svml_s_log10f16_core_avx512.S | 296 ++++++++----------
1 file changed, 125 insertions(+), 171 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f16_core_avx512.S
index bea2124519..5b68fbea61 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f16_core_avx512.S
@@ -27,211 +27,165 @@
*
*/
-/* Offsets for data table __svml_slog10_data_internal_avx512
- */
-#define One 0
-#define coeff4 64
-#define coeff3 128
-#define coeff2 192
-#define coeff1 256
-#define L2 320
+#define LOCAL_DATA_NAME __svml_slog10_data_internal
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog10_data_internal. */
+#define _Coeff_4 0
+#define _Coeff_3 64
+#define _Coeff_2 128
+#define _Coeff_1 192
+#define _L2 256
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_log10f_skx)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-64, %rsp
- subq $192, %rsp
vgetmantps $11, {sae}, %zmm0, %zmm3
- vmovups __svml_slog10_data_internal_avx512(%rip), %zmm1
+ vmovups COMMON_DATA(_OneF)(%rip), %zmm1
vgetexpps {sae}, %zmm0, %zmm5
- vmovups L2+__svml_slog10_data_internal_avx512(%rip), %zmm10
vpsrld $19, %zmm3, %zmm7
vgetexpps {sae}, %zmm3, %zmm6
vsubps {rn-sae}, %zmm1, %zmm3, %zmm11
- vpermps coeff4+__svml_slog10_data_internal_avx512(%rip), %zmm7, %zmm1
- vpermps coeff3+__svml_slog10_data_internal_avx512(%rip), %zmm7, %zmm2
+ vpermps LOCAL_DATA(_Coeff_4)(%rip), %zmm7, %zmm1
+ vpermps LOCAL_DATA(_Coeff_3)(%rip), %zmm7, %zmm2
vsubps {rn-sae}, %zmm6, %zmm5, %zmm9
- vpermps coeff2+__svml_slog10_data_internal_avx512(%rip), %zmm7, %zmm4
- vpermps coeff1+__svml_slog10_data_internal_avx512(%rip), %zmm7, %zmm8
+ vpermps LOCAL_DATA(_Coeff_2)(%rip), %zmm7, %zmm4
+ vpermps LOCAL_DATA(_Coeff_1)(%rip), %zmm7, %zmm8
- /* x<=0? */
- vfpclassps $94, %zmm0, %k0
+ /* x<=0? */
+ vfpclassps $0x5e, %zmm0, %k0
vfmadd213ps {rn-sae}, %zmm2, %zmm11, %zmm1
- vmulps {rn-sae}, %zmm10, %zmm9, %zmm12
+ vmulps LOCAL_DATA(_L2)(%rip), %zmm9, %zmm12
vfmadd213ps {rn-sae}, %zmm4, %zmm11, %zmm1
- kmovw %k0, %edx
vfmadd213ps {rn-sae}, %zmm8, %zmm11, %zmm1
vfmadd213ps {rn-sae}, %zmm12, %zmm11, %zmm1
+ kmovd %k0, %edx
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
-
- /* Restore registers
- * and exit the function
- */
-L(EXIT):
+ /* Restore registers * and exit the function. */
vmovaps %zmm1, %zmm0
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
ret
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- /* Branch to process
- * special inputs
- */
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanf call. Optimize for code size
+ moreso than speed here. */
L(SPECIAL_VALUES_BRANCH):
- vmovups %zmm0, 64(%rsp)
- vmovups %zmm1, 128(%rsp)
- # LOE rbx r12 r13 r14 r15 edx zmm1
- xorl %eax, %eax
- # LOE rbx r12 r13 r14 r15 eax edx
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_def_cfa (rsp, 16)
+ /* Need to callee save registers to preserve state across tanf
+ calls. */
+ pushq %rbx
+ cfi_def_cfa (rsp, 24)
+ pushq %rbp
+ cfi_def_cfa (rsp, 32)
+ movq %rsp, %r13
+ cfi_def_cfa (r13, 32)
+
+ /* Align stack and make room for 2x zmm vectors. */
+ andq $-64, %rsp
+ addq $-128, %rsp
+
+ /* Save original input. */
+ vmovaps %zmm0, 64(%rsp)
+ /* Save all already computed inputs. */
+ vmovaps %zmm1, (%rsp)
vzeroupper
- movq %r12, 16(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- movl %edx, %r13d
- movq %r14, (%rsp)
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $16, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- vmovups 128(%rsp), %zmm1
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r12 r13 r14 r15 zmm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- vmovss 64(%rsp, %r14, 4), %xmm0
+
+ /* use rbp as index for special value that is saved across calls
+ to tanf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 64(%rsp, %rbp, 4), %xmm0
call log10f@PLT
- # LOE rbx r14 r15 r12d r13d xmm0
- vmovss %xmm0, 128(%rsp, %r14, 4)
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, (%rsp, %rbp, 4)
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx r15 r12d r13d
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+
+ /* All results have been written to 64(%rsp). */
+ vmovaps (%rsp), %zmm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa (rsp, 32)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_def_cfa (rsp, 24)
+ popq %rbx
+ cfi_def_cfa (rsp, 16)
+ popq %r13
+ ret
END(_ZGVeN16v_log10f_skx)
- .section .rodata, "a"
+ .section .rodata.evex512, "a"
.align 64
-#ifdef __svml_slog10_data_internal_avx512_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(64)) VUINT32 One[16][1];
- __declspec(align(64)) VUINT32 coeff4[16][1];
- __declspec(align(64)) VUINT32 coeff3[16][1];
- __declspec(align(64)) VUINT32 coeff2[16][1];
- __declspec(align(64)) VUINT32 coeff1[16][1];
- __declspec(align(64)) VUINT32 L2[16][1];
-} __svml_slog10_data_internal_avx512;
-#endif
-__svml_slog10_data_internal_avx512:
- /* One */
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- // c4
- .align 64
- .long 0xbdc9ae9b, 0xbda6fcf4
- .long 0xbd8bac76, 0xbd6bca30
- .long 0xbd48a99b, 0xbd2c0a9f
- .long 0xbd1480db, 0xbd00faf2
- .long 0xbe823aa9, 0xbe656348
- .long 0xbe4afbb9, 0xbe346895
- .long 0xbe20ffff, 0xbe103a0b
- .long 0xbe01a91c, 0xbde9e84e
- // c3
- .align 64
- .long 0x3e13d888, 0x3e10a87c
- .long 0x3e0b95c3, 0x3e057f0b
- .long 0x3dfde038, 0x3df080d9
- .long 0x3de34c1e, 0x3dd68333
- .long 0x3dac6e8e, 0x3dd54a51
- .long 0x3df30f40, 0x3e04235d
- .long 0x3e0b7033, 0x3e102c90
- .long 0x3e12ebad, 0x3e141ff8
- // c2
- .align 64
- .long 0xbe5e5a9b, 0xbe5e2677
- .long 0xbe5d83f5, 0xbe5c6016
- .long 0xbe5abd0b, 0xbe58a6fd
- .long 0xbe562e02, 0xbe5362f8
- .long 0xbe68e27c, 0xbe646747
- .long 0xbe619a73, 0xbe5ff05a
- .long 0xbe5f0570, 0xbe5e92d0
- .long 0xbe5e662b, 0xbe5e5c08
- // c1
- .align 64
- .long 0x3ede5bd8, 0x3ede5b45
- .long 0x3ede57d8, 0x3ede4eb1
- .long 0x3ede3d37, 0x3ede2166
- .long 0x3eddf9d9, 0x3eddc5bb
- .long 0x3ede08ed, 0x3ede32e7
- .long 0x3ede4967, 0x3ede5490
- .long 0x3ede597f, 0x3ede5b50
- .long 0x3ede5bca, 0x3ede5bd9
- /* L2 */
- .align 64
- .long 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b
- .align 64
- .type __svml_slog10_data_internal_avx512, @object
- .size __svml_slog10_data_internal_avx512, .-__svml_slog10_data_internal_avx512
+LOCAL_DATA_NAME:
+ float_block (LOCAL_DATA_NAME, _Coeff_4,
+ 0xbdc9ae9b, 0xbda6fcf4,
+ 0xbd8bac76, 0xbd6bca30,
+ 0xbd48a99b, 0xbd2c0a9f,
+ 0xbd1480db, 0xbd00faf2,
+ 0xbe823aa9, 0xbe656348,
+ 0xbe4afbb9, 0xbe346895,
+ 0xbe20ffff, 0xbe103a0b,
+ 0xbe01a91c, 0xbde9e84e)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_3,
+ 0x3e13d888, 0x3e10a87c,
+ 0x3e0b95c3, 0x3e057f0b,
+ 0x3dfde038, 0x3df080d9,
+ 0x3de34c1e, 0x3dd68333,
+ 0x3dac6e8e, 0x3dd54a51,
+ 0x3df30f40, 0x3e04235d,
+ 0x3e0b7033, 0x3e102c90,
+ 0x3e12ebad, 0x3e141ff8)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_2,
+ 0xbe5e5a9b, 0xbe5e2677,
+ 0xbe5d83f5, 0xbe5c6016,
+ 0xbe5abd0b, 0xbe58a6fd,
+ 0xbe562e02, 0xbe5362f8,
+ 0xbe68e27c, 0xbe646747,
+ 0xbe619a73, 0xbe5ff05a,
+ 0xbe5f0570, 0xbe5e92d0,
+ 0xbe5e662b, 0xbe5e5c08)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_1,
+ 0x3ede5bd8, 0x3ede5b45,
+ 0x3ede57d8, 0x3ede4eb1,
+ 0x3ede3d37, 0x3ede2166,
+ 0x3eddf9d9, 0x3eddc5bb,
+ 0x3ede08ed, 0x3ede32e7,
+ 0x3ede4967, 0x3ede5490,
+ 0x3ede597f, 0x3ede5b50,
+ 0x3ede5bca, 0x3ede5bd9)
+
+ DATA_VEC (LOCAL_DATA_NAME, _L2, 0x3e9a209b)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 19/27] x86/fpu: Optimize svml_s_log10f4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (16 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 18/27] x86/fpu: Optimize svml_s_log10f16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 20/27] x86/fpu: Optimize svml_s_log10f8_core_avx2.S Noah Goldstein via Libc-alpha
` (8 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -61 Bytes (279 - 340)
Input New Time / Old Time
0F (0x00000000) -> 0.9395
0F (0x0000ffff, Denorm) -> 0.9729
.1F (0x3dcccccd) -> 0.9458
5F (0x40a00000) -> 0.9499
2315255808F (0x4f0a0000) -> 0.9437
-NaN (0xffffffff) -> 0.8284
---
.../fpu/multiarch/svml_s_log10f4_core_sse4.S | 319 +++++++-----------
1 file changed, 123 insertions(+), 196 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f4_core_sse4.S
index 58f54d62a3..faa0e79a24 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f4_core_sse4.S
@@ -27,216 +27,143 @@
*
*/
-/* Offsets for data table __svml_slog10_data_internal
- */
-#define MinNorm 0
-#define MaxNorm 16
-#define L2H 32
-#define L2L 48
-#define iBrkValue 64
-#define iOffExpoMask 80
-#define One 96
-#define sPoly 112
-#define L2 256
+#define LOCAL_DATA_NAME __svml_slog10_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog10_data_internal. */
+#define _L2L 0
+#define _Coeff_9 16
+#define _Coeff_8 32
+#define _Coeff_7 48
+#define _Coeff_6 64
+#define _Coeff_5 80
+#define _Coeff_4 96
+#define _Coeff_3 112
+#define _Coeff_2 128
+#define _Coeff_1 144
+#define _L2H 160
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_log10f_sse4)
- subq $72, %rsp
- cfi_def_cfa_offset(80)
- movaps %xmm0, %xmm1
-
- /* reduction: compute r, n */
- movdqu iBrkValue+__svml_slog10_data_internal(%rip), %xmm2
- movaps %xmm0, %xmm4
- movdqu iOffExpoMask+__svml_slog10_data_internal(%rip), %xmm10
- psubd %xmm2, %xmm1
- pand %xmm1, %xmm10
- psrad $23, %xmm1
- paddd %xmm2, %xmm10
+ movdqu COMMON_DATA(_NotiOffExpoMask)(%rip), %xmm2
movaps %xmm0, %xmm3
- movups sPoly+__svml_slog10_data_internal(%rip), %xmm5
- movups sPoly+32+__svml_slog10_data_internal(%rip), %xmm6
- movups sPoly+64+__svml_slog10_data_internal(%rip), %xmm7
- movups sPoly+96+__svml_slog10_data_internal(%rip), %xmm9
- cvtdq2ps %xmm1, %xmm12
- cmpltps MinNorm+__svml_slog10_data_internal(%rip), %xmm4
- cmpnleps MaxNorm+__svml_slog10_data_internal(%rip), %xmm3
- subps One+__svml_slog10_data_internal(%rip), %xmm10
- mulps %xmm10, %xmm5
- movaps %xmm10, %xmm8
- mulps %xmm10, %xmm6
- mulps %xmm10, %xmm8
- addps sPoly+16+__svml_slog10_data_internal(%rip), %xmm5
- mulps %xmm10, %xmm7
- addps sPoly+48+__svml_slog10_data_internal(%rip), %xmm6
- mulps %xmm10, %xmm9
- mulps %xmm8, %xmm5
- addps sPoly+80+__svml_slog10_data_internal(%rip), %xmm7
- addps sPoly+112+__svml_slog10_data_internal(%rip), %xmm9
- addps %xmm5, %xmm6
- mulps %xmm8, %xmm6
- orps %xmm3, %xmm4
-
- /* combine and get argument value range mask */
- movmskps %xmm4, %edx
- movups L2L+__svml_slog10_data_internal(%rip), %xmm1
- addps %xmm6, %xmm7
- mulps %xmm12, %xmm1
- mulps %xmm7, %xmm8
- movups L2H+__svml_slog10_data_internal(%rip), %xmm11
- addps %xmm8, %xmm9
- mulps %xmm11, %xmm12
- mulps %xmm10, %xmm9
- addps sPoly+128+__svml_slog10_data_internal(%rip), %xmm9
- mulps %xmm9, %xmm10
- addps %xmm10, %xmm1
- addps %xmm12, %xmm1
- testl %edx, %edx
-
- /* Go to special inputs processing branch */
+ psubd %xmm2, %xmm0
+ movaps COMMON_DATA(_ILoRange)(%rip), %xmm4
+ pcmpgtd %xmm0, %xmm4
+ /* combine and get argument value range mask. */
+ movmskps %xmm4, %eax
+ movups LOCAL_DATA(_L2L)(%rip), %xmm0
+ /* reduction: compute r, n. */
+ movdqu COMMON_DATA(_IBrkValue)(%rip), %xmm4
+ movaps %xmm3, %xmm6
+ psubd %xmm4, %xmm3
+ pandn %xmm3, %xmm2
+ paddd %xmm4, %xmm2
+ subps COMMON_DATA(_OneF)(%rip), %xmm2
+ psrad $0x17, %xmm3
+ cvtdq2ps %xmm3, %xmm4
+ mulps %xmm4, %xmm0
+ movaps %xmm2, %xmm3
+ mulps %xmm2, %xmm2
+ movups LOCAL_DATA(_Coeff_9)(%rip), %xmm1
+ mulps %xmm3, %xmm1
+ addps LOCAL_DATA(_Coeff_8)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ movups LOCAL_DATA(_Coeff_7)(%rip), %xmm5
+ mulps %xmm3, %xmm5
+ addps LOCAL_DATA(_Coeff_6)(%rip), %xmm5
+ addps %xmm1, %xmm5
+ mulps %xmm2, %xmm5
+ movups LOCAL_DATA(_Coeff_5)(%rip), %xmm1
+ mulps %xmm3, %xmm1
+ addps LOCAL_DATA(_Coeff_4)(%rip), %xmm1
+ addps %xmm5, %xmm1
+ mulps %xmm1, %xmm2
+ movups LOCAL_DATA(_Coeff_3)(%rip), %xmm1
+ mulps %xmm3, %xmm1
+ addps LOCAL_DATA(_Coeff_2)(%rip), %xmm1
+ addps %xmm2, %xmm1
+ mulps %xmm3, %xmm1
+ addps LOCAL_DATA(_Coeff_1)(%rip), %xmm1
+ mulps %xmm1, %xmm3
+ addps %xmm3, %xmm0
+ movups LOCAL_DATA(_L2H)(%rip), %xmm2
+ mulps %xmm4, %xmm2
+ addps %xmm2, %xmm0
+ testl %eax, %eax
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1
-
- /* Restore registers
- * and exit the function
- */
-
-L(EXIT):
- movaps %xmm1, %xmm0
- addq $72, %rsp
- cfi_def_cfa_offset(8)
ret
- cfi_def_cfa_offset(80)
-
- /* Branch to process
- * special inputs
- */
+ /* Cold case. edx has 1s where there was a special value that
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- movups %xmm0, 32(%rsp)
- movups %xmm1, 48(%rsp)
- # LOE rbx rbp r12 r13 r14 r15 edx
-
- xorl %eax, %eax
- movq %r12, 16(%rsp)
- cfi_offset(12, -64)
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- cfi_offset(13, -72)
- movl %edx, %r13d
- movq %r14, (%rsp)
- cfi_offset(14, -80)
- # LOE rbx rbp r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx rbp r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
-
+ /* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
+ call entry will be 16-byte aligned. */
+
+ subq $0x38, %rsp
+ movups %xmm0, 24(%rsp)
+ movups %xmm6, 40(%rsp)
+
+ /* Use rbx/rbp for callee save registers as they get short
+ encoding for many instructions (as compared with r12/r13). */
+ movq %rbx, (%rsp)
+ cfi_offset (rbx, -64)
+ movq %rbp, 8(%rsp)
+ cfi_offset (rbp, -56)
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
+ movl %eax, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $4, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx rbp r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- movups 48(%rsp), %xmm1
-
- /* Go to exit */
- jmp L(EXIT)
- cfi_offset(12, -64)
- cfi_offset(13, -72)
- cfi_offset(14, -80)
- # LOE rbx rbp r12 r13 r14 r15 xmm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- movss 32(%rsp, %r14, 4), %xmm0
- call log10f@PLT
- # LOE rbx rbp r14 r15 r12d r13d xmm0
- movss %xmm0, 48(%rsp, %r14, 4)
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
+ xorl %ebp, %ebp
+ bsfl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 40(%rsp, %rbp, 4), %xmm0
+ call log10f@PLT
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx rbp r15 r12d r13d
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, 24(%rsp, %rbp, 4)
+
+ leal -1(%rbx), %eax
+ andl %eax, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+ /* All results have been written to 24(%rsp). */
+ movups 24(%rsp), %xmm0
+ movq (%rsp), %rbx
+ cfi_restore (rbx)
+ movq 8(%rsp), %rbp
+ cfi_restore (rbp)
+ addq $56, %rsp
+ cfi_def_cfa_offset (8)
+ ret
END(_ZGVbN4v_log10f_sse4)
- .section .rodata, "a"
+ .section .rodata.sse4, "a"
.align 16
-#ifdef __svml_slog10_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(16)) VUINT32 MinNorm[4][1];
- __declspec(align(16)) VUINT32 MaxNorm[4][1];
- __declspec(align(16)) VUINT32 L2H[4][1];
- __declspec(align(16)) VUINT32 L2L[4][1];
- __declspec(align(16)) VUINT32 iBrkValue[4][1];
- __declspec(align(16)) VUINT32 iOffExpoMask[4][1];
- __declspec(align(16)) VUINT32 One[4][1];
- __declspec(align(16)) VUINT32 sPoly[9][4][1];
- __declspec(align(16)) VUINT32 L2[4][1];
-} __svml_slog10_data_internal;
-#endif
-__svml_slog10_data_internal:
- /* MinNorm */
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000
- /* MaxNorm */
- .align 16
- .long 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff
- /* L2H */
- .align 16
- .long 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100
- /* L2L */
- .align 16
- .long 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600
- /* iBrkValue = SP 2/3 */
- .align 16
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask */
- .align 16
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- /* sOne = SP 1.0 */
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* spoly[9] */
- .align 16
- .long 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4 /* coeff9 */
- .long 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073 /* coeff8 */
- .long 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317 /* coeff7 */
- .long 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27 /* coeff6 */
- .long 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96 /* coeff5 */
- .long 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20 /* coeff4 */
- .long 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5 /* coeff3 */
- .long 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5 /* coeff2 */
- .long 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9 /* coeff1 */
- /* L2 */
- .align 16
- .long 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b
- .align 16
- .type __svml_slog10_data_internal, @object
- .size __svml_slog10_data_internal, .-__svml_slog10_data_internal
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _L2L, 0xb64af600)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_9, 0x3d8063b4)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_8, 0xbd890073)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_7, 0x3d775317)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_6, 0xbd91fb27)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_5, 0x3db20b96)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_4, 0xbdde6e20)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_3, 0x3e143ce5)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_2, 0xbe5e5bc5)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_1, 0x3ede5bd9)
+ DATA_VEC (LOCAL_DATA_NAME, _L2H, 0x3e9a2100)
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 20/27] x86/fpu: Optimize svml_s_log10f8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (17 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 19/27] x86/fpu: Optimize svml_s_log10f4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 21/27] x86/fpu: Optimize svml_s_log2f16_core_avx512.S Noah Goldstein via Libc-alpha
` (7 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -43 Bytes (268 - 311)
Input New Time / Old Time
0F (0x00000000) -> 0.9483
0F (0x0000ffff, Denorm) -> 0.9718
.1F (0x3dcccccd) -> 0.9253
5F (0x40a00000) -> 0.9218
2315255808F (0x4f0a0000) -> 0.9199
-NaN (0xffffffff) -> 0.8258
---
.../fpu/multiarch/svml_s_log10f8_core_avx2.S | 316 ++++++++----------
1 file changed, 132 insertions(+), 184 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f8_core_avx2.S
index 4bdc62e90e..2e9db34f23 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log10f8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log10f8_core_avx2.S
@@ -27,216 +27,164 @@
*
*/
-/* Offsets for data table __svml_slog10_data_internal
- */
-#define MinNorm 0
-#define MaxNorm 32
-#define L2H 64
-#define L2L 96
-#define iBrkValue 128
-#define iOffExpoMask 160
-#define One 192
-#define sPoly 224
-#define L2 512
+#define LOCAL_DATA_NAME __svml_slog10_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog10_data_internal. */
+#define _Coeff_9 0
+#define _Coeff_8 32
+#define _Coeff_7 64
+#define _Coeff_6 96
+#define _Coeff_5 128
+#define _Coeff_4 160
+#define _Coeff_3 192
+#define _Coeff_2 224
+#define _Coeff_1 256
+#define _L2L 288
+#define _L2H 320
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_log10f_avx2)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-32, %rsp
- subq $96, %rsp
-
- /* reduction: compute r, n */
- vmovups iBrkValue+__svml_slog10_data_internal(%rip), %ymm4
- vmovups sPoly+__svml_slog10_data_internal(%rip), %ymm15
- vmovups sPoly+64+__svml_slog10_data_internal(%rip), %ymm9
- vmovups sPoly+128+__svml_slog10_data_internal(%rip), %ymm10
- vmovups sPoly+192+__svml_slog10_data_internal(%rip), %ymm12
+ /* reduction: compute r, n. */
+ vmovups COMMON_DATA(_IBrkValue)(%rip), %ymm4
vpsubd %ymm4, %ymm0, %ymm1
- vcmplt_oqps MinNorm+__svml_slog10_data_internal(%rip), %ymm0, %ymm5
- vcmpnle_uqps MaxNorm+__svml_slog10_data_internal(%rip), %ymm0, %ymm6
- vpand iOffExpoMask+__svml_slog10_data_internal(%rip), %ymm1, %ymm3
+ vmovups COMMON_DATA(_NotiOffExpoMask)(%rip), %ymm7
+ vpandn %ymm1, %ymm7, %ymm3
vpsrad $23, %ymm1, %ymm2
- vpaddd %ymm4, %ymm3, %ymm8
+
+ vpsubd %ymm7, %ymm0, %ymm5
+ vmovups COMMON_DATA(_ILoRange)(%rip), %ymm7
+ vpcmpgtd %ymm5, %ymm7, %ymm7
+
+
+ vpaddd %ymm4, %ymm3, %ymm5
vcvtdq2ps %ymm2, %ymm1
- vsubps One+__svml_slog10_data_internal(%rip), %ymm8, %ymm13
- vmulps L2L+__svml_slog10_data_internal(%rip), %ymm1, %ymm14
- vfmadd213ps sPoly+32+__svml_slog10_data_internal(%rip), %ymm13, %ymm15
- vfmadd213ps sPoly+96+__svml_slog10_data_internal(%rip), %ymm13, %ymm9
- vmulps %ymm13, %ymm13, %ymm11
- vfmadd213ps sPoly+160+__svml_slog10_data_internal(%rip), %ymm13, %ymm10
- vfmadd213ps sPoly+224+__svml_slog10_data_internal(%rip), %ymm13, %ymm12
- vfmadd213ps %ymm9, %ymm11, %ymm15
- vfmadd213ps %ymm10, %ymm11, %ymm15
- vfmadd213ps %ymm12, %ymm11, %ymm15
- vfmadd213ps sPoly+256+__svml_slog10_data_internal(%rip), %ymm13, %ymm15
- vfmadd213ps %ymm14, %ymm13, %ymm15
- vorps %ymm6, %ymm5, %ymm7
-
- /* combine and get argument value range mask */
+ vsubps COMMON_DATA(_OneF)(%rip), %ymm5, %ymm5
+
+ vmovups LOCAL_DATA(_Coeff_9)(%rip), %ymm2
+ vfmadd213ps LOCAL_DATA(_Coeff_8)(%rip), %ymm5, %ymm2
+ vmovups LOCAL_DATA(_Coeff_7)(%rip), %ymm3
+ vfmadd213ps LOCAL_DATA(_Coeff_6)(%rip), %ymm5, %ymm3
+ vmulps %ymm5, %ymm5, %ymm4
vmovmskps %ymm7, %edx
- vfmadd132ps L2H+__svml_slog10_data_internal(%rip), %ymm15, %ymm1
- testl %edx, %edx
+ vmovups LOCAL_DATA(_Coeff_5)(%rip), %ymm7
+ vfmadd213ps LOCAL_DATA(_Coeff_4)(%rip), %ymm5, %ymm7
+ vmovups LOCAL_DATA(_Coeff_3)(%rip), %ymm6
+ vfmadd213ps LOCAL_DATA(_Coeff_2)(%rip), %ymm5, %ymm6
+ vfmadd213ps %ymm3, %ymm4, %ymm2
+ vfmadd213ps %ymm7, %ymm4, %ymm2
+ vfmadd213ps %ymm6, %ymm4, %ymm2
+ vfmadd213ps LOCAL_DATA(_Coeff_1)(%rip), %ymm5, %ymm2
+ vmulps LOCAL_DATA(_L2L)(%rip), %ymm1, %ymm7
+ vfmadd213ps %ymm7, %ymm5, %ymm2
+
- /* Go to special inputs processing branch */
+
+ vfmadd132ps LOCAL_DATA(_L2H)(%rip), %ymm2, %ymm1
+ testl %edx, %edx
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1
- /* Restore registers
- * and exit the function
- */
-L(EXIT):
+ /* Restore registers * and exit the function. */
vmovaps %ymm1, %ymm0
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
ret
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
-
- /* Branch to process
- * special inputs
- */
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a atanhf call. Optimize for code size
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- vmovups %ymm0, 32(%rsp)
- vmovups %ymm1, 64(%rsp)
- # LOE rbx r12 r13 r14 r15 edx ymm1
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
+ pushq %rbx
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
+ pushq %rbp
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
+ movq %rsp, %r13
+ cfi_def_cfa_register (r13)
- xorl %eax, %eax
- # LOE rbx r12 r13 r14 r15 eax edx
+ /* Align stack and make room for 2x ymm vectors. */
+ andq $-32, %rsp
+ addq $-64, %rsp
+
+ /* Save all already computed inputs. */
+ vmovups %ymm1, (%rsp)
+ /* Save original input (ymm0 unchanged up to this point). */
+ vmovups %ymm0, 32(%rsp)
vzeroupper
- movq %r12, 16(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
- movl %edx, %r13d
- movq %r14, (%rsp)
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a atanhf call. */
+ movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $8, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- vmovups 64(%rsp), %ymm1
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r12 r13 r14 r15 ymm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- vmovss 32(%rsp, %r14, 4), %xmm0
+
+ /* use rbp as index for special value that is saved across calls
+ to atanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ vmovss 32(%rsp, %rbp, 4), %xmm0
call log10f@PLT
- # LOE rbx r14 r15 r12d r13d xmm0
- vmovss %xmm0, 64(%rsp, %r14, 4)
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ vmovss %xmm0, (%rsp, %rbp, 4)
+
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx r15 r12d r13d
+
+ /* All results have been written to (%rsp). */
+ vmovups (%rsp), %ymm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa_register (rsp)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %rbx
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %r13
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
+ ret
END(_ZGVdN8v_log10f_avx2)
- .section .rodata, "a"
+ .section .rodata.avx2, "a"
.align 32
-#ifdef __svml_slog10_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(32)) VUINT32 MinNorm[8][1];
- __declspec(align(32)) VUINT32 MaxNorm[8][1];
- __declspec(align(32)) VUINT32 L2H[8][1];
- __declspec(align(32)) VUINT32 L2L[8][1];
- __declspec(align(32)) VUINT32 iBrkValue[8][1];
- __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
- __declspec(align(32)) VUINT32 One[8][1];
- __declspec(align(32)) VUINT32 sPoly[9][8][1];
- __declspec(align(32)) VUINT32 L2[8][1];
-} __svml_slog10_data_internal;
-#endif
-__svml_slog10_data_internal:
- /* MinNorm */
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000
- /* MaxNorm */
- .align 32
- .long 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff
- /* L2H */
- .align 32
- .long 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100, 0x3e9a2100
- /* L2L */
- .align 32
- .long 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600, 0xb64AF600
- /* iBrkValue = SP 2/3 */
- .align 32
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask */
- .align 32
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- /* sOne = SP 1.0 */
- .align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* spoly[9] */
- .align 32
- .long 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4, 0x3d8063B4 /* coeff9 */
- .long 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073, 0xbd890073 /* coeff8 */
- .long 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317, 0x3d775317 /* coeff7 */
- .long 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27, 0xbd91FB27 /* coeff6 */
- .long 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96, 0x3dB20B96 /* coeff5 */
- .long 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20, 0xbdDE6E20 /* coeff4 */
- .long 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5, 0x3e143CE5 /* coeff3 */
- .long 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5, 0xbe5E5BC5 /* coeff2 */
- .long 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9, 0x3eDE5BD9 /* coeff1 */
- /* L2 */
- .align 32
- .long 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b
- .align 32
- .type __svml_slog10_data_internal, @object
- .size __svml_slog10_data_internal, .-__svml_slog10_data_internal
+LOCAL_DATA_NAME:
+
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_9, 0x3d8063b4)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_8, 0xbd890073)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_7, 0x3d775317)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_6, 0xbd91fb27)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_5, 0x3db20b96)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_4, 0xbdde6e20)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_3, 0x3e143ce5)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_2, 0xbe5e5bc5)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_1, 0x3ede5bd9)
+ DATA_VEC (LOCAL_DATA_NAME, _L2L, 0xb64af600)
+ DATA_VEC (LOCAL_DATA_NAME, _L2H, 0x3e9a2100)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 21/27] x86/fpu: Optimize svml_s_log2f16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (18 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 20/27] x86/fpu: Optimize svml_s_log10f8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 22/27] x86/fpu: Optimize svml_s_log2f4_core_sse4.S Noah Goldstein via Libc-alpha
` (6 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -46 Bytes (216 - 262)
Input New Time / Old Time
0F (0x00000000) -> 0.8641
0F (0x0000ffff, Denorm) -> 0.9888
.1F (0x3dcccccd) -> 0.9938
5F (0x40a00000) -> 0.9892
2315255808F (0x4f0a0000) -> 0.9953
-NaN (0xffffffff) -> 0.9769
---
.../multiarch/svml_s_log2f16_core_avx512.S | 288 ++++++++----------
1 file changed, 124 insertions(+), 164 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f16_core_avx512.S
index 3ada6ed349..61bfde1526 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f16_core_avx512.S
@@ -27,39 +27,35 @@
*
*/
-/* Offsets for data table __svml_slog2_data_internal_avx512
- */
-#define One 0
-#define coeff4 64
-#define coeff3 128
-#define coeff2 192
-#define coeff1 256
+#define LOCAL_DATA_NAME __svml_slog2_data_internal
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog2_data_internal. */
+#define _Coeff_4 0
+#define _Coeff_3 64
+#define _Coeff_2 128
+#define _Coeff_1 192
+
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_log2f_skx)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-64, %rsp
- subq $192, %rsp
vgetmantps $11, {sae}, %zmm0, %zmm3
- vmovups __svml_slog2_data_internal_avx512(%rip), %zmm1
+ vmovups COMMON_DATA(_OneF)(%rip), %zmm1
vgetexpps {sae}, %zmm0, %zmm5
- /* x<=0? */
- vfpclassps $94, %zmm0, %k0
+
vsubps {rn-sae}, %zmm1, %zmm3, %zmm9
vpsrld $19, %zmm3, %zmm7
vgetexpps {sae}, %zmm3, %zmm6
- vpermps coeff4+__svml_slog2_data_internal_avx512(%rip), %zmm7, %zmm1
- vpermps coeff3+__svml_slog2_data_internal_avx512(%rip), %zmm7, %zmm2
- vpermps coeff2+__svml_slog2_data_internal_avx512(%rip), %zmm7, %zmm4
- vpermps coeff1+__svml_slog2_data_internal_avx512(%rip), %zmm7, %zmm8
+ vpermps LOCAL_DATA(_Coeff_4)(%rip), %zmm7, %zmm1
+ vpermps LOCAL_DATA(_Coeff_3)(%rip), %zmm7, %zmm2
+ vpermps LOCAL_DATA(_Coeff_2)(%rip), %zmm7, %zmm4
+ vpermps LOCAL_DATA(_Coeff_1)(%rip), %zmm7, %zmm8
vsubps {rn-sae}, %zmm6, %zmm5, %zmm10
+ /* x<=0? */
+ vfpclassps $0x5e, %zmm0, %k0
vfmadd213ps {rn-sae}, %zmm2, %zmm9, %zmm1
kmovw %k0, %edx
vfmadd213ps {rn-sae}, %zmm4, %zmm9, %zmm1
@@ -67,164 +63,128 @@ ENTRY(_ZGVeN16v_log2f_skx)
vfmadd213ps {rn-sae}, %zmm10, %zmm9, %zmm1
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
-
- /* Restore registers
- * and exit the function
- */
-
-L(EXIT):
vmovaps %zmm1, %zmm0
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
ret
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- /* Branch to process
- * special inputs
- */
+ /* Restore registers * and exit the function. */
+
+ /* Branch to process * special inputs. */
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanf call. Optimize for code size
+ moreso than speed here. */
L(SPECIAL_VALUES_BRANCH):
- vmovups %zmm0, 64(%rsp)
- vmovups %zmm1, 128(%rsp)
- # LOE rbx r12 r13 r14 r15 edx zmm1
- xorl %eax, %eax
- # LOE rbx r12 r13 r14 r15 eax edx
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_def_cfa (rsp, 16)
+ /* Need to callee save registers to preserve state across tanf
+ calls. */
+ pushq %rbx
+ cfi_def_cfa (rsp, 24)
+ pushq %rbp
+ cfi_def_cfa (rsp, 32)
+ movq %rsp, %r13
+ cfi_def_cfa (r13, 32)
+
+ /* Align stack and make room for 2x zmm vectors. */
+ andq $-64, %rsp
+ addq $-128, %rsp
+
+ /* Save origional input. */
+ vmovaps %zmm0, 64(%rsp)
+ /* Save all already computed inputs. */
+ vmovaps %zmm1, (%rsp)
vzeroupper
- movq %r12, 16(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- movl %edx, %r13d
- movq %r14, (%rsp)
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $16, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- vmovups 128(%rsp), %zmm1
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r12 r13 r14 r15 zmm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- vmovss 64(%rsp, %r14, 4), %xmm0
+
+ /* use rbp as index for special value that is saved across calls
+ to tanf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 64(%rsp, %rbp, 4), %xmm0
call log2f@PLT
- # LOE rbx r14 r15 r12d r13d xmm0
- vmovss %xmm0, 128(%rsp, %r14, 4)
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, (%rsp, %rbp, 4)
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx r15 r12d r13d
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+
+ /* All results have been written to 64(%rsp). */
+ vmovaps (%rsp), %zmm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa (rsp, 32)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_def_cfa (rsp, 24)
+ popq %rbx
+ cfi_def_cfa (rsp, 16)
+ popq %r13
+ ret
END(_ZGVeN16v_log2f_skx)
- .section .rodata, "a"
+ .section .rodata.evex512, "a"
.align 64
-#ifdef __svml_slog2_data_internal_avx512_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(64)) VUINT32 One[16][1];
- __declspec(align(64)) VUINT32 coeff4[16][1];
- __declspec(align(64)) VUINT32 coeff3[16][1];
- __declspec(align(64)) VUINT32 coeff2[16][1];
- __declspec(align(64)) VUINT32 coeff1[16][1];
-} __svml_slog2_data_internal_avx512;
-#endif
-__svml_slog2_data_internal_avx512:
- /* One */
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- // c4
- .align 64
- .long 0xbea77e4a, 0xbe8aae3d
- .long 0xbe67fe32, 0xbe43d1b6
- .long 0xbe26a589, 0xbe0ee09b
- .long 0xbdf6a8a1, 0xbdd63b49
- .long 0xbf584e51, 0xbf3e80a1
- .long 0xbf2892f0, 0xbf15d377
- .long 0xbf05b525, 0xbeef8e30
- .long 0xbed75c8f, 0xbec24184
- // c3
- .align 64
- .long 0x3ef5910c, 0x3ef045a1
- .long 0x3ee7d87e, 0x3eddbb84
- .long 0x3ed2d6df, 0x3ec7bbd2
- .long 0x3ebcc42f, 0x3eb22616
- .long 0x3e8f3399, 0x3eb1223e
- .long 0x3ec9db4a, 0x3edb7a09
- .long 0x3ee79a1a, 0x3eef77cb
- .long 0x3ef407a4, 0x3ef607b4
- // c2
- .align 64
- .long 0xbf38a934, 0xbf387de6
- .long 0xbf37f6f0, 0xbf37048b
- .long 0xbf35a88a, 0xbf33ed04
- .long 0xbf31df56, 0xbf2f8d82
- .long 0xbf416814, 0xbf3daf58
- .long 0xbf3b5c08, 0xbf39fa2a
- .long 0xbf393713, 0xbf38d7e1
- .long 0xbf38b2cd, 0xbf38aa62
- // c1
- .align 64
- .long 0x3fb8aa3b, 0x3fb8a9c0
- .long 0x3fb8a6e8, 0x3fb89f4e
- .long 0x3fb890cb, 0x3fb879b1
- .long 0x3fb858d8, 0x3fb82d90
- .long 0x3fb8655e, 0x3fb8883a
- .long 0x3fb89aea, 0x3fb8a42f
- .long 0x3fb8a848, 0x3fb8a9c9
- .long 0x3fb8aa2f, 0x3fb8aa3b
- .align 64
- .type __svml_slog2_data_internal_avx512, @object
- .size __svml_slog2_data_internal_avx512, .-__svml_slog2_data_internal_avx512
+LOCAL_DATA_NAME:
+ float_block (LOCAL_DATA_NAME, _Coeff_4,
+ 0xbea77e4a, 0xbe8aae3d,
+ 0xbe67fe32, 0xbe43d1b6,
+ 0xbe26a589, 0xbe0ee09b,
+ 0xbdf6a8a1, 0xbdd63b49,
+ 0xbf584e51, 0xbf3e80a1,
+ 0xbf2892f0, 0xbf15d377,
+ 0xbf05b525, 0xbeef8e30,
+ 0xbed75c8f, 0xbec24184)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_3,
+ 0x3ef5910c, 0x3ef045a1,
+ 0x3ee7d87e, 0x3eddbb84,
+ 0x3ed2d6df, 0x3ec7bbd2,
+ 0x3ebcc42f, 0x3eb22616,
+ 0x3e8f3399, 0x3eb1223e,
+ 0x3ec9db4a, 0x3edb7a09,
+ 0x3ee79a1a, 0x3eef77cb,
+ 0x3ef407a4, 0x3ef607b4)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_2,
+ 0xbf38a934, 0xbf387de6,
+ 0xbf37f6f0, 0xbf37048b,
+ 0xbf35a88a, 0xbf33ed04,
+ 0xbf31df56, 0xbf2f8d82,
+ 0xbf416814, 0xbf3daf58,
+ 0xbf3b5c08, 0xbf39fa2a,
+ 0xbf393713, 0xbf38d7e1,
+ 0xbf38b2cd, 0xbf38aa62)
+
+ float_block (LOCAL_DATA_NAME, _Coeff_1,
+ 0x3fb8aa3b, 0x3fb8a9c0,
+ 0x3fb8a6e8, 0x3fb89f4e,
+ 0x3fb890cb, 0x3fb879b1,
+ 0x3fb858d8, 0x3fb82d90,
+ 0x3fb8655e, 0x3fb8883a,
+ 0x3fb89aea, 0x3fb8a42f,
+ 0x3fb8a848, 0x3fb8a9c9,
+ 0x3fb8aa2f, 0x3fb8aa3b)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 22/27] x86/fpu: Optimize svml_s_log2f4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (19 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 21/27] x86/fpu: Optimize svml_s_log2f16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 23/27] x86/fpu: Optimize svml_s_log2f8_core_avx2.S Noah Goldstein via Libc-alpha
` (5 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -56 Bytes (256 - 312)
Input New Time / Old Time
0F (0x00000000) -> 0.9048
0F (0x0000ffff, Denorm) -> 0.9910
.1F (0x3dcccccd) -> 0.9399
5F (0x40a00000) -> 0.9425
2315255808F (0x4f0a0000) -> 0.9312
-NaN (0xffffffff) -> 0.9230
---
.../fpu/multiarch/svml_s_log2f4_core_sse4.S | 292 +++++++-----------
1 file changed, 115 insertions(+), 177 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f4_core_sse4.S
index bc6a778b75..b877bbb034 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f4_core_sse4.S
@@ -27,196 +27,134 @@
*
*/
-/* Offsets for data table __svml_slog2_data_internal
- */
-#define MinNorm 0
-#define MaxNorm 16
-#define iBrkValue 32
-#define iOffExpoMask 48
-#define One 64
-#define sPoly 80
+#define LOCAL_DATA_NAME __svml_slog2_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+/* Offsets for data table __svml_slog2_data_internal. */
+#define _Coeff_3 0
+#define _Coeff_2 16
+#define _Coeff_7 32
+#define _Coeff_6 48
+#define _Coeff_9 64
+#define _Coeff_8 80
+#define _Coeff_5 96
+#define _Coeff_4 112
+#define _Coeff_1 128
+
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_log2f_sse4)
- subq $72, %rsp
- cfi_def_cfa_offset(80)
- movaps %xmm0, %xmm1
-
- /* reduction: compute r, n */
- movdqu iBrkValue+__svml_slog2_data_internal(%rip), %xmm2
- movaps %xmm0, %xmm4
- movdqu iOffExpoMask+__svml_slog2_data_internal(%rip), %xmm10
- psubd %xmm2, %xmm1
- pand %xmm1, %xmm10
- movaps %xmm0, %xmm3
- paddd %xmm2, %xmm10
- psrad $23, %xmm1
- movups sPoly+__svml_slog2_data_internal(%rip), %xmm5
- movups sPoly+32+__svml_slog2_data_internal(%rip), %xmm6
- movups sPoly+64+__svml_slog2_data_internal(%rip), %xmm7
- movups sPoly+96+__svml_slog2_data_internal(%rip), %xmm9
- cmpltps MinNorm+__svml_slog2_data_internal(%rip), %xmm4
- cmpnleps MaxNorm+__svml_slog2_data_internal(%rip), %xmm3
- cvtdq2ps %xmm1, %xmm1
- subps One+__svml_slog2_data_internal(%rip), %xmm10
- mulps %xmm10, %xmm5
- movaps %xmm10, %xmm8
- mulps %xmm10, %xmm6
- mulps %xmm10, %xmm8
- addps sPoly+16+__svml_slog2_data_internal(%rip), %xmm5
- mulps %xmm10, %xmm7
- addps sPoly+48+__svml_slog2_data_internal(%rip), %xmm6
- mulps %xmm10, %xmm9
- mulps %xmm8, %xmm5
- addps sPoly+80+__svml_slog2_data_internal(%rip), %xmm7
- addps sPoly+112+__svml_slog2_data_internal(%rip), %xmm9
- addps %xmm5, %xmm6
- mulps %xmm8, %xmm6
- orps %xmm3, %xmm4
-
- /* combine and get argument value range mask */
- movmskps %xmm4, %edx
- addps %xmm6, %xmm7
- mulps %xmm7, %xmm8
- addps %xmm8, %xmm9
- mulps %xmm10, %xmm9
- addps sPoly+128+__svml_slog2_data_internal(%rip), %xmm9
- mulps %xmm9, %xmm10
- addps %xmm10, %xmm1
- testl %edx, %edx
-
- /* Go to special inputs processing branch */
+ movdqu COMMON_DATA(_NotiOffExpoMask)(%rip), %xmm1
+ movaps %xmm0, %xmm2
+ psubd %xmm1, %xmm0
+ movaps COMMON_DATA(_ILoRange)(%rip), %xmm5
+
+ pcmpgtd %xmm0, %xmm5
+ /* combine and get argument value range mask. */
+ movmskps %xmm5, %eax
+ /* reduction: compute r, n. */
+ movdqu COMMON_DATA(_IBrkValue)(%rip), %xmm0
+ movaps %xmm2, %xmm5
+ psubd %xmm0, %xmm2
+ pandn %xmm2, %xmm1
+ paddd %xmm0, %xmm1
+ psrad $0x17, %xmm2
+ cvtdq2ps %xmm2, %xmm0
+ subps COMMON_DATA(_OneF)(%rip), %xmm1
+ movups LOCAL_DATA(_Coeff_3)(%rip), %xmm2
+ mulps %xmm1, %xmm2
+ addps LOCAL_DATA(_Coeff_2)(%rip), %xmm2
+ movups LOCAL_DATA(_Coeff_7)(%rip), %xmm4
+ mulps %xmm1, %xmm4
+ addps LOCAL_DATA(_Coeff_6)(%rip), %xmm4
+ movups LOCAL_DATA(_Coeff_9)(%rip), %xmm3
+ mulps %xmm1, %xmm3
+ addps LOCAL_DATA(_Coeff_8)(%rip), %xmm3
+ movaps %xmm1, %xmm6
+ mulps %xmm1, %xmm1
+ mulps %xmm1, %xmm3
+ addps %xmm3, %xmm4
+ mulps %xmm1, %xmm4
+ movups LOCAL_DATA(_Coeff_5)(%rip), %xmm3
+ mulps %xmm6, %xmm3
+ addps LOCAL_DATA(_Coeff_4)(%rip), %xmm3
+ addps %xmm4, %xmm3
+ mulps %xmm3, %xmm1
+ addps %xmm1, %xmm2
+ mulps %xmm6, %xmm2
+ addps LOCAL_DATA(_Coeff_1)(%rip), %xmm2
+ mulps %xmm2, %xmm6
+ addps %xmm6, %xmm0
+ testl %eax, %eax
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1
-
- /* Restore registers
- * and exit the function
- */
-
-L(EXIT):
- movaps %xmm1, %xmm0
- addq $72, %rsp
- cfi_def_cfa_offset(8)
ret
- cfi_def_cfa_offset(80)
-
- /* Branch to process
- * special inputs
- */
+ /* Cold case. edx has 1s where there was a special value that
+ more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
- movups %xmm0, 32(%rsp)
- movups %xmm1, 48(%rsp)
- # LOE rbx rbp r12 r13 r14 r15 edx
-
- xorl %eax, %eax
- movq %r12, 16(%rsp)
- cfi_offset(12, -64)
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- cfi_offset(13, -72)
- movl %edx, %r13d
- movq %r14, (%rsp)
- cfi_offset(14, -80)
- # LOE rbx rbp r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx rbp r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
-
+ /* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
+ call entry will be 16-byte aligned. */
+ subq $0x38, %rsp
+ movups %xmm0, 24(%rsp)
+ movups %xmm5, 40(%rsp)
+
+ /* Use rbx/rbp for callee save registers as they get short
+ encoding for many instructions (as compared with r12/r13). */
+ movq %rbx, (%rsp)
+ cfi_offset (rbx, -64)
+ movq %rbp, 8(%rsp)
+ cfi_offset (rbp, -56)
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
+ movl %eax, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $4, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx rbp r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- movups 48(%rsp), %xmm1
-
- /* Go to exit */
- jmp L(EXIT)
- cfi_offset(12, -64)
- cfi_offset(13, -72)
- cfi_offset(14, -80)
- # LOE rbx rbp r12 r13 r14 r15 xmm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- movss 32(%rsp, %r14, 4), %xmm0
- call log2f@PLT
- # LOE rbx rbp r14 r15 r12d r13d xmm0
- movss %xmm0, 48(%rsp, %r14, 4)
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
+ xorl %ebp, %ebp
+ bsfl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 40(%rsp, %rbp, 4), %xmm0
+ call log2f@PLT
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx rbp r15 r12d r13d
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, 24(%rsp, %rbp, 4)
+
+ leal -1(%rbx), %eax
+ andl %eax, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+ /* All results have been written to 24(%rsp). */
+ movups 24(%rsp), %xmm0
+ movq (%rsp), %rbx
+ cfi_restore (rbx)
+ movq 8(%rsp), %rbp
+ cfi_restore (rbp)
+ addq $56, %rsp
+ cfi_def_cfa_offset (8)
+ ret
END(_ZGVbN4v_log2f_sse4)
- .section .rodata, "a"
+ .section .rodata.sse4, "a"
.align 16
-#ifdef __svml_slog2_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(16)) VUINT32 MinNorm[4][1];
- __declspec(align(16)) VUINT32 MaxNorm[4][1];
- __declspec(align(16)) VUINT32 iBrkValue[4][1];
- __declspec(align(16)) VUINT32 iOffExpoMask[4][1];
- __declspec(align(16)) VUINT32 One[4][1];
- __declspec(align(16)) VUINT32 sPoly[9][4][1];
-} __svml_slog2_data_internal;
-#endif
-__svml_slog2_data_internal:
- /* MinNorm */
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000
- /* MaxNorm */
- .align 16
- .long 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff
- /* iBrkValue = SP 2/3 */
- .align 16
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask */
- .align 16
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- /* sOne = SP 1.0 */
- .align 16
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* spoly[9] */
- .align 16
- .long 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012 /* coeff9 */
- .long 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14 /* coeff8 */
- .long 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B /* coeff7 */
- .long 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824 /* coeff6 */
- .long 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07 /* coeff5 */
- .long 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969 /* coeff4 */
- .long 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0 /* coeff3 */
- .long 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B /* coeff2 */
- .long 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B /* coeff1 */
- .align 16
- .type __svml_slog2_data_internal, @object
- .size __svml_slog2_data_internal, .-__svml_slog2_data_internal
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_3, 0x3ef637c0)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_2, 0xbf38aa2b)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_7, 0x3e4d660b)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_6, 0xbe727824)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_9, 0x3e554012)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_8, 0xbe638e14)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_5, 0x3e93dd07)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_4, 0xbeb8b969)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_1, 0x3fb8aa3b)
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 23/27] x86/fpu: Optimize svml_s_log2f8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (20 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 22/27] x86/fpu: Optimize svml_s_log2f4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 24/27] x86/fpu: Optimize svml_s_logf16_core_avx512.S Noah Goldstein via Libc-alpha
` (4 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
Code Size Change: -43 Bytes (251 - 294)
Input New Time / Old Time
0F (0x00000000) -> 0.8543
0F (0x0000ffff, Denorm) -> 0.9722
.1F (0x3dcccccd) -> 0.9009
5F (0x40a00000) -> 0.9432
2315255808F (0x4f0a0000) -> 0.8680
-NaN (0xffffffff) -> 0.8154
---
.../fpu/multiarch/svml_s_log2f8_core_avx2.S | 290 ++++++++----------
1 file changed, 123 insertions(+), 167 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f8_core_avx2.S
index 2245d40f84..2c56159323 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_log2f8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_log2f8_core_avx2.S
@@ -27,199 +27,155 @@
*
*/
-/* Offsets for data table __svml_slog2_data_internal
- */
-#define MinNorm 0
-#define MaxNorm 32
-#define iBrkValue 64
-#define iOffExpoMask 96
-#define One 128
-#define sPoly 160
+#define LOCAL_DATA_NAME __svml_slog2_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+/* Offsets for data table __svml_slog2_data_internal. */
+#define _Coeff_9 0
+#define _Coeff_8 32
+#define _Coeff_7 64
+#define _Coeff_6 96
+#define _Coeff_5 128
+#define _Coeff_4 160
+#define _Coeff_3 192
+#define _Coeff_2 224
+#define _Coeff_1 256
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_log2f_avx2)
- pushq %rbp
- cfi_def_cfa_offset(16)
- movq %rsp, %rbp
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
- andq $-32, %rsp
- subq $96, %rsp
+ /* reduction: compute r, n. */
+ vmovups COMMON_DATA(_IBrkValue)(%rip), %ymm4
+
- /* reduction: compute r, n */
- vmovups iBrkValue+__svml_slog2_data_internal(%rip), %ymm4
- vmovups sPoly+64+__svml_slog2_data_internal(%rip), %ymm9
- vmovups sPoly+128+__svml_slog2_data_internal(%rip), %ymm10
- vmovups sPoly+192+__svml_slog2_data_internal(%rip), %ymm12
vpsubd %ymm4, %ymm0, %ymm1
- vcmplt_oqps MinNorm+__svml_slog2_data_internal(%rip), %ymm0, %ymm5
- vcmpnle_uqps MaxNorm+__svml_slog2_data_internal(%rip), %ymm0, %ymm6
- vpand iOffExpoMask+__svml_slog2_data_internal(%rip), %ymm1, %ymm3
+ vmovups COMMON_DATA(_NotiOffExpoMask)(%rip), %ymm2
+ vpsubd %ymm2, %ymm0, %ymm5
+ vmovups COMMON_DATA(_ILoRange)(%rip), %ymm6
+ vpcmpgtd %ymm5, %ymm6, %ymm6
+ vpandn %ymm1, %ymm2, %ymm3
vpsrad $23, %ymm1, %ymm2
- vmovups sPoly+__svml_slog2_data_internal(%rip), %ymm1
- vpaddd %ymm4, %ymm3, %ymm8
- vcvtdq2ps %ymm2, %ymm14
- vsubps One+__svml_slog2_data_internal(%rip), %ymm8, %ymm13
- vfmadd213ps sPoly+32+__svml_slog2_data_internal(%rip), %ymm13, %ymm1
- vfmadd213ps sPoly+96+__svml_slog2_data_internal(%rip), %ymm13, %ymm9
- vmulps %ymm13, %ymm13, %ymm11
- vfmadd213ps sPoly+160+__svml_slog2_data_internal(%rip), %ymm13, %ymm10
- vfmadd213ps sPoly+224+__svml_slog2_data_internal(%rip), %ymm13, %ymm12
- vfmadd213ps %ymm9, %ymm11, %ymm1
- vfmadd213ps %ymm10, %ymm11, %ymm1
- vfmadd213ps %ymm12, %ymm11, %ymm1
- vfmadd213ps sPoly+256+__svml_slog2_data_internal(%rip), %ymm13, %ymm1
- vorps %ymm6, %ymm5, %ymm7
-
- /* combine and get argument value range mask */
- vmovmskps %ymm7, %edx
- vfmadd213ps %ymm14, %ymm13, %ymm1
+ vmovups LOCAL_DATA(_Coeff_9)(%rip), %ymm1
+ vpaddd %ymm4, %ymm3, %ymm3
+
+ vsubps COMMON_DATA(_OneF)(%rip), %ymm3, %ymm3
+ vfmadd213ps LOCAL_DATA(_Coeff_8)(%rip), %ymm3, %ymm1
+ vmovups LOCAL_DATA(_Coeff_7)(%rip), %ymm4
+ vfmadd213ps LOCAL_DATA(_Coeff_6)(%rip), %ymm3, %ymm4
+ vmulps %ymm3, %ymm3, %ymm5
+ vmovups LOCAL_DATA(_Coeff_5)(%rip), %ymm7
+ vfmadd213ps LOCAL_DATA(_Coeff_4)(%rip), %ymm3, %ymm7
+ vmovmskps %ymm6, %edx
+
+ vmovups LOCAL_DATA(_Coeff_3)(%rip), %ymm6
+ vfmadd213ps LOCAL_DATA(_Coeff_2)(%rip), %ymm3, %ymm6
+ vfmadd213ps %ymm4, %ymm5, %ymm1
+ vfmadd213ps %ymm7, %ymm5, %ymm1
+ vfmadd213ps %ymm6, %ymm5, %ymm1
+ vfmadd213ps LOCAL_DATA(_Coeff_1)(%rip), %ymm3, %ymm1
+ vcvtdq2ps %ymm2, %ymm2
+
+ /* combine and get argument value range mask. */
+
+ vfmadd213ps %ymm2, %ymm3, %ymm1
testl %edx, %edx
- /* Go to special inputs processing branch */
+ /* Go to special inputs processing branch. */
jne L(SPECIAL_VALUES_BRANCH)
- # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1
- /* Restore registers
- * and exit the function
- */
-L(EXIT):
vmovaps %ymm1, %ymm0
- movq %rbp, %rsp
- popq %rbp
- cfi_def_cfa(7, 8)
- cfi_restore(6)
ret
- cfi_def_cfa(6, 16)
- cfi_offset(6, -16)
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a atanhf call. Optimize for code size
+ more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
- /* Branch to process
- * special inputs
- */
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
+ pushq %rbx
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
+ pushq %rbp
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
+ movq %rsp, %r13
+ cfi_def_cfa_register (r13)
-L(SPECIAL_VALUES_BRANCH):
- vmovups %ymm0, 32(%rsp)
- vmovups %ymm1, 64(%rsp)
- # LOE rbx r12 r13 r14 r15 edx ymm1
+ /* Align stack and make room for 2x ymm vectors. */
+ andq $-32, %rsp
+ addq $-64, %rsp
- xorl %eax, %eax
- # LOE rbx r12 r13 r14 r15 eax edx
+ /* Save all already computed inputs. */
+ vmovups %ymm1, (%rsp)
+ /* Save original input (ymm0 unchanged up to this point). */
+ vmovups %ymm0, 32(%rsp)
vzeroupper
- movq %r12, 16(%rsp)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
- movl %eax, %r12d
- movq %r13, 8(%rsp)
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
- movl %edx, %r13d
- movq %r14, (%rsp)
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r15 r12d r13d
-
- /* Range mask
- * bits check
- */
-
-L(RANGEMASK_CHECK):
- btl %r12d, %r13d
-
- /* Call scalar math function */
- jc L(SCALAR_MATH_CALL)
- # LOE rbx r15 r12d r13d
-
- /* Special inputs
- * processing loop
- */
+ /* edx has 1s where there was a special value that needs to be
+ handled by a atanhf call. */
+ movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
- incl %r12d
- cmpl $8, %r12d
-
- /* Check bits in range mask */
- jl L(RANGEMASK_CHECK)
- # LOE rbx r15 r12d r13d
-
- movq 16(%rsp), %r12
- cfi_restore(12)
- movq 8(%rsp), %r13
- cfi_restore(13)
- movq (%rsp), %r14
- cfi_restore(14)
- vmovups 64(%rsp), %ymm1
-
- /* Go to exit */
- jmp L(EXIT)
- /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
- .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
- .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
- /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
- .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
- # LOE rbx r12 r13 r14 r15 ymm1
-
- /* Scalar math fucntion call
- * to process special input
- */
-
-L(SCALAR_MATH_CALL):
- movl %r12d, %r14d
- vmovss 32(%rsp, %r14, 4), %xmm0
+
+ /* use rbp as index for special value that is saved across calls
+ to atanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ vmovss 32(%rsp, %rbp, 4), %xmm0
call log2f@PLT
- # LOE rbx r14 r15 r12d r13d xmm0
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ vmovss %xmm0, (%rsp, %rbp, 4)
+
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
- vmovss %xmm0, 64(%rsp, %r14, 4)
- /* Process special inputs in loop */
- jmp L(SPECIAL_VALUES_LOOP)
- # LOE rbx r15 r12d r13d
+ /* All results have been written to (%rsp). */
+ vmovups (%rsp), %ymm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa_register (rsp)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %rbx
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %r13
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
+ ret
END(_ZGVdN8v_log2f_avx2)
- .section .rodata, "a"
+ .section .rodata.avx2, "a"
.align 32
-#ifdef __svml_slog2_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
- __declspec(align(32)) VUINT32 MinNorm[8][1];
- __declspec(align(32)) VUINT32 MaxNorm[8][1];
- __declspec(align(32)) VUINT32 iBrkValue[8][1];
- __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
- __declspec(align(32)) VUINT32 One[8][1];
- __declspec(align(32)) VUINT32 sPoly[9][8][1];
-} __svml_slog2_data_internal;
-#endif
-__svml_slog2_data_internal:
- /* MinNorm */
- .long 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000, 0x00800000
- /* MaxNorm */
- .align 32
- .long 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff
- /* iBrkValue = SP 2/3 */
- .align 32
- .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
- /* iOffExpoMask = SP significand mask */
- .align 32
- .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
- /* sOne = SP 1.0 */
- .align 32
- .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
- /* spoly[9] */
- .align 32
- .long 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012, 0x3e554012 /* coeff9 */
- .long 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14, 0xbe638E14 /* coeff8 */
- .long 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B, 0x3e4D660B /* coeff7 */
- .long 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824, 0xbe727824 /* coeff6 */
- .long 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07, 0x3e93DD07 /* coeff5 */
- .long 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969, 0xbeB8B969 /* coeff4 */
- .long 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0, 0x3eF637C0 /* coeff3 */
- .long 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B, 0xbf38AA2B /* coeff2 */
- .long 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B /* coeff1 */
- .align 32
- .type __svml_slog2_data_internal, @object
- .size __svml_slog2_data_internal, .-__svml_slog2_data_internal
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_9, 0x3e554012)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_8, 0xbe638e14)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_7, 0x3e4d660b)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_6, 0xbe727824)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_5, 0x3e93dd07)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_4, 0xbeb8b969)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_3, 0x3ef637c0)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_2, 0xbf38aa2b)
+ DATA_VEC (LOCAL_DATA_NAME, _Coeff_1, 0x3fb8aa3b)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 24/27] x86/fpu: Optimize svml_s_logf16_core_avx512.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (21 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 23/27] x86/fpu: Optimize svml_s_log2f8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 25/27] x86/fpu: Optimize svml_s_logf4_core_sse4.S Noah Goldstein via Libc-alpha
` (3 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
As well instead of using the shared `__svml_slogf_data` just define
the data locally. This is because; 1) Its not really ideal for
the sse4/avx2 to reuse the avx512 tables as it pollute the cache
which unnecessarily large blocks. 2) Really only one of the
versions is ever expected to be used by a given process so there
isn't any constructive caching between them. And 3) there is not
enough data shared to make up for the first two reasons.
Lastly, the avx512-skl implementation no longer uses `vpternlogd` (the
only AVX512-DQ instruction) so make the avx512-knl implementation
just a alias to the SKL one.
Code Size Change: -1285 Bytes (267 - 1552) (With removing KNL impl)
Input New Time / Old Time
0F (0x00000000) -> 0.7324
0F (0x0000ffff, Denorm) -> 0.9708
.1F (0x3dcccccd) -> 0.9535
5F (0x40a00000) -> 0.9699
2315255808F (0x4f0a0000) -> 0.9909
-NaN (0xffffffff) -> 0.6798
---
.../fpu/multiarch/svml_s_logf16_core_avx512.S | 553 ++++++------------
1 file changed, 173 insertions(+), 380 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_logf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_logf16_core_avx512.S
index eb830a6579..ebc959aa74 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_logf16_core_avx512.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_logf16_core_avx512.S
@@ -16,388 +16,181 @@
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
+#define LOCAL_DATA_NAME __svml_slog_data_internal
+#define LOCAL_DATA_NAME_UNALIGNED __svml_slog_data_internal_unaligned
+#include "svml_s_common_evex512_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog_data_internal_unaligned.
+ 4 bytes each. */
+#define _iLoRange 0
+
+/* Offsets for data table __svml_slog_data_internal
+ 64 bytes each. */
+#define _iBrkValue 0
+#define _sPoly_7 64
+#define _sPoly_6 128
+#define _sPoly_5 192
+#define _sPoly_4 256
+#define _sPoly_3 320
+#define _sPoly_2 384
+#define _sLn2 448
+
#include <sysdep.h>
-#include "svml_s_logf_data.h"
-#include "svml_s_wrapper_impl.h"
.section .text.evex512, "ax", @progbits
-ENTRY (_ZGVeN16v_logf_knl)
-/*
- ALGORITHM DESCRIPTION:
-
- log(x) = exponent_x*log(2) + log(mantissa_x), if mantissa_x<4/3
- log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x), if mantissa_x>4/3
-
- R = mantissa_x - 1, if mantissa_x<4/3
- R = 0.5*mantissa_x - 1, if mantissa_x>4/3
- |R|< 1/3
-
- log(1+R) is approximated as a polynomial: degree 9 for 1-ulp,
- degree 7 for 4-ulp, degree 3 for half-precision. */
-
- pushq %rbp
- cfi_adjust_cfa_offset (8)
- cfi_rel_offset (%rbp, 0)
- movq %rsp, %rbp
- cfi_def_cfa_register (%rbp)
- andq $-64, %rsp
- subq $1280, %rsp
- movq __svml_slog_data@GOTPCREL(%rip), %rax
- movl $-1, %ecx
-
-/* reduction: compute r,n */
- vpsubd _iBrkValue(%rax), %zmm0, %zmm2
- vmovups _sPoly_7(%rax), %zmm7
- vpandd _iOffExpoMask(%rax), %zmm2, %zmm3
-
-/* exponent_x (mantissa_x<4/3) or exponent_x+1 (mantissa_x>4/3) */
- vpsrad $23, %zmm2, %zmm4
-
-/* check for working range,
- set special argument mask (denormals/zero/Inf/NaN)
- */
- vpaddd _iHiDelta(%rax), %zmm0, %zmm1
-
-/* mantissa_x (mantissa_x<4/3), or 0.5*mantissa_x (mantissa_x>4/3) */
- vpaddd _iBrkValue(%rax), %zmm3, %zmm6
- vpcmpd $1, _iLoRange(%rax), %zmm1, %k1
- vcvtdq2ps {rn-sae}, %zmm4, %zmm1
-
-/* reduced argument R */
- vsubps _sOne(%rax), %zmm6, %zmm8
- vpbroadcastd %ecx, %zmm5{%k1}{z}
-
-/* polynomial evaluation starts here */
- vfmadd213ps _sPoly_6(%rax), %zmm8, %zmm7
- vptestmd %zmm5, %zmm5, %k0
- kmovw %k0, %ecx
- vfmadd213ps _sPoly_5(%rax), %zmm8, %zmm7
- vfmadd213ps _sPoly_4(%rax), %zmm8, %zmm7
- vfmadd213ps _sPoly_3(%rax), %zmm8, %zmm7
- vfmadd213ps _sPoly_2(%rax), %zmm8, %zmm7
- vfmadd213ps _sPoly_1(%rax), %zmm8, %zmm7
- vmulps %zmm8, %zmm7, %zmm9
-
-/* polynomial evaluation end */
- vfmadd213ps %zmm8, %zmm8, %zmm9
-
-/*
- final reconstruction:
- add exponent_value*log2 to polynomial result
- */
- vfmadd132ps _sLn2(%rax), %zmm9, %zmm1
- testl %ecx, %ecx
- jne .LBL_1_3
-
-.LBL_1_2:
- cfi_remember_state
- vmovaps %zmm1, %zmm0
- movq %rbp, %rsp
- cfi_def_cfa_register (%rsp)
- popq %rbp
- cfi_adjust_cfa_offset (-8)
- cfi_restore (%rbp)
- ret
-
-.LBL_1_3:
- cfi_restore_state
- vmovups %zmm0, 1152(%rsp)
- vmovups %zmm1, 1216(%rsp)
- je .LBL_1_2
-
- xorb %dl, %dl
- kmovw %k4, 1048(%rsp)
- xorl %eax, %eax
- kmovw %k5, 1040(%rsp)
- kmovw %k6, 1032(%rsp)
- kmovw %k7, 1024(%rsp)
- vmovups %zmm16, 960(%rsp)
- vmovups %zmm17, 896(%rsp)
- vmovups %zmm18, 832(%rsp)
- vmovups %zmm19, 768(%rsp)
- vmovups %zmm20, 704(%rsp)
- vmovups %zmm21, 640(%rsp)
- vmovups %zmm22, 576(%rsp)
- vmovups %zmm23, 512(%rsp)
- vmovups %zmm24, 448(%rsp)
- vmovups %zmm25, 384(%rsp)
- vmovups %zmm26, 320(%rsp)
- vmovups %zmm27, 256(%rsp)
- vmovups %zmm28, 192(%rsp)
- vmovups %zmm29, 128(%rsp)
- vmovups %zmm30, 64(%rsp)
- vmovups %zmm31, (%rsp)
- movq %rsi, 1064(%rsp)
- movq %rdi, 1056(%rsp)
- movq %r12, 1096(%rsp)
- cfi_offset_rel_rsp (12, 1096)
- movb %dl, %r12b
- movq %r13, 1088(%rsp)
- cfi_offset_rel_rsp (13, 1088)
- movl %ecx, %r13d
- movq %r14, 1080(%rsp)
- cfi_offset_rel_rsp (14, 1080)
- movl %eax, %r14d
- movq %r15, 1072(%rsp)
- cfi_offset_rel_rsp (15, 1072)
- cfi_remember_state
-
-.LBL_1_6:
- btl %r14d, %r13d
- jc .LBL_1_12
-
-.LBL_1_7:
- lea 1(%r14), %esi
- btl %esi, %r13d
- jc .LBL_1_10
-
-.LBL_1_8:
- addb $1, %r12b
- addl $2, %r14d
- cmpb $16, %r12b
- jb .LBL_1_6
-
- kmovw 1048(%rsp), %k4
- movq 1064(%rsp), %rsi
- kmovw 1040(%rsp), %k5
- movq 1056(%rsp), %rdi
- kmovw 1032(%rsp), %k6
- movq 1096(%rsp), %r12
- cfi_restore (%r12)
- movq 1088(%rsp), %r13
- cfi_restore (%r13)
- kmovw 1024(%rsp), %k7
- vmovups 960(%rsp), %zmm16
- vmovups 896(%rsp), %zmm17
- vmovups 832(%rsp), %zmm18
- vmovups 768(%rsp), %zmm19
- vmovups 704(%rsp), %zmm20
- vmovups 640(%rsp), %zmm21
- vmovups 576(%rsp), %zmm22
- vmovups 512(%rsp), %zmm23
- vmovups 448(%rsp), %zmm24
- vmovups 384(%rsp), %zmm25
- vmovups 320(%rsp), %zmm26
- vmovups 256(%rsp), %zmm27
- vmovups 192(%rsp), %zmm28
- vmovups 128(%rsp), %zmm29
- vmovups 64(%rsp), %zmm30
- vmovups (%rsp), %zmm31
- movq 1080(%rsp), %r14
- cfi_restore (%r14)
- movq 1072(%rsp), %r15
- cfi_restore (%r15)
- vmovups 1216(%rsp), %zmm1
- jmp .LBL_1_2
-
-.LBL_1_10:
- cfi_restore_state
- movzbl %r12b, %r15d
- vmovss 1156(%rsp,%r15,8), %xmm0
- call JUMPTARGET(logf)
- vmovss %xmm0, 1220(%rsp,%r15,8)
- jmp .LBL_1_8
-
-.LBL_1_12:
- movzbl %r12b, %r15d
- vmovss 1152(%rsp,%r15,8), %xmm0
- call JUMPTARGET(logf)
- vmovss %xmm0, 1216(%rsp,%r15,8)
- jmp .LBL_1_7
-END (_ZGVeN16v_logf_knl)
-
ENTRY (_ZGVeN16v_logf_skx)
-/*
- ALGORITHM DESCRIPTION:
-
- log(x) = exponent_x*log(2) + log(mantissa_x), if mantissa_x<4/3
- log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x), if mantissa_x>4/3
-
- R = mantissa_x - 1, if mantissa_x<4/3
- R = 0.5*mantissa_x - 1, if mantissa_x>4/3
- |R|< 1/3
-
- log(1+R) is approximated as a polynomial: degree 9 for 1-ulp,
- degree 7 for 4-ulp, degree 3 for half-precision. */
-
- pushq %rbp
- cfi_adjust_cfa_offset (8)
- cfi_rel_offset (%rbp, 0)
- movq %rsp, %rbp
- cfi_def_cfa_register (%rbp)
- andq $-64, %rsp
- subq $1280, %rsp
- movq __svml_slog_data@GOTPCREL(%rip), %rax
- vpternlogd $0xff, %zmm6, %zmm6, %zmm6
- vmovups _iBrkValue(%rax), %zmm4
- vmovups _sPoly_7(%rax), %zmm8
-
-/*
- check for working range,
- set special argument mask (denormals/zero/Inf/NaN)
- */
- vpaddd _iHiDelta(%rax), %zmm0, %zmm1
-
-/* reduction: compute r,n */
- vpsubd %zmm4, %zmm0, %zmm2
- vpcmpd $5, _iLoRange(%rax), %zmm1, %k1
-
-/* exponent_x (mantissa_x<4/3) or exponent_x+1 (mantissa_x>4/3) */
- vpsrad $23, %zmm2, %zmm5
- vpandd _iOffExpoMask(%rax), %zmm2, %zmm3
-
-/* mantissa_x (mantissa_x<4/3), or 0.5*mantissa_x (mantissa_x>4/3) */
- vpaddd %zmm4, %zmm3, %zmm7
-
-/* reduced argument R */
- vsubps _sOne(%rax), %zmm7, %zmm9
-
-/* polynomial evaluation starts here */
- vfmadd213ps _sPoly_6(%rax), %zmm9, %zmm8
- vfmadd213ps _sPoly_5(%rax), %zmm9, %zmm8
- vfmadd213ps _sPoly_4(%rax), %zmm9, %zmm8
- vfmadd213ps _sPoly_3(%rax), %zmm9, %zmm8
- vfmadd213ps _sPoly_2(%rax), %zmm9, %zmm8
- vfmadd213ps _sPoly_1(%rax), %zmm9, %zmm8
- vmulps %zmm9, %zmm8, %zmm10
-
-/* polynomial evaluation end */
- vfmadd213ps %zmm9, %zmm9, %zmm10
- vpandnd %zmm1, %zmm1, %zmm6{%k1}
- vptestmd %zmm6, %zmm6, %k0
- vcvtdq2ps {rn-sae}, %zmm5, %zmm1
- kmovw %k0, %ecx
-
-/*
- final reconstruction:
- add exponent_value*log2 to polynomial result
- */
- vfmadd132ps _sLn2(%rax), %zmm10, %zmm1
- testl %ecx, %ecx
- jne .LBL_2_3
-
-.LBL_2_2:
- cfi_remember_state
- vmovaps %zmm1, %zmm0
- movq %rbp, %rsp
- cfi_def_cfa_register (%rsp)
- popq %rbp
- cfi_adjust_cfa_offset (-8)
- cfi_restore (%rbp)
- ret
-
-.LBL_2_3:
- cfi_restore_state
- vmovups %zmm0, 1152(%rsp)
- vmovups %zmm1, 1216(%rsp)
- je .LBL_2_2
-
- xorb %dl, %dl
- xorl %eax, %eax
- kmovw %k4, 1048(%rsp)
- kmovw %k5, 1040(%rsp)
- kmovw %k6, 1032(%rsp)
- kmovw %k7, 1024(%rsp)
- vmovups %zmm16, 960(%rsp)
- vmovups %zmm17, 896(%rsp)
- vmovups %zmm18, 832(%rsp)
- vmovups %zmm19, 768(%rsp)
- vmovups %zmm20, 704(%rsp)
- vmovups %zmm21, 640(%rsp)
- vmovups %zmm22, 576(%rsp)
- vmovups %zmm23, 512(%rsp)
- vmovups %zmm24, 448(%rsp)
- vmovups %zmm25, 384(%rsp)
- vmovups %zmm26, 320(%rsp)
- vmovups %zmm27, 256(%rsp)
- vmovups %zmm28, 192(%rsp)
- vmovups %zmm29, 128(%rsp)
- vmovups %zmm30, 64(%rsp)
- vmovups %zmm31, (%rsp)
- movq %rsi, 1064(%rsp)
- movq %rdi, 1056(%rsp)
- movq %r12, 1096(%rsp)
- cfi_offset_rel_rsp (12, 1096)
- movb %dl, %r12b
- movq %r13, 1088(%rsp)
- cfi_offset_rel_rsp (13, 1088)
- movl %ecx, %r13d
- movq %r14, 1080(%rsp)
- cfi_offset_rel_rsp (14, 1080)
- movl %eax, %r14d
- movq %r15, 1072(%rsp)
- cfi_offset_rel_rsp (15, 1072)
- cfi_remember_state
-
-.LBL_2_6:
- btl %r14d, %r13d
- jc .LBL_2_12
-
-.LBL_2_7:
- lea 1(%r14), %esi
- btl %esi, %r13d
- jc .LBL_2_10
-
-.LBL_2_8:
- incb %r12b
- addl $2, %r14d
- cmpb $16, %r12b
- jb .LBL_2_6
-
- kmovw 1048(%rsp), %k4
- kmovw 1040(%rsp), %k5
- kmovw 1032(%rsp), %k6
- kmovw 1024(%rsp), %k7
- vmovups 960(%rsp), %zmm16
- vmovups 896(%rsp), %zmm17
- vmovups 832(%rsp), %zmm18
- vmovups 768(%rsp), %zmm19
- vmovups 704(%rsp), %zmm20
- vmovups 640(%rsp), %zmm21
- vmovups 576(%rsp), %zmm22
- vmovups 512(%rsp), %zmm23
- vmovups 448(%rsp), %zmm24
- vmovups 384(%rsp), %zmm25
- vmovups 320(%rsp), %zmm26
- vmovups 256(%rsp), %zmm27
- vmovups 192(%rsp), %zmm28
- vmovups 128(%rsp), %zmm29
- vmovups 64(%rsp), %zmm30
- vmovups (%rsp), %zmm31
- vmovups 1216(%rsp), %zmm1
- movq 1064(%rsp), %rsi
- movq 1056(%rsp), %rdi
- movq 1096(%rsp), %r12
- cfi_restore (%r12)
- movq 1088(%rsp), %r13
- cfi_restore (%r13)
- movq 1080(%rsp), %r14
- cfi_restore (%r14)
- movq 1072(%rsp), %r15
- cfi_restore (%r15)
- jmp .LBL_2_2
-
-.LBL_2_10:
- cfi_restore_state
- movzbl %r12b, %r15d
- vmovss 1156(%rsp,%r15,8), %xmm0
- vzeroupper
- vmovss 1156(%rsp,%r15,8), %xmm0
-
- call JUMPTARGET(logf)
-
- vmovss %xmm0, 1220(%rsp,%r15,8)
- jmp .LBL_2_8
-
-.LBL_2_12:
- movzbl %r12b, %r15d
- vmovss 1152(%rsp,%r15,8), %xmm0
- vzeroupper
- vmovss 1152(%rsp,%r15,8), %xmm0
-
- call JUMPTARGET(logf)
-
- vmovss %xmm0, 1216(%rsp,%r15,8)
- jmp .LBL_2_7
-
+ /* ALGORITHM DESCRIPTION:
+ if mantissa_x<4/3
+ log(x) = exponent_x*log(2) + log(mantissa_x)
+ if mantissa_x>4/3
+ log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x)
+
+ R = mantissa_x - 1, if mantissa_x<4/3
+ R = 0.5*mantissa_x - 1, if mantissa_x>4/3
+ |R|< 1/3
+
+ log(1+R) is approximated as a polynomial: degree 9 for
+ 1-ulp, degree 7 for 4-ulp, degree 3 for half-precision. */
+ vmovups LOCAL_DATA(_iBrkValue)(%rip), %zmm4
+ vmovups LOCAL_DATA(_sPoly_7)(%rip), %zmm8
+
+ /* check for working range, set special argument mask
+ (denormals/zero/Inf/NaN). */
+ vmovups COMMON_DATA(_NotiOffExpoMask)(%rip), %zmm3
+ vpsubd %zmm3, %zmm0, %zmm1
+
+ /* reduction: compute r,n. */
+ vpsubd %zmm4, %zmm0, %zmm2
+ vpcmpd $2, LOCAL_DATA_UNALIGNED(_iLoRange)(%rip){1to16}, %zmm1, %k0
+
+ /* exponent_x (mantissa_x<4/3),
+ or exponent_x+1 (mantissa_x>4/3). */
+ vpsrad $23, %zmm2, %zmm5
+ vpandnd %zmm2, %zmm3, %zmm3
+
+ /* mantissa_x (mantissa_x<4/3),
+ or 0.5 mantissa_x (mantissa_x>4/3). */
+ vpaddd %zmm4, %zmm3, %zmm7
+
+ /* reduced argument R. */
+ vsubps COMMON_DATA(_OneF)(%rip), %zmm7, %zmm9
+
+ /* polynomial evaluation starts here. */
+ vfmadd213ps LOCAL_DATA(_sPoly_6)(%rip), %zmm9, %zmm8
+ vfmadd213ps LOCAL_DATA(_sPoly_5)(%rip), %zmm9, %zmm8
+ vfmadd213ps LOCAL_DATA(_sPoly_4)(%rip), %zmm9, %zmm8
+ vfmadd213ps LOCAL_DATA(_sPoly_3)(%rip), %zmm9, %zmm8
+ vfmadd213ps LOCAL_DATA(_sPoly_2)(%rip), %zmm9, %zmm8
+ vfmadd213ps COMMON_DATA(_Neg5F)(%rip), %zmm9, %zmm8
+ vmulps %zmm9, %zmm8, %zmm10
+
+ /* polynomial evaluation end. */
+ vfmadd213ps %zmm9, %zmm9, %zmm10
+ vcvtdq2ps {rn-sae}, %zmm5, %zmm1
+ kmovw %k0, %ecx
+ /* final reconstruction: add exponent_value
+ log2 to polynomial result. */
+ vfmadd132ps LOCAL_DATA(_sLn2)(%rip), %zmm10, %zmm1
+ /* Branch to process special inputs. */
+ testl %ecx, %ecx
+ jne L(SPECIAL_VALUES_BRANCH)
+
+ vmovaps %zmm1, %zmm0
+ ret
+
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a tanf call. Optimize for code size
+ moreso than speed here. */
+L(SPECIAL_VALUES_BRANCH):
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_def_cfa (rsp, 16)
+ /* Need to callee save registers to preserve state across tanf
+ calls. */
+ pushq %rbx
+ cfi_def_cfa (rsp, 24)
+ pushq %rbp
+ cfi_def_cfa (rsp, 32)
+ movq %rsp, %r13
+ cfi_def_cfa (r13, 32)
+
+ /* Align stack and make room for 2x zmm vectors. */
+ andq $-64, %rsp
+ addq $-128, %rsp
+
+ /* Save origional input. */
+ vmovaps %zmm0, 64(%rsp)
+ /* Save all already computed inputs. */
+ vmovaps %zmm1, (%rsp)
+
+ vzeroupper
+
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanf call. */
+ movl %ecx, %ebx
+L(SPECIAL_VALUES_LOOP):
+
+ /* use rbp as index for special value that is saved across calls
+ to tanf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 56] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 64(%rsp, %rbp, 4), %xmm0
+ call logf@PLT
+
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, (%rsp, %rbp, 4)
+
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+
+ /* All results have been written to 64(%rsp). */
+ vmovaps (%rsp), %zmm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa (rsp, 32)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_def_cfa (rsp, 24)
+ popq %rbx
+ cfi_def_cfa (rsp, 16)
+ popq %r13
+ ret
END (_ZGVeN16v_logf_skx)
+
+strong_alias (_ZGVeN16v_logf_skx, _ZGVeN16v_logf_knl)
+
+ .section .rodata.evex512, "a"
+ .align 64
+
+ /* Data table for vector implementations of function logf. The
+ table may contain polynomial, reduction, lookup coefficients
+ and other coefficients obtained through different methods of
+ research and experimental work. */
+LOCAL_DATA_NAME_UNALIGNED:
+ float_block (LOCAL_DATA_NAME_UNALIGNED, _iLoRange, 0x00ffffff)
+
+ .type LOCAL_DATA_NAME_UNALIGNED, @object
+ .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
+
+LOCAL_DATA_NAME:
+ DATA_VEC (LOCAL_DATA_NAME, _iBrkValue, 0x3f2aaaab)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_7, 0xbe1b6a22)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_6, 0x3e2db86b)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_5, 0xbe289358)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_4, 0x3e4afb81)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_3, 0xbe80061d)
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_2, 0x3eaaaee7)
+ DATA_VEC (LOCAL_DATA_NAME, _sLn2, 0x3f317218)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 25/27] x86/fpu: Optimize svml_s_logf4_core_sse4.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (22 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 24/27] x86/fpu: Optimize svml_s_logf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 26/27] x86/fpu: Optimize svml_s_logf8_core_avx2.S Noah Goldstein via Libc-alpha
` (2 subsequent siblings)
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
As well instead of using the shared `__svml_slogf_data` just define
the data locally. This is because; 1) Its not really ideal for
the sse4/avx2 to reuse the avx512 tables as it pollute the cache
which unnecessarily large blocks. 2) Really only one of the
versions is ever expected to be used by a given process so there
isn't any constructive caching between them. And 3) there is not
enough data shared to make up for the first two reasons.
Code Size Change: -286 Bytes (235 - 521)
Input New Time / Old Time
0F (0x00000000) -> 0.5750
0F (0x0000ffff, Denorm) -> 0.9206
.1F (0x3dcccccd) -> 0.9389
5F (0x40a00000) -> 0.9361
2315255808F (0x4f0a0000) -> 0.9306
-NaN (0xffffffff) -> 0.5226
---
.../fpu/multiarch/svml_s_logf4_core_sse4.S | 327 +++++++++---------
1 file changed, 156 insertions(+), 171 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_logf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_logf4_core_sse4.S
index 20ad054eac..42d09db8df 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_logf4_core_sse4.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_logf4_core_sse4.S
@@ -16,179 +16,164 @@
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
+
+
+#define LOCAL_DATA_NAME __svml_slog_data_internal
+#include "svml_s_common_sse4_rodata_offsets.h"
+
+#define _sPoly_7 0
+#define _sPoly_6 16
+#define _sPoly_5 32
+#define _sPoly_4 48
+#define _sPoly_3 64
+#define _sPoly_2 80
+
#include <sysdep.h>
-#include "svml_s_logf_data.h"
.section .text.sse4, "ax", @progbits
ENTRY (_ZGVbN4v_logf_sse4)
-/*
- ALGORITHM DESCRIPTION:
-
- log(x) = exponent_x*log(2) + log(mantissa_x), if mantissa_x<4/3
- log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x), if mantissa_x>4/3
-
- R = mantissa_x - 1, if mantissa_x<4/3
- R = 0.5*mantissa_x - 1, if mantissa_x>4/3
- |R|< 1/3
-
- log(1+R) is approximated as a polynomial: degree 9 for 1-ulp,
- degree 7 for 4-ulp, degree 3 for half-precision. */
-
- pushq %rbp
- cfi_adjust_cfa_offset (8)
- cfi_rel_offset (%rbp, 0)
- movq %rsp, %rbp
- cfi_def_cfa_register (%rbp)
- andq $-64, %rsp
- subq $320, %rsp
-
-/* reduction: compute r,n */
- movaps %xmm0, %xmm2
-
-/* check for working range,
- set special argument mask (denormals/zero/Inf/NaN) */
- movq __svml_slog_data@GOTPCREL(%rip), %rax
- movdqu _iHiDelta(%rax), %xmm1
- movdqu _iLoRange(%rax), %xmm4
- paddd %xmm0, %xmm1
- movdqu _iBrkValue(%rax), %xmm3
- pcmpgtd %xmm1, %xmm4
- movdqu _iOffExpoMask(%rax), %xmm1
- psubd %xmm3, %xmm2
- pand %xmm2, %xmm1
-
-/* exponent_x (mantissa_x<4/3) or exponent_x+1 (mantissa_x>4/3) */
- psrad $23, %xmm2
- paddd %xmm3, %xmm1
- movups _sPoly_7(%rax), %xmm5
-
-/* mantissa_x (mantissa_x<4/3), or 0.5*mantissa_x (mantissa_x>4/3) */
- cvtdq2ps %xmm2, %xmm6
-
-/* reduced argument R */
- subps _sOne(%rax), %xmm1
- movmskps %xmm4, %ecx
-
-/* final reconstruction:
- add exponent_value*log2 to polynomial result */
- mulps _sLn2(%rax), %xmm6
-
-/* polynomial evaluation starts here */
- mulps %xmm1, %xmm5
- addps _sPoly_6(%rax), %xmm5
- mulps %xmm1, %xmm5
- addps _sPoly_5(%rax), %xmm5
- mulps %xmm1, %xmm5
- addps _sPoly_4(%rax), %xmm5
- mulps %xmm1, %xmm5
- addps _sPoly_3(%rax), %xmm5
- mulps %xmm1, %xmm5
- addps _sPoly_2(%rax), %xmm5
- mulps %xmm1, %xmm5
- addps _sPoly_1(%rax), %xmm5
- mulps %xmm1, %xmm5
-
-/* polynomial evaluation end */
- mulps %xmm1, %xmm5
- addps %xmm5, %xmm1
- addps %xmm6, %xmm1
- testl %ecx, %ecx
- jne .LBL_1_3
-
-.LBL_1_2:
- cfi_remember_state
- movdqa %xmm1, %xmm0
- movq %rbp, %rsp
- cfi_def_cfa_register (%rsp)
- popq %rbp
- cfi_adjust_cfa_offset (-8)
- cfi_restore (%rbp)
- ret
-
-.LBL_1_3:
- cfi_restore_state
- movups %xmm0, 192(%rsp)
- movups %xmm1, 256(%rsp)
- je .LBL_1_2
-
- xorb %dl, %dl
- xorl %eax, %eax
- movups %xmm8, 112(%rsp)
- movups %xmm9, 96(%rsp)
- movups %xmm10, 80(%rsp)
- movups %xmm11, 64(%rsp)
- movups %xmm12, 48(%rsp)
- movups %xmm13, 32(%rsp)
- movups %xmm14, 16(%rsp)
- movups %xmm15, (%rsp)
- movq %rsi, 136(%rsp)
- movq %rdi, 128(%rsp)
- movq %r12, 168(%rsp)
- cfi_offset_rel_rsp (12, 168)
- movb %dl, %r12b
- movq %r13, 160(%rsp)
- cfi_offset_rel_rsp (13, 160)
- movl %ecx, %r13d
- movq %r14, 152(%rsp)
- cfi_offset_rel_rsp (14, 152)
- movl %eax, %r14d
- movq %r15, 144(%rsp)
- cfi_offset_rel_rsp (15, 144)
- cfi_remember_state
-
-.LBL_1_6:
- btl %r14d, %r13d
- jc .LBL_1_12
-
-.LBL_1_7:
- lea 1(%r14), %esi
- btl %esi, %r13d
- jc .LBL_1_10
-
-.LBL_1_8:
- incb %r12b
- addl $2, %r14d
- cmpb $16, %r12b
- jb .LBL_1_6
-
- movups 112(%rsp), %xmm8
- movups 96(%rsp), %xmm9
- movups 80(%rsp), %xmm10
- movups 64(%rsp), %xmm11
- movups 48(%rsp), %xmm12
- movups 32(%rsp), %xmm13
- movups 16(%rsp), %xmm14
- movups (%rsp), %xmm15
- movq 136(%rsp), %rsi
- movq 128(%rsp), %rdi
- movq 168(%rsp), %r12
- cfi_restore (%r12)
- movq 160(%rsp), %r13
- cfi_restore (%r13)
- movq 152(%rsp), %r14
- cfi_restore (%r14)
- movq 144(%rsp), %r15
- cfi_restore (%r15)
- movups 256(%rsp), %xmm1
- jmp .LBL_1_2
-
-.LBL_1_10:
- cfi_restore_state
- movzbl %r12b, %r15d
- movss 196(%rsp,%r15,8), %xmm0
-
- call JUMPTARGET(logf)
-
- movss %xmm0, 260(%rsp,%r15,8)
- jmp .LBL_1_8
-
-.LBL_1_12:
- movzbl %r12b, %r15d
- movss 192(%rsp,%r15,8), %xmm0
-
- call JUMPTARGET(logf)
-
- movss %xmm0, 256(%rsp,%r15,8)
- jmp .LBL_1_7
-
+ movdqu COMMON_DATA(_ILoRange)(%rip), %xmm1
+ /* ALGORITHM DESCRIPTION:
+ if mantissa_x<4/3
+ log(x) = exponent_x*log(2) + log(mantissa_x)
+ if mantissa_x>4/3
+ log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x)
+
+ R = mantissa_x - 1, if mantissa_x<4/3
+ R = 0.5*mantissa_x - 1, if mantissa_x>4/3
+ |R|< 1/3
+
+ log(1+R) is approximated as a polynomial: degree 9 for
+ 1-ulp, degree 7 for 4-ulp, degree 3 for half-precision. */
+
+ /* check for working range, set special argument mask
+ (denormals/zero/Inf/NaN). */
+ movdqu COMMON_DATA(_NotiOffExpoMask)(%rip), %xmm2
+ movaps %xmm0, %xmm3
+ psubd %xmm2, %xmm3
+ pcmpgtd %xmm3, %xmm1
+ movmskps %xmm1, %eax
+
+ movdqu COMMON_DATA(_IBrkValue)(%rip), %xmm1
+ movaps %xmm0, %xmm3
+ psubd %xmm1, %xmm0
+ pandn %xmm0, %xmm2
+ paddd %xmm1, %xmm2
+ /* reduced argument R. */
+ subps COMMON_DATA(_OneF)(%rip), %xmm2
+ /* exponent_x (mantissa_x<4/3),
+ or exponent_x+1 (mantissa_x>4/3). */
+ psrad $0x17, %xmm0
+ /* mantissa_x (mantissa_x<4/3),
+ or 0.5 mantissa_x (mantissa_x>4/3). */
+ cvtdq2ps %xmm0, %xmm0
+ /* final reconstruction: add exponent_value * log2 to polynomial
+ result. */
+ mulps COMMON_DATA(_Ln2)(%rip), %xmm0
+ movups LOCAL_DATA(_sPoly_7)(%rip), %xmm1
+ /* polynomial evaluation starts here. */
+ mulps %xmm2, %xmm1
+ addps LOCAL_DATA(_sPoly_6)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ addps LOCAL_DATA(_sPoly_5)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ addps LOCAL_DATA(_sPoly_4)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ addps LOCAL_DATA(_sPoly_3)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ addps LOCAL_DATA(_sPoly_2)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ addps COMMON_DATA(_Neg5F)(%rip), %xmm1
+ mulps %xmm2, %xmm1
+ /* polynomial evaluation end. */
+ mulps %xmm2, %xmm1
+ addps %xmm1, %xmm2
+ addps %xmm2, %xmm0
+ testl %eax, %eax
+ jne L(SPECIAL_VALUES_BRANCH)
+ ret
+
+ /* Cold case. edx has 1s where there was a special value that
+ more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
+ /* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
+ call entry will be 16-byte aligned. */
+ subq $0x38, %rsp
+ movups %xmm0, 24(%rsp)
+ movups %xmm3, 40(%rsp)
+
+ /* Use rbx/rbp for callee save registers as they get short
+ encoding for many instructions (as compared with r12/r13). */
+ movq %rbx, (%rsp)
+ cfi_offset (rbx, -64)
+ movq %rbp, 8(%rsp)
+ cfi_offset (rbp, -56)
+ /* edx has 1s where there was a special value that needs to be
+ handled by a tanhf call. */
+ movl %eax, %ebx
+L(SPECIAL_VALUES_LOOP):
+
+ /* use rbp as index for special value that is saved across calls
+ to tanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 12] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. */
+ xorl %ebp, %ebp
+ bsfl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ movss 40(%rsp, %rbp, 4), %xmm0
+ call logf@PLT
+
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ movss %xmm0, 24(%rsp, %rbp, 4)
+
+ leal -1(%rbx), %eax
+ andl %eax, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+ /* All results have been written to 24(%rsp). */
+ movups 24(%rsp), %xmm0
+ movq (%rsp), %rbx
+ cfi_restore (rbx)
+ movq 8(%rsp), %rbp
+ cfi_restore (rbp)
+ addq $56, %rsp
+ cfi_def_cfa_offset (8)
+ ret
END (_ZGVbN4v_logf_sse4)
+
+ .section .rodata.sse4, "a"
+ .align 16
+
+ /* Data table for vector implementations of function logf. The
+ table may contain polynomial, reduction, lookup coefficients
+ and other coefficients obtained through different methods of
+ research and experimental work. */
+
+ .globl LOCAL_DATA_NAME
+LOCAL_DATA_NAME:
+ /* Polynomial sPoly[] coefficients:. */
+ /* -1.5177205204963684082031250e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_7, 0xbe1b6a22)
+
+ /* 1.6964881122112274169921875e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_6, 0x3e2db86b)
+
+ /* -1.6462457180023193359375000e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_5, 0xbe289358)
+
+ /* 1.9822503626346588134765625e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_4, 0x3e4afb81)
+
+ /* -2.5004664063453674316406250e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_3, 0xbe80061d)
+
+ /* 3.3336564898490905761718750e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_2, 0x3eaaaee7)
+
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 26/27] x86/fpu: Optimize svml_s_logf8_core_avx2.S
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (23 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 25/27] x86/fpu: Optimize svml_s_logf4_core_sse4.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 27/27] x86/fpu: Remove unused svml_s_logf_data.S file Noah Goldstein via Libc-alpha
2022-12-07 23:53 ` [PATCH v1 01/27] x86/fpu: Create helper file for common data macros H.J. Lu via Libc-alpha
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
1. Improve special values case which ends up covering ~half of all
float bit patterns.
2. Cleanup some missed optimizations in instruction selection /
unnecissary repeated rodata references.
3. Remove unused rodata.
4. Use common data definitions where possible.
As well instead of using the shared `__svml_slogf_data` just define
the data locally. This is because; 1) Its not really ideal for
the sse4/avx2 to reuse the avx512 tables as it pollute the cache
which unnecessarily large blocks. 2) Really only one of the
versions is ever expected to be used by a given process so there
isn't any constructive caching between them. And 3) there is not
enough data shared to make up for the first two reasons.
Code Size Change: -314 Bytes (230 - 544)
Input New Time / Old Time
0F (0x00000000) -> 0.6246
0F (0x0000ffff, Denorm) -> 0.9525
.1F (0x3dcccccd) -> 0.9021
5F (0x40a00000) -> 0.9113
2315255808F (0x4f0a0000) -> 0.8293
-NaN (0xffffffff) -> 0.5745
---
.../fpu/multiarch/svml_s_logf8_core_avx2.S | 342 +++++++++---------
1 file changed, 181 insertions(+), 161 deletions(-)
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_logf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_logf8_core_avx2.S
index 616312c695..35f63b7879 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_logf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_logf8_core_avx2.S
@@ -16,169 +16,189 @@
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
+#define LOCAL_DATA_NAME __svml_slog_data_internal
+#include "svml_s_common_avx2_rodata_offsets.h"
+
+/* Offsets for data table __svml_slog_data_internal. */
+#define _sPoly_7 0
+#define _sPoly_6 32
+#define _sPoly_5 64
+#define _sPoly_4 96
+#define _sPoly_3 128
+#define _sPoly_2 160
+
#include <sysdep.h>
-#include "svml_s_logf_data.h"
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_logf_avx2)
-/*
- ALGORITHM DESCRIPTION:
-
- log(x) = exponent_x*log(2) + log(mantissa_x), if mantissa_x<4/3
- log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x), if mantissa_x>4/3
-
- R = mantissa_x - 1, if mantissa_x<4/3
- R = 0.5*mantissa_x - 1, if mantissa_x>4/3
- |R|< 1/3
-
- log(1+R) is approximated as a polynomial: degree 9 for 1-ulp,
- degree 7 for 4-ulp, degree 3 for half-precision. */
-
- pushq %rbp
- cfi_adjust_cfa_offset (8)
- cfi_rel_offset (%rbp, 0)
- movq %rsp, %rbp
- cfi_def_cfa_register (%rbp)
- andq $-64, %rsp
- subq $448, %rsp
- movq __svml_slog_data@GOTPCREL(%rip), %rax
- vmovaps %ymm0, %ymm2
- vmovups _iBrkValue(%rax), %ymm6
- vmovups _iLoRange(%rax), %ymm1
-/* check for working range,
- set special argument mask (denormals/zero/Inf/NaN) */
- vpaddd _iHiDelta(%rax), %ymm2, %ymm7
-
-/* reduction: compute r,n */
- vpsubd %ymm6, %ymm2, %ymm4
-
-/* exponent_x (mantissa_x<4/3) or exponent_x+1 (mantissa_x>4/3) */
- vpsrad $23, %ymm4, %ymm3
- vpand _iOffExpoMask(%rax), %ymm4, %ymm5
- vmovups _sPoly_7(%rax), %ymm4
- vcvtdq2ps %ymm3, %ymm0
-
-/* mantissa_x (mantissa_x<4/3), or 0.5*mantissa_x (mantissa_x>4/3) */
- vpaddd %ymm6, %ymm5, %ymm3
-
-/* reduced argument R */
- vsubps _sOne(%rax), %ymm3, %ymm5
-
-/* polynomial evaluation starts here */
- vfmadd213ps _sPoly_6(%rax), %ymm5, %ymm4
- vfmadd213ps _sPoly_5(%rax), %ymm5, %ymm4
- vfmadd213ps _sPoly_4(%rax), %ymm5, %ymm4
- vfmadd213ps _sPoly_3(%rax), %ymm5, %ymm4
- vfmadd213ps _sPoly_2(%rax), %ymm5, %ymm4
- vfmadd213ps _sPoly_1(%rax), %ymm5, %ymm4
- vmulps %ymm5, %ymm4, %ymm6
-
-/* polynomial evaluation end */
- vfmadd213ps %ymm5, %ymm5, %ymm6
- vpcmpgtd %ymm7, %ymm1, %ymm1
- vmovmskps %ymm1, %ecx
-
-/* final reconstruction:
- add exponent_value*log2 to polynomial result */
- vfmadd132ps _sLn2(%rax), %ymm6, %ymm0
- testl %ecx, %ecx
- jne .LBL_1_3
-
-.LBL_1_2:
- cfi_remember_state
- movq %rbp, %rsp
- cfi_def_cfa_register (%rsp)
- popq %rbp
- cfi_adjust_cfa_offset (-8)
- cfi_restore (%rbp)
- ret
-
-.LBL_1_3:
- cfi_restore_state
- vmovups %ymm2, 320(%rsp)
- vmovups %ymm0, 384(%rsp)
- je .LBL_1_2
-
- xorb %dl, %dl
- xorl %eax, %eax
- vmovups %ymm8, 224(%rsp)
- vmovups %ymm9, 192(%rsp)
- vmovups %ymm10, 160(%rsp)
- vmovups %ymm11, 128(%rsp)
- vmovups %ymm12, 96(%rsp)
- vmovups %ymm13, 64(%rsp)
- vmovups %ymm14, 32(%rsp)
- vmovups %ymm15, (%rsp)
- movq %rsi, 264(%rsp)
- movq %rdi, 256(%rsp)
- movq %r12, 296(%rsp)
- cfi_offset_rel_rsp (12, 296)
- movb %dl, %r12b
- movq %r13, 288(%rsp)
- cfi_offset_rel_rsp (13, 288)
- movl %ecx, %r13d
- movq %r14, 280(%rsp)
- cfi_offset_rel_rsp (14, 280)
- movl %eax, %r14d
- movq %r15, 272(%rsp)
- cfi_offset_rel_rsp (15, 272)
- cfi_remember_state
-
-.LBL_1_6:
- btl %r14d, %r13d
- jc .LBL_1_12
-
-.LBL_1_7:
- lea 1(%r14), %esi
- btl %esi, %r13d
- jc .LBL_1_10
-
-.LBL_1_8:
- incb %r12b
- addl $2, %r14d
- cmpb $16, %r12b
- jb .LBL_1_6
-
- vmovups 224(%rsp), %ymm8
- vmovups 192(%rsp), %ymm9
- vmovups 160(%rsp), %ymm10
- vmovups 128(%rsp), %ymm11
- vmovups 96(%rsp), %ymm12
- vmovups 64(%rsp), %ymm13
- vmovups 32(%rsp), %ymm14
- vmovups (%rsp), %ymm15
- vmovups 384(%rsp), %ymm0
- movq 264(%rsp), %rsi
- movq 256(%rsp), %rdi
- movq 296(%rsp), %r12
- cfi_restore (%r12)
- movq 288(%rsp), %r13
- cfi_restore (%r13)
- movq 280(%rsp), %r14
- cfi_restore (%r14)
- movq 272(%rsp), %r15
- cfi_restore (%r15)
- jmp .LBL_1_2
-
-.LBL_1_10:
- cfi_restore_state
- movzbl %r12b, %r15d
- vmovss 324(%rsp,%r15,8), %xmm0
- vzeroupper
-
- call JUMPTARGET(logf)
-
- vmovss %xmm0, 388(%rsp,%r15,8)
- jmp .LBL_1_8
-
-.LBL_1_12:
- movzbl %r12b, %r15d
- vmovss 320(%rsp,%r15,8), %xmm0
- vzeroupper
-
- call JUMPTARGET(logf)
-
- vmovss %xmm0, 384(%rsp,%r15,8)
- jmp .LBL_1_7
-
+ /* ALGORITHM DESCRIPTION:
+ if mantissa_x<4/3
+ log(x) = exponent_x*log(2) + log(mantissa_x)
+ if mantissa_x>4/3
+ log(x) = (exponent_x+1)*log(2) + log(0.5*mantissa_x)
+
+ R = mantissa_x - 1, if mantissa_x<4/3
+ R = 0.5*mantissa_x - 1, if mantissa_x>4/3
+ |R|< 1/3
+
+ log(1+R) is approximated as a polynomial: degree 9 for
+ 1-ulp, degree 7 for 4-ulp, degree 3 for half-precision. */
+ vmovups COMMON_DATA(_IBrkValue)(%rip), %ymm6
+
+
+ vmovups COMMON_DATA(_NotiOffExpoMask)(%rip), %ymm7
+
+ /* reduction: compute r,n. */
+ vpsubd %ymm6, %ymm0, %ymm4
+
+ /* exponent_x (mantissa_x<4/3) or
+ exponent_x+1 (mantissa_x>4/3). */
+ vpsrad $23, %ymm4, %ymm3
+ vpandn %ymm4, %ymm7, %ymm5
+ vmovups LOCAL_DATA(_sPoly_7)(%rip), %ymm4
+ vcvtdq2ps %ymm3, %ymm2
+
+ /* mantissa_x (mantissa_x<4/3),
+ or 0.5*mantissa_x (mantissa_x>4/3). */
+ vpaddd %ymm6, %ymm5, %ymm3
+
+ /* reduced argument R. */
+ vsubps COMMON_DATA(_OneF)(%rip), %ymm3, %ymm5
+
+ /* polynomial evaluation starts here. */
+ vfmadd213ps LOCAL_DATA(_sPoly_6)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPoly_5)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPoly_4)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPoly_3)(%rip), %ymm5, %ymm4
+ vfmadd213ps LOCAL_DATA(_sPoly_2)(%rip), %ymm5, %ymm4
+ vfmadd213ps COMMON_DATA(_Neg5F)(%rip), %ymm5, %ymm4
+ vmulps %ymm5, %ymm4, %ymm6
+
+ /* polynomial evaluation end. */
+ vfmadd213ps %ymm5, %ymm5, %ymm6
+
+ vmovups COMMON_DATA(_ILoRange)(%rip), %ymm1
+ /* check for working range, set special argument mask
+ (denormals/zero/Inf/NaN). */
+ vpsubd %ymm7, %ymm0, %ymm7
+
+
+ vpcmpgtd %ymm7, %ymm1, %ymm1
+ vmovmskps %ymm1, %ecx
+
+ /* final reconstruction: add exponent_value*log2 to polynomial
+ result. */
+ vfmadd132ps COMMON_DATA(_Ln2)(%rip), %ymm6, %ymm2
+ testl %ecx, %ecx
+ /* Branch to process special inputs. */
+ jne L(SPECIAL_VALUES_BRANCH)
+ vmovaps %ymm2, %ymm0
+ ret
+
+
+ /* Cold case. edx has 1s where there was a special value that
+ needs to be handled by a atanhf call. Optimize for code size
+ more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
+ /* Use r13 to save/restore the stack. This allows us to use rbp
+ as callee save register saving code size. */
+ pushq %r13
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (r13, -16)
+ /* Need to callee save registers to preserve state across tanhf
+ calls. */
+ pushq %rbx
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbx, -24)
+ pushq %rbp
+ cfi_adjust_cfa_offset (8)
+ cfi_offset (rbp, -32)
+ movq %rsp, %r13
+ cfi_def_cfa_register (r13)
+
+ /* Align stack and make room for 2x ymm vectors. */
+ andq $-32, %rsp
+ addq $-64, %rsp
+
+ /* Save all already computed inputs. */
+ vmovups %ymm2, (%rsp)
+ /* Save original input (ymm2 unchanged up to this point). */
+ vmovups %ymm0, 32(%rsp)
+
+ vzeroupper
+
+ /* edx has 1s where there was a special value that needs to be
+ handled by a atanhf call. */
+ movl %ecx, %ebx
+L(SPECIAL_VALUES_LOOP):
+
+ /* use rbp as index for special value that is saved across calls
+ to atanhf. We technically don't need a callee save register
+ here as offset to rsp is always [0, 28] so we can restore
+ rsp by realigning to 64. Essentially the tradeoff is 1 extra
+ save/restore vs 2 extra instructions in the loop. Realigning
+ also costs more code size. */
+ xorl %ebp, %ebp
+ tzcntl %ebx, %ebp
+
+ /* Scalar math fucntion call to process special input. */
+ vmovss 32(%rsp, %rbp, 4), %xmm0
+ call logf@PLT
+
+ /* No good way to avoid the store-forwarding fault this will
+ cause on return. `lfence` avoids the SF fault but at greater
+ cost as it serialized stack/callee save restoration. */
+ vmovss %xmm0, (%rsp, %rbp, 4)
+
+ blsrl %ebx, %ebx
+ jnz L(SPECIAL_VALUES_LOOP)
+
+
+
+ /* All results have been written to (%rsp). */
+ vmovups (%rsp), %ymm0
+ /* Restore rsp. */
+ movq %r13, %rsp
+ cfi_def_cfa_register (rsp)
+ /* Restore callee save registers. */
+ popq %rbp
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %rbx
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (rbp)
+ popq %r13
+ cfi_adjust_cfa_offset (-8)
+ cfi_restore (r13)
+ ret
END(_ZGVdN8v_logf_avx2)
+
+ .section .rodata.avx2, "a"
+ .align 32
+
+ /* Data table for vector implementations of function logf. The
+ table may contain polynomial, reduction, lookup coefficients
+ and other coefficients obtained through different methods of
+ research and experimental work. */
+LOCAL_DATA_NAME:
+ /* Polynomial sPoly[] coefficients:. */
+ /* -1.5177205204963684082031250e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_7, 0xbe1b6a22)
+
+ /* 1.6964881122112274169921875e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_6, 0x3e2db86b)
+
+ /* -1.6462457180023193359375000e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_5, 0xbe289358)
+
+ /* 1.9822503626346588134765625e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_4, 0x3e4afb81)
+
+ /* -2.5004664063453674316406250e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_3, 0xbe80061d)
+
+ /* 3.3336564898490905761718750e-01. */
+ DATA_VEC (LOCAL_DATA_NAME, _sPoly_2, 0x3eaaaee7)
+
+ .type LOCAL_DATA_NAME, @object
+ .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* [PATCH v1 27/27] x86/fpu: Remove unused svml_s_logf_data.S file
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (24 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 26/27] x86/fpu: Optimize svml_s_logf8_core_avx2.S Noah Goldstein via Libc-alpha
@ 2022-12-07 8:52 ` Noah Goldstein via Libc-alpha
2022-12-07 23:53 ` [PATCH v1 01/27] x86/fpu: Create helper file for common data macros H.J. Lu via Libc-alpha
26 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-07 8:52 UTC (permalink / raw)
To: libc-alpha; +Cc: goldstein.w.n, hjl.tools, andrey.kolesov, carlos
The common data definitions inside the file are no longer used so
delete it.
---
sysdeps/x86_64/fpu/Makefile | 1 -
sysdeps/x86_64/fpu/svml_s_logf_data.S | 102 --------------------------
sysdeps/x86_64/fpu/svml_s_logf_data.h | 48 ------------
3 files changed, 151 deletions(-)
delete mode 100644 sysdeps/x86_64/fpu/svml_s_logf_data.S
delete mode 100644 sysdeps/x86_64/fpu/svml_s_logf_data.h
diff --git a/sysdeps/x86_64/fpu/Makefile b/sysdeps/x86_64/fpu/Makefile
index e7e747e920..72375170a5 100644
--- a/sysdeps/x86_64/fpu/Makefile
+++ b/sysdeps/x86_64/fpu/Makefile
@@ -18,7 +18,6 @@ libmvec-support += \
svml_s_common_evex512_rodata \
svml_s_common_sse4_rodata \
svml_s_expf_data \
- svml_s_logf_data \
svml_s_powf_data \
svml_s_trig_data \
$(foreach l,$(libmvec-double-func-list), \
diff --git a/sysdeps/x86_64/fpu/svml_s_logf_data.S b/sysdeps/x86_64/fpu/svml_s_logf_data.S
deleted file mode 100644
index 73c05e1734..0000000000
--- a/sysdeps/x86_64/fpu/svml_s_logf_data.S
+++ /dev/null
@@ -1,102 +0,0 @@
-/* Data for vector function logf.
- Copyright (C) 2014-2022 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
-
- The GNU C Library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- The GNU C Library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with the GNU C Library; if not, see
- <https://www.gnu.org/licenses/>. */
-
-#include "svml_s_logf_data.h"
-
- .section .rodata, "a"
- .align 64
-
-/* Data table for vector implementations of function logf.
- The table may contain polynomial, reduction, lookup coefficients and
- other coefficients obtained through different methods of research and
- experimental work. */
-
- .globl __svml_slog_data
-__svml_slog_data:
-
-/* Polynomial sPoly[] coefficients:
- * -5.0000000000000000000000000e-01 */
-float_vector _sPoly_1 0xbf000000
-
-/* 3.3336564898490905761718750e-01 */
-float_vector _sPoly_2 0x3eaaaee7
-
-/* -2.5004664063453674316406250e-01 */
-float_vector _sPoly_3 0xbe80061d
-
-/* 1.9822503626346588134765625e-01 */
-float_vector _sPoly_4 0x3e4afb81
-
-/* -1.6462457180023193359375000e-01 */
-float_vector _sPoly_5 0xbe289358
-
-/* 1.6964881122112274169921875e-01 */
-float_vector _sPoly_6 0x3e2db86b
-
-/* -1.5177205204963684082031250e-01 */
-float_vector _sPoly_7 0xbe1b6a22
-
-/* Constant for work range check: Delta 80000000-7f800000 */
-float_vector _iHiDelta 0x00800000
-
-/* Constant for work range check: 00800000 + Delta */
-float_vector _iLoRange 0x01000000
-
-/* Mantissa break point SP 2/3 */
-float_vector _iBrkValue 0x3f2aaaab
-
-/* SP significand mask */
-float_vector _iOffExpoMask 0x007fffff
-
-/* 1.0f */
-float_vector _sOne 0x3f800000
-
-/* SP log(2) */
-float_vector _sLn2 0x3f317218
-
-/* SP infinity, +/- */
-.if .-__svml_slog_data != _sInfs
-.err
-.endif
- .long 0x7f800000
- .long 0xff800000
- .rept 56
- .byte 0
- .endr
-
-/* SP one, +/- */
-.if .-__svml_slog_data != _sOnes
-.err
-.endif
- .long 0x3f800000
- .long 0xbf800000
- .rept 56
- .byte 0
- .endr
-
-/* SP zero +/- */
-.if .-__svml_slog_data != _sZeros
-.err
-.endif
- .long 0x00000000
- .long 0x80000000
- .rept 56
- .byte 0
- .endr
- .type __svml_slog_data,@object
- .size __svml_slog_data,.-__svml_slog_data
diff --git a/sysdeps/x86_64/fpu/svml_s_logf_data.h b/sysdeps/x86_64/fpu/svml_s_logf_data.h
deleted file mode 100644
index 72e66081c5..0000000000
--- a/sysdeps/x86_64/fpu/svml_s_logf_data.h
+++ /dev/null
@@ -1,48 +0,0 @@
-/* Offsets for data table for vectorized function logf.
- Copyright (C) 2014-2022 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
-
- The GNU C Library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- The GNU C Library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with the GNU C Library; if not, see
- <https://www.gnu.org/licenses/>. */
-
-#ifndef S_LOGF_DATA_H
-#define S_LOGF_DATA_H
-
-#define _sPoly_1 0
-#define _sPoly_2 64
-#define _sPoly_3 128
-#define _sPoly_4 192
-#define _sPoly_5 256
-#define _sPoly_6 320
-#define _sPoly_7 384
-#define _iHiDelta 448
-#define _iLoRange 512
-#define _iBrkValue 576
-#define _iOffExpoMask 640
-#define _sOne 704
-#define _sLn2 768
-#define _sInfs 832
-#define _sOnes 896
-#define _sZeros 960
-
-.macro float_vector offset value
-.if .-__svml_slog_data != \offset
-.err
-.endif
-.rept 16
-.long \value
-.endr
-.endm
-
-#endif
--
2.34.1
^ permalink raw reply related [flat|nested] 38+ messages in thread
* Re: [PATCH v1 01/27] x86/fpu: Create helper file for common data macros
2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
` (25 preceding siblings ...)
2022-12-07 8:52 ` [PATCH v1 27/27] x86/fpu: Remove unused svml_s_logf_data.S file Noah Goldstein via Libc-alpha
@ 2022-12-07 23:53 ` H.J. Lu via Libc-alpha
2022-12-08 0:13 ` Noah Goldstein via Libc-alpha
26 siblings, 1 reply; 38+ messages in thread
From: H.J. Lu via Libc-alpha @ 2022-12-07 23:53 UTC (permalink / raw)
To: Noah Goldstein; +Cc: libc-alpha, andrey.kolesov, carlos
On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
>
> The macros are useful for creating .rodata definitions and checking
> that the offset is correct.
> ---
> .../x86_64/fpu/svml_common_data_macros.h.S | 50 +++++++++++++++++++
> 1 file changed, 50 insertions(+)
> create mode 100644 sysdeps/x86_64/fpu/svml_common_data_macros.h.S
>
> diff --git a/sysdeps/x86_64/fpu/svml_common_data_macros.h.S b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> new file mode 100644
> index 0000000000..31bd66835d
> --- /dev/null
> +++ b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> @@ -0,0 +1,50 @@
> +/* Helper macros for creating rodata
> + Copyright (C) 2022 Free Software Foundation, Inc.
> + This file is part of the GNU C Library.
> +
> + The GNU C Library is free software; you can redistribute it and/or
> + modify it under the terms of the GNU Lesser General Public
> + License as published by the Free Software Foundation; either
> + version 2.1 of the License, or (at your option) any later version.
> +
> + The GNU C Library is distributed in the hope that it will be useful,
> + but WITHOUT ANY WARRANTY; without even the implied warranty of
> + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
> + Lesser General Public License for more details.
> +
> + You should have received a copy of the GNU Lesser General Public
> + License along with the GNU C Library; if not, see
> + https://www.gnu.org/licenses/. */
> +
> +#ifndef _SVML_COMMON_DATA_MACROS_H_S
> +#define _SVML_COMMON_DATA_MACROS_H_S 1
> +
> +
> +.macro check_offset data_section offset
> + .if .-\data_section != \offset
> + .err
> + .endif
> +.endm
> +
> +
> +/* Only used in floating point functions at the moment. */
> +.macro float_vectorN data_section N offset value
> + check_offset \data_section \offset
> + .rept \N
> + .long \value
> + .endr
> +.endm
> +
> +#define float_block(data_section, offset, ...) \
> + check_offset data_section offset; \
> + .long __VA_ARGS__
> +
> +
> +#define float_vector16(data_section, offset, value) \
> + float_vectorN data_section 4 offset value
> +#define float_vector32(data_section, offset, value) \
> + float_vectorN data_section 8 offset value
> +#define float_vector64(data_section, offset, value) \
> + float_vectorN data_section 16 offset value
> +
> +#endif
> --
> 2.34.1
>
Please use .h files in fpu directory.
--
H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 01/27] x86/fpu: Create helper file for common data macros
2022-12-07 23:53 ` [PATCH v1 01/27] x86/fpu: Create helper file for common data macros H.J. Lu via Libc-alpha
@ 2022-12-08 0:13 ` Noah Goldstein via Libc-alpha
2022-12-08 0:22 ` H.J. Lu via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-08 0:13 UTC (permalink / raw)
To: H.J. Lu; +Cc: libc-alpha, andrey.kolesov, carlos
On Wed, Dec 7, 2022 at 3:53 PM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > The macros are useful for creating .rodata definitions and checking
> > that the offset is correct.
> > ---
> > .../x86_64/fpu/svml_common_data_macros.h.S | 50 +++++++++++++++++++
> > 1 file changed, 50 insertions(+)
> > create mode 100644 sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> >
> > diff --git a/sysdeps/x86_64/fpu/svml_common_data_macros.h.S b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > new file mode 100644
> > index 0000000000..31bd66835d
> > --- /dev/null
> > +++ b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > @@ -0,0 +1,50 @@
> > +/* Helper macros for creating rodata
> > + Copyright (C) 2022 Free Software Foundation, Inc.
> > + This file is part of the GNU C Library.
> > +
> > + The GNU C Library is free software; you can redistribute it and/or
> > + modify it under the terms of the GNU Lesser General Public
> > + License as published by the Free Software Foundation; either
> > + version 2.1 of the License, or (at your option) any later version.
> > +
> > + The GNU C Library is distributed in the hope that it will be useful,
> > + but WITHOUT ANY WARRANTY; without even the implied warranty of
> > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
> > + Lesser General Public License for more details.
> > +
> > + You should have received a copy of the GNU Lesser General Public
> > + License along with the GNU C Library; if not, see
> > + https://www.gnu.org/licenses/. */
> > +
> > +#ifndef _SVML_COMMON_DATA_MACROS_H_S
> > +#define _SVML_COMMON_DATA_MACROS_H_S 1
> > +
> > +
> > +.macro check_offset data_section offset
> > + .if .-\data_section != \offset
> > + .err
> > + .endif
> > +.endm
> > +
> > +
> > +/* Only used in floating point functions at the moment. */
> > +.macro float_vectorN data_section N offset value
> > + check_offset \data_section \offset
> > + .rept \N
> > + .long \value
> > + .endr
> > +.endm
> > +
> > +#define float_block(data_section, offset, ...) \
> > + check_offset data_section offset; \
> > + .long __VA_ARGS__
> > +
> > +
> > +#define float_vector16(data_section, offset, value) \
> > + float_vectorN data_section 4 offset value
> > +#define float_vector32(data_section, offset, value) \
> > + float_vectorN data_section 8 offset value
> > +#define float_vector64(data_section, offset, value) \
> > + float_vectorN data_section 16 offset value
> > +
> > +#endif
> > --
> > 2.34.1
> >
>
> Please use .h files in fpu directory.
Are .S files globbed somewhere or something?
It uses assembler macros so its convenient for the
extension to match.
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 01/27] x86/fpu: Create helper file for common data macros
2022-12-08 0:13 ` Noah Goldstein via Libc-alpha
@ 2022-12-08 0:22 ` H.J. Lu via Libc-alpha
2022-12-08 0:46 ` Noah Goldstein via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: H.J. Lu via Libc-alpha @ 2022-12-08 0:22 UTC (permalink / raw)
To: Noah Goldstein; +Cc: libc-alpha, andrey.kolesov, carlos
On Wed, Dec 7, 2022 at 4:13 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
>
> On Wed, Dec 7, 2022 at 3:53 PM H.J. Lu <hjl.tools@gmail.com> wrote:
> >
> > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > >
> > > The macros are useful for creating .rodata definitions and checking
> > > that the offset is correct.
> > > ---
> > > .../x86_64/fpu/svml_common_data_macros.h.S | 50 +++++++++++++++++++
> > > 1 file changed, 50 insertions(+)
> > > create mode 100644 sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > >
> > > diff --git a/sysdeps/x86_64/fpu/svml_common_data_macros.h.S b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > > new file mode 100644
> > > index 0000000000..31bd66835d
> > > --- /dev/null
> > > +++ b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > > @@ -0,0 +1,50 @@
> > > +/* Helper macros for creating rodata
> > > + Copyright (C) 2022 Free Software Foundation, Inc.
> > > + This file is part of the GNU C Library.
> > > +
> > > + The GNU C Library is free software; you can redistribute it and/or
> > > + modify it under the terms of the GNU Lesser General Public
> > > + License as published by the Free Software Foundation; either
> > > + version 2.1 of the License, or (at your option) any later version.
> > > +
> > > + The GNU C Library is distributed in the hope that it will be useful,
> > > + but WITHOUT ANY WARRANTY; without even the implied warranty of
> > > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
> > > + Lesser General Public License for more details.
> > > +
> > > + You should have received a copy of the GNU Lesser General Public
> > > + License along with the GNU C Library; if not, see
> > > + https://www.gnu.org/licenses/. */
> > > +
> > > +#ifndef _SVML_COMMON_DATA_MACROS_H_S
> > > +#define _SVML_COMMON_DATA_MACROS_H_S 1
> > > +
> > > +
> > > +.macro check_offset data_section offset
> > > + .if .-\data_section != \offset
> > > + .err
> > > + .endif
> > > +.endm
> > > +
> > > +
> > > +/* Only used in floating point functions at the moment. */
> > > +.macro float_vectorN data_section N offset value
> > > + check_offset \data_section \offset
> > > + .rept \N
> > > + .long \value
> > > + .endr
> > > +.endm
> > > +
> > > +#define float_block(data_section, offset, ...) \
> > > + check_offset data_section offset; \
> > > + .long __VA_ARGS__
> > > +
> > > +
> > > +#define float_vector16(data_section, offset, value) \
> > > + float_vectorN data_section 4 offset value
> > > +#define float_vector32(data_section, offset, value) \
> > > + float_vectorN data_section 8 offset value
> > > +#define float_vector64(data_section, offset, value) \
> > > + float_vectorN data_section 16 offset value
> > > +
> > > +#endif
> > > --
> > > 2.34.1
> > >
> >
> > Please use .h files in fpu directory.
>
> Are .S files globbed somewhere or something?
>
> It uses assembler macros so its convenient for the
> extension to match.
Use new macros or rename files before commit.
--
H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 01/27] x86/fpu: Create helper file for common data macros
2022-12-08 0:22 ` H.J. Lu via Libc-alpha
@ 2022-12-08 0:46 ` Noah Goldstein via Libc-alpha
0 siblings, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-08 0:46 UTC (permalink / raw)
To: H.J. Lu; +Cc: libc-alpha, andrey.kolesov, carlos
On Wed, Dec 7, 2022 at 4:22 PM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Wed, Dec 7, 2022 at 4:13 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > On Wed, Dec 7, 2022 at 3:53 PM H.J. Lu <hjl.tools@gmail.com> wrote:
> > >
> > > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > >
> > > > The macros are useful for creating .rodata definitions and checking
> > > > that the offset is correct.
> > > > ---
> > > > .../x86_64/fpu/svml_common_data_macros.h.S | 50 +++++++++++++++++++
> > > > 1 file changed, 50 insertions(+)
> > > > create mode 100644 sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > > >
> > > > diff --git a/sysdeps/x86_64/fpu/svml_common_data_macros.h.S b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > > > new file mode 100644
> > > > index 0000000000..31bd66835d
> > > > --- /dev/null
> > > > +++ b/sysdeps/x86_64/fpu/svml_common_data_macros.h.S
> > > > @@ -0,0 +1,50 @@
> > > > +/* Helper macros for creating rodata
> > > > + Copyright (C) 2022 Free Software Foundation, Inc.
> > > > + This file is part of the GNU C Library.
> > > > +
> > > > + The GNU C Library is free software; you can redistribute it and/or
> > > > + modify it under the terms of the GNU Lesser General Public
> > > > + License as published by the Free Software Foundation; either
> > > > + version 2.1 of the License, or (at your option) any later version.
> > > > +
> > > > + The GNU C Library is distributed in the hope that it will be useful,
> > > > + but WITHOUT ANY WARRANTY; without even the implied warranty of
> > > > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
> > > > + Lesser General Public License for more details.
> > > > +
> > > > + You should have received a copy of the GNU Lesser General Public
> > > > + License along with the GNU C Library; if not, see
> > > > + https://www.gnu.org/licenses/. */
> > > > +
> > > > +#ifndef _SVML_COMMON_DATA_MACROS_H_S
> > > > +#define _SVML_COMMON_DATA_MACROS_H_S 1
> > > > +
> > > > +
> > > > +.macro check_offset data_section offset
> > > > + .if .-\data_section != \offset
> > > > + .err
> > > > + .endif
> > > > +.endm
> > > > +
> > > > +
> > > > +/* Only used in floating point functions at the moment. */
> > > > +.macro float_vectorN data_section N offset value
> > > > + check_offset \data_section \offset
> > > > + .rept \N
> > > > + .long \value
> > > > + .endr
> > > > +.endm
> > > > +
> > > > +#define float_block(data_section, offset, ...) \
> > > > + check_offset data_section offset; \
> > > > + .long __VA_ARGS__
> > > > +
> > > > +
> > > > +#define float_vector16(data_section, offset, value) \
> > > > + float_vectorN data_section 4 offset value
> > > > +#define float_vector32(data_section, offset, value) \
> > > > + float_vectorN data_section 8 offset value
> > > > +#define float_vector64(data_section, offset, value) \
> > > > + float_vectorN data_section 16 offset value
> > > > +
> > > > +#endif
> > > > --
> > > > 2.34.1
> > > >
> > >
> > > Please use .h files in fpu directory.
> >
> > Are .S files globbed somewhere or something?
> >
> > It uses assembler macros so its convenient for the
> > extension to match.
>
> Use new macros or rename files before commit.
Okay.
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-07 8:52 ` [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S Noah Goldstein via Libc-alpha
@ 2022-12-16 17:05 ` H.J. Lu via Libc-alpha
2022-12-16 18:17 ` Noah Goldstein via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: H.J. Lu via Libc-alpha @ 2022-12-16 17:05 UTC (permalink / raw)
To: Noah Goldstein, Sunil K Pandey; +Cc: libc-alpha, andrey.kolesov, carlos
On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
>
> No changes to the logic, just change how rodata is handled.
>
> 1. Define the rodatas using the new macros so they check that the
> offset is correct.
>
> 2. Use common data where applicable.
> ---
> .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> 1 file changed, 197 insertions(+), 253 deletions(-)
>
> diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> index d74fc7731d..765e9ed7f7 100644
> --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> @@ -70,94 +70,99 @@
> *
> */
>
> -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> - by use in the function. On cold-starts this might help the
> - prefetcher. Possibly a better idea is to interleave start/end so
> - that the prefetcher is less likely to detect a stream and pull
> - irrelivant lines into cache. */
>
> -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> - */
> +
> +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> +#include "svml_s_common_evex512_rodata_offsets.h"
> +
> +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> + 4 bytes each. */
> #define _iExpMantMask_UISA 0
> #define _iMinIdxOfsMask_UISA 4
> #define _iMaxIdxMask_UISA 8
> #define _iExpMask 12
>
> -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> - each. */
> -#define _sC_lo 0
> -#define _sC_hi 64
> -#define _sP7_lo 128
> -#define _sP7_hi 192
> -#define _sSignMask 256
> -#define _sP6_lo 320
> -#define _sP6_hi 384
> -#define _sP5_lo 448
> -#define _sP5_hi 512
> -#define _sP4_lo 576
> -#define _sP4_hi 640
> -#define _sP3_lo 704
> -#define _sP3_hi 768
> -#define _sP2_lo 832
> -#define _sP2_hi 896
> -#define _sP0_lo 960
> -#define _sP0_hi 1024
> +/* Offsets for data table __svml_stanh_data_internal. Ordered
> + by use in the function. On cold-starts this might help the
> + prefetcher. Possibly a better idea is to interleave start/end so
> + that the prefetcher is less likely to detect a stream and pull
> + irrelivant lines into cache. */
> +
> +/* Offsets for data table __svml_stanh_data_internal.
> + 64 bytes each. */
> +#define _sC_lo 0
> +#define _sC_hi 64
> +#define _sP7_lo 128
> +#define _sP7_hi 192
> +#define _sP6_lo 256
> +#define _sP6_hi 320
> +#define _sP5_lo 384
> +#define _sP5_hi 448
> +#define _sP4_lo 512
> +#define _sP4_hi 576
> +#define _sP3_lo 640
> +#define _sP3_hi 704
> +#define _sP2_lo 768
> +#define _sP2_hi 832
> +#define _sP0_lo 896
> +#define _sP0_hi 960
> +
>
> #include <sysdep.h>
> -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
>
> .section .text.evex512, "ax", @progbits
> ENTRY(_ZGVeN16v_tanhf_skx)
> - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> + /* Here huge arguments, INF and NaNs are filtered out to
> + callout. */
> + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
>
> /* Selection arguments between [0, 0x03e00000] into zmm3. */
> vpxord %zmm3, %zmm3, %zmm3
> vpmaxsd %zmm3, %zmm2, %zmm3
> - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
>
> /* Setup permute indices in zmm3. */
> vpsrld $21, %zmm3, %zmm3
>
> /* Store if there are any special cases in k1. */
> - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
>
> - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
>
> - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
>
> /* Store absolute values of inputs in zmm1. */
> - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> vandnps %zmm0, %zmm4, %zmm1
> vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
>
> - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
>
> - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
>
> vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
>
> - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
>
> - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
>
> vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
>
> - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
>
> - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
>
> vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
>
> /* Go to special inputs processing branch. */
> jne L(SPECIAL_VALUES_BRANCH)
> - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> +
> /* Wait until after branch of write over zmm0. */
> vpternlogd $0xec, %zmm4, %zmm2, %zmm0
>
> @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
>
> /* Cold case. edx has 1s where there was a special value that
> needs to be handled by a tanhf call. Optimize for code size
> - more so than speed here. */
> + more so than speed here. */
> L(SPECIAL_VALUES_BRANCH):
> - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> - /* Use r13 to save/restore the stack. This allows us to use rbp as
> - callee save register saving code size. */
> +
> + /* Use r13 to save/restore the stack. This allows us to use rbp
> + as callee save register saving code size. */
> pushq %r13
> - cfi_adjust_cfa_offset(8)
> - cfi_offset(r13, -16)
> - /* Need to callee save registers to preserve state across tanhf calls.
> - */
> + cfi_adjust_cfa_offset (8)
> + cfi_offset (r13, -16)
> + /* Need to callee save registers to preserve state across tanhf
> + calls. */
> pushq %rbx
> - cfi_adjust_cfa_offset(8)
> - cfi_offset(rbx, -24)
> + cfi_adjust_cfa_offset (8)
> + cfi_offset (rbx, -24)
> pushq %rbp
> - cfi_adjust_cfa_offset(8)
> - cfi_offset(rbp, -32)
> + cfi_adjust_cfa_offset (8)
> + cfi_offset (rbp, -32)
> movq %rsp, %r13
> - cfi_def_cfa_register(r13)
> + cfi_def_cfa_register (r13)
>
> /* Align stack and make room for 2x zmm vectors. */
> andq $-64, %rsp
> @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
>
> vzeroupper
>
> - /* edx has 1s where there was a special value that needs to be handled
> - by a tanhf call. */
> + /* edx has 1s where there was a special value that needs to be
> + handled by a tanhf call. */
> movl %edx, %ebx
> L(SPECIAL_VALUES_LOOP):
> - # LOE rbx rbp r12 r13 r14 r15
> - /* use rbp as index for special value that is saved across calls to
> - tanhf. We technically don't need a callee save register here as offset
> - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> - in the loop. Realigning also costs more code size. */
> +
> + /* use rbp as index for special value that is saved across calls
> + to tanhf. We technically don't need a callee save register
> + here as offset to rsp is always [0, 56] so we can restore
> + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> + save/restore vs 2 extra instructions in the loop. Realigning
> + also costs more code size. */
> xorl %ebp, %ebp
> tzcntl %ebx, %ebp
>
> @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> vmovss 64(%rsp, %rbp, 4), %xmm0
> call tanhf@PLT
>
> - /* No good way to avoid the store-forwarding fault this will cause on
> - return. `lfence` avoids the SF fault but at greater cost as it
> - serialized stack/callee save restoration. */
> + /* No good way to avoid the store-forwarding fault this will
> + cause on return. `lfence` avoids the SF fault but at greater
> + cost as it serialized stack/callee save restoration. */
> vmovss %xmm0, (%rsp, %rbp, 4)
>
> - blsrl %ebx, %ebx
> + blsrl %ebx, %ebx
> jnz L(SPECIAL_VALUES_LOOP)
> - # LOE r12 r13 r14 r15
> +
>
> /* All results have been written to (%rsp). */
> vmovaps (%rsp), %zmm0
> /* Restore rsp. */
> movq %r13, %rsp
> - cfi_def_cfa_register(rsp)
> + cfi_def_cfa_register (rsp)
> /* Restore callee save registers. */
> popq %rbp
> - cfi_adjust_cfa_offset(-8)
> - cfi_restore(rbp)
> + cfi_adjust_cfa_offset (-8)
> + cfi_restore (rbp)
> popq %rbx
> - cfi_adjust_cfa_offset(-8)
> - cfi_restore(rbp)
> + cfi_adjust_cfa_offset (-8)
> + cfi_restore (rbp)
> popq %r13
> - cfi_adjust_cfa_offset(-8)
> - cfi_restore(r13)
> + cfi_adjust_cfa_offset (-8)
> + cfi_restore (r13)
> ret
> END(_ZGVeN16v_tanhf_skx)
>
> - .section .rodata, "a"
> + .section .rodata.evex512, "a"
> .align 16
> -#ifdef __svml_stanh_data_internal_typedef
> -typedef unsigned int VUINT32;
> -typedef struct
> - {
> - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> -} __svml_stanh_data_internal;
> -#endif
> -
> -__svml_stanh_data_internal:
> - .align 4
> - /* _iExpMantMask_UISA */
> - .long 0x7fe00000
> -
> - .align 4
> - /* _iMinIdxOfsMask_UISA */
> - .long 0x3d400000
> -
> - .align 4
> - /* _iMaxIdxMask_UISA */
> - .long 0x03e00000
> -
> - .align 4
> - /* _iExpMask */
> - .long 0x7f000000
> -
> - .align 64
> -__svml_stanh_data_internal_al64:
> - .align 64
> - /* _sC_lo */
> - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> -
> - .align 64
> - /* _sC_hi */
> - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> -
> - .align 64
> - /* _sP7_lo */
> - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> -
> - .align 64
> - /* _sP7_hi */
> - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
>
> - .align 64
> - /* _sSignMask */
> - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> -
> - .align 64
> - /* _sP6_lo */
> - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> -
> - .align 64
> - /* _sP6_hi */
> - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> -
> - .align 64
> - /* _sP5_lo */
> - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> -
> - .align 64
> - /* _sP5_hi */
> - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> -
> - .align 64
> - /* _sP4_lo */
> - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> -
> - .align 64
> - /* _sP4_hi */
> - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> -
> - .align 64
> - /* _sP3_lo */
> - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> -
> - .align 64
> - /* _sP3_hi */
> - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> -
> - .align 64
> - /* _sP2_lo */
> - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> -
> - .align 64
> - /* _sP2_hi */
> - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> -
> - .align 64
> - /* _sP0_lo */
> - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> -
> - .align 64
> - /* _sP0_hi */
> - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> +LOCAL_DATA_NAME_UNALIGNED:
> + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> + .type LOCAL_DATA_NAME_UNALIGNED, @object
> + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
>
> .align 64
> - .type __svml_stanh_data_internal_al64, @object
> - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> - .type __svml_stanh_data_internal, @object
> - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> +LOCAL_DATA_NAME:
> + float_block (LOCAL_DATA_NAME, _sC_lo,
> + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> +
> + float_block (LOCAL_DATA_NAME, _sC_hi,
> + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP7_lo,
> + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> +
> + float_block (LOCAL_DATA_NAME, _sP7_hi,
> + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP6_lo,
> + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> +
> + float_block (LOCAL_DATA_NAME, _sP6_hi,
> + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP5_lo,
> + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> +
> + float_block (LOCAL_DATA_NAME, _sP5_hi,
> + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP4_lo,
> + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> +
> + float_block (LOCAL_DATA_NAME, _sP4_hi,
> + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP3_lo,
> + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> +
> + float_block (LOCAL_DATA_NAME, _sP3_hi,
> + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP2_lo,
> + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> +
> + float_block (LOCAL_DATA_NAME, _sP2_hi,
> + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> +
> + float_block (LOCAL_DATA_NAME, _sP0_lo,
> + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> +
> + float_block (LOCAL_DATA_NAME, _sP0_hi,
> + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> +
> + .type LOCAL_DATA_NAME, @object
> + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> --
> 2.34.1
>
The data movement makes the assembler codes much harder to follow.
Sunil, what do you think of this patch series?
--
H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 17:05 ` H.J. Lu via Libc-alpha
@ 2022-12-16 18:17 ` Noah Goldstein via Libc-alpha
2022-12-16 21:37 ` H.J. Lu via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-16 18:17 UTC (permalink / raw)
To: H.J. Lu; +Cc: Sunil K Pandey, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > No changes to the logic, just change how rodata is handled.
> >
> > 1. Define the rodatas using the new macros so they check that the
> > offset is correct.
> >
> > 2. Use common data where applicable.
> > ---
> > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > 1 file changed, 197 insertions(+), 253 deletions(-)
> >
> > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > index d74fc7731d..765e9ed7f7 100644
> > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > @@ -70,94 +70,99 @@
> > *
> > */
> >
> > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > - by use in the function. On cold-starts this might help the
> > - prefetcher. Possibly a better idea is to interleave start/end so
> > - that the prefetcher is less likely to detect a stream and pull
> > - irrelivant lines into cache. */
> >
> > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > - */
> > +
> > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > +#include "svml_s_common_evex512_rodata_offsets.h"
> > +
> > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > + 4 bytes each. */
> > #define _iExpMantMask_UISA 0
> > #define _iMinIdxOfsMask_UISA 4
> > #define _iMaxIdxMask_UISA 8
> > #define _iExpMask 12
> >
> > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > - each. */
> > -#define _sC_lo 0
> > -#define _sC_hi 64
> > -#define _sP7_lo 128
> > -#define _sP7_hi 192
> > -#define _sSignMask 256
> > -#define _sP6_lo 320
> > -#define _sP6_hi 384
> > -#define _sP5_lo 448
> > -#define _sP5_hi 512
> > -#define _sP4_lo 576
> > -#define _sP4_hi 640
> > -#define _sP3_lo 704
> > -#define _sP3_hi 768
> > -#define _sP2_lo 832
> > -#define _sP2_hi 896
> > -#define _sP0_lo 960
> > -#define _sP0_hi 1024
> > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > + by use in the function. On cold-starts this might help the
> > + prefetcher. Possibly a better idea is to interleave start/end so
> > + that the prefetcher is less likely to detect a stream and pull
> > + irrelivant lines into cache. */
> > +
> > +/* Offsets for data table __svml_stanh_data_internal.
> > + 64 bytes each. */
> > +#define _sC_lo 0
> > +#define _sC_hi 64
> > +#define _sP7_lo 128
> > +#define _sP7_hi 192
> > +#define _sP6_lo 256
> > +#define _sP6_hi 320
> > +#define _sP5_lo 384
> > +#define _sP5_hi 448
> > +#define _sP4_lo 512
> > +#define _sP4_hi 576
> > +#define _sP3_lo 640
> > +#define _sP3_hi 704
> > +#define _sP2_lo 768
> > +#define _sP2_hi 832
> > +#define _sP0_lo 896
> > +#define _sP0_hi 960
> > +
> >
> > #include <sysdep.h>
> > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> >
> > .section .text.evex512, "ax", @progbits
> > ENTRY(_ZGVeN16v_tanhf_skx)
> > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > + /* Here huge arguments, INF and NaNs are filtered out to
> > + callout. */
> > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> >
> > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > vpxord %zmm3, %zmm3, %zmm3
> > vpmaxsd %zmm3, %zmm2, %zmm3
> > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> >
> > /* Setup permute indices in zmm3. */
> > vpsrld $21, %zmm3, %zmm3
> >
> > /* Store if there are any special cases in k1. */
> > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> >
> > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> >
> > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> >
> > /* Store absolute values of inputs in zmm1. */
> > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > vandnps %zmm0, %zmm4, %zmm1
> > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> >
> > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> >
> > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> >
> > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> >
> > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> >
> > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> >
> > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> >
> > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> >
> > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> >
> > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> >
> > /* Go to special inputs processing branch. */
> > jne L(SPECIAL_VALUES_BRANCH)
> > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > +
> > /* Wait until after branch of write over zmm0. */
> > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> >
> > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> >
> > /* Cold case. edx has 1s where there was a special value that
> > needs to be handled by a tanhf call. Optimize for code size
> > - more so than speed here. */
> > + more so than speed here. */
> > L(SPECIAL_VALUES_BRANCH):
> > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > - callee save register saving code size. */
> > +
> > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > + as callee save register saving code size. */
> > pushq %r13
> > - cfi_adjust_cfa_offset(8)
> > - cfi_offset(r13, -16)
> > - /* Need to callee save registers to preserve state across tanhf calls.
> > - */
> > + cfi_adjust_cfa_offset (8)
> > + cfi_offset (r13, -16)
> > + /* Need to callee save registers to preserve state across tanhf
> > + calls. */
> > pushq %rbx
> > - cfi_adjust_cfa_offset(8)
> > - cfi_offset(rbx, -24)
> > + cfi_adjust_cfa_offset (8)
> > + cfi_offset (rbx, -24)
> > pushq %rbp
> > - cfi_adjust_cfa_offset(8)
> > - cfi_offset(rbp, -32)
> > + cfi_adjust_cfa_offset (8)
> > + cfi_offset (rbp, -32)
> > movq %rsp, %r13
> > - cfi_def_cfa_register(r13)
> > + cfi_def_cfa_register (r13)
> >
> > /* Align stack and make room for 2x zmm vectors. */
> > andq $-64, %rsp
> > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> >
> > vzeroupper
> >
> > - /* edx has 1s where there was a special value that needs to be handled
> > - by a tanhf call. */
> > + /* edx has 1s where there was a special value that needs to be
> > + handled by a tanhf call. */
> > movl %edx, %ebx
> > L(SPECIAL_VALUES_LOOP):
> > - # LOE rbx rbp r12 r13 r14 r15
> > - /* use rbp as index for special value that is saved across calls to
> > - tanhf. We technically don't need a callee save register here as offset
> > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > - in the loop. Realigning also costs more code size. */
> > +
> > + /* use rbp as index for special value that is saved across calls
> > + to tanhf. We technically don't need a callee save register
> > + here as offset to rsp is always [0, 56] so we can restore
> > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > + save/restore vs 2 extra instructions in the loop. Realigning
> > + also costs more code size. */
> > xorl %ebp, %ebp
> > tzcntl %ebx, %ebp
> >
> > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > vmovss 64(%rsp, %rbp, 4), %xmm0
> > call tanhf@PLT
> >
> > - /* No good way to avoid the store-forwarding fault this will cause on
> > - return. `lfence` avoids the SF fault but at greater cost as it
> > - serialized stack/callee save restoration. */
> > + /* No good way to avoid the store-forwarding fault this will
> > + cause on return. `lfence` avoids the SF fault but at greater
> > + cost as it serialized stack/callee save restoration. */
> > vmovss %xmm0, (%rsp, %rbp, 4)
> >
> > - blsrl %ebx, %ebx
> > + blsrl %ebx, %ebx
> > jnz L(SPECIAL_VALUES_LOOP)
> > - # LOE r12 r13 r14 r15
> > +
> >
> > /* All results have been written to (%rsp). */
> > vmovaps (%rsp), %zmm0
> > /* Restore rsp. */
> > movq %r13, %rsp
> > - cfi_def_cfa_register(rsp)
> > + cfi_def_cfa_register (rsp)
> > /* Restore callee save registers. */
> > popq %rbp
> > - cfi_adjust_cfa_offset(-8)
> > - cfi_restore(rbp)
> > + cfi_adjust_cfa_offset (-8)
> > + cfi_restore (rbp)
> > popq %rbx
> > - cfi_adjust_cfa_offset(-8)
> > - cfi_restore(rbp)
> > + cfi_adjust_cfa_offset (-8)
> > + cfi_restore (rbp)
> > popq %r13
> > - cfi_adjust_cfa_offset(-8)
> > - cfi_restore(r13)
> > + cfi_adjust_cfa_offset (-8)
> > + cfi_restore (r13)
> > ret
> > END(_ZGVeN16v_tanhf_skx)
> >
> > - .section .rodata, "a"
> > + .section .rodata.evex512, "a"
> > .align 16
> > -#ifdef __svml_stanh_data_internal_typedef
> > -typedef unsigned int VUINT32;
> > -typedef struct
> > - {
> > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > -} __svml_stanh_data_internal;
> > -#endif
> > -
> > -__svml_stanh_data_internal:
> > - .align 4
> > - /* _iExpMantMask_UISA */
> > - .long 0x7fe00000
> > -
> > - .align 4
> > - /* _iMinIdxOfsMask_UISA */
> > - .long 0x3d400000
> > -
> > - .align 4
> > - /* _iMaxIdxMask_UISA */
> > - .long 0x03e00000
> > -
> > - .align 4
> > - /* _iExpMask */
> > - .long 0x7f000000
> > -
> > - .align 64
> > -__svml_stanh_data_internal_al64:
> > - .align 64
> > - /* _sC_lo */
> > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > -
> > - .align 64
> > - /* _sC_hi */
> > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > -
> > - .align 64
> > - /* _sP7_lo */
> > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > -
> > - .align 64
> > - /* _sP7_hi */
> > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> >
> > - .align 64
> > - /* _sSignMask */
> > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > -
> > - .align 64
> > - /* _sP6_lo */
> > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > -
> > - .align 64
> > - /* _sP6_hi */
> > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > -
> > - .align 64
> > - /* _sP5_lo */
> > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > -
> > - .align 64
> > - /* _sP5_hi */
> > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > -
> > - .align 64
> > - /* _sP4_lo */
> > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > -
> > - .align 64
> > - /* _sP4_hi */
> > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > -
> > - .align 64
> > - /* _sP3_lo */
> > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > -
> > - .align 64
> > - /* _sP3_hi */
> > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > -
> > - .align 64
> > - /* _sP2_lo */
> > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > -
> > - .align 64
> > - /* _sP2_hi */
> > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > -
> > - .align 64
> > - /* _sP0_lo */
> > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > -
> > - .align 64
> > - /* _sP0_hi */
> > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > +LOCAL_DATA_NAME_UNALIGNED:
> > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> >
> > .align 64
> > - .type __svml_stanh_data_internal_al64, @object
> > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > - .type __svml_stanh_data_internal, @object
> > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > +LOCAL_DATA_NAME:
> > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > +
> > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > +
> > + .type LOCAL_DATA_NAME, @object
> > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > --
> > 2.34.1
> >
>
> The data movement makes the assembler codes much harder to follow.
> Sunil, what do you think of this patch series?
What do you mean? The change on in how we define rodata or the movement
to multiple files or something else?
>
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 18:17 ` Noah Goldstein via Libc-alpha
@ 2022-12-16 21:37 ` H.J. Lu via Libc-alpha
2022-12-16 21:51 ` Noah Goldstein via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: H.J. Lu via Libc-alpha @ 2022-12-16 21:37 UTC (permalink / raw)
To: Noah Goldstein; +Cc: Sunil K Pandey, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 10:18 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
>
> On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
> >
> > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > >
> > > No changes to the logic, just change how rodata is handled.
> > >
> > > 1. Define the rodatas using the new macros so they check that the
> > > offset is correct.
> > >
> > > 2. Use common data where applicable.
> > > ---
> > > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > > 1 file changed, 197 insertions(+), 253 deletions(-)
> > >
> > > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > index d74fc7731d..765e9ed7f7 100644
> > > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > @@ -70,94 +70,99 @@
> > > *
> > > */
> > >
> > > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > > - by use in the function. On cold-starts this might help the
> > > - prefetcher. Possibly a better idea is to interleave start/end so
> > > - that the prefetcher is less likely to detect a stream and pull
> > > - irrelivant lines into cache. */
> > >
> > > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > > - */
> > > +
> > > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > > +#include "svml_s_common_evex512_rodata_offsets.h"
> > > +
> > > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > > + 4 bytes each. */
> > > #define _iExpMantMask_UISA 0
> > > #define _iMinIdxOfsMask_UISA 4
> > > #define _iMaxIdxMask_UISA 8
> > > #define _iExpMask 12
> > >
> > > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > > - each. */
> > > -#define _sC_lo 0
> > > -#define _sC_hi 64
> > > -#define _sP7_lo 128
> > > -#define _sP7_hi 192
> > > -#define _sSignMask 256
> > > -#define _sP6_lo 320
> > > -#define _sP6_hi 384
> > > -#define _sP5_lo 448
> > > -#define _sP5_hi 512
> > > -#define _sP4_lo 576
> > > -#define _sP4_hi 640
> > > -#define _sP3_lo 704
> > > -#define _sP3_hi 768
> > > -#define _sP2_lo 832
> > > -#define _sP2_hi 896
> > > -#define _sP0_lo 960
> > > -#define _sP0_hi 1024
> > > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > > + by use in the function. On cold-starts this might help the
> > > + prefetcher. Possibly a better idea is to interleave start/end so
> > > + that the prefetcher is less likely to detect a stream and pull
> > > + irrelivant lines into cache. */
> > > +
> > > +/* Offsets for data table __svml_stanh_data_internal.
> > > + 64 bytes each. */
> > > +#define _sC_lo 0
> > > +#define _sC_hi 64
> > > +#define _sP7_lo 128
> > > +#define _sP7_hi 192
> > > +#define _sP6_lo 256
> > > +#define _sP6_hi 320
> > > +#define _sP5_lo 384
> > > +#define _sP5_hi 448
> > > +#define _sP4_lo 512
> > > +#define _sP4_hi 576
> > > +#define _sP3_lo 640
> > > +#define _sP3_hi 704
> > > +#define _sP2_lo 768
> > > +#define _sP2_hi 832
> > > +#define _sP0_lo 896
> > > +#define _sP0_hi 960
> > > +
> > >
> > > #include <sysdep.h>
> > > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> > >
> > > .section .text.evex512, "ax", @progbits
> > > ENTRY(_ZGVeN16v_tanhf_skx)
> > > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > + /* Here huge arguments, INF and NaNs are filtered out to
> > > + callout. */
> > > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > >
> > > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > > vpxord %zmm3, %zmm3, %zmm3
> > > vpmaxsd %zmm3, %zmm2, %zmm3
> > > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > >
> > > /* Setup permute indices in zmm3. */
> > > vpsrld $21, %zmm3, %zmm3
> > >
> > > /* Store if there are any special cases in k1. */
> > > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > >
> > > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > >
> > > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > >
> > > /* Store absolute values of inputs in zmm1. */
> > > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > > vandnps %zmm0, %zmm4, %zmm1
> > > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> > >
> > > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > >
> > > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > >
> > > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> > >
> > > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > >
> > > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > >
> > > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> > >
> > > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > >
> > > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > >
> > > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > >
> > > /* Go to special inputs processing branch. */
> > > jne L(SPECIAL_VALUES_BRANCH)
> > > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > +
> > > /* Wait until after branch of write over zmm0. */
> > > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> > >
> > > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > >
> > > /* Cold case. edx has 1s where there was a special value that
> > > needs to be handled by a tanhf call. Optimize for code size
> > > - more so than speed here. */
> > > + more so than speed here. */
> > > L(SPECIAL_VALUES_BRANCH):
> > > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > > - callee save register saving code size. */
> > > +
> > > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > > + as callee save register saving code size. */
> > > pushq %r13
> > > - cfi_adjust_cfa_offset(8)
> > > - cfi_offset(r13, -16)
> > > - /* Need to callee save registers to preserve state across tanhf calls.
> > > - */
> > > + cfi_adjust_cfa_offset (8)
> > > + cfi_offset (r13, -16)
> > > + /* Need to callee save registers to preserve state across tanhf
> > > + calls. */
> > > pushq %rbx
> > > - cfi_adjust_cfa_offset(8)
> > > - cfi_offset(rbx, -24)
> > > + cfi_adjust_cfa_offset (8)
> > > + cfi_offset (rbx, -24)
> > > pushq %rbp
> > > - cfi_adjust_cfa_offset(8)
> > > - cfi_offset(rbp, -32)
> > > + cfi_adjust_cfa_offset (8)
> > > + cfi_offset (rbp, -32)
> > > movq %rsp, %r13
> > > - cfi_def_cfa_register(r13)
> > > + cfi_def_cfa_register (r13)
> > >
> > > /* Align stack and make room for 2x zmm vectors. */
> > > andq $-64, %rsp
> > > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> > >
> > > vzeroupper
> > >
> > > - /* edx has 1s where there was a special value that needs to be handled
> > > - by a tanhf call. */
> > > + /* edx has 1s where there was a special value that needs to be
> > > + handled by a tanhf call. */
> > > movl %edx, %ebx
> > > L(SPECIAL_VALUES_LOOP):
> > > - # LOE rbx rbp r12 r13 r14 r15
> > > - /* use rbp as index for special value that is saved across calls to
> > > - tanhf. We technically don't need a callee save register here as offset
> > > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > > - in the loop. Realigning also costs more code size. */
> > > +
> > > + /* use rbp as index for special value that is saved across calls
> > > + to tanhf. We technically don't need a callee save register
> > > + here as offset to rsp is always [0, 56] so we can restore
> > > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > > + save/restore vs 2 extra instructions in the loop. Realigning
> > > + also costs more code size. */
> > > xorl %ebp, %ebp
> > > tzcntl %ebx, %ebp
> > >
> > > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > > vmovss 64(%rsp, %rbp, 4), %xmm0
> > > call tanhf@PLT
> > >
> > > - /* No good way to avoid the store-forwarding fault this will cause on
> > > - return. `lfence` avoids the SF fault but at greater cost as it
> > > - serialized stack/callee save restoration. */
> > > + /* No good way to avoid the store-forwarding fault this will
> > > + cause on return. `lfence` avoids the SF fault but at greater
> > > + cost as it serialized stack/callee save restoration. */
> > > vmovss %xmm0, (%rsp, %rbp, 4)
> > >
> > > - blsrl %ebx, %ebx
> > > + blsrl %ebx, %ebx
> > > jnz L(SPECIAL_VALUES_LOOP)
> > > - # LOE r12 r13 r14 r15
> > > +
> > >
> > > /* All results have been written to (%rsp). */
> > > vmovaps (%rsp), %zmm0
> > > /* Restore rsp. */
> > > movq %r13, %rsp
> > > - cfi_def_cfa_register(rsp)
> > > + cfi_def_cfa_register (rsp)
> > > /* Restore callee save registers. */
> > > popq %rbp
> > > - cfi_adjust_cfa_offset(-8)
> > > - cfi_restore(rbp)
> > > + cfi_adjust_cfa_offset (-8)
> > > + cfi_restore (rbp)
> > > popq %rbx
> > > - cfi_adjust_cfa_offset(-8)
> > > - cfi_restore(rbp)
> > > + cfi_adjust_cfa_offset (-8)
> > > + cfi_restore (rbp)
> > > popq %r13
> > > - cfi_adjust_cfa_offset(-8)
> > > - cfi_restore(r13)
> > > + cfi_adjust_cfa_offset (-8)
> > > + cfi_restore (r13)
> > > ret
> > > END(_ZGVeN16v_tanhf_skx)
> > >
> > > - .section .rodata, "a"
> > > + .section .rodata.evex512, "a"
> > > .align 16
> > > -#ifdef __svml_stanh_data_internal_typedef
> > > -typedef unsigned int VUINT32;
> > > -typedef struct
> > > - {
> > > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > > -} __svml_stanh_data_internal;
> > > -#endif
> > > -
> > > -__svml_stanh_data_internal:
> > > - .align 4
> > > - /* _iExpMantMask_UISA */
> > > - .long 0x7fe00000
> > > -
> > > - .align 4
> > > - /* _iMinIdxOfsMask_UISA */
> > > - .long 0x3d400000
> > > -
> > > - .align 4
> > > - /* _iMaxIdxMask_UISA */
> > > - .long 0x03e00000
> > > -
> > > - .align 4
> > > - /* _iExpMask */
> > > - .long 0x7f000000
> > > -
> > > - .align 64
> > > -__svml_stanh_data_internal_al64:
> > > - .align 64
> > > - /* _sC_lo */
> > > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > > -
> > > - .align 64
> > > - /* _sC_hi */
> > > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP7_lo */
> > > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > > -
> > > - .align 64
> > > - /* _sP7_hi */
> > > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> > >
> > > - .align 64
> > > - /* _sSignMask */
> > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > -
> > > - .align 64
> > > - /* _sP6_lo */
> > > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > > -
> > > - .align 64
> > > - /* _sP6_hi */
> > > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP5_lo */
> > > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > > -
> > > - .align 64
> > > - /* _sP5_hi */
> > > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP4_lo */
> > > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > > -
> > > - .align 64
> > > - /* _sP4_hi */
> > > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP3_lo */
> > > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > > -
> > > - .align 64
> > > - /* _sP3_hi */
> > > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP2_lo */
> > > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > > -
> > > - .align 64
> > > - /* _sP2_hi */
> > > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > > -
> > > - .align 64
> > > - /* _sP0_lo */
> > > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > > -
> > > - .align 64
> > > - /* _sP0_hi */
> > > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > > +LOCAL_DATA_NAME_UNALIGNED:
> > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> > >
> > > .align 64
> > > - .type __svml_stanh_data_internal_al64, @object
> > > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > > - .type __svml_stanh_data_internal, @object
> > > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > > +LOCAL_DATA_NAME:
> > > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > > +
> > > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > > +
> > > + .type LOCAL_DATA_NAME, @object
> > > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > > --
> > > 2.34.1
> > >
> >
> > The data movement makes the assembler codes much harder to follow.
> > Sunil, what do you think of this patch series?
>
> What do you mean? The change on in how we define rodata or the movement
> to multiple files or something else?
The glibc way to support data files for assembly codes is to define
data in C and use *.sym to generate offsets for assembly files, like
sysdeps/x86/cpu-features-offsets.sym:XSAVE_STATE_SIZE_OFFSET
offsetof (struct cpu_features, xsave_state_size)
sysdeps/x86_64/dl-trampoline.h: sub
_rtld_local_ro+RTLD_GLOBAL_RO_DL_X86_CPU_FEATURES_OFFSET+XSAVE_STATE_SIZE_OFFSET(%rip),
%RSP_LP
sysdeps/x86_64/dl-trampoline.h: sub
_dl_x86_cpu_features+XSAVE_STATE_SIZE_OFFSET(%rip), %RSP_LP
--
H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 21:37 ` H.J. Lu via Libc-alpha
@ 2022-12-16 21:51 ` Noah Goldstein via Libc-alpha
2022-12-16 22:01 ` H.J. Lu via Libc-alpha
0 siblings, 1 reply; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2022-12-16 21:51 UTC (permalink / raw)
To: H.J. Lu; +Cc: Sunil K Pandey, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 1:38 PM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Fri, Dec 16, 2022 at 10:18 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
> > >
> > > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > >
> > > > No changes to the logic, just change how rodata is handled.
> > > >
> > > > 1. Define the rodatas using the new macros so they check that the
> > > > offset is correct.
> > > >
> > > > 2. Use common data where applicable.
> > > > ---
> > > > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > > > 1 file changed, 197 insertions(+), 253 deletions(-)
> > > >
> > > > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > index d74fc7731d..765e9ed7f7 100644
> > > > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > @@ -70,94 +70,99 @@
> > > > *
> > > > */
> > > >
> > > > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > > > - by use in the function. On cold-starts this might help the
> > > > - prefetcher. Possibly a better idea is to interleave start/end so
> > > > - that the prefetcher is less likely to detect a stream and pull
> > > > - irrelivant lines into cache. */
> > > >
> > > > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > > > - */
> > > > +
> > > > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > > > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > > > +#include "svml_s_common_evex512_rodata_offsets.h"
> > > > +
> > > > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > > > + 4 bytes each. */
> > > > #define _iExpMantMask_UISA 0
> > > > #define _iMinIdxOfsMask_UISA 4
> > > > #define _iMaxIdxMask_UISA 8
> > > > #define _iExpMask 12
> > > >
> > > > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > > > - each. */
> > > > -#define _sC_lo 0
> > > > -#define _sC_hi 64
> > > > -#define _sP7_lo 128
> > > > -#define _sP7_hi 192
> > > > -#define _sSignMask 256
> > > > -#define _sP6_lo 320
> > > > -#define _sP6_hi 384
> > > > -#define _sP5_lo 448
> > > > -#define _sP5_hi 512
> > > > -#define _sP4_lo 576
> > > > -#define _sP4_hi 640
> > > > -#define _sP3_lo 704
> > > > -#define _sP3_hi 768
> > > > -#define _sP2_lo 832
> > > > -#define _sP2_hi 896
> > > > -#define _sP0_lo 960
> > > > -#define _sP0_hi 1024
> > > > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > > > + by use in the function. On cold-starts this might help the
> > > > + prefetcher. Possibly a better idea is to interleave start/end so
> > > > + that the prefetcher is less likely to detect a stream and pull
> > > > + irrelivant lines into cache. */
> > > > +
> > > > +/* Offsets for data table __svml_stanh_data_internal.
> > > > + 64 bytes each. */
> > > > +#define _sC_lo 0
> > > > +#define _sC_hi 64
> > > > +#define _sP7_lo 128
> > > > +#define _sP7_hi 192
> > > > +#define _sP6_lo 256
> > > > +#define _sP6_hi 320
> > > > +#define _sP5_lo 384
> > > > +#define _sP5_hi 448
> > > > +#define _sP4_lo 512
> > > > +#define _sP4_hi 576
> > > > +#define _sP3_lo 640
> > > > +#define _sP3_hi 704
> > > > +#define _sP2_lo 768
> > > > +#define _sP2_hi 832
> > > > +#define _sP0_lo 896
> > > > +#define _sP0_hi 960
> > > > +
> > > >
> > > > #include <sysdep.h>
> > > > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > > > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> > > >
> > > > .section .text.evex512, "ax", @progbits
> > > > ENTRY(_ZGVeN16v_tanhf_skx)
> > > > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > > > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > + /* Here huge arguments, INF and NaNs are filtered out to
> > > > + callout. */
> > > > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > >
> > > > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > > > vpxord %zmm3, %zmm3, %zmm3
> > > > vpmaxsd %zmm3, %zmm2, %zmm3
> > > > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > >
> > > > /* Setup permute indices in zmm3. */
> > > > vpsrld $21, %zmm3, %zmm3
> > > >
> > > > /* Store if there are any special cases in k1. */
> > > > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > >
> > > > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > > > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > > > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > >
> > > > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > > > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > > > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > >
> > > > /* Store absolute values of inputs in zmm1. */
> > > > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > > > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > > > vandnps %zmm0, %zmm4, %zmm1
> > > > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> > > >
> > > > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > > > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > > > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > >
> > > > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > > > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > > > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > >
> > > > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > > > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> > > >
> > > > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > > > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > > > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > >
> > > > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > > > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > > > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > >
> > > > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > > > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> > > >
> > > > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > > > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > > > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > >
> > > > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > > > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > > > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > >
> > > > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > > > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > > > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > >
> > > > /* Go to special inputs processing branch. */
> > > > jne L(SPECIAL_VALUES_BRANCH)
> > > > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > +
> > > > /* Wait until after branch of write over zmm0. */
> > > > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> > > >
> > > > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > >
> > > > /* Cold case. edx has 1s where there was a special value that
> > > > needs to be handled by a tanhf call. Optimize for code size
> > > > - more so than speed here. */
> > > > + more so than speed here. */
> > > > L(SPECIAL_VALUES_BRANCH):
> > > > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > > > - callee save register saving code size. */
> > > > +
> > > > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > > > + as callee save register saving code size. */
> > > > pushq %r13
> > > > - cfi_adjust_cfa_offset(8)
> > > > - cfi_offset(r13, -16)
> > > > - /* Need to callee save registers to preserve state across tanhf calls.
> > > > - */
> > > > + cfi_adjust_cfa_offset (8)
> > > > + cfi_offset (r13, -16)
> > > > + /* Need to callee save registers to preserve state across tanhf
> > > > + calls. */
> > > > pushq %rbx
> > > > - cfi_adjust_cfa_offset(8)
> > > > - cfi_offset(rbx, -24)
> > > > + cfi_adjust_cfa_offset (8)
> > > > + cfi_offset (rbx, -24)
> > > > pushq %rbp
> > > > - cfi_adjust_cfa_offset(8)
> > > > - cfi_offset(rbp, -32)
> > > > + cfi_adjust_cfa_offset (8)
> > > > + cfi_offset (rbp, -32)
> > > > movq %rsp, %r13
> > > > - cfi_def_cfa_register(r13)
> > > > + cfi_def_cfa_register (r13)
> > > >
> > > > /* Align stack and make room for 2x zmm vectors. */
> > > > andq $-64, %rsp
> > > > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> > > >
> > > > vzeroupper
> > > >
> > > > - /* edx has 1s where there was a special value that needs to be handled
> > > > - by a tanhf call. */
> > > > + /* edx has 1s where there was a special value that needs to be
> > > > + handled by a tanhf call. */
> > > > movl %edx, %ebx
> > > > L(SPECIAL_VALUES_LOOP):
> > > > - # LOE rbx rbp r12 r13 r14 r15
> > > > - /* use rbp as index for special value that is saved across calls to
> > > > - tanhf. We technically don't need a callee save register here as offset
> > > > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > > > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > > > - in the loop. Realigning also costs more code size. */
> > > > +
> > > > + /* use rbp as index for special value that is saved across calls
> > > > + to tanhf. We technically don't need a callee save register
> > > > + here as offset to rsp is always [0, 56] so we can restore
> > > > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > > > + save/restore vs 2 extra instructions in the loop. Realigning
> > > > + also costs more code size. */
> > > > xorl %ebp, %ebp
> > > > tzcntl %ebx, %ebp
> > > >
> > > > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > > > vmovss 64(%rsp, %rbp, 4), %xmm0
> > > > call tanhf@PLT
> > > >
> > > > - /* No good way to avoid the store-forwarding fault this will cause on
> > > > - return. `lfence` avoids the SF fault but at greater cost as it
> > > > - serialized stack/callee save restoration. */
> > > > + /* No good way to avoid the store-forwarding fault this will
> > > > + cause on return. `lfence` avoids the SF fault but at greater
> > > > + cost as it serialized stack/callee save restoration. */
> > > > vmovss %xmm0, (%rsp, %rbp, 4)
> > > >
> > > > - blsrl %ebx, %ebx
> > > > + blsrl %ebx, %ebx
> > > > jnz L(SPECIAL_VALUES_LOOP)
> > > > - # LOE r12 r13 r14 r15
> > > > +
> > > >
> > > > /* All results have been written to (%rsp). */
> > > > vmovaps (%rsp), %zmm0
> > > > /* Restore rsp. */
> > > > movq %r13, %rsp
> > > > - cfi_def_cfa_register(rsp)
> > > > + cfi_def_cfa_register (rsp)
> > > > /* Restore callee save registers. */
> > > > popq %rbp
> > > > - cfi_adjust_cfa_offset(-8)
> > > > - cfi_restore(rbp)
> > > > + cfi_adjust_cfa_offset (-8)
> > > > + cfi_restore (rbp)
> > > > popq %rbx
> > > > - cfi_adjust_cfa_offset(-8)
> > > > - cfi_restore(rbp)
> > > > + cfi_adjust_cfa_offset (-8)
> > > > + cfi_restore (rbp)
> > > > popq %r13
> > > > - cfi_adjust_cfa_offset(-8)
> > > > - cfi_restore(r13)
> > > > + cfi_adjust_cfa_offset (-8)
> > > > + cfi_restore (r13)
> > > > ret
> > > > END(_ZGVeN16v_tanhf_skx)
> > > >
> > > > - .section .rodata, "a"
> > > > + .section .rodata.evex512, "a"
> > > > .align 16
> > > > -#ifdef __svml_stanh_data_internal_typedef
> > > > -typedef unsigned int VUINT32;
> > > > -typedef struct
> > > > - {
> > > > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > > > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > > > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > > > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > > > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > > > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > > > -} __svml_stanh_data_internal;
> > > > -#endif
> > > > -
> > > > -__svml_stanh_data_internal:
> > > > - .align 4
> > > > - /* _iExpMantMask_UISA */
> > > > - .long 0x7fe00000
> > > > -
> > > > - .align 4
> > > > - /* _iMinIdxOfsMask_UISA */
> > > > - .long 0x3d400000
> > > > -
> > > > - .align 4
> > > > - /* _iMaxIdxMask_UISA */
> > > > - .long 0x03e00000
> > > > -
> > > > - .align 4
> > > > - /* _iExpMask */
> > > > - .long 0x7f000000
> > > > -
> > > > - .align 64
> > > > -__svml_stanh_data_internal_al64:
> > > > - .align 64
> > > > - /* _sC_lo */
> > > > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > > > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > > > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > > > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > > > -
> > > > - .align 64
> > > > - /* _sC_hi */
> > > > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > > > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > > > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > > > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP7_lo */
> > > > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > > > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > > > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > > > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > > > -
> > > > - .align 64
> > > > - /* _sP7_hi */
> > > > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > > > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > > > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > > > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> > > >
> > > > - .align 64
> > > > - /* _sSignMask */
> > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > -
> > > > - .align 64
> > > > - /* _sP6_lo */
> > > > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > > > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > > > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > > > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > > > -
> > > > - .align 64
> > > > - /* _sP6_hi */
> > > > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > > > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > > > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > > > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP5_lo */
> > > > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > > > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > > > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > > > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > > > -
> > > > - .align 64
> > > > - /* _sP5_hi */
> > > > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > > > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > > > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > > > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP4_lo */
> > > > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > > > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > > > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > > > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > > > -
> > > > - .align 64
> > > > - /* _sP4_hi */
> > > > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > > > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > > > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > > > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP3_lo */
> > > > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > > > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > > > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > > > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > > > -
> > > > - .align 64
> > > > - /* _sP3_hi */
> > > > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > > > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > > > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > > > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP2_lo */
> > > > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > > > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > > > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > > > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > > > -
> > > > - .align 64
> > > > - /* _sP2_hi */
> > > > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > > > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > > > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > > > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > > > -
> > > > - .align 64
> > > > - /* _sP0_lo */
> > > > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > > > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > > > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > > > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > > > -
> > > > - .align 64
> > > > - /* _sP0_hi */
> > > > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > > > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > > > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > > > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > > > +LOCAL_DATA_NAME_UNALIGNED:
> > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > > > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > > > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> > > >
> > > > .align 64
> > > > - .type __svml_stanh_data_internal_al64, @object
> > > > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > > > - .type __svml_stanh_data_internal, @object
> > > > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > > > +LOCAL_DATA_NAME:
> > > > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > > > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > > > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > > > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > > > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > > > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > > > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > > > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > > > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > > > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > > > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > > > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > > > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > > > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > > > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > > > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > > > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > > > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > > > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > > > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > > > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > > > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > > > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > > > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > > > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > > > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > > > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > > > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > > > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > > > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > > > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > > > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > > > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > > > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > > > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > > > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > > > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > > > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > > > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > > > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > > > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > > > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > > > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > > > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > > > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > > > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > > > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > > > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > > > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > > > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > > > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > > > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > > > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > > > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > > > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > > > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > > > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > > > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > > > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > > > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > > > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > > > +
> > > > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > > > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > > > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > > > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > > > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > > > +
> > > > + .type LOCAL_DATA_NAME, @object
> > > > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > > > --
> > > > 2.34.1
> > > >
> > >
> > > The data movement makes the assembler codes much harder to follow.
> > > Sunil, what do you think of this patch series?
> >
> > What do you mean? The change on in how we define rodata or the movement
> > to multiple files or something else?
>
> The glibc way to support data files for assembly codes is to define
> data in C and use *.sym to generate offsets for assembly files, like
I see. Although to be fair the entire SVML codebase bucks that trend.
Seems like a more dramatic trend to move all the offsets to C.
>
> sysdeps/x86/cpu-features-offsets.sym:XSAVE_STATE_SIZE_OFFSET
> offsetof (struct cpu_features, xsave_state_size)
> sysdeps/x86_64/dl-trampoline.h: sub
> _rtld_local_ro+RTLD_GLOBAL_RO_DL_X86_CPU_FEATURES_OFFSET+XSAVE_STATE_SIZE_OFFSET(%rip),
> %RSP_LP
> sysdeps/x86_64/dl-trampoline.h: sub
> _dl_x86_cpu_features+XSAVE_STATE_SIZE_OFFSET(%rip), %RSP_LP
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 21:51 ` Noah Goldstein via Libc-alpha
@ 2022-12-16 22:01 ` H.J. Lu via Libc-alpha
2022-12-16 22:54 ` Sunil Pandey via Libc-alpha
2023-06-27 18:23 ` Noah Goldstein via Libc-alpha
0 siblings, 2 replies; 38+ messages in thread
From: H.J. Lu via Libc-alpha @ 2022-12-16 22:01 UTC (permalink / raw)
To: Noah Goldstein; +Cc: Sunil K Pandey, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 1:52 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
>
> On Fri, Dec 16, 2022 at 1:38 PM H.J. Lu <hjl.tools@gmail.com> wrote:
> >
> > On Fri, Dec 16, 2022 at 10:18 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > >
> > > On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
> > > >
> > > > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > > >
> > > > > No changes to the logic, just change how rodata is handled.
> > > > >
> > > > > 1. Define the rodatas using the new macros so they check that the
> > > > > offset is correct.
> > > > >
> > > > > 2. Use common data where applicable.
> > > > > ---
> > > > > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > > > > 1 file changed, 197 insertions(+), 253 deletions(-)
> > > > >
> > > > > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > index d74fc7731d..765e9ed7f7 100644
> > > > > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > @@ -70,94 +70,99 @@
> > > > > *
> > > > > */
> > > > >
> > > > > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > > > > - by use in the function. On cold-starts this might help the
> > > > > - prefetcher. Possibly a better idea is to interleave start/end so
> > > > > - that the prefetcher is less likely to detect a stream and pull
> > > > > - irrelivant lines into cache. */
> > > > >
> > > > > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > > > > - */
> > > > > +
> > > > > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > > > > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > > > > +#include "svml_s_common_evex512_rodata_offsets.h"
> > > > > +
> > > > > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > > > > + 4 bytes each. */
> > > > > #define _iExpMantMask_UISA 0
> > > > > #define _iMinIdxOfsMask_UISA 4
> > > > > #define _iMaxIdxMask_UISA 8
> > > > > #define _iExpMask 12
> > > > >
> > > > > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > > > > - each. */
> > > > > -#define _sC_lo 0
> > > > > -#define _sC_hi 64
> > > > > -#define _sP7_lo 128
> > > > > -#define _sP7_hi 192
> > > > > -#define _sSignMask 256
> > > > > -#define _sP6_lo 320
> > > > > -#define _sP6_hi 384
> > > > > -#define _sP5_lo 448
> > > > > -#define _sP5_hi 512
> > > > > -#define _sP4_lo 576
> > > > > -#define _sP4_hi 640
> > > > > -#define _sP3_lo 704
> > > > > -#define _sP3_hi 768
> > > > > -#define _sP2_lo 832
> > > > > -#define _sP2_hi 896
> > > > > -#define _sP0_lo 960
> > > > > -#define _sP0_hi 1024
> > > > > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > > > > + by use in the function. On cold-starts this might help the
> > > > > + prefetcher. Possibly a better idea is to interleave start/end so
> > > > > + that the prefetcher is less likely to detect a stream and pull
> > > > > + irrelivant lines into cache. */
> > > > > +
> > > > > +/* Offsets for data table __svml_stanh_data_internal.
> > > > > + 64 bytes each. */
> > > > > +#define _sC_lo 0
> > > > > +#define _sC_hi 64
> > > > > +#define _sP7_lo 128
> > > > > +#define _sP7_hi 192
> > > > > +#define _sP6_lo 256
> > > > > +#define _sP6_hi 320
> > > > > +#define _sP5_lo 384
> > > > > +#define _sP5_hi 448
> > > > > +#define _sP4_lo 512
> > > > > +#define _sP4_hi 576
> > > > > +#define _sP3_lo 640
> > > > > +#define _sP3_hi 704
> > > > > +#define _sP2_lo 768
> > > > > +#define _sP2_hi 832
> > > > > +#define _sP0_lo 896
> > > > > +#define _sP0_hi 960
> > > > > +
> > > > >
> > > > > #include <sysdep.h>
> > > > > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > > > > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> > > > >
> > > > > .section .text.evex512, "ax", @progbits
> > > > > ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > > > > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > > + /* Here huge arguments, INF and NaNs are filtered out to
> > > > > + callout. */
> > > > > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > >
> > > > > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > > > > vpxord %zmm3, %zmm3, %zmm3
> > > > > vpmaxsd %zmm3, %zmm2, %zmm3
> > > > > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > >
> > > > > /* Setup permute indices in zmm3. */
> > > > > vpsrld $21, %zmm3, %zmm3
> > > > >
> > > > > /* Store if there are any special cases in k1. */
> > > > > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > >
> > > > > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > > > > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > > > > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > > > > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > > > > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > >
> > > > > /* Store absolute values of inputs in zmm1. */
> > > > > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > > > > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > > > > vandnps %zmm0, %zmm4, %zmm1
> > > > > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > > > > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > > > > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > > > > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > > > > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > >
> > > > > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > > > > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > > > > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > > > > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > > > > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > > > > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > >
> > > > > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > > > > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > > > > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > > > > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > >
> > > > > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > > > > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > > > > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > >
> > > > > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > > > > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > > > > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > >
> > > > > /* Go to special inputs processing branch. */
> > > > > jne L(SPECIAL_VALUES_BRANCH)
> > > > > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > +
> > > > > /* Wait until after branch of write over zmm0. */
> > > > > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> > > > >
> > > > > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > >
> > > > > /* Cold case. edx has 1s where there was a special value that
> > > > > needs to be handled by a tanhf call. Optimize for code size
> > > > > - more so than speed here. */
> > > > > + more so than speed here. */
> > > > > L(SPECIAL_VALUES_BRANCH):
> > > > > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > > > > - callee save register saving code size. */
> > > > > +
> > > > > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > > > > + as callee save register saving code size. */
> > > > > pushq %r13
> > > > > - cfi_adjust_cfa_offset(8)
> > > > > - cfi_offset(r13, -16)
> > > > > - /* Need to callee save registers to preserve state across tanhf calls.
> > > > > - */
> > > > > + cfi_adjust_cfa_offset (8)
> > > > > + cfi_offset (r13, -16)
> > > > > + /* Need to callee save registers to preserve state across tanhf
> > > > > + calls. */
> > > > > pushq %rbx
> > > > > - cfi_adjust_cfa_offset(8)
> > > > > - cfi_offset(rbx, -24)
> > > > > + cfi_adjust_cfa_offset (8)
> > > > > + cfi_offset (rbx, -24)
> > > > > pushq %rbp
> > > > > - cfi_adjust_cfa_offset(8)
> > > > > - cfi_offset(rbp, -32)
> > > > > + cfi_adjust_cfa_offset (8)
> > > > > + cfi_offset (rbp, -32)
> > > > > movq %rsp, %r13
> > > > > - cfi_def_cfa_register(r13)
> > > > > + cfi_def_cfa_register (r13)
> > > > >
> > > > > /* Align stack and make room for 2x zmm vectors. */
> > > > > andq $-64, %rsp
> > > > > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> > > > >
> > > > > vzeroupper
> > > > >
> > > > > - /* edx has 1s where there was a special value that needs to be handled
> > > > > - by a tanhf call. */
> > > > > + /* edx has 1s where there was a special value that needs to be
> > > > > + handled by a tanhf call. */
> > > > > movl %edx, %ebx
> > > > > L(SPECIAL_VALUES_LOOP):
> > > > > - # LOE rbx rbp r12 r13 r14 r15
> > > > > - /* use rbp as index for special value that is saved across calls to
> > > > > - tanhf. We technically don't need a callee save register here as offset
> > > > > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > > > > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > > > > - in the loop. Realigning also costs more code size. */
> > > > > +
> > > > > + /* use rbp as index for special value that is saved across calls
> > > > > + to tanhf. We technically don't need a callee save register
> > > > > + here as offset to rsp is always [0, 56] so we can restore
> > > > > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > > > > + save/restore vs 2 extra instructions in the loop. Realigning
> > > > > + also costs more code size. */
> > > > > xorl %ebp, %ebp
> > > > > tzcntl %ebx, %ebp
> > > > >
> > > > > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > > > > vmovss 64(%rsp, %rbp, 4), %xmm0
> > > > > call tanhf@PLT
> > > > >
> > > > > - /* No good way to avoid the store-forwarding fault this will cause on
> > > > > - return. `lfence` avoids the SF fault but at greater cost as it
> > > > > - serialized stack/callee save restoration. */
> > > > > + /* No good way to avoid the store-forwarding fault this will
> > > > > + cause on return. `lfence` avoids the SF fault but at greater
> > > > > + cost as it serialized stack/callee save restoration. */
> > > > > vmovss %xmm0, (%rsp, %rbp, 4)
> > > > >
> > > > > - blsrl %ebx, %ebx
> > > > > + blsrl %ebx, %ebx
> > > > > jnz L(SPECIAL_VALUES_LOOP)
> > > > > - # LOE r12 r13 r14 r15
> > > > > +
> > > > >
> > > > > /* All results have been written to (%rsp). */
> > > > > vmovaps (%rsp), %zmm0
> > > > > /* Restore rsp. */
> > > > > movq %r13, %rsp
> > > > > - cfi_def_cfa_register(rsp)
> > > > > + cfi_def_cfa_register (rsp)
> > > > > /* Restore callee save registers. */
> > > > > popq %rbp
> > > > > - cfi_adjust_cfa_offset(-8)
> > > > > - cfi_restore(rbp)
> > > > > + cfi_adjust_cfa_offset (-8)
> > > > > + cfi_restore (rbp)
> > > > > popq %rbx
> > > > > - cfi_adjust_cfa_offset(-8)
> > > > > - cfi_restore(rbp)
> > > > > + cfi_adjust_cfa_offset (-8)
> > > > > + cfi_restore (rbp)
> > > > > popq %r13
> > > > > - cfi_adjust_cfa_offset(-8)
> > > > > - cfi_restore(r13)
> > > > > + cfi_adjust_cfa_offset (-8)
> > > > > + cfi_restore (r13)
> > > > > ret
> > > > > END(_ZGVeN16v_tanhf_skx)
> > > > >
> > > > > - .section .rodata, "a"
> > > > > + .section .rodata.evex512, "a"
> > > > > .align 16
> > > > > -#ifdef __svml_stanh_data_internal_typedef
> > > > > -typedef unsigned int VUINT32;
> > > > > -typedef struct
> > > > > - {
> > > > > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > > > > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > > > > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > > > > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > > > > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > > > > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > > > > -} __svml_stanh_data_internal;
> > > > > -#endif
> > > > > -
> > > > > -__svml_stanh_data_internal:
> > > > > - .align 4
> > > > > - /* _iExpMantMask_UISA */
> > > > > - .long 0x7fe00000
> > > > > -
> > > > > - .align 4
> > > > > - /* _iMinIdxOfsMask_UISA */
> > > > > - .long 0x3d400000
> > > > > -
> > > > > - .align 4
> > > > > - /* _iMaxIdxMask_UISA */
> > > > > - .long 0x03e00000
> > > > > -
> > > > > - .align 4
> > > > > - /* _iExpMask */
> > > > > - .long 0x7f000000
> > > > > -
> > > > > - .align 64
> > > > > -__svml_stanh_data_internal_al64:
> > > > > - .align 64
> > > > > - /* _sC_lo */
> > > > > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > > > > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > > > > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > > > > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sC_hi */
> > > > > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > > > > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > > > > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > > > > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP7_lo */
> > > > > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > > > > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > > > > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > > > > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP7_hi */
> > > > > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > > > > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > > > > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > > > > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> > > > >
> > > > > - .align 64
> > > > > - /* _sSignMask */
> > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP6_lo */
> > > > > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > > > > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > > > > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > > > > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP6_hi */
> > > > > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > > > > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > > > > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > > > > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP5_lo */
> > > > > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > > > > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > > > > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > > > > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP5_hi */
> > > > > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > > > > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > > > > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > > > > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP4_lo */
> > > > > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > > > > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > > > > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > > > > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP4_hi */
> > > > > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > > > > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > > > > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > > > > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP3_lo */
> > > > > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > > > > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > > > > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > > > > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP3_hi */
> > > > > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > > > > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > > > > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > > > > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP2_lo */
> > > > > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > > > > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > > > > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > > > > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP2_hi */
> > > > > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > > > > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > > > > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > > > > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP0_lo */
> > > > > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > > > > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > > > > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > > > > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > > > > -
> > > > > - .align 64
> > > > > - /* _sP0_hi */
> > > > > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > > > > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > > > > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > > > > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > > > > +LOCAL_DATA_NAME_UNALIGNED:
> > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > > > > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > > > > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> > > > >
> > > > > .align 64
> > > > > - .type __svml_stanh_data_internal_al64, @object
> > > > > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > > > > - .type __svml_stanh_data_internal, @object
> > > > > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > > > > +LOCAL_DATA_NAME:
> > > > > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > > > > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > > > > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > > > > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > > > > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > > > > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > > > > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > > > > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > > > > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > > > > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > > > > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > > > > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > > > > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > > > > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > > > > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > > > > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > > > > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > > > > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > > > > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > > > > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > > > > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > > > > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > > > > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > > > > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > > > > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > > > > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > > > > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > > > > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > > > > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > > > > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > > > > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > > > > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > > > > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > > > > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > > > > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > > > > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > > > > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > > > > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > > > > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > > > > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > > > > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > > > > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > > > > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > > > > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > > > > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > > > > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > > > > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > > > > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > > > > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > > > > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > > > > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > > > > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > > > > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > > > > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > > > > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > > > > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > > > > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > > > > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > > > > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > > > > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > > > > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > > > > +
> > > > > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > > > > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > > > > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > > > > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > > > > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > > > > +
> > > > > + .type LOCAL_DATA_NAME, @object
> > > > > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > > > > --
> > > > > 2.34.1
> > > > >
> > > >
> > > > The data movement makes the assembler codes much harder to follow.
> > > > Sunil, what do you think of this patch series?
> > >
> > > What do you mean? The change on in how we define rodata or the movement
> > > to multiple files or something else?
> >
> > The glibc way to support data files for assembly codes is to define
> > data in C and use *.sym to generate offsets for assembly files, like
>
> I see. Although to be fair the entire SVML codebase bucks that trend.
It is because libmvec codes were generated by ICC and processed
by scripts.
> Seems like a more dramatic trend to move all the offsets to C.
Since you are adding data by hand, you should do it in C.
> >
> > sysdeps/x86/cpu-features-offsets.sym:XSAVE_STATE_SIZE_OFFSET
> > offsetof (struct cpu_features, xsave_state_size)
> > sysdeps/x86_64/dl-trampoline.h: sub
> > _rtld_local_ro+RTLD_GLOBAL_RO_DL_X86_CPU_FEATURES_OFFSET+XSAVE_STATE_SIZE_OFFSET(%rip),
> > %RSP_LP
> > sysdeps/x86_64/dl-trampoline.h: sub
> > _dl_x86_cpu_features+XSAVE_STATE_SIZE_OFFSET(%rip), %RSP_LP
> >
> > --
> > H.J.
--
H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 22:01 ` H.J. Lu via Libc-alpha
@ 2022-12-16 22:54 ` Sunil Pandey via Libc-alpha
2023-06-27 18:23 ` Noah Goldstein via Libc-alpha
1 sibling, 0 replies; 38+ messages in thread
From: Sunil Pandey via Libc-alpha @ 2022-12-16 22:54 UTC (permalink / raw)
To: H.J. Lu; +Cc: Noah Goldstein, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 2:01 PM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Fri, Dec 16, 2022 at 1:52 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > On Fri, Dec 16, 2022 at 1:38 PM H.J. Lu <hjl.tools@gmail.com> wrote:
> > >
> > > On Fri, Dec 16, 2022 at 10:18 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > >
> > > > On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
> > > > >
> > > > > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > > > >
> > > > > > No changes to the logic, just change how rodata is handled.
> > > > > >
> > > > > > 1. Define the rodatas using the new macros so they check that the
> > > > > > offset is correct.
> > > > > >
> > > > > > 2. Use common data where applicable.
> > > > > > ---
> > > > > > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > > > > > 1 file changed, 197 insertions(+), 253 deletions(-)
> > > > > >
> > > > > > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > index d74fc7731d..765e9ed7f7 100644
> > > > > > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > @@ -70,94 +70,99 @@
> > > > > > *
> > > > > > */
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > > > > > - by use in the function. On cold-starts this might help the
> > > > > > - prefetcher. Possibly a better idea is to interleave start/end so
> > > > > > - that the prefetcher is less likely to detect a stream and pull
> > > > > > - irrelivant lines into cache. */
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > > > > > - */
> > > > > > +
> > > > > > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > > > > > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > > > > > +#include "svml_s_common_evex512_rodata_offsets.h"
> > > > > > +
> > > > > > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > > > > > + 4 bytes each. */
> > > > > > #define _iExpMantMask_UISA 0
> > > > > > #define _iMinIdxOfsMask_UISA 4
> > > > > > #define _iMaxIdxMask_UISA 8
> > > > > > #define _iExpMask 12
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > > > > > - each. */
> > > > > > -#define _sC_lo 0
> > > > > > -#define _sC_hi 64
> > > > > > -#define _sP7_lo 128
> > > > > > -#define _sP7_hi 192
> > > > > > -#define _sSignMask 256
> > > > > > -#define _sP6_lo 320
> > > > > > -#define _sP6_hi 384
> > > > > > -#define _sP5_lo 448
> > > > > > -#define _sP5_hi 512
> > > > > > -#define _sP4_lo 576
> > > > > > -#define _sP4_hi 640
> > > > > > -#define _sP3_lo 704
> > > > > > -#define _sP3_hi 768
> > > > > > -#define _sP2_lo 832
> > > > > > -#define _sP2_hi 896
> > > > > > -#define _sP0_lo 960
> > > > > > -#define _sP0_hi 1024
> > > > > > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > > > > > + by use in the function. On cold-starts this might help the
> > > > > > + prefetcher. Possibly a better idea is to interleave start/end so
> > > > > > + that the prefetcher is less likely to detect a stream and pull
> > > > > > + irrelivant lines into cache. */
> > > > > > +
> > > > > > +/* Offsets for data table __svml_stanh_data_internal.
> > > > > > + 64 bytes each. */
> > > > > > +#define _sC_lo 0
> > > > > > +#define _sC_hi 64
> > > > > > +#define _sP7_lo 128
> > > > > > +#define _sP7_hi 192
> > > > > > +#define _sP6_lo 256
> > > > > > +#define _sP6_hi 320
> > > > > > +#define _sP5_lo 384
> > > > > > +#define _sP5_hi 448
> > > > > > +#define _sP4_lo 512
> > > > > > +#define _sP4_hi 576
> > > > > > +#define _sP3_lo 640
> > > > > > +#define _sP3_hi 704
> > > > > > +#define _sP2_lo 768
> > > > > > +#define _sP2_hi 832
> > > > > > +#define _sP0_lo 896
> > > > > > +#define _sP0_hi 960
> > > > > > +
> > > > > >
> > > > > > #include <sysdep.h>
> > > > > > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > > > > > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> > > > > >
> > > > > > .section .text.evex512, "ax", @progbits
> > > > > > ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > > > > > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > > > + /* Here huge arguments, INF and NaNs are filtered out to
> > > > > > + callout. */
> > > > > > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > > >
> > > > > > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > > > > > vpxord %zmm3, %zmm3, %zmm3
> > > > > > vpmaxsd %zmm3, %zmm2, %zmm3
> > > > > > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > > > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > > >
> > > > > > /* Setup permute indices in zmm3. */
> > > > > > vpsrld $21, %zmm3, %zmm3
> > > > > >
> > > > > > /* Store if there are any special cases in k1. */
> > > > > > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > > > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > > > > > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > > > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > > > > > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > > > > > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > > > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > > > > > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > > >
> > > > > > /* Store absolute values of inputs in zmm1. */
> > > > > > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > > > > > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > > > > > vandnps %zmm0, %zmm4, %zmm1
> > > > > > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > > > > > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > > > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > > > > > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > > > > > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > > > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > > > > > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > > > > > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > > > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > > > > > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > > > > > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > > > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > > > > > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > > > > > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > > > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > > > > > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > > > > > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > > > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > > > > > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > > > > > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > /* Go to special inputs processing branch. */
> > > > > > jne L(SPECIAL_VALUES_BRANCH)
> > > > > > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > > +
> > > > > > /* Wait until after branch of write over zmm0. */
> > > > > > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> > > > > >
> > > > > > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > /* Cold case. edx has 1s where there was a special value that
> > > > > > needs to be handled by a tanhf call. Optimize for code size
> > > > > > - more so than speed here. */
> > > > > > + more so than speed here. */
> > > > > > L(SPECIAL_VALUES_BRANCH):
> > > > > > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > > > > > - callee save register saving code size. */
> > > > > > +
> > > > > > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > > > > > + as callee save register saving code size. */
> > > > > > pushq %r13
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(r13, -16)
> > > > > > - /* Need to callee save registers to preserve state across tanhf calls.
> > > > > > - */
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (r13, -16)
> > > > > > + /* Need to callee save registers to preserve state across tanhf
> > > > > > + calls. */
> > > > > > pushq %rbx
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(rbx, -24)
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (rbx, -24)
> > > > > > pushq %rbp
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(rbp, -32)
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (rbp, -32)
> > > > > > movq %rsp, %r13
> > > > > > - cfi_def_cfa_register(r13)
> > > > > > + cfi_def_cfa_register (r13)
> > > > > >
> > > > > > /* Align stack and make room for 2x zmm vectors. */
> > > > > > andq $-64, %rsp
> > > > > > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> > > > > >
> > > > > > vzeroupper
> > > > > >
> > > > > > - /* edx has 1s where there was a special value that needs to be handled
> > > > > > - by a tanhf call. */
> > > > > > + /* edx has 1s where there was a special value that needs to be
> > > > > > + handled by a tanhf call. */
> > > > > > movl %edx, %ebx
> > > > > > L(SPECIAL_VALUES_LOOP):
> > > > > > - # LOE rbx rbp r12 r13 r14 r15
> > > > > > - /* use rbp as index for special value that is saved across calls to
> > > > > > - tanhf. We technically don't need a callee save register here as offset
> > > > > > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > > > > > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > > > > > - in the loop. Realigning also costs more code size. */
> > > > > > +
> > > > > > + /* use rbp as index for special value that is saved across calls
> > > > > > + to tanhf. We technically don't need a callee save register
> > > > > > + here as offset to rsp is always [0, 56] so we can restore
> > > > > > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > > > > > + save/restore vs 2 extra instructions in the loop. Realigning
> > > > > > + also costs more code size. */
> > > > > > xorl %ebp, %ebp
> > > > > > tzcntl %ebx, %ebp
> > > > > >
> > > > > > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > > > > > vmovss 64(%rsp, %rbp, 4), %xmm0
> > > > > > call tanhf@PLT
> > > > > >
> > > > > > - /* No good way to avoid the store-forwarding fault this will cause on
> > > > > > - return. `lfence` avoids the SF fault but at greater cost as it
> > > > > > - serialized stack/callee save restoration. */
> > > > > > + /* No good way to avoid the store-forwarding fault this will
> > > > > > + cause on return. `lfence` avoids the SF fault but at greater
> > > > > > + cost as it serialized stack/callee save restoration. */
> > > > > > vmovss %xmm0, (%rsp, %rbp, 4)
> > > > > >
> > > > > > - blsrl %ebx, %ebx
> > > > > > + blsrl %ebx, %ebx
> > > > > > jnz L(SPECIAL_VALUES_LOOP)
> > > > > > - # LOE r12 r13 r14 r15
> > > > > > +
> > > > > >
> > > > > > /* All results have been written to (%rsp). */
> > > > > > vmovaps (%rsp), %zmm0
> > > > > > /* Restore rsp. */
> > > > > > movq %r13, %rsp
> > > > > > - cfi_def_cfa_register(rsp)
> > > > > > + cfi_def_cfa_register (rsp)
> > > > > > /* Restore callee save registers. */
> > > > > > popq %rbp
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(rbp)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (rbp)
> > > > > > popq %rbx
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(rbp)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (rbp)
> > > > > > popq %r13
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(r13)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (r13)
> > > > > > ret
> > > > > > END(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > - .section .rodata, "a"
> > > > > > + .section .rodata.evex512, "a"
> > > > > > .align 16
> > > > > > -#ifdef __svml_stanh_data_internal_typedef
> > > > > > -typedef unsigned int VUINT32;
> > > > > > -typedef struct
> > > > > > - {
> > > > > > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > > > > > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > > > > > -} __svml_stanh_data_internal;
> > > > > > -#endif
> > > > > > -
> > > > > > -__svml_stanh_data_internal:
> > > > > > - .align 4
> > > > > > - /* _iExpMantMask_UISA */
> > > > > > - .long 0x7fe00000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iMinIdxOfsMask_UISA */
> > > > > > - .long 0x3d400000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iMaxIdxMask_UISA */
> > > > > > - .long 0x03e00000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iExpMask */
> > > > > > - .long 0x7f000000
> > > > > > -
> > > > > > - .align 64
> > > > > > -__svml_stanh_data_internal_al64:
> > > > > > - .align 64
> > > > > > - /* _sC_lo */
> > > > > > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > > > > > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > > > > > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > > > > > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sC_hi */
> > > > > > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > > > > > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > > > > > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > > > > > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP7_lo */
> > > > > > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > > > > > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > > > > > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > > > > > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP7_hi */
> > > > > > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > > > > > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > > > > > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > > > > > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> > > > > >
> > > > > > - .align 64
> > > > > > - /* _sSignMask */
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP6_lo */
> > > > > > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > > > > > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > > > > > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > > > > > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP6_hi */
> > > > > > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > > > > > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > > > > > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > > > > > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP5_lo */
> > > > > > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > > > > > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > > > > > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > > > > > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP5_hi */
> > > > > > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > > > > > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > > > > > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > > > > > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP4_lo */
> > > > > > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > > > > > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > > > > > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > > > > > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP4_hi */
> > > > > > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > > > > > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > > > > > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > > > > > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP3_lo */
> > > > > > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > > > > > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > > > > > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > > > > > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP3_hi */
> > > > > > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > > > > > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > > > > > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > > > > > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP2_lo */
> > > > > > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > > > > > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > > > > > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > > > > > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP2_hi */
> > > > > > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > > > > > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > > > > > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > > > > > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP0_lo */
> > > > > > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > > > > > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > > > > > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > > > > > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP0_hi */
> > > > > > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > > > > > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > > > > > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > > > > > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > > > > > +LOCAL_DATA_NAME_UNALIGNED:
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > > > > > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > > > > > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> > > > > >
> > > > > > .align 64
> > > > > > - .type __svml_stanh_data_internal_al64, @object
> > > > > > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > > > > > - .type __svml_stanh_data_internal, @object
> > > > > > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > > > > > +LOCAL_DATA_NAME:
> > > > > > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > > > > > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > > > > > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > > > > > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > > > > > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > > > > > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > > > > > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > > > > > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > > > > > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > > > > > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > > > > > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > > > > > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > > > > > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > > > > > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > > > > > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > > > > > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > > > > > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > > > > > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > > > > > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > > > > > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > > > > > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > > > > > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > > > > > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > > > > > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > > > > > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > > > > > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > > > > > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > > > > > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > > > > > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > > > > > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > > > > > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > > > > > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > > > > > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > > > > > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > > > > > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > > > > > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > > > > > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > > > > > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > > > > > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > > > > > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > > > > > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > > > > > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > > > > > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > > > > > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > > > > > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > > > > > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > > > > > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > > > > > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > > > > > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > > > > > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > > > > > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > > > > > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > > > > > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > > > > > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > > > > > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > > > > > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > > > > > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > > > > > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > > > > > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > > > > > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > > > > > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > > > > > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > > > > > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > > > > > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > > > > > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > > > > > +
> > > > > > + .type LOCAL_DATA_NAME, @object
> > > > > > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > > > > > --
> > > > > > 2.34.1
> > > > > >
> > > > >
> > > > > The data movement makes the assembler codes much harder to follow.
> > > > > Sunil, what do you think of this patch series?
> > > >
> > > > What do you mean? The change on in how we define rodata or the movement
> > > > to multiple files or something else?
> > >
> > > The glibc way to support data files for assembly codes is to define
> > > data in C and use *.sym to generate offsets for assembly files, like
> >
> > I see. Although to be fair the entire SVML codebase bucks that trend.
>
> It is because libmvec codes were generated by ICC and processed
> by scripts.
>
> > Seems like a more dramatic trend to move all the offsets to C.
>
> Since you are adding data by hand, you should do it in C.
>
> > >
> > > sysdeps/x86/cpu-features-offsets.sym:XSAVE_STATE_SIZE_OFFSET
> > > offsetof (struct cpu_features, xsave_state_size)
> > > sysdeps/x86_64/dl-trampoline.h: sub
> > > _rtld_local_ro+RTLD_GLOBAL_RO_DL_X86_CPU_FEATURES_OFFSET+XSAVE_STATE_SIZE_OFFSET(%rip),
> > > %RSP_LP
> > > sysdeps/x86_64/dl-trampoline.h: sub
> > > _dl_x86_cpu_features+XSAVE_STATE_SIZE_OFFSET(%rip), %RSP_LP
> > >
> > > --
> > > H.J.
>
>
Does this restructuring provide any performance benefit as measured by
libmvec microbenchmark?
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
* Re: [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S
2022-12-16 22:01 ` H.J. Lu via Libc-alpha
2022-12-16 22:54 ` Sunil Pandey via Libc-alpha
@ 2023-06-27 18:23 ` Noah Goldstein via Libc-alpha
1 sibling, 0 replies; 38+ messages in thread
From: Noah Goldstein via Libc-alpha @ 2023-06-27 18:23 UTC (permalink / raw)
To: H.J. Lu; +Cc: Sunil K Pandey, libc-alpha, andrey.kolesov, carlos
On Fri, Dec 16, 2022 at 4:01 PM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Fri, Dec 16, 2022 at 1:52 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > On Fri, Dec 16, 2022 at 1:38 PM H.J. Lu <hjl.tools@gmail.com> wrote:
> > >
> > > On Fri, Dec 16, 2022 at 10:18 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > >
> > > > On Fri, Dec 16, 2022 at 9:06 AM H.J. Lu <hjl.tools@gmail.com> wrote:
> > > > >
> > > > > On Wed, Dec 7, 2022 at 12:52 AM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> > > > > >
> > > > > > No changes to the logic, just change how rodata is handled.
> > > > > >
> > > > > > 1. Define the rodatas using the new macros so they check that the
> > > > > > offset is correct.
> > > > > >
> > > > > > 2. Use common data where applicable.
> > > > > > ---
> > > > > > .../multiarch/svml_s_tanhf16_core_avx512.S | 450 ++++++++----------
> > > > > > 1 file changed, 197 insertions(+), 253 deletions(-)
> > > > > >
> > > > > > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > index d74fc7731d..765e9ed7f7 100644
> > > > > > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S
> > > > > > @@ -70,94 +70,99 @@
> > > > > > *
> > > > > > */
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
> > > > > > - by use in the function. On cold-starts this might help the
> > > > > > - prefetcher. Possibly a better idea is to interleave start/end so
> > > > > > - that the prefetcher is less likely to detect a stream and pull
> > > > > > - irrelivant lines into cache. */
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
> > > > > > - */
> > > > > > +
> > > > > > +#define LOCAL_DATA_NAME __svml_stanh_data_internal
> > > > > > +#define LOCAL_DATA_NAME_UNALIGNED __svml_stanh_data_internal_unaligned
> > > > > > +#include "svml_s_common_evex512_rodata_offsets.h"
> > > > > > +
> > > > > > +/* Offsets for data table __svml_stanh_data_internal_unaligned.
> > > > > > + 4 bytes each. */
> > > > > > #define _iExpMantMask_UISA 0
> > > > > > #define _iMinIdxOfsMask_UISA 4
> > > > > > #define _iMaxIdxMask_UISA 8
> > > > > > #define _iExpMask 12
> > > > > >
> > > > > > -/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
> > > > > > - each. */
> > > > > > -#define _sC_lo 0
> > > > > > -#define _sC_hi 64
> > > > > > -#define _sP7_lo 128
> > > > > > -#define _sP7_hi 192
> > > > > > -#define _sSignMask 256
> > > > > > -#define _sP6_lo 320
> > > > > > -#define _sP6_hi 384
> > > > > > -#define _sP5_lo 448
> > > > > > -#define _sP5_hi 512
> > > > > > -#define _sP4_lo 576
> > > > > > -#define _sP4_hi 640
> > > > > > -#define _sP3_lo 704
> > > > > > -#define _sP3_hi 768
> > > > > > -#define _sP2_lo 832
> > > > > > -#define _sP2_hi 896
> > > > > > -#define _sP0_lo 960
> > > > > > -#define _sP0_hi 1024
> > > > > > +/* Offsets for data table __svml_stanh_data_internal. Ordered
> > > > > > + by use in the function. On cold-starts this might help the
> > > > > > + prefetcher. Possibly a better idea is to interleave start/end so
> > > > > > + that the prefetcher is less likely to detect a stream and pull
> > > > > > + irrelivant lines into cache. */
> > > > > > +
> > > > > > +/* Offsets for data table __svml_stanh_data_internal.
> > > > > > + 64 bytes each. */
> > > > > > +#define _sC_lo 0
> > > > > > +#define _sC_hi 64
> > > > > > +#define _sP7_lo 128
> > > > > > +#define _sP7_hi 192
> > > > > > +#define _sP6_lo 256
> > > > > > +#define _sP6_hi 320
> > > > > > +#define _sP5_lo 384
> > > > > > +#define _sP5_hi 448
> > > > > > +#define _sP4_lo 512
> > > > > > +#define _sP4_hi 576
> > > > > > +#define _sP3_lo 640
> > > > > > +#define _sP3_hi 704
> > > > > > +#define _sP2_lo 768
> > > > > > +#define _sP2_hi 832
> > > > > > +#define _sP0_lo 896
> > > > > > +#define _sP0_hi 960
> > > > > > +
> > > > > >
> > > > > > #include <sysdep.h>
> > > > > > -#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
> > > > > > -#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
> > > > > >
> > > > > > .section .text.evex512, "ax", @progbits
> > > > > > ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > > - /* Here huge arguments, INF and NaNs are filtered out to callout. */
> > > > > > - vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > > - vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > > > + /* Here huge arguments, INF and NaNs are filtered out to
> > > > > > + callout. */
> > > > > > + vpandd LOCAL_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
> > > > > > + vpsubd LOCAL_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
> > > > > >
> > > > > > /* Selection arguments between [0, 0x03e00000] into zmm3. */
> > > > > > vpxord %zmm3, %zmm3, %zmm3
> > > > > > vpmaxsd %zmm3, %zmm2, %zmm3
> > > > > > - vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > > > + vpminsd LOCAL_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
> > > > > >
> > > > > > /* Setup permute indices in zmm3. */
> > > > > > vpsrld $21, %zmm3, %zmm3
> > > > > >
> > > > > > /* Store if there are any special cases in k1. */
> > > > > > - vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > > > + vpcmpd $6, LOCAL_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
> > > > > > - vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > > > + vmovaps LOCAL_DATA(_sC_lo)(%rip), %zmm5
> > > > > > + vpermt2ps LOCAL_DATA(_sC_hi)(%rip), %zmm3, %zmm5
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
> > > > > > - vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > > > + vmovaps LOCAL_DATA(_sP7_lo)(%rip), %zmm2
> > > > > > + vpermt2ps LOCAL_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
> > > > > >
> > > > > > /* Store absolute values of inputs in zmm1. */
> > > > > > - vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
> > > > > > + vmovaps COMMON_DATA(_SignMask)(%rip), %zmm4
> > > > > > vandnps %zmm0, %zmm4, %zmm1
> > > > > > vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
> > > > > > - vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > > > + vmovaps LOCAL_DATA(_sP6_lo)(%rip), %zmm5
> > > > > > + vpermt2ps LOCAL_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
> > > > > > - vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > > > + vmovaps LOCAL_DATA(_sP5_lo)(%rip), %zmm6
> > > > > > + vpermt2ps LOCAL_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
> > > > > > - vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > > > + vmovaps LOCAL_DATA(_sP4_lo)(%rip), %zmm7
> > > > > > + vpermt2ps LOCAL_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
> > > > > > - vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > > > + vmovaps LOCAL_DATA(_sP3_lo)(%rip), %zmm8
> > > > > > + vpermt2ps LOCAL_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
> > > > > > - vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > > > + vmovaps LOCAL_DATA(_sP2_lo)(%rip), %zmm9
> > > > > > + vpermt2ps LOCAL_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
> > > > > >
> > > > > > - vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
> > > > > > - vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > > > + vmovaps LOCAL_DATA(_sP0_lo)(%rip), %zmm10
> > > > > > + vpermt2ps LOCAL_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
> > > > > >
> > > > > > vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
> > > > > > vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
> > > > > > @@ -167,7 +172,7 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > /* Go to special inputs processing branch. */
> > > > > > jne L(SPECIAL_VALUES_BRANCH)
> > > > > > - # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > > +
> > > > > > /* Wait until after branch of write over zmm0. */
> > > > > > vpternlogd $0xec, %zmm4, %zmm2, %zmm0
> > > > > >
> > > > > > @@ -176,24 +181,24 @@ ENTRY(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > /* Cold case. edx has 1s where there was a special value that
> > > > > > needs to be handled by a tanhf call. Optimize for code size
> > > > > > - more so than speed here. */
> > > > > > + more so than speed here. */
> > > > > > L(SPECIAL_VALUES_BRANCH):
> > > > > > - # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
> > > > > > - /* Use r13 to save/restore the stack. This allows us to use rbp as
> > > > > > - callee save register saving code size. */
> > > > > > +
> > > > > > + /* Use r13 to save/restore the stack. This allows us to use rbp
> > > > > > + as callee save register saving code size. */
> > > > > > pushq %r13
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(r13, -16)
> > > > > > - /* Need to callee save registers to preserve state across tanhf calls.
> > > > > > - */
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (r13, -16)
> > > > > > + /* Need to callee save registers to preserve state across tanhf
> > > > > > + calls. */
> > > > > > pushq %rbx
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(rbx, -24)
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (rbx, -24)
> > > > > > pushq %rbp
> > > > > > - cfi_adjust_cfa_offset(8)
> > > > > > - cfi_offset(rbp, -32)
> > > > > > + cfi_adjust_cfa_offset (8)
> > > > > > + cfi_offset (rbp, -32)
> > > > > > movq %rsp, %r13
> > > > > > - cfi_def_cfa_register(r13)
> > > > > > + cfi_def_cfa_register (r13)
> > > > > >
> > > > > > /* Align stack and make room for 2x zmm vectors. */
> > > > > > andq $-64, %rsp
> > > > > > @@ -207,16 +212,17 @@ L(SPECIAL_VALUES_BRANCH):
> > > > > >
> > > > > > vzeroupper
> > > > > >
> > > > > > - /* edx has 1s where there was a special value that needs to be handled
> > > > > > - by a tanhf call. */
> > > > > > + /* edx has 1s where there was a special value that needs to be
> > > > > > + handled by a tanhf call. */
> > > > > > movl %edx, %ebx
> > > > > > L(SPECIAL_VALUES_LOOP):
> > > > > > - # LOE rbx rbp r12 r13 r14 r15
> > > > > > - /* use rbp as index for special value that is saved across calls to
> > > > > > - tanhf. We technically don't need a callee save register here as offset
> > > > > > - to rsp is always [0, 56] so we can restore rsp by realigning to 64.
> > > > > > - Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > > > > > - in the loop. Realigning also costs more code size. */
> > > > > > +
> > > > > > + /* use rbp as index for special value that is saved across calls
> > > > > > + to tanhf. We technically don't need a callee save register
> > > > > > + here as offset to rsp is always [0, 56] so we can restore
> > > > > > + rsp by realigning to 64. Essentially the tradeoff is 1 extra
> > > > > > + save/restore vs 2 extra instructions in the loop. Realigning
> > > > > > + also costs more code size. */
> > > > > > xorl %ebp, %ebp
> > > > > > tzcntl %ebx, %ebp
> > > > > >
> > > > > > @@ -224,203 +230,141 @@ L(SPECIAL_VALUES_LOOP):
> > > > > > vmovss 64(%rsp, %rbp, 4), %xmm0
> > > > > > call tanhf@PLT
> > > > > >
> > > > > > - /* No good way to avoid the store-forwarding fault this will cause on
> > > > > > - return. `lfence` avoids the SF fault but at greater cost as it
> > > > > > - serialized stack/callee save restoration. */
> > > > > > + /* No good way to avoid the store-forwarding fault this will
> > > > > > + cause on return. `lfence` avoids the SF fault but at greater
> > > > > > + cost as it serialized stack/callee save restoration. */
> > > > > > vmovss %xmm0, (%rsp, %rbp, 4)
> > > > > >
> > > > > > - blsrl %ebx, %ebx
> > > > > > + blsrl %ebx, %ebx
> > > > > > jnz L(SPECIAL_VALUES_LOOP)
> > > > > > - # LOE r12 r13 r14 r15
> > > > > > +
> > > > > >
> > > > > > /* All results have been written to (%rsp). */
> > > > > > vmovaps (%rsp), %zmm0
> > > > > > /* Restore rsp. */
> > > > > > movq %r13, %rsp
> > > > > > - cfi_def_cfa_register(rsp)
> > > > > > + cfi_def_cfa_register (rsp)
> > > > > > /* Restore callee save registers. */
> > > > > > popq %rbp
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(rbp)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (rbp)
> > > > > > popq %rbx
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(rbp)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (rbp)
> > > > > > popq %r13
> > > > > > - cfi_adjust_cfa_offset(-8)
> > > > > > - cfi_restore(r13)
> > > > > > + cfi_adjust_cfa_offset (-8)
> > > > > > + cfi_restore (r13)
> > > > > > ret
> > > > > > END(_ZGVeN16v_tanhf_skx)
> > > > > >
> > > > > > - .section .rodata, "a"
> > > > > > + .section .rodata.evex512, "a"
> > > > > > .align 16
> > > > > > -#ifdef __svml_stanh_data_internal_typedef
> > > > > > -typedef unsigned int VUINT32;
> > > > > > -typedef struct
> > > > > > - {
> > > > > > - __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
> > > > > > - __declspec(align(4)) VUINT32 _iExpMask[1][1];
> > > > > > - __declspec(align(64)) VUINT32 _sC_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sC_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP7_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP7_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sSignMask[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP6_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP6_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP5_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP5_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP4_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP4_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP3_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP3_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP2_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP2_hi[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP0_lo[16][1];
> > > > > > - __declspec(align(64)) VUINT32 _sP0_hi[16][1];
> > > > > > -} __svml_stanh_data_internal;
> > > > > > -#endif
> > > > > > -
> > > > > > -__svml_stanh_data_internal:
> > > > > > - .align 4
> > > > > > - /* _iExpMantMask_UISA */
> > > > > > - .long 0x7fe00000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iMinIdxOfsMask_UISA */
> > > > > > - .long 0x3d400000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iMaxIdxMask_UISA */
> > > > > > - .long 0x03e00000
> > > > > > -
> > > > > > - .align 4
> > > > > > - /* _iExpMask */
> > > > > > - .long 0x7f000000
> > > > > > -
> > > > > > - .align 64
> > > > > > -__svml_stanh_data_internal_al64:
> > > > > > - .align 64
> > > > > > - /* _sC_lo */
> > > > > > - .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
> > > > > > - .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
> > > > > > - .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
> > > > > > - .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sC_hi */
> > > > > > - .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
> > > > > > - .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
> > > > > > - .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
> > > > > > - .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP7_lo */
> > > > > > - .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
> > > > > > - .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
> > > > > > - .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
> > > > > > - .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP7_hi */
> > > > > > - .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
> > > > > > - .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
> > > > > > - .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
> > > > > > - .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
> > > > > >
> > > > > > - .align 64
> > > > > > - /* _sSignMask */
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP6_lo */
> > > > > > - .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
> > > > > > - .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
> > > > > > - .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
> > > > > > - .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP6_hi */
> > > > > > - .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
> > > > > > - .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
> > > > > > - .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
> > > > > > - .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP5_lo */
> > > > > > - .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
> > > > > > - .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
> > > > > > - .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
> > > > > > - .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP5_hi */
> > > > > > - .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
> > > > > > - .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
> > > > > > - .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
> > > > > > - .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP4_lo */
> > > > > > - .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
> > > > > > - .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
> > > > > > - .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
> > > > > > - .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP4_hi */
> > > > > > - .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
> > > > > > - .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
> > > > > > - .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
> > > > > > - .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP3_lo */
> > > > > > - .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
> > > > > > - .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
> > > > > > - .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
> > > > > > - .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP3_hi */
> > > > > > - .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
> > > > > > - .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
> > > > > > - .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
> > > > > > - .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP2_lo */
> > > > > > - .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
> > > > > > - .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
> > > > > > - .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
> > > > > > - .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP2_hi */
> > > > > > - .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
> > > > > > - .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
> > > > > > - .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
> > > > > > - .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP0_lo */
> > > > > > - .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
> > > > > > - .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
> > > > > > - .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
> > > > > > - .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
> > > > > > -
> > > > > > - .align 64
> > > > > > - /* _sP0_hi */
> > > > > > - .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
> > > > > > - .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
> > > > > > - .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
> > > > > > - .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
> > > > > > +LOCAL_DATA_NAME_UNALIGNED:
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMantMask_UISA, 0x7fe00000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMinIdxOfsMask_UISA, 0x3d400000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iMaxIdxMask_UISA, 0x03e00000)
> > > > > > + float_block (LOCAL_DATA_NAME_UNALIGNED, _iExpMask, 0x7f000000)
> > > > > > + .type LOCAL_DATA_NAME_UNALIGNED, @object
> > > > > > + .size LOCAL_DATA_NAME_UNALIGNED, .-LOCAL_DATA_NAME_UNALIGNED
> > > > > >
> > > > > > .align 64
> > > > > > - .type __svml_stanh_data_internal_al64, @object
> > > > > > - .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
> > > > > > - .type __svml_stanh_data_internal, @object
> > > > > > - .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
> > > > > > +LOCAL_DATA_NAME:
> > > > > > + float_block (LOCAL_DATA_NAME, _sC_lo,
> > > > > > + 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000,
> > > > > > + 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000,
> > > > > > + 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000,
> > > > > > + 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sC_hi,
> > > > > > + 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000,
> > > > > > + 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000,
> > > > > > + 0x40500000, 0x40700000, 0x40900000, 0x40b00000,
> > > > > > + 0x40d00000, 0x40f00000, 0x41100000, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP7_lo,
> > > > > > + 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e,
> > > > > > + 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57,
> > > > > > + 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f,
> > > > > > + 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP7_hi,
> > > > > > + 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b,
> > > > > > + 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22,
> > > > > > + 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950,
> > > > > > + 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP6_lo,
> > > > > > + 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756,
> > > > > > + 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0,
> > > > > > + 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17,
> > > > > > + 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP6_hi,
> > > > > > + 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63,
> > > > > > + 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66,
> > > > > > + 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3,
> > > > > > + 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP5_lo,
> > > > > > + 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d,
> > > > > > + 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670,
> > > > > > + 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405,
> > > > > > + 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP5_hi,
> > > > > > + 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9,
> > > > > > + 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd,
> > > > > > + 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232,
> > > > > > + 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP4_lo,
> > > > > > + 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120,
> > > > > > + 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a,
> > > > > > + 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88,
> > > > > > + 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP4_hi,
> > > > > > + 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96,
> > > > > > + 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67,
> > > > > > + 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9,
> > > > > > + 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP3_lo,
> > > > > > + 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d,
> > > > > > + 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3,
> > > > > > + 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca,
> > > > > > + 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP3_hi,
> > > > > > + 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704,
> > > > > > + 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06,
> > > > > > + 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2,
> > > > > > + 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP2_lo,
> > > > > > + 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f,
> > > > > > + 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580,
> > > > > > + 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92,
> > > > > > + 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP2_hi,
> > > > > > + 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2,
> > > > > > + 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4,
> > > > > > + 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b,
> > > > > > + 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP0_lo,
> > > > > > + 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169,
> > > > > > + 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984,
> > > > > > + 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163,
> > > > > > + 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0)
> > > > > > +
> > > > > > + float_block (LOCAL_DATA_NAME, _sP0_hi,
> > > > > > + 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53,
> > > > > > + 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85,
> > > > > > + 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0,
> > > > > > + 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000)
> > > > > > +
> > > > > > + .type LOCAL_DATA_NAME, @object
> > > > > > + .size LOCAL_DATA_NAME, .-LOCAL_DATA_NAME
> > > > > > --
> > > > > > 2.34.1
> > > > > >
> > > > >
> > > > > The data movement makes the assembler codes much harder to follow.
> > > > > Sunil, what do you think of this patch series?
> > > >
> > > > What do you mean? The change on in how we define rodata or the movement
> > > > to multiple files or something else?
> > >
> > > The glibc way to support data files for assembly codes is to define
> > > data in C and use *.sym to generate offsets for assembly files, like
> >
> > I see. Although to be fair the entire SVML codebase bucks that trend.
>
> It is because libmvec codes were generated by ICC and processed
> by scripts.
>
> > Seems like a more dramatic trend to move all the offsets to C.
>
> Since you are adding data by hand, you should do it in C.
Since the plan is to integrate this piece-meal (function by function), think
it's easier to integrate into a system that matches the rest of the
unyet changed
files.
Once all of the SVML functions have been updated it will be simple
enough to script
the change from ASM -> C.
Thoughts?
>
> > >
> > > sysdeps/x86/cpu-features-offsets.sym:XSAVE_STATE_SIZE_OFFSET
> > > offsetof (struct cpu_features, xsave_state_size)
> > > sysdeps/x86_64/dl-trampoline.h: sub
> > > _rtld_local_ro+RTLD_GLOBAL_RO_DL_X86_CPU_FEATURES_OFFSET+XSAVE_STATE_SIZE_OFFSET(%rip),
> > > %RSP_LP
> > > sysdeps/x86_64/dl-trampoline.h: sub
> > > _dl_x86_cpu_features+XSAVE_STATE_SIZE_OFFSET(%rip), %RSP_LP
> > >
> > > --
> > > H.J.
>
>
>
> --
> H.J.
^ permalink raw reply [flat|nested] 38+ messages in thread
end of thread, other threads:[~2023-06-27 18:24 UTC | newest]
Thread overview: 38+ messages (download: mbox.gz / follow: Atom feed)
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2022-12-07 8:52 [PATCH v1 01/27] x86/fpu: Create helper file for common data macros Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 02/27] x86/fpu: Add file for common data used across svml_s_*_avx2.S files Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 03/27] x86/fpu: Add file for common data used across svml_s_*_avx512.S files Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 04/27] x86/fpu: Add file for common data used across svml_s_*_sse4.S files Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 05/27] x86/fpu: Build common data files for svml_s_*_{avx512, avx2, sse4}.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 06/27] x86/fpu: Update rodata usage in svml_s_tanhf_*_{avx2, sse4} Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 07/27] x86/fpu: Update rodata usage in svml_s_tanhf16_core_avx512.S Noah Goldstein via Libc-alpha
2022-12-16 17:05 ` H.J. Lu via Libc-alpha
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2022-12-16 22:54 ` Sunil Pandey via Libc-alpha
2023-06-27 18:23 ` Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 08/27] x86/fpu: Update rodata usage in svml_s_atanhf16_core_avx512.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 09/27] x86/fpu: Update rodata usage in svml_s_atanhf4_core_sse4.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 10/27] x86/fpu: Update rodata usage in svml_s_atanhf8_core_avx2.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 11/27] x86/fpu: Optimize svml_s_atanf16_core_avx512.S Noah Goldstein via Libc-alpha
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2022-12-07 8:52 ` [PATCH v1 15/27] x86/fpu: Optimize svml_s_tanf16_core_avx512.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 16/27] x86/fpu: Optimize svml_s_tanf4_core_sse4.S Noah Goldstein via Libc-alpha
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2022-12-07 8:52 ` [PATCH v1 19/27] x86/fpu: Optimize svml_s_log10f4_core_sse4.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 20/27] x86/fpu: Optimize svml_s_log10f8_core_avx2.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 21/27] x86/fpu: Optimize svml_s_log2f16_core_avx512.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 22/27] x86/fpu: Optimize svml_s_log2f4_core_sse4.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 23/27] x86/fpu: Optimize svml_s_log2f8_core_avx2.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 24/27] x86/fpu: Optimize svml_s_logf16_core_avx512.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 25/27] x86/fpu: Optimize svml_s_logf4_core_sse4.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 26/27] x86/fpu: Optimize svml_s_logf8_core_avx2.S Noah Goldstein via Libc-alpha
2022-12-07 8:52 ` [PATCH v1 27/27] x86/fpu: Remove unused svml_s_logf_data.S file Noah Goldstein via Libc-alpha
2022-12-07 23:53 ` [PATCH v1 01/27] x86/fpu: Create helper file for common data macros H.J. Lu via Libc-alpha
2022-12-08 0:13 ` Noah Goldstein via Libc-alpha
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