[PATCH 09/11] math: Use erfcf from CORE-MATH
Adhemerval Zanella
adhemerval.zanella@linaro.org
Mon Nov 11 13:45:47 GMT 2024
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic erfcf.
The code was adapted to glibc style and to use the definition of
math_config.h.
Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (M1,
gcc 13.2.1), and powerpc (POWER10, gcc 13.2.1):
latency master patched improvement
x86_64 98.8796 66.2142 33.04%
x86_64v2 98.9617 67.4221 31.87%
x86_64v3 87.4161 53.1754 39.17%
aarch64 33.8336 22.0781 34.75%
power10 21.1750 13.5864 35.84%
powerpc 21.4694 13.8149 35.65%
reciprocal-throughput master patched improvement
x86_64 48.5620 27.6731 43.01%
x86_64v2 47.9497 28.3804 40.81%
x86_64v3 42.0255 18.1355 56.85%
aarch64 24.3938 13.4041 45.05%
power10 10.4919 6.1881 41.02%
powerpc 11.763 6.76468 42.49%
Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
---
SHARED-FILES | 4 +
sysdeps/alpha/fpu/libm-test-ulps | 4 -
sysdeps/arc/fpu/libm-test-ulps | 4 -
sysdeps/arc/nofpu/libm-test-ulps | 1 -
sysdeps/arm/libm-test-ulps | 4 -
sysdeps/csky/fpu/libm-test-ulps | 4 -
sysdeps/csky/nofpu/libm-test-ulps | 4 -
sysdeps/hppa/fpu/libm-test-ulps | 4 -
sysdeps/i386/fpu/libm-test-ulps | 4 -
.../i386/i686/fpu/multiarch/libm-test-ulps | 4 -
sysdeps/ieee754/flt-32/s_erfcf.c | 332 +++++++++---------
sysdeps/loongarch/lp64/libm-test-ulps | 4 -
sysdeps/m68k/m680x0/fpu/libm-test-ulps | 4 -
sysdeps/microblaze/libm-test-ulps | 1 -
sysdeps/mips/mips32/libm-test-ulps | 4 -
sysdeps/mips/mips64/libm-test-ulps | 4 -
sysdeps/nios2/libm-test-ulps | 1 -
sysdeps/or1k/fpu/libm-test-ulps | 4 -
sysdeps/or1k/nofpu/libm-test-ulps | 4 -
sysdeps/powerpc/fpu/libm-test-ulps | 4 -
sysdeps/powerpc/nofpu/libm-test-ulps | 4 -
sysdeps/riscv/nofpu/libm-test-ulps | 4 -
sysdeps/riscv/rvd/libm-test-ulps | 4 -
sysdeps/s390/fpu/libm-test-ulps | 4 -
sysdeps/sh/libm-test-ulps | 2 -
sysdeps/sparc/fpu/libm-test-ulps | 4 -
sysdeps/x86_64/fpu/libm-test-ulps | 4 -
27 files changed, 176 insertions(+), 249 deletions(-)
diff --git a/SHARED-FILES b/SHARED-FILES
index ccc5179f80..e6e29bcadc 100644
--- a/SHARED-FILES
+++ b/SHARED-FILES
@@ -276,3 +276,7 @@ sysdeps/ieee754/flt-32/s_erff.c
(file src/binary32/erf/erff.c in CORE-MATH)
- The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow.
+sysdeps/ieee754/flt-32/s_erfcf.c
+ (file src/binary32/erfc/erfcf.c in CORE-MATH)
+ - The code was adapted to use glibc code style and internal
+ functions to handle errno, overflow, and underflow.
diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps
index bbb3a5c459..3678bc38e3 100644
--- a/sysdeps/alpha/fpu/libm-test-ulps
+++ b/sysdeps/alpha/fpu/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 4
Function: "erfc_downward":
double: 5
-float: 6
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
ldouble: 5
Function: "exp":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index 9e422da289..68d67b6a67 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -745,19 +745,15 @@ double: 2
Function: "erfc":
double: 5
-float: 5
Function: "erfc_downward":
double: 4
-float: 4
Function: "erfc_towardzero":
double: 4
-float: 4
Function: "erfc_upward":
double: 5
-float: 5
Function: "exp":
double: 1
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index 2c24fdf663..dc2499b56a 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -180,7 +180,6 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "exp":
double: 1
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index 153cd1f3d7..000a5af492 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -738,19 +738,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps
index d276db245b..ed373cd353 100644
--- a/sysdeps/csky/fpu/libm-test-ulps
+++ b/sysdeps/csky/fpu/libm-test-ulps
@@ -731,19 +731,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps
index ea08fd5378..48a8c7351f 100644
--- a/sysdeps/csky/nofpu/libm-test-ulps
+++ b/sysdeps/csky/nofpu/libm-test-ulps
@@ -729,19 +729,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index 7e4f6ebe77..19087298e9 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -752,20 +752,16 @@ double: 1
Function: "erfc":
double: 5
-float: 3
ldouble: 1
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 041c180f7a..5284078bee 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1098,25 +1098,21 @@ ldouble: 1
Function: "erfc":
double: 5
-float: 3
float128: 4
ldouble: 5
Function: "erfc_downward":
double: 5
-float: 6
float128: 5
ldouble: 4
Function: "erfc_towardzero":
double: 3
-float: 4
float128: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
float128: 5
ldouble: 5
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index e3ee0c61f6..da00d80ba7 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -1101,25 +1101,21 @@ ldouble: 1
Function: "erfc":
double: 5
-float: 3
float128: 4
ldouble: 5
Function: "erfc_downward":
double: 5
-float: 6
float128: 5
ldouble: 4
Function: "erfc_towardzero":
double: 3
-float: 4
float128: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
float128: 5
ldouble: 5
diff --git a/sysdeps/ieee754/flt-32/s_erfcf.c b/sysdeps/ieee754/flt-32/s_erfcf.c
index fdba278eff..6f8c7c6a57 100644
--- a/sysdeps/ieee754/flt-32/s_erfcf.c
+++ b/sysdeps/ieee754/flt-32/s_erfcf.c
@@ -1,173 +1,185 @@
-/* s_erfcf.c -- float version of s_erfc.c.
- */
+/* Correctly-rounded complementary error function for the binary32 format
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
+Copyright (c) 2023, 2024 Alexei Sibidanov.
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
-#endif
+This file is part of the CORE-MATH project
+project (file src/binary32/erfc/erfcf.c revision bc385c2).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
#include <errno.h>
-#include <fix-int-fp-convert-zero.h>
-#include <libm-alias-float.h>
-#include <math-narrow-eval.h>
#include <math.h>
-#include <math_private.h>
-
+#include <stdint.h>
+#include <libm-alias-float.h>
+#include "math_config.h"
-static const float
-tiny = 1e-30,
-half= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
- /* c = (subfloat)0.84506291151 */
-erx = 8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to erf on [0,0.84375]
- */
-pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
-pp1 = -3.2504209876e-01, /* 0xbea66beb */
-pp2 = -2.8481749818e-02, /* 0xbce9528f */
-pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
-qq2 = 6.5022252500e-02, /* 0x3d852a63 */
-qq3 = 5.0813062117e-03, /* 0x3ba68116 */
-qq4 = 1.3249473704e-04, /* 0x390aee49 */
-qq5 = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to erf in [0.84375,1.25]
- */
-pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1 = 4.1485610604e-01, /* 0x3ed46805 */
-pa2 = -3.7220788002e-01, /* 0xbebe9208 */
-pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
-pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
-pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
-qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
-qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
-qa4 = 1.2617121637e-01, /* 0x3e013307 */
-qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
-qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
-/*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
- */
-ra0 = -9.8649440333e-03, /* 0xbc21a093 */
-ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2 = -1.0558626175e+01, /* 0xc128f022 */
-ra3 = -6.2375331879e+01, /* 0xc2798057 */
-ra4 = -1.6239666748e+02, /* 0xc322658c */
-ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6 = -8.1287437439e+01, /* 0xc2a2932b */
-ra7 = -9.8143291473e+00, /* 0xc11d077e */
-sa1 = 1.9651271820e+01, /* 0x419d35ce */
-sa2 = 1.3765776062e+02, /* 0x4309a863 */
-sa3 = 4.3456588745e+02, /* 0x43d9486f */
-sa4 = 6.4538726807e+02, /* 0x442158c9 */
-sa5 = 4.2900814819e+02, /* 0x43d6810b */
-sa6 = 1.0863500214e+02, /* 0x42d9451f */
-sa7 = 6.5702495575e+00, /* 0x40d23f7c */
-sa8 = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to erfc in [1/.35,28]
- */
-rb0 = -9.8649431020e-03, /* 0xbc21a092 */
-rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2 = -1.7757955551e+01, /* 0xc18e104b */
-rb3 = -1.6063638306e+02, /* 0xc320a2ea */
-rb4 = -6.3756646729e+02, /* 0xc41f6441 */
-rb5 = -1.0250950928e+03, /* 0xc480230b */
-rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1 = 3.0338060379e+01, /* 0x41f2b459 */
-sb2 = 3.2579251099e+02, /* 0x43a2e571 */
-sb3 = 1.5367296143e+03, /* 0x44c01759 */
-sb4 = 3.1998581543e+03, /* 0x4547fdbb */
-sb5 = 2.5530502930e+03, /* 0x451f90ce */
-sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
-sb7 = -2.2440952301e+01; /* 0xc1b38712 */
+static const double E[] =
+ {
+ 0x1p+0, 0x1.0163da9fb3335p+0, 0x1.02c9a3e778061p+0,
+ 0x1.04315e86e7f85p+0, 0x1.059b0d3158574p+0, 0x1.0706b29ddf6dep+0,
+ 0x1.0874518759bc8p+0, 0x1.09e3ecac6f383p+0, 0x1.0b5586cf9890fp+0,
+ 0x1.0cc922b7247f7p+0, 0x1.0e3ec32d3d1a2p+0, 0x1.0fb66affed31bp+0,
+ 0x1.11301d0125b51p+0, 0x1.12abdc06c31ccp+0, 0x1.1429aaea92dep+0,
+ 0x1.15a98c8a58e51p+0, 0x1.172b83c7d517bp+0, 0x1.18af9388c8deap+0,
+ 0x1.1a35beb6fcb75p+0, 0x1.1bbe084045cd4p+0, 0x1.1d4873168b9aap+0,
+ 0x1.1ed5022fcd91dp+0, 0x1.2063b88628cd6p+0, 0x1.21f49917ddc96p+0,
+ 0x1.2387a6e756238p+0, 0x1.251ce4fb2a63fp+0, 0x1.26b4565e27cddp+0,
+ 0x1.284dfe1f56381p+0, 0x1.29e9df51fdee1p+0, 0x1.2b87fd0dad99p+0,
+ 0x1.2d285a6e4030bp+0, 0x1.2ecafa93e2f56p+0, 0x1.306fe0a31b715p+0,
+ 0x1.32170fc4cd831p+0, 0x1.33c08b26416ffp+0, 0x1.356c55f929ff1p+0,
+ 0x1.371a7373aa9cbp+0, 0x1.38cae6d05d866p+0, 0x1.3a7db34e59ff7p+0,
+ 0x1.3c32dc313a8e5p+0, 0x1.3dea64c123422p+0, 0x1.3fa4504ac801cp+0,
+ 0x1.4160a21f72e2ap+0, 0x1.431f5d950a897p+0, 0x1.44e086061892dp+0,
+ 0x1.46a41ed1d0057p+0, 0x1.486a2b5c13cdp+0, 0x1.4a32af0d7d3dep+0,
+ 0x1.4bfdad5362a27p+0, 0x1.4dcb299fddd0dp+0, 0x1.4f9b2769d2ca7p+0,
+ 0x1.516daa2cf6642p+0, 0x1.5342b569d4f82p+0, 0x1.551a4ca5d920fp+0,
+ 0x1.56f4736b527dap+0, 0x1.58d12d497c7fdp+0, 0x1.5ab07dd485429p+0,
+ 0x1.5c9268a5946b7p+0, 0x1.5e76f15ad2148p+0, 0x1.605e1b976dc09p+0,
+ 0x1.6247eb03a5585p+0, 0x1.6434634ccc32p+0, 0x1.6623882552225p+0,
+ 0x1.68155d44ca973p+0, 0x1.6a09e667f3bcdp+0, 0x1.6c012750bdabfp+0,
+ 0x1.6dfb23c651a2fp+0, 0x1.6ff7df9519484p+0, 0x1.71f75e8ec5f74p+0,
+ 0x1.73f9a48a58174p+0, 0x1.75feb564267c9p+0, 0x1.780694fde5d3fp+0,
+ 0x1.7a11473eb0187p+0, 0x1.7c1ed0130c132p+0, 0x1.7e2f336cf4e62p+0,
+ 0x1.80427543e1a12p+0, 0x1.82589994cce13p+0, 0x1.8471a4623c7adp+0,
+ 0x1.868d99b4492edp+0, 0x1.88ac7d98a6699p+0, 0x1.8ace5422aa0dbp+0,
+ 0x1.8cf3216b5448cp+0, 0x1.8f1ae99157736p+0, 0x1.9145b0b91ffc6p+0,
+ 0x1.93737b0cdc5e5p+0, 0x1.95a44cbc8520fp+0, 0x1.97d829fde4e5p+0,
+ 0x1.9a0f170ca07bap+0, 0x1.9c49182a3f09p+0, 0x1.9e86319e32323p+0,
+ 0x1.a0c667b5de565p+0, 0x1.a309bec4a2d33p+0, 0x1.a5503b23e255dp+0,
+ 0x1.a799e1330b358p+0, 0x1.a9e6b5579fdbfp+0, 0x1.ac36bbfd3f37ap+0,
+ 0x1.ae89f995ad3adp+0, 0x1.b0e07298db666p+0, 0x1.b33a2b84f15fbp+0,
+ 0x1.b59728de5593ap+0, 0x1.b7f76f2fb5e47p+0, 0x1.ba5b030a1064ap+0,
+ 0x1.bcc1e904bc1d2p+0, 0x1.bf2c25bd71e09p+0, 0x1.c199bdd85529cp+0,
+ 0x1.c40ab5fffd07ap+0, 0x1.c67f12e57d14bp+0, 0x1.c8f6d9406e7b5p+0,
+ 0x1.cb720dcef9069p+0, 0x1.cdf0b555dc3fap+0, 0x1.d072d4a07897cp+0,
+ 0x1.d2f87080d89f2p+0, 0x1.d5818dcfba487p+0, 0x1.d80e316c98398p+0,
+ 0x1.da9e603db3285p+0, 0x1.dd321f301b46p+0, 0x1.dfc97337b9b5fp+0,
+ 0x1.e264614f5a129p+0, 0x1.e502ee78b3ff6p+0, 0x1.e7a51fbc74c83p+0,
+ 0x1.ea4afa2a490dap+0, 0x1.ecf482d8e67f1p+0, 0x1.efa1bee615a27p+0,
+ 0x1.f252b376bba97p+0, 0x1.f50765b6e454p+0, 0x1.f7bfdad9cbe14p+0,
+ 0x1.fa7c1819e90d8p+0, 0x1.fd3c22b8f71f1p+0
+ };
-float __erfcf(float x)
+float
+__erfcf (float xf)
{
- int32_t hx,ix;
- float R,S,P,Q,s,y,z,r;
- GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erfc(nan)=nan */
- /* erfc(+-inf)=0,2 */
- float ret = (float)(((uint32_t)hx>>31)<<1)+one/x;
- if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f)
- return 0.0f;
- return ret;
- }
-
- if(ix < 0x3f580000) { /* |x|<0.84375 */
- if(ix < 0x32800000) /* |x|<2**-26 */
- return one-x;
- z = x*x;
- r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
- s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
- y = r/s;
- if(hx < 0x3e800000) { /* x<1/4 */
- return one-(x+x*y);
- } else {
- r = x*y;
- r += (x-half);
- return half - r ;
- }
+ float axf = fabsf (xf);
+ double axd = axf;
+ double x2 = axd * axd;
+ uint32_t t = asuint (xf);
+ unsigned int at = t & (~0u >> 1);
+ unsigned int sgn = t >> 31;
+ int64_t i = at > 0x40051000;
+ /* for x < -0x1.ea8f94p+1, erfc(x) rounds to 2 (to nearest) */
+ if (__glibc_unlikely (t > 0xc07547ca))
+ { /* xf < -0x1.ea8f94p+1 */
+ if (__glibc_unlikely (t >= 0xff800000))
+ { /* -Inf or NaN */
+ if (t == 0xff800000)
+ return 2.0f; /* -Inf */
+ return xf + xf; /* NaN */
}
- if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = fabsf(x)-one;
- P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
- Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
- if(hx>=0) {
- z = one-erx; return z - P/Q;
- } else {
- z = erx+P/Q; return one+z;
- }
+ return 2.0f - 0x1p-25f; /* rounds to 2 or nextbelow(2) */
+ }
+ /* at is the absolute value of xf
+ for x >= 0x1.41bbf8p+3, erfc(x) < 2^-150, thus rounds to 0 or 2^-149 */
+ if (__glibc_unlikely (at >= 0x4120ddfc))
+ { /* |xf| >= 0x1.41bbf8p+3 */
+ if (__glibc_unlikely (at >= 0x7f800000))
+ { /* +Inf or NaN */
+ if (at == 0x7f800000)
+ return 0.0f; /* +Inf */
+ return xf + xf; /* NaN */
}
- if (ix < 0x41e00000) { /* |x|<28 */
- x = fabsf(x);
- s = one/(x*x);
- if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
- ra5+s*(ra6+s*ra7))))));
- S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
- sa5+s*(sa6+s*(sa7+s*sa8)))))));
- } else { /* |x| >= 1/.35 ~ 2.857143 */
- if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
- R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
- rb5+s*rb6)))));
- S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
- sb5+s*(sb6+s*sb7))))));
- }
- GET_FLOAT_WORD(ix,x);
- SET_FLOAT_WORD(z,ix&0xffffe000);
- r = __ieee754_expf(-z*z-(float)0.5625)*
- __ieee754_expf((z-x)*(z+x)+R/S);
- if(hx>0) {
- float ret = math_narrow_eval (r/x);
- if (ret == 0)
- __set_errno (ERANGE);
- return ret;
- } else
- return two-r/x;
- } else {
- if(hx>0) {
- __set_errno (ERANGE);
- return tiny*tiny;
- } else
- return two-tiny;
+ __set_errno (ERANGE);
+ return 0x1p-149f * 0.25f; /* 0 or 2^-149 wrt rounding */
+ }
+ if (__glibc_unlikely (at <= 0x3db80000))
+ { /* |x| <= 0x1.7p-4 */
+ if (__glibc_unlikely (t == 0xb76c9f62))
+ return 0x1.00010ap+0f + 0x1p-25f; /* exceptional case */
+ /* for |x| <= 0x1.c5bf88p-26. erfc(x) rounds to 1 (to nearest) */
+ if (__glibc_unlikely (at <= 0x32e2dfc4))
+ { /* |x| <= 0x1.c5bf88p-26 */
+ if (__glibc_unlikely (at == 0))
+ return 1.0f;
+ static const float d[] = { -0x1p-26, 0x1p-25 };
+ return 1.0f + d[sgn];
}
+ /* around 0, erfc(x) behaves as 1 + (odd polynomial) */
+ static const double c[] =
+ {
+ 0x1.20dd750429b6dp+0, -0x1.812746b03610bp-2, 0x1.ce2f218831d2fp-4,
+ -0x1.b82c609607dcbp-6, 0x1.553af09b8008ep-8
+ };
+ double f0 = xf
+ * (c[0] + x2 * (c[1] + x2 * (c[2] + x2 * (c[3] + x2 * (c[4])))));
+ return 1.0 - f0;
+ }
+
+ /* now -0x1.ea8f94p+1 <= x <= 0x1.41bbf8p+3, with |x| > 0x1.7p-4 */
+ const double iln2 = 0x1.71547652b82fep+0;
+ const double ln2h = 0x1.62e42fefap-8;
+ const double ln2l = 0x1.cf79abd6f5dc8p-47;
+ uint64_t jt = asuint64 (fma (x2, iln2, -(1024 + 0x1p-8)));
+ int64_t j = (int64_t) (jt << 12) >> 48;
+ double S = asdouble (((j >> 7) + (0x3ff | sgn << 11)) << 52);
+ static const double ch[] =
+ {
+ -0x1.ffffffffff333p-2, 0x1.5555555556a14p-3, -0x1.55556666659b4p-5,
+ 0x1.1111074cc7b22p-7
+ };
+ double d = (x2 + ln2h * j) + ln2l * j;
+ double d2 = d * d;
+ double e0 = E[j & 127];
+ double f = d + d2 * ((ch[0] + d * ch[1]) + d2 * (ch[2] + d * ch[3]));
+ static const double ct[][16] =
+ {
+ {
+ 0x1.c162355429b28p-1, 3.70, 0x1.da951cece2b85p-2,
+ -0x1.70ef6cff4bcc4p+0, 0x1.3d7f7b3d617dep+1, -0x1.9d0aa47537c51p+1,
+ 0x1.9754ea9a3fcb1p+1, -0x1.27a5453fcc015p+1, 0x1.1ef2e0531aebap+0,
+ -0x1.eca090f5a1c06p-3, -0x1.7a3cd173a063cp-4, 0x1.30fa68a68fdddp-4,
+ 0x1.55ad9a326993ap-10, -0x1.07e7b0bb39fbfp-6, 0x1.2328706c0e95p-10,
+ 0x1.d6aa0b7b19cfep-9
+ },
+ {
+ 0x1.137c8983f8516p+2, 2.95, 0x1.05b53aa241333p-3,
+ -0x1.a3f53872bf87p-3, 0x1.de4c30742c9d5p-4, -0x1.cb24bfa591986p-5,
+ 0x1.666aec059ca5fp-6, -0x1.a61250eb26b0bp-8, 0x1.2b28b7924b34dp-10,
+ 0x1.41b13a9d45013p-15, -0x1.6dd5e8a273613p-14, 0x1.09ce8ea5e8da5p-16,
+ 0x1.33923b4102981p-18, -0x1.1dfd161e3f984p-19, -0x1.c87618fcae3b3p-23,
+ 0x1.e8a6ffa0ba2c7p-23
+ }
+ };
+ double z = (axd - ct[i][0]) / (axd + ct[i][1]);
+ double z2 = z * z, z4 = z2 * z2;
+ double z8 = z4 * z4;
+ const double *c = ct[i] + 3;
+ double s = (((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
+ + z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])))
+ + z8 * (((c[8] + z * c[9]) + z2 * (c[10] + z * c[11])) + z4 * (c[12]));
+ s = ct[i][2] + z * s;
+ static const double off[] = { 0, 2 };
+ double r = (S * (e0 - f * e0)) * s;
+ double y = off[sgn] + r;
+ return y;
}
libm_alias_float (__erfc, erfc)
diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
index 2af6da3638..759050a3c3 100644
--- a/sysdeps/loongarch/lp64/libm-test-ulps
+++ b/sysdeps/loongarch/lp64/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 4
Function: "erfc_downward":
double: 5
-float: 6
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
ldouble: 5
Function: "exp":
diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
index 3ea3f74e89..08fbad9c4a 100644
--- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps
+++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
@@ -854,22 +854,18 @@ ldouble: 1
Function: "erfc":
double: 1
-float: 2
ldouble: 2
Function: "erfc_downward":
double: 1
-float: 4
ldouble: 4
Function: "erfc_towardzero":
double: 1
-float: 4
ldouble: 4
Function: "erfc_upward":
double: 1
-float: 3
ldouble: 3
Function: "exp10m1":
diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps
index c079a4f501..5382a18115 100644
--- a/sysdeps/microblaze/libm-test-ulps
+++ b/sysdeps/microblaze/libm-test-ulps
@@ -175,7 +175,6 @@ double: 1
Function: "erfc":
double: 3
-float: 2
Function: "exp":
float: 1
diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
index ebd88e0cef..0fe27ef417 100644
--- a/sysdeps/mips/mips32/libm-test-ulps
+++ b/sysdeps/mips/mips32/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
index ca658b945c..ce7dde2e65 100644
--- a/sysdeps/mips/mips64/libm-test-ulps
+++ b/sysdeps/mips/mips64/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 4
Function: "erfc_downward":
double: 5
-float: 6
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
ldouble: 5
Function: "exp":
diff --git a/sysdeps/nios2/libm-test-ulps b/sysdeps/nios2/libm-test-ulps
index 6416c7ff38..cc63f8fe9f 100644
--- a/sysdeps/nios2/libm-test-ulps
+++ b/sysdeps/nios2/libm-test-ulps
@@ -180,7 +180,6 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "exp":
double: 1
diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
index fb1606801b..5677a353ed 100644
--- a/sysdeps/or1k/fpu/libm-test-ulps
+++ b/sysdeps/or1k/fpu/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
index 2742e3b8be..c7ba12fe19 100644
--- a/sysdeps/or1k/nofpu/libm-test-ulps
+++ b/sysdeps/or1k/nofpu/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
Function: "erfc":
double: 5
-float: 3
Function: "erfc_downward":
double: 5
-float: 6
Function: "erfc_towardzero":
double: 3
-float: 4
Function: "erfc_upward":
double: 5
-float: 6
Function: "exp":
double: 1
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index b22aaf90bd..4e448a263b 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1125,25 +1125,21 @@ ldouble: 3
Function: "erfc":
double: 2
-float: 2
float128: 4
ldouble: 3
Function: "erfc_downward":
double: 4
-float: 4
float128: 5
ldouble: 10
Function: "erfc_towardzero":
double: 3
-float: 3
float128: 4
ldouble: 11
Function: "erfc_upward":
double: 4
-float: 4
float128: 5
ldouble: 7
diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
index 98cd67bd07..d9555e7706 100644
--- a/sysdeps/powerpc/nofpu/libm-test-ulps
+++ b/sysdeps/powerpc/nofpu/libm-test-ulps
@@ -935,22 +935,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 3
Function: "erfc_downward":
double: 5
-float: 6
ldouble: 10
Function: "erfc_towardzero":
double: 3
-float: 4
ldouble: 11
Function: "erfc_upward":
double: 5
-float: 6
ldouble: 7
Function: "exp":
diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
index 8cfeb7bcb2..23228a80a9 100644
--- a/sysdeps/riscv/nofpu/libm-test-ulps
+++ b/sysdeps/riscv/nofpu/libm-test-ulps
@@ -922,22 +922,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 4
Function: "erfc_downward":
double: 3
-float: 4
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 3
ldouble: 4
Function: "erfc_upward":
double: 3
-float: 4
ldouble: 5
Function: "exp":
diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
index f7c6c82dd1..74bde1024a 100644
--- a/sysdeps/riscv/rvd/libm-test-ulps
+++ b/sysdeps/riscv/rvd/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc":
double: 2
-float: 2
ldouble: 4
Function: "erfc_downward":
double: 4
-float: 4
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 3
ldouble: 4
Function: "erfc_upward":
double: 4
-float: 4
ldouble: 5
Function: "exp":
diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
index 36da5d742a..6747fd4f7b 100644
--- a/sysdeps/s390/fpu/libm-test-ulps
+++ b/sysdeps/s390/fpu/libm-test-ulps
@@ -926,22 +926,18 @@ ldouble: 2
Function: "erfc":
double: 2
-float: 2
ldouble: 4
Function: "erfc_downward":
double: 4
-float: 4
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 3
ldouble: 4
Function: "erfc_upward":
double: 4
-float: 4
ldouble: 5
Function: "exp":
diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps
index 6b55797f81..69fe20bc0a 100644
--- a/sysdeps/sh/libm-test-ulps
+++ b/sysdeps/sh/libm-test-ulps
@@ -361,11 +361,9 @@ double: 1
Function: "erfc":
double: 5
-float: 2
Function: "erfc_towardzero":
double: 3
-float: 3
Function: "exp":
double: 1
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 3aed9d4d06..98f7a07190 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc":
double: 5
-float: 3
ldouble: 4
Function: "erfc_downward":
double: 5
-float: 6
ldouble: 5
Function: "erfc_towardzero":
double: 3
-float: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
ldouble: 5
Function: "exp":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index e00ad56c62..b7400e9969 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1330,25 +1330,21 @@ float: 2
Function: "erfc":
double: 5
-float: 3
float128: 4
ldouble: 5
Function: "erfc_downward":
double: 5
-float: 6
float128: 5
ldouble: 4
Function: "erfc_towardzero":
double: 3
-float: 4
float128: 4
ldouble: 4
Function: "erfc_upward":
double: 5
-float: 6
float128: 5
ldouble: 5
--
2.43.0
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