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math: Use acosf from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic acosf. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): Latency master patched improvement x86_64 52.5098 36.6312 30.24% x86_64v2 53.0217 37.3091 29.63% x86_64v3 42.8501 32.3977 24.39% i686 207.3960 109.4000 47.25% aarch64 21.3694 13.7871 35.48% power10 14.5542 7.2891 49.92% reciprocal-throughput master patched improvement x86_64 14.1487 15.9508 -12.74% x86_64v2 14.3293 16.1899 -12.98% x86_64v3 13.6563 12.6161 7.62% i686 158.4060 45.7354 71.13% aarch64 12.5515 9.19233 26.76% power10 5.7868 3.3487 42.13% 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
45126f866c
commit
66fa7ad437
@ -294,3 +294,7 @@ sysdeps/ieee754/flt-32/s_tanf.c:
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functions to handle errno, overflow, and underflow. It was changed
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to use an internal wrapper for 128 bit unsigned integer operations
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for ABIs that do not support the type natively.
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sysdeps/ieee754/flt-32/e_acosf.c:
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(src/binary32/acos/acosf.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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@ -3,7 +3,6 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_advsimd":
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@ -12,7 +11,6 @@ float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_sve":
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@ -21,12 +19,10 @@ float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_upward":
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double: 1
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float: 1
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ldouble: 1
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Function: "acosh":
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@ -3,22 +3,18 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_downward":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "acos_upward":
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double: 1
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float: 1
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ldouble: 1
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Function: "acosh":
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@ -3,19 +3,15 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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Function: "acos_upward":
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double: 1
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float: 1
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Function: "acosh":
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double: 3
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@ -3,7 +3,6 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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Function: "acosh":
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double: 2
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@ -3,19 +3,15 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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Function: "acos_upward":
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double: 1
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float: 1
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Function: "acosh":
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double: 2
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@ -2,19 +2,15 @@
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# Maximal error of functions:
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Function: "acos":
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float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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Function: "acos_upward":
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double: 1
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float: 1
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Function: "acosh":
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double: 2
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@ -2,19 +2,15 @@
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# Maximal error of functions:
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Function: "acos":
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float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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Function: "acos_upward":
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double: 1
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float: 1
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Function: "acosh":
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double: 2
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@ -3,19 +3,15 @@
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# Maximal error of functions:
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Function: "acos":
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double: 1
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float: 1
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Function: "acos_downward":
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double: 1
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float: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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Function: "acos_upward":
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double: 1
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float: 1
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Function: "acosh":
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double: 2
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@ -1,23 +0,0 @@
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/*
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* Public domain.
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*/
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#include <machine/asm.h>
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#include <libm-alias-finite.h>
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RCSID("$NetBSD: $")
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/* acos = atan (sqrt(1 - x^2) / x) */
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ENTRY(__ieee754_acosf)
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flds 4(%esp) /* x */
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fld %st
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fmul %st(0) /* x^2 */
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fld1
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fsubp /* 1 - x^2 */
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fsqrt /* sqrt (1 - x^2) */
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fabs
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fxch %st(1)
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fpatan
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ret
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END (__ieee754_acosf)
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libm_alias_finite (__ieee754_acosf, __acosf)
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@ -47,13 +47,13 @@ ldouble: 1
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Function: "acospi_downward":
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double: 1
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float: 1
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float: 2
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float128: 1
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ldouble: 3
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Function: "acospi_towardzero":
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double: 1
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float: 1
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float: 2
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float128: 1
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ldouble: 3
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@ -47,13 +47,13 @@ ldouble: 1
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Function: "acospi_downward":
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double: 1
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float: 1
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float: 2
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float128: 1
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ldouble: 3
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Function: "acospi_towardzero":
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double: 1
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float: 1
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float: 2
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float128: 1
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ldouble: 3
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@ -1,78 +1,139 @@
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/* e_acosf.c -- float version of e_acos.c.
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*/
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/* Correctly-rounded arc-cosine 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) 2023-2024 Alexei Sibidanov.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/acos/acosf.c, revision 61d7bef).
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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 <math.h>
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#include <math_private.h>
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#include <libm-alias-finite.h>
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#include "math_config.h"
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static const float
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one = 1.0000000000e+00, /* 0x3F800000 */
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pi = 3.1415925026e+00, /* 0x40490fda */
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pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
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pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
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pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
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pS1 = -3.2556581497e-01, /* 0xbea6b090 */
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pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
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pS3 = -4.0055535734e-02, /* 0xbd241146 */
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pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
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pS5 = 3.4793309169e-05, /* 0x3811ef08 */
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qS1 = -2.4033949375e+00, /* 0xc019d139 */
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qS2 = 2.0209457874e+00, /* 0x4001572d */
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qS3 = -6.8828397989e-01, /* 0xbf303361 */
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qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
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static __attribute__ ((noinline)) float
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as_special (float x)
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{
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const float pih = 0x1.921fb6p+1;
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const float pil = -0x1p-24f;
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uint32_t t = asuint (x);
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if (t == (0x7fu << 23))
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return 0.0f; /* x=1 */
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if (t == (0x17fu << 23))
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return pih + pil; /* x=-1 */
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uint32_t ax = t << 1;
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if (ax > (0xffu << 24))
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return x + x; /* nan */
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return __math_invalidf (0.0);
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}
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static inline double
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poly12 (double z, const double *c)
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{
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double z2 = z * z, z4 = z2 * z2;
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double c0 = c[0] + z * c[1];
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double c2 = c[2] + z * c[3];
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double c4 = c[4] + z * c[5];
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double c6 = c[6] + z * c[7];
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double c8 = c[8] + z * c[9];
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double c10 = c[10] + z * c[11];
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c0 += c2 * z2;
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c4 += c6 * z2;
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c8 += z2 * c10;
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c0 += z4 * (c4 + z4 * c8);
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return c0;
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}
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float
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__ieee754_acosf(float x)
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__ieee754_acosf (float x)
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{
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float z,p,q,r,w,s,c,df;
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int32_t hx,ix;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix==0x3f800000) { /* |x|==1 */
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if(hx>0) return 0.0; /* acos(1) = 0 */
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else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
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} else if(ix>0x3f800000) { /* |x| >= 1 */
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return (x-x)/(x-x); /* acos(|x|>1) is NaN */
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}
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if(ix<0x3f000000) { /* |x| < 0.5 */
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if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<=2**-26*/
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z = x*x;
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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r = p/q;
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return pio2_hi - (x - (pio2_lo-x*r));
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} else if (hx<0) { /* x < -0.5 */
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z = (one+x)*(float)0.5;
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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s = sqrtf(z);
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r = p/q;
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w = r*s-pio2_lo;
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return pi - (float)2.0*(s+w);
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} else { /* x > 0.5 */
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int32_t idf;
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z = (one-x)*(float)0.5;
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s = sqrtf(z);
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df = s;
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GET_FLOAT_WORD(idf,df);
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SET_FLOAT_WORD(df,idf&0xfffff000);
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c = (z-df*df)/(s+df);
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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r = p/q;
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w = r*s+c;
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return (float)2.0*(df+w);
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}
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const double pi2 = 0x1.921fb54442d18p+0;
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static const double o[] = { 0, 0x1.921fb54442d18p+1 };
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double xs = x;
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double r;
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uint32_t t = asuint (x);
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uint32_t ax = t << 1;
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if (__glibc_unlikely (ax >= 0x7f<<24))
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return as_special (x);
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if (__glibc_likely (ax < 0x7ec2a1dcu)) /* |x| < 0x1.c2a1dcp-1 */
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{
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static const double b[] =
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{
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0x1.fffffffd9ccb8p-1, 0x1.5555c94838007p-3, 0x1.32ded4b7c20fap-4,
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0x1.8566df703309ep-5, -0x1.980c959bec9a3p-6, 0x1.56fbb04998344p-1,
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-0x1.403d8e4c49f52p+2, 0x1.b06c3e9f311eap+4, -0x1.9ea97c4e2c21fp+6,
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0x1.200b8261cc61bp+8, -0x1.2274c2799a5c7p+9, 0x1.a558a59cc19d3p+9,
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-0x1.aca4b6a529ffp+9, 0x1.228744703f813p+9, -0x1.d7dbb0b322228p+7,
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0x1.5c2018c0c0105p+5
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};
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/* Avoid spurious underflow exception. */
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if (__glibc_unlikely (ax <= 0x40000000u)) /* |x| < 2^-63 */
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return (float) pi2;
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double z = xs;
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double z2 = z * z;
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double z4 = z2 * z2;
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double z8 = z4 * z4;
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double z16 = z8 * z8;
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r = z * ((((b[0] + z2 * b[1]) + z4 * (b[2] + z2 * b[3]))
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+ z8 * ((b[4] + z2 * b[5]) + z4 * (b[6] + z2 * b[7])))
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+ z16 * (((b[8] + z2 * b[9]) + z4 * (b[10] + z2 * b[11]))
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+ z8
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* ((b[12] + z2 * b[13])+ z4 * (b[14] + z2 * b[15]))));
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float ub = 0x1.921fb54574191p+0 - r;
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float lb = 0x1.921fb543118ap+0 - r;
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if (ub == lb)
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return ub;
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}
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/* accurate path */
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if (ax < (0x7eu << 24))
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{
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static const double c[] =
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{
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0x1.555555555529cp-3, 0x1.333333337e0ddp-4, 0x1.6db6db3b4465ep-5,
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0x1.f1c72e13ac306p-6, 0x1.6e89cebe06bc4p-6, 0x1.1c6dcf5289094p-6,
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0x1.c6dbbcc7c6315p-7, 0x1.8f8dc2615e996p-7, 0x1.a5833b7bf15e8p-8,
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0x1.43f44ace1665cp-6, -0x1.0fb17df881c73p-6, 0x1.07520c026b2d6p-5
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};
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if (t == 0x328885a3u)
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return 0x1.921fb6p+0f + 0x1p-25;
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if (t == 0x39826222u)
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return 0x1.920f6ap+0f + 0x1p-25;
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double x2 = xs * xs;
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r = (pi2 - xs) - (xs * x2) * poly12 (x2, c);
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}
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else
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{
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static const double c[] =
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{
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0x1.6a09e667f3bcbp+0, 0x1.e2b7dddff2db9p-4, 0x1.b27247ab42dbcp-6,
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0x1.02995cc4e0744p-7, 0x1.5ffb0276ec8eap-9, 0x1.033885a928decp-10,
|
||||
0x1.911f2be23f8c7p-12, 0x1.4c3c55d2437fdp-13, 0x1.af477e1d7b461p-15,
|
||||
0x1.abd6bdff67dcbp-15, -0x1.1717e86d0fa28p-16, 0x1.6ff526de46023p-16
|
||||
};
|
||||
double bx = fabs (xs);
|
||||
double z = 1.0 - bx;
|
||||
double s = copysign (sqrt (z), xs);
|
||||
r = o[t >> 31] + s * poly12 (z, c);
|
||||
}
|
||||
return r;
|
||||
}
|
||||
libm_alias_finite (__ieee754_acosf, __acosf)
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -2,7 +2,6 @@
|
||||
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
float: 1
|
||||
|
||||
Function: "acosh":
|
||||
double: 2
|
||||
|
||||
@ -3,19 +3,15 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acosh":
|
||||
double: 2
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -3,19 +3,15 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acosh":
|
||||
double: 2
|
||||
|
||||
@ -3,19 +3,15 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acosh":
|
||||
double: 2
|
||||
|
||||
@ -3,25 +3,21 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -2,11 +2,9 @@
|
||||
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
float: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "acosh":
|
||||
double: 2
|
||||
|
||||
@ -3,22 +3,18 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "acosh":
|
||||
|
||||
@ -3,25 +3,21 @@
|
||||
# Maximal error of functions:
|
||||
Function: "acos":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "acos_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "acos_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "acos_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user