From: Paul Zimmermann <Paul.Zimmermann@inria.fr>
To: Florian Weimer <fweimer@redhat.com>
Cc: libc-alpha@sourceware.org
Subject: fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny (v4)
Date: Mon, 03 Aug 2020 15:19:25 +0200 [thread overview]
Message-ID: <mwwo2fvpcy.fsf@tomate.loria.fr> (raw)
In-Reply-To: <87lfj1jse3.fsf@oldenburg2.str.redhat.com> (message from Florian Weimer on Thu, 30 Jul 2020 10:53:24 +0200)
Dear Florian,
> I suggest to leave it at 6, other CPU variants may still need the 6
> there.
here is a new version.
Paul
From 971c832c2087e9463951d1b07b48d4d9a998e8c0 Mon Sep 17 00:00:00 2001
From: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Date: Mon, 3 Aug 2020 15:16:39 +0200
Subject: [PATCH] fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is
tiny (v4)
---
math/auto-libm-test-in | 2 ++
sysdeps/ieee754/flt-32/e_j0f.c | 17 ++++++++++++++++-
2 files changed, 18 insertions(+), 1 deletion(-)
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 4414e54d93..5d488a8711 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -5748,6 +5748,8 @@ j0 0x1p16382
j0 0x1p16383
# the next value generates larger error bounds on x86_64 (binary32)
j0 0x2.602774p+0 xfail-rounding:ibm128-libgcc
+# the next value exercises the flt-32 code path for x >= 2^127
+j0 0x8.2f4ecp+124
j1 -1.0
j1 0.0
diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c
index c89b9f2688..91e8de8fe3 100644
--- a/sysdeps/ieee754/flt-32/e_j0f.c
+++ b/sysdeps/ieee754/flt-32/e_j0f.c
@@ -55,7 +55,22 @@ __ieee754_j0f(float x)
z = -__cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
- }
+ } else {
+ /* We subtract (exactly) a value x0 such that cos(x0)+sin(x0)
+ is very near to 0, and use the identity
+ sin(x-x0) = sin(x)*cos(x0)-cos(x)*sin(x0) to get
+ sin(x) + cos(x) with extra accuracy. */
+ float x0 = 0xe.d4108p+124f;
+ float y = x - x0; /* exact */
+ /* sin(y) = sin(x)*cos(x0)-cos(x)*sin(x0) */
+ z = __sinf (y);
+ float eps = 0x1.5f263ep-24f;
+ /* cos(x0) ~ -sin(x0) + eps */
+ z += eps * __cosf (x);
+ /* now z ~ (sin(x)-cos(x))*cos(x0) */
+ float cosx0 = -0xb.504f3p-4f;
+ cc = z / cosx0;
+ }
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
--
2.27.0
next prev parent reply other threads:[~2020-08-03 13:19 UTC|newest]
Thread overview: 16+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-07-27 17:15 fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny Paul Zimmermann
2020-07-27 21:35 ` Joseph Myers
2020-07-28 8:23 ` Paul Zimmermann
2020-07-28 9:19 ` Andreas Schwab
2020-07-28 10:50 ` Paul Zimmermann
2020-07-28 18:09 ` Adhemerval Zanella via Libc-alpha
2020-07-29 7:03 ` fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny (v2) Paul Zimmermann
2020-07-29 20:25 ` Adhemerval Zanella via Libc-alpha
2020-07-30 7:20 ` fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny (v3) Paul Zimmermann
2020-07-30 8:53 ` Florian Weimer via Libc-alpha
2020-08-03 13:19 ` Paul Zimmermann [this message]
-- strict thread matches above, loose matches on Subject: below --
2020-08-07 11:25 fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny (v4) Paul Zimmermann
2020-08-07 19:33 ` Adhemerval Zanella via Libc-alpha
2020-08-07 20:30 ` Joseph Myers
2020-08-08 19:53 ` Adhemerval Zanella via Libc-alpha
2020-08-11 11:31 ` Paul Zimmermann
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