From: Adhemerval Zanella via Libc-alpha <libc-alpha@sourceware.org>
To: libc-alpha@sourceware.org
Cc: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
Subject: [PATCH v3 0/7] Improve hypot()
Date: Mon, 1 Nov 2021 17:20:52 -0300 [thread overview]
Message-ID: <20211101202059.1026032-1-adhemerval.zanella@linaro.org> (raw)
This patchset uses a different algorithm for hypot() based on the
'An Improved Algorithm for hypot(a,b)' by Carlos F. Borges [1]. This
method is also used by Julia language. The motivation for this change
are:
1. The new algorithm is more precise without minimum performance
difference.
2. It allows to consolidate the implementations, since it favor
floating-point operations over integer ones (as done for powerpc).
This might be a boost for some architectures as well.
The current hypot() implementation seems already to be bounded to a
maximum of 1 ulp of error, however the new proposed algorithm shows an
slight precision improvement by showing more correctly rounded results.
With a random 1e9 inputs for different float format I see:
- An improvement from 3427362 to 18457 results with 1 ulp of
error for Binary64.
- An improvement from 233442 to 1274 results with 1 ulp of
error for Binary96 (x86_64).
- An improvement from 453045 to 1294 results with 1 ulp of
error for Binary96 (x86_64).
Also for the maximal known error master shows (in ulps, with
corresponding inputs), determined with [3]:
binary32 0.500 0x1.3ac98p+67,-0x1.ba5ec2p+77
binary64 0.987 -0x0.5a934b7eac967p-1022,-0x0.b5265a7e06b82p-1022
binary96 0.981 0x1.73f339f61eda21dp-16384l,0x2.e45f9f9500877e2p-16384l
binary128 0.985 -0x2.d8311789103b76133ea1d5bc38c4p-16384,-0x1.6d85492006d7dcc6cc52938684p-16384
With the new implementation:
binary32 0.500 0x1.3ac98p+67,-0x1.ba5ec2p+77 [same]
binary64 0.792 0x0.603e52daf0bfdp-1022,-0x0.a622d0a9a433bp-1022
binary96 0.584 -0x2.97b86706043d619p+7240l,0x1.8256bdd12d2e163ep+7240l
binary128 0.749 0x2.2d5faf4036d6e68566f01054612p-8192,0x3.5738e8e2505f5d1fc2973716f05p-8192
Along with the newer implementation, the last patch also optimizes the
call with similar work done for other math functions by removing the
POSIX error handling (which is a big performance boost in some cases
and architectures).
I have adapted the dbl-64, ldbl-96, and ldbl-128, the flt-32 is not
required since it calls the dbl-64 one. I have not adapated ldbl-128ibm
since the format has a lot of caveats and IBM aims to move to ldbl-128.
[1] https://arxiv.org/pdf/1904.09481.pdf
[2] https://github.com/JuliaLang/julia/commit/4a046009a3362ab5e17d369641dbbc9657eb680c
[3] https://gitlab.inria.fr/zimmerma/math_accuracy/-/blob/master/binary64/check_sample2.c
---
Changes from v2:
- Improved the NaN and infinity checks.
- Fixed i386 C implementation.
Adhemerval Zanella (7):
math: Simplify hypotf implementation
math: Use an improved algorithm for hypot (dbl-64)
math: Use an improved algorithm for hypotl (ldbl-96)
math: Use an improved algorithm for hypotl (ldbl-128)
math: Remove powerpc e_hypot
i386: Move hypot implementation to C
math: Remove the error handling wrapper from hypot and hypotf
math/Versions | 2 +
math/w_hypot.c | 8 +
math/w_hypot_compat.c | 13 +-
math/w_hypotf.c | 8 +
math/w_hypotf_compat.c | 6 +-
sysdeps/i386/fpu/e_hypot.S | 75 ------
sysdeps/i386/fpu/e_hypot.c | 58 ++++
sysdeps/i386/fpu/e_hypotf.S | 64 -----
sysdeps/ieee754/dbl-64/e_hypot.c | 247 ++++++++----------
sysdeps/ieee754/dbl-64/w_hypot.c | 1 +
sysdeps/ieee754/flt-32/e_hypotf.c | 75 +++---
sysdeps/ieee754/flt-32/math_config.h | 9 +
sysdeps/ieee754/flt-32/w_hypotf.c | 1 +
sysdeps/ieee754/ldbl-128/e_hypotl.c | 224 +++++++---------
sysdeps/ieee754/ldbl-96/e_hypotl.c | 229 +++++++---------
sysdeps/mach/hurd/i386/libm.abilist | 2 +
sysdeps/powerpc/fpu/e_hypot.c | 87 ------
sysdeps/powerpc/fpu/e_hypotf.c | 78 ------
.../powerpc32/power4/fpu/multiarch/Makefile | 5 +-
.../power4/fpu/multiarch/e_hypot-power7.c | 23 --
.../power4/fpu/multiarch/e_hypot-ppc32.c | 23 --
.../powerpc32/power4/fpu/multiarch/e_hypot.c | 33 ---
.../power4/fpu/multiarch/e_hypotf-power7.c | 23 --
.../power4/fpu/multiarch/e_hypotf-ppc32.c | 23 --
.../powerpc32/power4/fpu/multiarch/e_hypotf.c | 33 ---
sysdeps/unix/sysv/linux/aarch64/libm.abilist | 2 +
sysdeps/unix/sysv/linux/alpha/libm.abilist | 2 +
sysdeps/unix/sysv/linux/arm/be/libm.abilist | 2 +
sysdeps/unix/sysv/linux/arm/le/libm.abilist | 2 +
sysdeps/unix/sysv/linux/hppa/libm.abilist | 2 +
sysdeps/unix/sysv/linux/i386/libm.abilist | 2 +
.../sysv/linux/m68k/coldfire/libm.abilist | 2 +
.../unix/sysv/linux/m68k/m680x0/libm.abilist | 2 +
.../sysv/linux/microblaze/be/libm.abilist | 2 +
.../sysv/linux/microblaze/le/libm.abilist | 2 +
.../unix/sysv/linux/mips/mips32/libm.abilist | 2 +
.../unix/sysv/linux/mips/mips64/libm.abilist | 2 +
sysdeps/unix/sysv/linux/nios2/libm.abilist | 2 +
.../linux/powerpc/powerpc32/fpu/libm.abilist | 2 +
.../powerpc/powerpc32/nofpu/libm.abilist | 2 +
.../linux/powerpc/powerpc64/be/libm.abilist | 2 +
.../linux/powerpc/powerpc64/le/libm.abilist | 2 +
.../unix/sysv/linux/s390/s390-32/libm.abilist | 2 +
.../unix/sysv/linux/s390/s390-64/libm.abilist | 2 +
sysdeps/unix/sysv/linux/sh/be/libm.abilist | 2 +
sysdeps/unix/sysv/linux/sh/le/libm.abilist | 2 +
.../sysv/linux/sparc/sparc32/libm.abilist | 2 +
.../sysv/linux/sparc/sparc64/libm.abilist | 2 +
.../unix/sysv/linux/x86_64/64/libm.abilist | 2 +
.../unix/sysv/linux/x86_64/x32/libm.abilist | 2 +
50 files changed, 495 insertions(+), 905 deletions(-)
create mode 100644 math/w_hypot.c
create mode 100644 math/w_hypotf.c
delete mode 100644 sysdeps/i386/fpu/e_hypot.S
create mode 100644 sysdeps/i386/fpu/e_hypot.c
delete mode 100644 sysdeps/i386/fpu/e_hypotf.S
create mode 100644 sysdeps/ieee754/dbl-64/w_hypot.c
create mode 100644 sysdeps/ieee754/flt-32/w_hypotf.c
delete mode 100644 sysdeps/powerpc/fpu/e_hypot.c
delete mode 100644 sysdeps/powerpc/fpu/e_hypotf.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot-power7.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot-ppc32.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypot.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf-power7.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf-ppc32.c
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/multiarch/e_hypotf.c
--
2.32.0
next reply other threads:[~2021-11-01 20:21 UTC|newest]
Thread overview: 16+ messages / expand[flat|nested] mbox.gz Atom feed top
2021-11-01 20:20 Adhemerval Zanella via Libc-alpha [this message]
2021-11-01 20:20 ` [PATCH v3 1/7] math: Simplify hypotf implementation Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 2/7] math: Use an improved algorithm for hypot (dbl-64) Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 3/7] math: Use an improved algorithm for hypotl (ldbl-96) Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 4/7] math: Use an improved algorithm for hypotl (ldbl-128) Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 5/7] math: Remove powerpc e_hypot Adhemerval Zanella via Libc-alpha
2021-11-09 19:28 ` Paul A. Clarke via Libc-alpha
2021-11-10 14:34 ` Wilco Dijkstra via Libc-alpha
2021-11-10 14:43 ` Paul A. Clarke via Libc-alpha
2021-11-10 14:47 ` Adhemerval Zanella via Libc-alpha
2021-11-11 17:05 ` Wilco Dijkstra via Libc-alpha
2021-11-11 17:13 ` Adhemerval Zanella via Libc-alpha
2021-11-11 19:48 ` Wilco Dijkstra via Libc-alpha
2021-11-11 20:54 ` Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 6/7] i386: Move hypot implementation to C Adhemerval Zanella via Libc-alpha
2021-11-01 20:20 ` [PATCH v3 7/7] math: Remove the error handling wrapper from hypot and hypotf Adhemerval Zanella via Libc-alpha
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