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math: Use erff from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance to the generic erff. 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 85.7363 45.1372 47.35% x86_64v2 86.6337 38.5816 55.47% x86_64v3 71.3810 34.0843 52.25% i686 190.143 97.5014 48.72% aarch64 34.9091 14.9320 57.23% power10 38.6160 8.5188 77.94% powerpc 39.7446 8.45781 78.72% reciprocal-throughput master patched improvement x86_64 35.1739 14.7603 58.04% x86_64v2 34.5976 11.2283 67.55% x86_64v3 27.3260 9.8550 63.94% i686 91.0282 30.8840 66.07% aarch64 22.5831 6.9615 69.17% power10 18.0386 3.0918 82.86% powerpc 20.7277 3.63396 82.47% 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
parent
c4c64ba5d1
commit
994fec2397
@ -272,3 +272,7 @@ sysdeps/ieee754/flt-32/s_cbrtf.c
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(file src/binary32/cbrt/cbrtf.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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sysdeps/ieee754/flt-32/s_erff.c
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(file src/binary32/erf/erff.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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@ -991,7 +991,6 @@ ldouble: 5
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Function: "erf":
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double: 1
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float: 1
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ldouble: 1
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Function: "erf_advsimd":
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@ -909,22 +909,18 @@ ldouble: 5
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Function: "erf":
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double: 1
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float: 1
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ldouble: 1
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Function: "erf_downward":
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double: 1
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float: 1
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ldouble: 2
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Function: "erf_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "erf_upward":
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double: 1
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float: 1
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ldouble: 2
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Function: "erfc":
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@ -733,19 +733,15 @@ float: 6
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Function: "erf":
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double: 1
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float: 1
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Function: "erf_downward":
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double: 1
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float: 1
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Function: "erf_towardzero":
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double: 1
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float: 2
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Function: "erf_upward":
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double: 2
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float: 2
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Function: "erfc":
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double: 5
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@ -177,7 +177,6 @@ float: 2
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Function: "erf":
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double: 1
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float: 1
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Function: "erfc":
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double: 5
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@ -726,19 +726,15 @@ float: 3
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Function: "erf":
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double: 1
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float: 1
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Function: "erf_downward":
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double: 1
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float: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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Function: "erf_upward":
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double: 1
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float: 1
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Function: "erfc":
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double: 5
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@ -719,19 +719,15 @@ float: 3
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Function: "erf":
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double: 1
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float: 1
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Function: "erf_downward":
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double: 1
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float: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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Function: "erf_upward":
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double: 1
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float: 1
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Function: "erfc":
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double: 5
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@ -717,19 +717,15 @@ float: 3
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Function: "erf":
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double: 1
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float: 1
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Function: "erf_downward":
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double: 1
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float: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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Function: "erf_upward":
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double: 1
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float: 1
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Function: "erfc":
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double: 5
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@ -742,20 +742,16 @@ float: 3
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Function: "erf":
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double: 1
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float: 1
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ldouble: 1
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Function: "erf_downward":
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double: 1
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float: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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Function: "erf_upward":
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double: 1
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float: 1
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Function: "erfc":
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double: 5
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@ -1078,25 +1078,21 @@ ldouble: 3
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Function: "erf":
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double: 1
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float: 1
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float128: 1
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ldouble: 1
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Function: "erf_downward":
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double: 1
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float: 1
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float128: 2
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ldouble: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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float128: 1
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ldouble: 1
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Function: "erf_upward":
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double: 1
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float: 1
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float128: 2
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ldouble: 1
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@ -1081,25 +1081,21 @@ ldouble: 3
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Function: "erf":
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double: 1
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float: 1
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float128: 1
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ldouble: 1
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Function: "erf_downward":
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double: 1
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float: 1
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float128: 2
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ldouble: 1
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Function: "erf_towardzero":
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double: 1
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float: 1
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float128: 1
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ldouble: 1
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Function: "erf_upward":
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double: 1
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float: 1
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float128: 2
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ldouble: 1
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@ -1,154 +1,256 @@
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/* s_erff.c -- float version of s_erf.c.
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*/
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/* Correctly-rounded error function for binary32 value.
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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Copyright (c) 2022-2024 Alexei Sibidanov.
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
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#endif
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This file is part of the CORE-MATH project
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project (file src/binary32/erf/erff.c revision bc385c2).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <errno.h>
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#include <float.h>
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <math-underflow.h>
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#include <stdint.h>
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#include <libm-alias-float.h>
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#include <fix-int-fp-convert-zero.h>
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#include "math_config.h"
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static const float
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tiny = 1e-30,
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one = 1.0000000000e+00, /* 0x3F800000 */
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erx = 8.4506291151e-01, /* 0x3f58560b */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx = 1.2837916613e-01, /* 0x3e0375d4 */
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pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
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pp1 = -3.2504209876e-01, /* 0xbea66beb */
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pp2 = -2.8481749818e-02, /* 0xbce9528f */
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pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
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pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
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qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
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qq2 = 6.5022252500e-02, /* 0x3d852a63 */
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qq3 = 5.0813062117e-03, /* 0x3ba68116 */
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qq4 = 1.3249473704e-04, /* 0x390aee49 */
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qq5 = -3.9602282413e-06, /* 0xb684e21a */
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/*
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* Coefficients for approximation to erf in [0.84375,1.25]
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*/
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pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
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pa1 = 4.1485610604e-01, /* 0x3ed46805 */
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pa2 = -3.7220788002e-01, /* 0xbebe9208 */
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pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
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pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
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pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
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pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
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qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
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qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
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qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
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qa4 = 1.2617121637e-01, /* 0x3e013307 */
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qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
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qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
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/*
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* Coefficients for approximation to erfc in [1.25,1/0.35]
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*/
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ra0 = -9.8649440333e-03, /* 0xbc21a093 */
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ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
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ra2 = -1.0558626175e+01, /* 0xc128f022 */
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ra3 = -6.2375331879e+01, /* 0xc2798057 */
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ra4 = -1.6239666748e+02, /* 0xc322658c */
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ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
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ra6 = -8.1287437439e+01, /* 0xc2a2932b */
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ra7 = -9.8143291473e+00, /* 0xc11d077e */
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sa1 = 1.9651271820e+01, /* 0x419d35ce */
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sa2 = 1.3765776062e+02, /* 0x4309a863 */
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sa3 = 4.3456588745e+02, /* 0x43d9486f */
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sa4 = 6.4538726807e+02, /* 0x442158c9 */
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sa5 = 4.2900814819e+02, /* 0x43d6810b */
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sa6 = 1.0863500214e+02, /* 0x42d9451f */
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sa7 = 6.5702495575e+00, /* 0x40d23f7c */
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sa8 = -6.0424413532e-02, /* 0xbd777f97 */
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/*
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* Coefficients for approximation to erfc in [1/.35,28]
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*/
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rb0 = -9.8649431020e-03, /* 0xbc21a092 */
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rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
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rb2 = -1.7757955551e+01, /* 0xc18e104b */
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rb3 = -1.6063638306e+02, /* 0xc320a2ea */
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rb4 = -6.3756646729e+02, /* 0xc41f6441 */
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rb5 = -1.0250950928e+03, /* 0xc480230b */
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rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
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sb1 = 3.0338060379e+01, /* 0x41f2b459 */
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sb2 = 3.2579251099e+02, /* 0x43a2e571 */
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sb3 = 1.5367296143e+03, /* 0x44c01759 */
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sb4 = 3.1998581543e+03, /* 0x4547fdbb */
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sb5 = 2.5530502930e+03, /* 0x451f90ce */
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sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
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sb7 = -2.2440952301e+01; /* 0xc1b38712 */
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float __erff(float x)
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float
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__erff (float x)
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{
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int32_t hx,ix,i;
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float R,S,P,Q,s,y,z,r;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix>=0x7f800000) { /* erf(nan)=nan */
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i = ((uint32_t)hx>>31)<<1;
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return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
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}
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if(ix < 0x3f580000) { /* |x|<0.84375 */
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if(ix < 0x31800000) { /* |x|<2**-28 */
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if (ix < 0x04000000)
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/* for 7 <= i < 63, C[i-7] is a degree-7 polynomial approximation of
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erf(i/16+1/32+x) for -1/32 <= x <= 1/32 */
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static const double C[56][8] = {
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{ 0x1.f86faa9428f9cp-2, 0x1.cfc41e36c7dfap-1, -0x1.b2c7dc53508b9p-2,
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-0x1.5a9de93fa556ep-3, 0x1.731793dbb01b5p-3, 0x1.133e06426cf18p-6,
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-0x1.a12a6289cafd8p-5, 0x1.717d6f1d6f557p-9 },
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{ 0x1.1855a5fd3dd50p-1, 0x1.b3aafcc27502fp-1, -0x1.cee5ac8e92bb2p-2,
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-0x1.fa02983ca2d79p-4, 0x1.77cd746cb1922p-3, -0x1.fa6f277886487p-10,
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-0x1.8de75458db416p-5, 0x1.00899c98551c9p-7 },
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{ 0x1.32a54cb8db67ap-1, 0x1.96164fafd8de5p-1, -0x1.e23a7ea0c9ad3p-2,
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-0x1.3f5ee15671cf4p-4, 0x1.70e468a3d72d9p-3, -0x1.3da68037cfc99p-6,
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-0x1.69ed9ba1f9839p-5, 0x1.8cab9244a4ff4p-7 },
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{ 0x1.4b13713ad3513p-1, 0x1.7791b886e7405p-1, -0x1.ecef423109bf5p-2,
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-0x1.15c3c5cec6847p-5, 0x1.5f688fc931ba6p-3, -0x1.1da63ed190037p-5,
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-0x1.38427ca63cca4p-5, 0x1.fa00e52525e17p-7 },
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{ 0x1.61955607dd15dp-1, 0x1.58a445da7c74ep-1, -0x1.ef6c246a0f66cp-2,
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0x1.e83e0d9d61330p-8, 0x1.44cc65535bc9fp-3, -0x1.87d3c4860435dp-5,
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-0x1.f90b10501169bp-6, 0x1.22295856d427ap-6 },
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{ 0x1.762870f720c6fp-1, 0x1.39ccc1b136d5cp-1, -0x1.ea4feea4e4744p-2,
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0x1.715e5952ebfbap-5, 0x1.22cdbd83c75c4p-3, -0x1.da50aa1d925b6p-5,
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-0x1.754dc0a29b4ddp-6, 0x1.350b6bef9392cp-6 },
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{ 0x1.88d1cd474a2e0p-1, 0x1.1b7e98fe26219p-1, -0x1.de65a22ce1419p-2,
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0x1.40686a3f16400p-4, 0x1.f6b0cbb216b2bp-4, -0x1.09c7c903edd57p-4,
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-0x1.da7529fde641p-7, 0x1.362a7a0588eabp-6 },
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{ 0x1.999d4192a5717p-1, 0x1.fc3ee5d1524b3p-2, -0x1.cc990045b55c8p-2,
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0x1.b37338e68b37dp-4, 0x1.a0d120c872ea7p-4, -0x1.19bb2b07ecff6p-4,
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-0x1.a110f5f593aafp-8, 0x1.272c15a57720ep-6 },
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{ 0x1.a89c850b7d54dp-1, 0x1.c40b0729ed54ap-2, -0x1.b5eaaef0a2346p-2,
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0x1.0847c7dacbae1p-3, 0x1.47de0ba6d18fbp-4, -0x1.1d9de77a4b648p-4,
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0x1.30ffbe56f0726p-10, 0x1.0a9cb99feea01p-6 },
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{ 0x1.b5e62fce16096p-1, 0x1.8eed36b886d95p-2, -0x1.9b64a06e50705p-2,
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0x1.2bb6e2c744df5p-3, 0x1.dee3261ca61bcp-5, -0x1.16996004f7da5p-4,
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0x1.fdff37bae983ep-8, 0x1.c750083e65f9ap-7 },
|
||||
{ 0x1.c194b1d49a184p-1, 0x1.5d4fd33729015p-2, -0x1.7e0f4f045addbp-2,
|
||||
0x1.444bc66c31a1bp-3, 0x1.356dbf16ec8f1p-5, -0x1.0643de0906cd8p-4,
|
||||
0x1.b281af7bd3a2cp-7, 0x1.6b97eaa2c6abdp-7 },
|
||||
{ 0x1.cbc54b476248ep-1, 0x1.2f7cc3fe6f423p-2, -0x1.5ee8429e36de8p-2,
|
||||
0x1.52a8395f96177p-3, 0x1.313761ba257dcp-6, -0x1.dcf844d5fed8fp-5,
|
||||
0x1.1e1420f475fa9p-6, 0x1.091c7dc1e18b2p-7 },
|
||||
{ 0x1.d4970f9ce00d9p-1, 0x1.059f59af7a905p-2, -0x1.3eda354de36c3p-2,
|
||||
0x1.57b85ad439779p-3, 0x1.8e913b9778136p-10, -0x1.a2893bd3435f4p-5,
|
||||
0x1.4d3a90e37164ap-6, 0x1.4ce7f6e19a902p-8 },
|
||||
{ 0x1.dc29fb60715b0p-1, 0x1.bf8e1b1ca2277p-3, -0x1.1eb7095e5d6d2p-2,
|
||||
0x1.549ea6f7a64f4p-3, -0x1.b10f12f3877a3p-7, -0x1.61420c8f7156ap-5,
|
||||
0x1.674f1f92a8812p-6, 0x1.25543ffd74d52p-9 },
|
||||
{ 0x1.e29e22a89d767p-1, 0x1.7bd5c7df3fe99p-3, -0x1.fe674494077bfp-3,
|
||||
0x1.4a9feacf86578p-3, -0x1.a008269076644p-6, -0x1.1cf0e8fb4f1cbp-5,
|
||||
0x1.6e0d2ef105fb3p-6, -0x1.367205fbd7876p-12 },
|
||||
{ 0x1.e812fc64db36ap-1, 0x1.3fda6bc016991p-3, -0x1.c1cb278627920p-3,
|
||||
0x1.3b10512314f1ep-3, -0x1.1e6457bb1b9a9p-5, -0x1.b1f6474e2388cp-6,
|
||||
0x1.640a5345f7ec7p-6, -0x1.3dae5a997fdbp-9 },
|
||||
{ 0x1.eca6ccd709544p-1, 0x1.0b3f52ce8c380p-3, -0x1.8885019f63c6dp-3,
|
||||
0x1.274275fc91a05p-3, -0x1.57f73699a8372p-5, -0x1.3076a305fc7cep-6,
|
||||
0x1.4c6ae04843a41p-6, -0x1.0be5fcf5ecc91p-8 },
|
||||
{ 0x1.f0762fde45ee7p-1, 0x1.bb1c972f23e4ap-4, -0x1.5341e3c01b58dp-3,
|
||||
0x1.107929f6f0b60p-3, -0x1.7e1b34f976c02p-5, -0x1.73b62589c234ap-7,
|
||||
0x1.2a97ee1876486p-6, -0x1.595f40a3150fep-8 },
|
||||
{ 0x1.f39bc242e43e6p-1, 0x1.6c7e64e7281c5p-4, -0x1.2274b86835fd3p-3,
|
||||
0x1.efb890e5c770dp-4, -0x1.92c7db16847e0p-5, -0x1.45477db5e2dd4p-8,
|
||||
0x1.01fc6165fc866p-6, -0x1.8845509030c2cp-8 },
|
||||
{ 0x1.f62fe80272419p-1, 0x1.297db960e4f5dp-4, -0x1.ecb83b087c04fp-4,
|
||||
0x1.bce18363ca3d1p-4, -0x1.985aaf776482cp-5, 0x1.cd953efdae886p-12,
|
||||
0x1.ab9a0b89b54ffp-7, -0x1.9b5e576ccc31cp-8 },
|
||||
{ 0x1.f848acb544e95p-1, 0x1.e1d4cf1e24501p-5, -0x1.9e12e1fde5552p-4,
|
||||
0x1.8a27806df3d1bp-4, -0x1.91674e5eb3319p-5, 0x1.3bc75595b2db8p-8,
|
||||
0x1.51bc537ac61afp-7, -0x1.96b23b19ea04dp-8 },
|
||||
{ 0x1.f9f9ba8d3c733p-1, 0x1.83298d7172108p-5, -0x1.58d101f905a75p-4,
|
||||
0x1.58f1456f8639bp-4, -0x1.808d1850b8231p-5, 0x1.0c1bd99c348a7p-7,
|
||||
0x1.f61e9d7bc48cap-8, -0x1.7f07c13441774p-8 },
|
||||
{ 0x1.fb54641aebbc9p-1, 0x1.34ac36ad8dafap-5, -0x1.1c8ec267f9405p-4,
|
||||
0x1.2a52c5d841848p-4, -0x1.68541c02b3b6bp-5, 0x1.5afe400196379p-7,
|
||||
0x1.565b2d6eda3d6p-8, -0x1.596aaff29e739p-8 },
|
||||
{ 0x1.fc67bcf2d7b8fp-1, 0x1.e85c449e377efp-6, -0x1.d177f166c07c6p-5,
|
||||
0x1.fe23b7584b504p-5, -0x1.4b12109613313p-5, 0x1.8d9905c0acf7dp-7,
|
||||
0x1.9265032a669dap-9, -0x1.2ac4a6dbcbf3ep-8 },
|
||||
{ 0x1.fd40bd6d7a785p-1, 0x1.7f5188610ddc7p-6, -0x1.7954423f7c998p-5,
|
||||
0x1.af5baae33887fp-5, -0x1.2ad77c7cbc474p-5, 0x1.a7b8c47ec2a51p-7,
|
||||
0x1.46646ee094bccp-10, -0x1.ef19d8db8673p-9 },
|
||||
{ 0x1.fdea6e062d0c9p-1, 0x1.2a875b5ffab58p-6, -0x1.2f3178cd6dcd5p-5,
|
||||
0x1.68d1c45b94182p-5, -0x1.09648ed3aeaefp-5, 0x1.ad8b150d38164p-7,
|
||||
-0x1.e9a6023d9429fp-13, -0x1.8722d19ee2e8ep-9 },
|
||||
{ 0x1.fe6e1742f7cf5p-1, 0x1.cd5ec93c1243ap-7, -0x1.e2ff3aaacb386p-6,
|
||||
0x1.2aa4e5823cc89p-5, -0x1.d049842dbe399p-6, 0x1.a34edb21ab302p-7,
|
||||
-0x1.676e5996c7f9bp-10, -0x1.23b01a35140bfp-9 },
|
||||
{ 0x1.fed37386190fbp-1, 0x1.61beae53b72c2p-7, -0x1.7d6193f22c3c1p-6,
|
||||
0x1.e947279e3bb7dp-6, -0x1.906031b97ca97p-6, 0x1.8d14d62561755p-7,
|
||||
-0x1.1f245e7178882p-9, -0x1.9257d4eb47685p-10 },
|
||||
{ 0x1.ff20e0a7ba8c2p-1, 0x1.0d1d69569b839p-7, -0x1.2a8ca0dc02752p-6,
|
||||
0x1.8cc071b709751p-6, -0x1.54a149f1b070cp-6, 0x1.6e9137b13412cp-7,
|
||||
-0x1.6577ed3d8e83bp-9, -0x1.e9c1a5178a289p-11 },
|
||||
{ 0x1.ff5b8fb26f5f6p-1, 0x1.9646f35a7663cp-8, -0x1.cf68ed9311b0bp-7,
|
||||
0x1.3e8735b5a694fp-6, -0x1.1e1612d026fdfp-6, 0x1.4afd8e6ca636dp-7,
|
||||
-0x1.8c375170ccb22p-9, -0x1.c799443c4fd3bp-12 },
|
||||
{ 0x1.ff87b1913e853p-1, 0x1.30499b5039596p-8, -0x1.64964201ec8bap-7,
|
||||
0x1.fa73d7eafba98p-7, -0x1.daa3022141fbbp-7, 0x1.2509444c063b7p-7,
|
||||
-0x1.99482a2f8a0a1p-9, -0x1.403d1f76c9454p-15 },
|
||||
{ 0x1.ffa89fe5b3625p-1, 0x1.c4412bf4b8f35p-9, -0x1.100f347126cf0p-7,
|
||||
0x1.8ebda07671d40p-7, -0x1.850c6a31c98c1p-7, 0x1.fdac860c67d21p-8,
|
||||
-0x1.927d03d2ba12cp-9, 0x1.0ff620b4190fep-12 },
|
||||
{ 0x1.ffc10194fcb64p-1, 0x1.4d78bba8ca621p-9, -0x1.9ba107a443e02p-8,
|
||||
0x1.36f273fbc04ccp-7, -0x1.3b38716ac7e6fp-7, 0x1.b3fe0181914acp-8,
|
||||
-0x1.7d3fe7de98c5cp-9, 0x1.ea31f8e5317f7p-12 },
|
||||
{ 0x1.ffd2eae369a07p-1, 0x1.e7f232d9e266cp-10, -0x1.34c7442dd48d9p-8,
|
||||
0x1.e066bed070a0bp-8, -0x1.f914f3c42fc0dp-8, 0x1.6f4664ed2260fp-8,
|
||||
-0x1.5e59910761d24p-9, 0x1.39cbb6e84c126p-11 },
|
||||
{ 0x1.ffdff92db56e5p-1, 0x1.6235fbd7a4373p-10, -0x1.cb5e029b9e56ap-9,
|
||||
0x1.6fa4c7ef274dap-8, -0x1.903a089a835f3p-8, 0x1.30f12e0ca1901p-8,
|
||||
-0x1.39d21b6957f99p-9, 0x1.5d3f8495a703cp-11 },
|
||||
{ 0x1.ffe96a78a04a9p-1, 0x1.fe41cd9bb4f2cp-11, -0x1.52d7b28966c0cp-9,
|
||||
0x1.16c192d86a1a7p-8, -0x1.39bfce951100cp-8, 0x1.f376a7869f9e3p-9,
|
||||
-0x1.12e6cef999c4fp-9, 0x1.66acd4d667b5p-11 },
|
||||
{ 0x1.fff0312b010b5p-1, 0x1.6caa0d3583018p-11, -0x1.efb729f4cf75bp-10,
|
||||
0x1.a2da7cebe12acp-9, -0x1.e6c27a24bc759p-9, 0x1.93b1f4d8ea65p-9,
|
||||
-0x1.d82050aa94a08p-10, 0x1.5cd7dc75d6cbap-11 },
|
||||
{ 0x1.fff50456dab8cp-1, 0x1.0295ef6591865p-11, -0x1.679880e95a4dap-10,
|
||||
0x1.37d38e3a5c8ebp-9, -0x1.75b3708aebb8fp-9, 0x1.4231c4b4b0296p-9,
|
||||
-0x1.8e26476489318p-10, 0x1.45c3b570dd924p-11 },
|
||||
{ 0x1.fff86cfd3e657p-1, 0x1.6be02102b353dp-12, -0x1.02b157780d6aep-10,
|
||||
0x1.cc1d886861133p-10, -0x1.1bff6f12ec9abp-9, 0x1.fc0f77bd9c736p-10,
|
||||
-0x1.4a3320bd0959dp-10, 0x1.267f8b4f95d2p-11 },
|
||||
{ 0x1.fffad0b901755p-1, 0x1.fc0d55470cf5ep-13, -0x1.7121aff5e820ep-11,
|
||||
0x1.506d6992f7de5p-10, -0x1.ab595d3ecd0d6p-10, 0x1.8bdd79daaf754p-10,
|
||||
-0x1.0d9b090f997c1p-10, 0x1.031ab9fd1c7dap-11 },
|
||||
{ 0x1.fffc7a37857d2p-1, 0x1.5feada379d8a5p-13, -0x1.05304df58f3aap-11,
|
||||
0x1.e79c081b8600fp-11, -0x1.3e5dbe33232e0p-10, 0x1.30eb208200729p-10,
|
||||
-0x1.b1d493b147945p-11, 0x1.bd587bbc071bep-12 },
|
||||
{ 0x1.fffd9fdeabccep-1, 0x1.e3bcf436a1a49p-14, -0x1.6e953111ef0a1p-12,
|
||||
0x1.5e3edf6768654p-11, -0x1.d5be67c0547a4p-11, 0x1.d07d9ffa1d435p-11,
|
||||
-0x1.58328f5f358cap-11, 0x1.76d42d95c42c4p-12 },
|
||||
{ 0x1.fffe68f4fa777p-1, 0x1.49e17724f4cddp-14, -0x1.fe48c44e229c1p-13,
|
||||
0x1.f2bd95d76f188p-12, -0x1.57388cb12d011p-11, 0x1.5decc25c5c079p-11,
|
||||
-0x1.0d7499d1b0d2dp-11, 0x1.359332c94ecdcp-12 },
|
||||
{ 0x1.fffef1960d85dp-1, 0x1.be6abbb10a4cdp-15, -0x1.6040381a8c313p-13,
|
||||
0x1.5fff1dde9ee9dp-12, -0x1.f0c933efa9971p-12, 0x1.04cbf4a5cd760p-11,
|
||||
-0x1.a07f150af6dadp-12, 0x1.f68dd183426bap-13 },
|
||||
{ 0x1.ffff4db27f146p-1, 0x1.2bb5cc22e5cd8p-15, -0x1.e25894899f526p-14,
|
||||
0x1.ec8a8e5a72757p-13, -0x1.64256ae0a3cf9p-12, 0x1.80a836c18c46cp-12,
|
||||
-0x1.3dea401af6775p-12, 0x1.915ddff3fe0d1p-13 },
|
||||
{ 0x1.ffff8b500e77cp-1, 0x1.8f4ccca7fc769p-16, -0x1.478cffe305946p-14,
|
||||
0x1.559f04adde504p-13, -0x1.f9e1577d6961dp-13, 0x1.18bda53c14716p-12,
|
||||
-0x1.df8634c35541cp-13, 0x1.3bb5c6b616337p-13 },
|
||||
{ 0x1.ffffb43555b5fp-1, 0x1.07ebd2a2d26c8p-16, -0x1.b93e442a37f2bp-15,
|
||||
0x1.d5cf15159ce28p-14, -0x1.63f5e1469c006p-13, 0x1.95a03acebac18p-13,
|
||||
-0x1.656e5e2a1f8e2p-13, 0x1.e98c437189bdep-14 },
|
||||
{ 0x1.ffffcf23ff5fcp-1, 0x1.5a2adfa0b492cp-17, -0x1.26c88270759f0p-15,
|
||||
0x1.40473572b99a8p-14, -0x1.f057cbde578a5p-14, 0x1.22178d1c3c948p-13,
|
||||
-0x1.0765b61a0d859p-13, 0x1.765b3ea03ddbep-14 },
|
||||
{ 0x1.ffffe0bd3e852p-1, 0x1.c282cd3957a72p-18, -0x1.86ad6dfa44faap-16,
|
||||
0x1.b0f313f03a029p-15, -0x1.56e44abecd255p-14, 0x1.9ad1ecfe34a89p-14,
|
||||
-0x1.7fe4033478618p-14, 0x1.1a8184e049fbfp-14 },
|
||||
{ 0x1.ffffec2641a9ep-1, 0x1.22df29821407ep-18, -0x1.00c902a6cfd98p-16,
|
||||
0x1.22234eb88671fp-15, -0x1.d57a181c9e6e1p-15, 0x1.200c283b54a90p-14,
|
||||
-0x1.14b4c3295a7d0p-14, 0x1.a4f966f713bdep-15 },
|
||||
{ 0x1.fffff37d63a36p-1, 0x1.74adc8f405eecp-19, -0x1.4ed4228e44858p-17,
|
||||
0x1.81918baea92bap-16, -0x1.3e81b17a0009cp-15, 0x1.9004a36116436p-15,
|
||||
-0x1.8aa1ba400e076p-15, 0x1.35cd4e2340a9ep-15 },
|
||||
{ 0x1.fffff82cdcf1bp-1, 0x1.d9c73698fa87dp-20, -0x1.b11017ec67115p-18,
|
||||
0x1.fc0dfadf653f8p-17, -0x1.ac4e03cd2dfc2p-16, 0x1.131806b5abbc5p-15,
|
||||
-0x1.1672ef66fcaafp-15, 0x1.c2882c7debed7p-16 },
|
||||
{ 0x1.fffffb248c39dp-1, 0x1.2acee2f5ec66ap-20, -0x1.15cc570408a36p-18,
|
||||
0x1.4be757bbb75a3p-17, -0x1.1d6aa5f8d2940p-16, 0x1.76c5937d5105ep-16,
|
||||
-0x1.84dffc3ca9302p-16, 0x1.43c8315f2c30ap-16 },
|
||||
{ 0x1.fffffd01f36afp-1, 0x1.75fa8dbc840bap-21, -0x1.6186da0133f5ap-19,
|
||||
0x1.ae023231e1af5p-18, -0x1.790812f7ca394p-17, 0x1.f9c25656d0ef2p-17,
|
||||
-0x1.0cc66682e304cp-16, 0x1.cc170a75d6f9cp-17 },
|
||||
{ 0x1.fffffe2ba0ea5p-1, 0x1.d06ad6ecde88ep-22, -0x1.be46aa8edc9a1p-20,
|
||||
0x1.143860c7840b8p-18, -0x1.edaba78fb1260p-18, 0x1.52138a96ecee2p-17,
|
||||
-0x1.6fca538c4e2eep-17, 0x1.434040640bcefp-17 },
|
||||
{ 0x1.fffffee3cc32cp-1, 0x1.1e1e857adb8ddp-22, -0x1.1769ce5f2a6e8p-20,
|
||||
0x1.5fe5d479b0543p-19, -0x1.405d865c94c2ap-18, 0x1.bfc94feb96afcp-18,
|
||||
-0x1.f245d5f3e8358p-18, 0x1.c142456acf443p-18 },
|
||||
};
|
||||
float ax = fabsf (x);
|
||||
uint32_t ux = asuint (ax);
|
||||
double s = x;
|
||||
double z = ax;
|
||||
/* 0x407ad444 corresponds to x = 0x1.f5a888p+1 = 3.91921..., which is the
|
||||
largest float such that erf(x) does not round to 1 (to nearest). */
|
||||
if (__glibc_unlikely (ux > 0x407ad444u))
|
||||
{
|
||||
/* Avoid spurious underflow. */
|
||||
float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
|
||||
math_check_force_underflow (ret);
|
||||
return ret;
|
||||
float os = copysignf (1.0f, x);
|
||||
if (ux > (0xffu << 23))
|
||||
return x + x; /* nan */
|
||||
if (ux == (0xffu << 23))
|
||||
return os; /* +-inf */
|
||||
return os - 0x1p-25f * os;
|
||||
}
|
||||
return x + efx*x;
|
||||
double v = floor (16.0 * z);
|
||||
uint32_t i = 16.0f * ax;
|
||||
/* 0x3ee00000 corresponds to x = 0.4375, for smaller x we have i < 7. */
|
||||
if (__glibc_unlikely (ux < 0x3ee00000u))
|
||||
{
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.20dd750429b6dp+0, -0x1.812746b0375fbp-2,
|
||||
0x1.ce2f219fd6f45p-4, -0x1.b82ce2cbf0838p-6,
|
||||
0x1.565bb655adb85p-8, -0x1.c025bfc879c94p-11,
|
||||
0x1.f81718f61309cp-14, -0x1.cc67bd88f5867p-17
|
||||
};
|
||||
double z2 = s * s, z4 = z2 * z2, z8 = z4 * z4;
|
||||
double c0 = c[0] + z2 * c[1];
|
||||
double c2 = c[2] + z2 * c[3];
|
||||
double c4 = c[4] + z2 * c[5];
|
||||
double c6 = c[6] + z2 * c[7];
|
||||
c0 += z4 * c2;
|
||||
c4 += z4 * c6;
|
||||
c0 += z8 * c4;
|
||||
return s * c0;
|
||||
}
|
||||
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;
|
||||
return x + x*y;
|
||||
}
|
||||
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) return erx + P/Q; else return -erx - P/Q;
|
||||
}
|
||||
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
|
||||
if(hx>=0) return one-tiny; else return tiny-one;
|
||||
}
|
||||
x = fabsf(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
|
||||
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| >= 1/0.35 */
|
||||
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&0xfffff000);
|
||||
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
|
||||
if(hx>=0) return one-r/x; else return r/x-one;
|
||||
z = (z - 0.03125) - 0.0625 * v;
|
||||
const double *c = C[i - 7];
|
||||
double z2 = z * z, z4 = z2 * z2;
|
||||
double c0 = c[0] + z * c[1];
|
||||
double c2 = c[2] + z * c[3];
|
||||
double c4 = c[4] + z * c[5];
|
||||
double c6 = c[6] + z * c[7];
|
||||
c0 += z2 * c2;
|
||||
c4 += z2 * c6;
|
||||
c0 += z4 * c4;
|
||||
return copysign (c0, s);
|
||||
}
|
||||
libm_alias_float (__erf, erf)
|
||||
|
||||
@ -910,22 +910,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -839,21 +839,17 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -172,7 +172,6 @@ float: 2
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 3
|
||||
|
||||
@ -723,19 +723,15 @@ float: 3
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 5
|
||||
|
||||
@ -909,22 +909,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -177,7 +177,6 @@ float: 2
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 5
|
||||
|
||||
@ -723,19 +723,15 @@ float: 3
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 5
|
||||
|
||||
@ -723,19 +723,15 @@ float: 3
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 5
|
||||
|
||||
@ -1105,25 +1105,21 @@ double: 1
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 3
|
||||
|
||||
|
||||
@ -919,22 +919,18 @@ double: 1
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -906,22 +906,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -909,22 +909,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -910,22 +910,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -355,11 +355,9 @@ float: 3
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "erfc":
|
||||
double: 5
|
||||
|
||||
@ -909,22 +909,18 @@ ldouble: 5
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "erfc":
|
||||
|
||||
@ -1290,25 +1290,21 @@ ldouble: 3
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "erf_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 1
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user