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math: Use asinf from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic asinf. 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 42.8237 35.2460 17.70% x86_64v2 43.3711 35.9406 17.13% x86_64v3 35.0335 30.5744 12.73% i686 213.8780 104.4710 51.15% aarch64 (Neoverse) 17.2937 13.6025 21.34% power10 12.0227 7.4241 38.25% reciprocal-throughput master patched improvement x86_64 13.6770 15.5231 -13.50% x86_64v2 13.8722 16.0446 -15.66% x86_64v3 13.6211 13.2753 2.54% i686 186.7670 45.4388 75.67% aarch64 (Neoverse) 9.96089 9.39285 5.70% power10 4.9862 3.7819 24.15% 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
673e6fe110
commit
5fb4b566ef
27 changed files with 124 additions and 214 deletions
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@ -302,3 +302,7 @@ sysdeps/ieee754/flt-32/e_acoshf.c:
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(src/binary32/acosh/acoshf.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/e_asinf.c:
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(src/binary32/asin/asinf.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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@ -71,7 +71,6 @@ ldouble: 2
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Function: "asin":
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double: 1
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float: 1
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ldouble: 1
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Function: "asin_advsimd":
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@ -80,7 +79,6 @@ float: 2
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Function: "asin_downward":
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double: 1
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float: 1
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ldouble: 2
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Function: "asin_sve":
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@ -89,12 +87,10 @@ float: 2
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Function: "asin_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "asin_upward":
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double: 2
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float: 1
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ldouble: 2
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Function: "asinh":
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@ -35,22 +35,18 @@ ldouble: 3
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Function: "asin":
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double: 1
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float: 1
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ldouble: 1
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Function: "asin_downward":
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double: 1
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float: 1
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ldouble: 2
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Function: "asin_towardzero":
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double: 1
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float: 1
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ldouble: 1
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Function: "asin_upward":
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double: 2
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float: 1
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ldouble: 2
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Function: "asinh":
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@ -27,19 +27,15 @@ double: 3
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Function: "asin":
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double: 1
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float: 1
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Function: "asin_downward":
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double: 1
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float: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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Function: "asin_upward":
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double: 2
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float: 1
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Function: "asinh":
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double: 3
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@ -9,7 +9,6 @@ double: 2
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Function: "asin":
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double: 1
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float: 1
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Function: "asinh":
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double: 2
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@ -43,19 +43,15 @@ float: 1
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Function: "asin":
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double: 1
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float: 1
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Function: "asin_downward":
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double: 1
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float: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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Function: "asin_upward":
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double: 2
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float: 1
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Function: "asinh":
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double: 2
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@ -25,19 +25,15 @@ Function: "acosh_upward":
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double: 2
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Function: "asin":
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float: 1
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Function: "asin_downward":
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double: 1
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float: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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Function: "asin_upward":
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double: 1
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float: 1
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Function: "asinh":
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double: 2
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@ -25,19 +25,15 @@ Function: "acosh_upward":
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double: 2
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Function: "asin":
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float: 1
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Function: "asin_downward":
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double: 1
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float: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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Function: "asin_upward":
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double: 1
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float: 1
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Function: "asinh":
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double: 2
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@ -43,19 +43,15 @@ float: 1
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Function: "asin":
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double: 1
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float: 1
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Function: "asin_downward":
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double: 1
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float: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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Function: "asin_upward":
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double: 2
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float: 1
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Function: "asinh":
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double: 2
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@ -1,38 +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 <i386-math-asm.h>
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#include <libm-alias-finite.h>
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RCSID("$NetBSD: $")
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.section .rodata.cst4,"aM",@progbits,4
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DEFINE_FLT_MIN
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#ifdef PIC
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# define MO(op) op##@GOTOFF(%ecx)
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#else
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# define MO(op) op
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#endif
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.text
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/* asin = atan (x / sqrt(1 - x^2)) */
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ENTRY(__ieee754_asinf)
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#ifdef PIC
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LOAD_PIC_REG (cx)
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#endif
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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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fpatan
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FLT_CHECK_FORCE_UFLOW
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ret
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END (__ieee754_asinf)
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libm_alias_finite (__ieee754_asinf, __asinf)
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@ -80,7 +80,6 @@ ldouble: 1
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Function: "asin_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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@ -80,7 +80,6 @@ ldouble: 1
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Function: "asin_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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@ -1,105 +1,131 @@
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/* e_asinf.c -- float version of e_asin.c.
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*/
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/* Correctly-rounded arc-sine 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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/*
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Modifications for single precision expansion are
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Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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and are incorporated herein by permission of the author. The author
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reserves the right to distribute this material elsewhere under different
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copying permissions. These modifications are distributed here under
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the following terms:
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/asin/asinf.c, revision bc385c2).
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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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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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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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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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<https://www.gnu.org/licenses/>. */
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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
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#endif
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#include <float.h>
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#include <math.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 <errno.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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huge = 1.000e+30,
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pio2_hi = 1.57079637050628662109375f,
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pio2_lo = -4.37113900018624283e-8f,
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pio4_hi = 0.785398185253143310546875f,
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/* asin x = x + x^3 p(x^2)
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-0.5 <= x <= 0.5;
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Peak relative error 4.8e-9 */
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p0 = 1.666675248e-1f,
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p1 = 7.495297643e-2f,
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p2 = 4.547037598e-2f,
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p3 = 2.417951451e-2f,
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p4 = 4.216630880e-2f;
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float __ieee754_asinf(float x)
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static __attribute__ ((noinline)) float
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as_special (float x)
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{
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float t,w,p,q,c,r,s;
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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) {
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/* asin(1)=+-pi/2 with inexact */
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return x*pio2_hi+x*pio2_lo;
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} else if(ix> 0x3f800000) { /* |x|>= 1 */
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return (x-x)/(x-x); /* asin(|x|>1) is NaN */
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} else if (ix<0x3f000000) { /* |x|<0.5 */
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if(ix<0x32000000) { /* if |x| < 2**-27 */
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math_check_force_underflow (x);
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if(huge+x>one) return x;/* return x with inexact if x!=0*/
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} else {
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t = x*x;
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w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
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return x+x*w;
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}
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}
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/* 1> |x|>= 0.5 */
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w = one-fabsf(x);
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t = w*0.5f;
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p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
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s = sqrtf(t);
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if(ix>=0x3F79999A) { /* if |x| > 0.975 */
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t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
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} else {
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int32_t iw;
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w = s;
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GET_FLOAT_WORD(iw,w);
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SET_FLOAT_WORD(w,iw&0xfffff000);
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c = (t-w*w)/(s+w);
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r = p;
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p = 2.0f*s*r-(pio2_lo-2.0f*c);
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q = pio4_hi-2.0f*w;
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t = pio4_hi-(p-q);
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}
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if(hx>0) return t; else return -t;
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uint32_t ax = asuint (x) << 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 double
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poly12 (double z, const double *c)
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{
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double z2 = z * z;
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double 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_asinf (float x)
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{
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const double pi2 = 0x1.921fb54442d18p+0;
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double xs = x;
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double r;
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uint32_t ax = asuint (x) << 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 < 0x7ec29000u))
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{
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if (__glibc_unlikely (ax < 115 << 24))
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return fmaf (x, 0x1p-25, x);
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static const double b[] =
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{
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0x1.0000000000005p+0, 0x1.55557aeca105dp-3, 0x1.3314ec3db7d12p-4,
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0x1.775738a5a6f92p-5, 0x1.5d5f7ce1c8538p-8, 0x1.605c6d58740fp-2,
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-0x1.5728b732d73c6p+1, 0x1.f152170f151ebp+3, -0x1.f962ea3ca992ep+5,
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0x1.71971e17375ap+7, -0x1.860512b4ba23p+8, 0x1.26a3b8d4bdb14p+9,
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-0x1.36f2ea5698b51p+9, 0x1.b3d722aebfa2ep+8, -0x1.6cf89703b1289p+7,
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0x1.1518af6a65e2dp+5
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};
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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 * ((b[12] + z2 * b[13])
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+ z4 * (b[14] + z2 * b[15]))));
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float ub = r;
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float lb = r - z * 0x1.efa8ebp-31;
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if (ub == lb)
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return ub;
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}
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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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double z = xs;
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double z2 = z * z;
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double c0 = poly12 (z2, c);
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r = z + (z * z2) * c0;
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}
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else
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{
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if (__glibc_unlikely (ax == 0x7e55688au))
|
||||
return copysignf (0x1.75b8a2p-1f, x) + copysignf (0x1p-26f, x);
|
||||
if (__glibc_unlikely (ax == 0x7e107434u))
|
||||
return copysignf (0x1.1f4b64p-1f, x) + copysignf (0x1p-26f, x);
|
||||
double bx = fabs (xs);
|
||||
double z = 1.0 - bx;
|
||||
double s = sqrt (z);
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.6a09e667f3bcbp+0, 0x1.e2b7dddff2db9p-4, 0x1.b27247ab42dbcp-6,
|
||||
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
|
||||
};
|
||||
r = pi2 - s * poly12 (z, c);
|
||||
r = copysign (r, xs);
|
||||
}
|
||||
return r;
|
||||
}
|
||||
libm_alias_finite (__ieee754_asinf, __asinf)
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 3
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -7,7 +7,6 @@ Function: "acosh":
|
|||
double: 2
|
||||
|
||||
Function: "asin":
|
||||
float: 1
|
||||
|
||||
Function: "asinh":
|
||||
double: 1
|
||||
|
|
|
|||
|
|
@ -27,19 +27,15 @@ double: 2
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
|
||||
Function: "asinh":
|
||||
double: 2
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 3
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -27,19 +27,15 @@ double: 2
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
|
||||
Function: "asinh":
|
||||
double: 2
|
||||
|
|
|
|||
|
|
@ -31,19 +31,15 @@ float: 1
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asinh":
|
||||
double: 2
|
||||
|
|
|
|||
|
|
@ -71,25 +71,21 @@ float: 1
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 2
|
||||
|
||||
|
|
|
|||
|
|
@ -39,22 +39,18 @@ float: 1
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 2
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 3
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 3
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -13,11 +13,9 @@ Function: "acosh_towardzero":
|
|||
double: 2
|
||||
|
||||
Function: "asin":
|
||||
float: 1
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "asinh":
|
||||
double: 2
|
||||
|
|
|
|||
|
|
@ -35,22 +35,18 @@ ldouble: 3
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "asinh":
|
||||
|
|
|
|||
|
|
@ -107,25 +107,21 @@ ldouble: 2
|
|||
|
||||
Function: "asin":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "asin_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "asin_upward":
|
||||
double: 2
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 1
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue