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math: Use erfcf from CORE-MATH

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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>
Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella
2024-10-29 10:02:20 -03:00
parent 994fec2397
commit baa495f231
27 changed files with 179 additions and 250 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
SHARED-FILES
View File

@@ -276,3 +276,7 @@ sysdeps/ieee754/flt-32/s_erff.c
(file src/binary32/erf/erff.c in CORE-MATH) (file src/binary32/erf/erff.c in CORE-MATH)
- The code was adapted to use glibc code style and internal - The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow. 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.

4
sysdeps/alpha/fpu/libm-test-ulps
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@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

4
sysdeps/arc/fpu/libm-test-ulps
View File

@@ -745,19 +745,15 @@ double: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 5
Function: "erfc_downward": Function: "erfc_downward":
double: 4 double: 4
float: 4
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 4 double: 4
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 5
Function: "exp": Function: "exp":
double: 1 double: 1

1
sysdeps/arc/nofpu/libm-test-ulps
View File

@@ -180,7 +180,6 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/arm/libm-test-ulps
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@@ -738,19 +738,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/csky/fpu/libm-test-ulps
View File

@@ -731,19 +731,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/csky/nofpu/libm-test-ulps
View File

@@ -729,19 +729,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/hppa/fpu/libm-test-ulps
View File

@@ -755,20 +755,16 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 1 ldouble: 1
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/i386/fpu/libm-test-ulps
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@@ -1098,25 +1098,21 @@ ldouble: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
float128: 4 float128: 4
ldouble: 5 ldouble: 5
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 4 ldouble: 4
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 5 ldouble: 5

4
sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
View File

@@ -1101,25 +1101,21 @@ ldouble: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
float128: 4 float128: 4
ldouble: 5 ldouble: 5
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 4 ldouble: 4
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 5 ldouble: 5

336
sysdeps/ieee754/flt-32/s_erfcf.c
View File

@@ -1,173 +1,187 @@
/* s_erfcf.c -- float version of s_erfc.c. /* Correctly-rounded complementary error function for the binary32 format
*/
/* Copyright (c) 2023, 2024 Alexei Sibidanov.
* ====================================================
* 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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint) This file is part of the CORE-MATH project
static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $"; project (file src/binary32/erfc/erfcf.c revision bc385c2).
#endif
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 <errno.h>
#include <fix-int-fp-convert-zero.h>
#include <libm-alias-float.h>
#include <math-narrow-eval.h>
#include <math.h> #include <math.h>
#include <math_private.h> #include <stdint.h>
#include <libm-alias-float.h>
#include "math_config.h"
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
};
static const float float
tiny = 1e-30, __erfcf (float xf)
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 */
float __erfcf(float x)
{ {
int32_t hx,ix; float axf = fabsf (xf);
float R,S,P,Q,s,y,z,r; double axd = axf;
GET_FLOAT_WORD(hx,x); double x2 = axd * axd;
ix = hx&0x7fffffff; uint32_t t = asuint (xf);
if(ix>=0x7f800000) { /* erfc(nan)=nan */ unsigned int at = t & (~0u >> 1);
/* erfc(+-inf)=0,2 */ unsigned int sgn = t >> 31;
float ret = (float)(((uint32_t)hx>>31)<<1)+one/x; int64_t i = at > 0x40051000;
if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f) /* for x < -0x1.ea8f94p+1, erfc(x) rounds to 2 (to nearest) */
return 0.0f; if (__glibc_unlikely (t > 0xc07547ca))
return ret; { /* xf < -0x1.ea8f94p+1 */
if (__glibc_unlikely (t >= 0xff800000))
{ /* -Inf or NaN */
if (t == 0xff800000)
return 2.0f; /* -Inf */
return xf + xf; /* NaN */
} }
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 to 2^-149
depending on the rounding mode */
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 */
}
__set_errno (ERANGE);
/* 0x1p-149f * 0.25f rounds to 0 or 2^-149 depending on rounding */
return 0x1p-149f * 0.25f;
}
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;
}
if(ix < 0x3f580000) { /* |x|<0.84375 */ /* now -0x1.ea8f94p+1 <= x <= 0x1.41bbf8p+3, with |x| > 0x1.7p-4 */
if(ix < 0x32800000) /* |x|<2**-26 */ const double iln2 = 0x1.71547652b82fep+0;
return one-x; const double ln2h = 0x1.62e42fefap-8;
z = x*x; const double ln2l = 0x1.cf79abd6f5dc8p-47;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); uint64_t jt = asuint64 (fma (x2, iln2, -(1024 + 0x1p-8)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); int64_t j = (int64_t) (jt << 12) >> 48;
y = r/s; double S = asdouble (((j >> 7) + (0x3ff | sgn << 11)) << 52);
if(hx < 0x3e800000) { /* x<1/4 */ static const double ch[] =
return one-(x+x*y); {
} else { -0x1.ffffffffff333p-2, 0x1.5555555556a14p-3, -0x1.55556666659b4p-5,
r = x*y; 0x1.1111074cc7b22p-7
r += (x-half); };
return half - r ; double d = (x2 + ln2h * j) + ln2l * j;
} double d2 = d * d;
} double e0 = E[j & 127];
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ double f = d + d2 * ((ch[0] + d * ch[1]) + d2 * (ch[2] + d * ch[3]));
s = fabsf(x)-one; static const double ct[][16] =
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) { 0x1.c162355429b28p-1, 0x1.d99999999999ap+1, 0x1.da951cece2b85p-2,
z = one-erx; return z - P/Q; -0x1.70ef6cff4bcc4p+0, 0x1.3d7f7b3d617dep+1, -0x1.9d0aa47537c51p+1,
} else { 0x1.9754ea9a3fcb1p+1, -0x1.27a5453fcc015p+1, 0x1.1ef2e0531aebap+0,
z = erx+P/Q; return one+z; -0x1.eca090f5a1c06p-3, -0x1.7a3cd173a063cp-4, 0x1.30fa68a68fdddp-4,
} 0x1.55ad9a326993ap-10, -0x1.07e7b0bb39fbfp-6, 0x1.2328706c0e95p-10,
} 0x1.d6aa0b7b19cfep-9
if (ix < 0x41e00000) { /* |x|<28 */ },
x = fabsf(x); {
s = one/(x*x); 0x1.137c8983f8516p+2, 0x1.799999999999ap+1, 0x1.05b53aa241333p-3,
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ -0x1.a3f53872bf87p-3, 0x1.de4c30742c9d5p-4, -0x1.cb24bfa591986p-5,
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 0x1.666aec059ca5fp-6, -0x1.a61250eb26b0bp-8, 0x1.2b28b7924b34dp-10,
ra5+s*(ra6+s*ra7)))))); 0x1.41b13a9d45013p-15, -0x1.6dd5e8a273613p-14, 0x1.09ce8ea5e8da5p-16,
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 0x1.33923b4102981p-18, -0x1.1dfd161e3f984p-19, -0x1.c87618fcae3b3p-23,
sa5+s*(sa6+s*(sa7+s*sa8))))))); 0x1.e8a6ffa0ba2c7p-23
} 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*( double z = (axd - ct[i][0]) / (axd + ct[i][1]);
rb5+s*rb6))))); double z2 = z * z, z4 = z2 * z2;
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( double z8 = z4 * z4;
sb5+s*(sb6+s*sb7)))))); const double *c = ct[i] + 3;
} double s = (((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
GET_FLOAT_WORD(ix,x); + z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])))
SET_FLOAT_WORD(z,ix&0xffffe000); + z8 * (((c[8] + z * c[9]) + z2 * (c[10] + z * c[11])) + z4 * (c[12]));
r = __ieee754_expf(-z*z-(float)0.5625)* s = ct[i][2] + z * s;
__ieee754_expf((z-x)*(z+x)+R/S); static const double off[] = { 0, 2 };
if(hx>0) { double r = (S * (e0 - f * e0)) * s;
float ret = math_narrow_eval (r/x); double y = off[sgn] + r;
if (ret == 0) return y;
__set_errno (ERANGE);
return ret;
} else
return two-r/x;
} else {
if(hx>0) {
__set_errno (ERANGE);
return tiny*tiny;
} else
return two-tiny;
}
} }
libm_alias_float (__erfc, erfc) libm_alias_float (__erfc, erfc)

4
sysdeps/loongarch/lp64/libm-test-ulps
View File

@@ -926,22 +926,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

4
sysdeps/m68k/m680x0/fpu/libm-test-ulps
View File

@@ -854,22 +854,18 @@ ldouble: 1
Function: "erfc": Function: "erfc":
double: 1 double: 1
float: 2
ldouble: 2 ldouble: 2
Function: "erfc_downward": Function: "erfc_downward":
double: 1 double: 1
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 1 double: 1
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 1 double: 1
float: 3
ldouble: 3 ldouble: 3
Function: "exp10m1": Function: "exp10m1":

1
sysdeps/microblaze/libm-test-ulps
View File

@@ -175,7 +175,6 @@ double: 1
Function: "erfc": Function: "erfc":
double: 3 double: 3
float: 2
Function: "exp": Function: "exp":
float: 1 float: 1

4
sysdeps/mips/mips32/libm-test-ulps
View File

@@ -735,19 +735,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/mips/mips64/libm-test-ulps
View File

@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

1
sysdeps/nios2/libm-test-ulps
View File

@@ -180,7 +180,6 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/or1k/fpu/libm-test-ulps
View File

@@ -735,19 +735,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/or1k/nofpu/libm-test-ulps
View File

@@ -735,19 +735,15 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/powerpc/fpu/libm-test-ulps
View File

@@ -1125,25 +1125,21 @@ ldouble: 3
Function: "erfc": Function: "erfc":
double: 2 double: 2
float: 2
float128: 4 float128: 4
ldouble: 3 ldouble: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 4 double: 4
float: 4
float128: 5 float128: 5
ldouble: 10 ldouble: 10
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 3
float128: 4 float128: 4
ldouble: 11 ldouble: 11
Function: "erfc_upward": Function: "erfc_upward":
double: 4 double: 4
float: 4
float128: 5 float128: 5
ldouble: 7 ldouble: 7

4
sysdeps/powerpc/nofpu/libm-test-ulps
View File

@@ -935,22 +935,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 3 ldouble: 3
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
ldouble: 10 ldouble: 10
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
ldouble: 11 ldouble: 11
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
ldouble: 7 ldouble: 7
Function: "exp": Function: "exp":

4
sysdeps/riscv/nofpu/libm-test-ulps
View File

@@ -922,22 +922,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 3 double: 3
float: 4
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 3 double: 3
float: 4
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

4
sysdeps/riscv/rvd/libm-test-ulps
View File

@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 2 double: 2
float: 2
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 4 double: 4
float: 4
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 4 double: 4
float: 4
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

4
sysdeps/s390/fpu/libm-test-ulps
View File

@@ -926,22 +926,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 2 double: 2
float: 2
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 4 double: 4
float: 4
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 4 double: 4
float: 4
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

2
sysdeps/sh/libm-test-ulps
View File

@@ -361,11 +361,9 @@ double: 1
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 2
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 3
Function: "exp": Function: "exp":
double: 1 double: 1

4
sysdeps/sparc/fpu/libm-test-ulps
View File

@@ -925,22 +925,18 @@ ldouble: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
ldouble: 4 ldouble: 4
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
ldouble: 5 ldouble: 5
Function: "exp": Function: "exp":

4
sysdeps/x86_64/fpu/libm-test-ulps
View File

@@ -1330,25 +1330,21 @@ float: 2
Function: "erfc": Function: "erfc":
double: 5 double: 5
float: 3
float128: 4 float128: 4
ldouble: 5 ldouble: 5
Function: "erfc_downward": Function: "erfc_downward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 4 ldouble: 4
Function: "erfc_towardzero": Function: "erfc_towardzero":
double: 3 double: 3
float: 4
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "erfc_upward": Function: "erfc_upward":
double: 5 double: 5
float: 6
float128: 5 float128: 5
ldouble: 5 ldouble: 5