From ed608a40e2903351c64a3cea51ce8bd7c62996ef Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Thu, 14 Nov 2024 11:07:11 -0300 Subject: [PATCH] math: Use asinhf from CORE-MATH The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic asinhf. 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 64.5128 56.9717 11.69% x86_64v2 63.3065 57.2666 9.54% x86_64v3 62.8719 51.4170 18.22% i686 189.1630 137.635 27.24% aarch64 (Neoverse) 25.3551 20.5757 18.85% power10 17.9712 13.3302 25.82% reciprocal-throughput master patched improvement x86_64 20.0844 15.4731 22.96% x86_64v2 19.2919 15.4000 20.17% x86_64v3 18.7226 11.9009 36.44% i686 103.7670 80.2681 22.65% aarch64 (Neoverse) 12.5005 8.68969 30.49% power10 7.2220 5.03617 30.27% Signed-off-by: Alexei Sibidanov Signed-off-by: Paul Zimmermann Signed-off-by: Adhemerval Zanella : Reviewed-by: DJ Delorie --- SHARED-FILES | 4 + sysdeps/aarch64/libm-test-ulps | 4 - sysdeps/alpha/fpu/libm-test-ulps | 4 - sysdeps/arc/fpu/libm-test-ulps | 4 - sysdeps/arc/nofpu/libm-test-ulps | 1 - sysdeps/arm/libm-test-ulps | 4 - sysdeps/csky/fpu/libm-test-ulps | 4 - sysdeps/csky/nofpu/libm-test-ulps | 4 - sysdeps/hppa/fpu/libm-test-ulps | 4 - sysdeps/i386/fpu/libm-test-ulps | 3 - sysdeps/i386/fpu/s_asinhf.S | 139 ----------- .../i386/i686/fpu/multiarch/libm-test-ulps | 3 - sysdeps/ieee754/flt-32/s_asinhf.c | 217 ++++++++++++++---- sysdeps/loongarch/lp64/libm-test-ulps | 4 - sysdeps/m68k/m680x0/fpu/libm-test-ulps | 4 - sysdeps/microblaze/libm-test-ulps | 1 - sysdeps/mips/mips32/libm-test-ulps | 4 - sysdeps/mips/mips64/libm-test-ulps | 4 - sysdeps/or1k/fpu/libm-test-ulps | 4 - sysdeps/or1k/nofpu/libm-test-ulps | 4 - sysdeps/powerpc/fpu/libm-test-ulps | 4 - sysdeps/powerpc/nofpu/libm-test-ulps | 4 - sysdeps/riscv/nofpu/libm-test-ulps | 4 - sysdeps/riscv/rvd/libm-test-ulps | 4 - sysdeps/s390/fpu/libm-test-ulps | 4 - sysdeps/sh/libm-test-ulps | 2 - sysdeps/sparc/fpu/libm-test-ulps | 4 - sysdeps/x86_64/fpu/libm-test-ulps | 4 - 28 files changed, 182 insertions(+), 268 deletions(-) delete mode 100644 sysdeps/i386/fpu/s_asinhf.S diff --git a/SHARED-FILES b/SHARED-FILES index 6a6ff76b31..18b3244e44 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -306,3 +306,7 @@ sysdeps/ieee754/flt-32/e_asinf.c: (src/binary32/asin/asinf.c in CORE-MATH) - The code was adapted to use glibc code style and internal functions to handle errno, overflow, and underflow. +sysdeps/ieee754/flt-32/s_asinhf.c: + (src/binary32/asinh/asinhf.c in CORE-MATH) + - The code was adapted to use glibc code style and internal + functions to handle errno, overflow, and underflow. diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index da054b62e7..44493b3f02 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -95,7 +95,6 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_advsimd": @@ -104,7 +103,6 @@ float: 2 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_sve": @@ -113,12 +111,10 @@ float: 2 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "asinpi": diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps index cda6ece49e..708299915d 100644 --- a/sysdeps/alpha/fpu/libm-test-ulps +++ b/sysdeps/alpha/fpu/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index 3c08593d99..1c34bd36d6 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -39,19 +39,15 @@ double: 2 Function: "asinh": double: 3 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "atan": double: 1 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index c3548a9807..58fc499f53 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -12,7 +12,6 @@ double: 1 Function: "asinh": double: 2 -float: 2 Function: "atan": double: 1 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index 8e55b23f41..60f483ec31 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -55,19 +55,15 @@ double: 2 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "asinpi": double: 1 diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps index b04ed2a161..2b7b5cfc92 100644 --- a/sysdeps/csky/fpu/libm-test-ulps +++ b/sysdeps/csky/fpu/libm-test-ulps @@ -37,19 +37,15 @@ double: 1 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "atan": float: 1 diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps index 612bd19eda..0eb62de8b2 100644 --- a/sysdeps/csky/nofpu/libm-test-ulps +++ b/sysdeps/csky/nofpu/libm-test-ulps @@ -37,19 +37,15 @@ double: 1 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "atan": float: 1 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index bb7e30f255..f48a12f511 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -55,19 +55,15 @@ double: 2 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "asinpi": double: 1 diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 11606b93d9..669ecbe3ac 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -90,19 +90,16 @@ ldouble: 3 Function: "asinh_downward": double: 1 -float: 1 float128: 4 ldouble: 5 Function: "asinh_towardzero": double: 1 -float: 1 float128: 2 ldouble: 4 Function: "asinh_upward": double: 1 -float: 1 float128: 4 ldouble: 5 diff --git a/sysdeps/i386/fpu/s_asinhf.S b/sysdeps/i386/fpu/s_asinhf.S deleted file mode 100644 index fe52e20886..0000000000 --- a/sysdeps/i386/fpu/s_asinhf.S +++ /dev/null @@ -1,139 +0,0 @@ -/* ix87 specific implementation of arcsinh. - Copyright (C) 1996-2024 Free Software Foundation, Inc. - This file is part of the GNU C Library. - - The GNU C Library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - The GNU C Library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with the GNU C Library; if not, see - . */ - -#include -#include - - .section .rodata - - .align ALIGNARG(4) - .type huge,@object -huge: .double 1e+36 - ASM_SIZE_DIRECTIVE(huge) - .type one,@object -one: .double 1.0 - ASM_SIZE_DIRECTIVE(one) - .type limit,@object -limit: .double 0.29 - ASM_SIZE_DIRECTIVE(limit) - -#ifdef PIC -#define MO(op) op##@GOTOFF(%edx) -#else -#define MO(op) op -#endif - - .text -ENTRY(__asinhf) - movl 4(%esp), %ecx - movl $0x7fffffff, %eax - andl %ecx, %eax - andl $0x80000000, %ecx - movl %eax, %edx - orl $0x807fffff, %edx - incl %edx - jz 7f // x in ħInf or NaN - xorl %ecx, 4(%esp) - flds 4(%esp) // |x| - cmpl $0x38000000, %eax - jb 2f // |x| < 2^-14 - fldln2 // log(2) : |x| - cmpl $0x47000000, %eax - fxch // |x| : log(2) - ja 3f // |x| > 2^14 -#ifdef PIC - LOAD_PIC_REG (dx) -#endif - cmpl $0x40000000, %eax - ja 5f // |x| > 2 - - // 2^-14 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2))) - fld %st // |x| : |x| : log(2) - fmul %st(1) // |x|^2 : |x| : log(2) - fld %st // |x|^2 : |x|^2 : |x| : log(2) - faddl MO(one) // 1+|x|^2 : |x|^2 : |x| : log(2) - fsqrt // sqrt(1+|x|^2) : |x|^2 : |x| : log(2) - faddl MO(one) // 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2) - fdivrp // |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2) - faddp // |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2) - fcoml MO(limit) - fnstsw - sahf - ja 6f - fyl2xp1 - jecxz 4f - fchs -4: ret - -7: flds 4(%esp) - ret - -6: faddl MO(one) - fyl2x - jecxz 4f - fchs -4: ret - - // |x| < 2^-14 => y = x (inexact iff |x| != 0.0) - .align ALIGNARG(4) -2: -#ifdef PIC - LOAD_PIC_REG (dx) -#endif - jecxz 4f - fchs // x -4: fld %st // x : x - faddl MO(huge) // huge+x : x - fstp %st(0) // x - cmpl $0x00800000, %eax - jae 8f - subl $4, %esp - cfi_adjust_cfa_offset (4) - fld %st(0) - fmul %st(0) - fstps (%esp) - addl $4, %esp - cfi_adjust_cfa_offset (-4) -8: ret - - // |x| > 2^14 => y = sign(x) * (log(|x|) + log(2)) - .align ALIGNARG(4) -3: fyl2x // log(|x|) - fldln2 // log(2) : log(|x|) - faddp // log(|x|)+log(2) - jecxz 4f - fchs -4: ret - - // |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1))) - .align ALIGNARG(4) -5: fld %st // |x| : |x| : log(2) - fadd %st, %st(1) // |x| : 2*|x| : log(2) - fld %st // |x| : |x| : 2*|x| : log(2) - fmul %st(1) // |x|^2 : |x| : 2*|x| : log(2) - faddl MO(one) // 1+|x|^2 : |x| : 2*|x| : log(2) - fsqrt // sqrt(1+|x|^2) : |x| : 2*|x| : log(2) - faddp // |x|+sqrt(1+|x|^2) : 2*|x| : log(2) - fdivrl MO(one) // 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2) - faddp // 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2) - fyl2x // log(2*|x|+1/(|x|+sqrt(1+|x|^2))) - jecxz 4f - fchs -4: ret -END(__asinhf) -libm_alias_float (__asinh, asinh) diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps index f416f8d1f0..e5bc05eed1 100644 --- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps +++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps @@ -90,19 +90,16 @@ ldouble: 3 Function: "asinh_downward": double: 1 -float: 1 float128: 4 ldouble: 5 Function: "asinh_towardzero": double: 1 -float: 1 float128: 2 ldouble: 4 Function: "asinh_upward": double: 1 -float: 1 float128: 4 ldouble: 5 diff --git a/sysdeps/ieee754/flt-32/s_asinhf.c b/sysdeps/ieee754/flt-32/s_asinhf.c index a94676fbda..93750f5dae 100644 --- a/sysdeps/ieee754/flt-32/s_asinhf.c +++ b/sysdeps/ieee754/flt-32/s_asinhf.c @@ -1,51 +1,190 @@ -/* s_asinhf.c -- float version of s_asinh.c. - */ +/* Correctly-rounded inverse hyperbolic sine function for binary32 format. -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ +Copyright (c) 2023-2024 Alexei Sibidanov. + +The original version of this file was copied from the CORE-MATH +project (file src/binary32/asinh/asinhf.c, revision e8774b3). + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +*/ -#include #include -#include -#include +#include #include - -static const float -one = 1.0000000000e+00, /* 0x3F800000 */ -ln2 = 6.9314718246e-01, /* 0x3f317218 */ -huge= 1.0000000000e+30; +#include "math_config.h" float -__asinhf(float x) +__asinhf (float x) { - float w; - int32_t hx,ix; - GET_FLOAT_WORD(hx,x); - ix = hx&0x7fffffff; - if(__builtin_expect(ix< 0x38000000, 0)) { /* |x|<2**-14 */ - math_check_force_underflow (x); - if(huge+x>one) return x; /* return x inexact except 0 */ + static const double ix[] = + { + 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, + 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, + 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, + 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, + 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, + 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, + 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, + 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, + 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, + 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, + 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, + 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, + 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, + 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, + 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, + 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, + 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, + 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, + 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, + 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, + 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, + 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, + 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, + 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, + 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, + 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, + 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, + 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, + 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, + 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, + 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, + 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, + 0x1p-1 + }; + + static const double lix[] = + { + 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, + 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, + 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, + 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, + 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, + 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, + 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, + 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, + 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, + 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, + 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, + 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, + 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, + 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, + 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, + 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, + 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, + 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, + 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, + 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, + 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, + 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, + 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, + 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, + 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, + 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, + 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, + 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, + 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, + 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, + 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, + 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, + 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, + 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, + 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, + 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, + 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, + 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, + 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, + 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, + 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, + 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, + 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 + }; + + uint32_t t = asuint (x); + t &= ~0u >> 1; + double xs = x; + if (__glibc_unlikely (t <= 0x3e815667u)) + { + if (__glibc_unlikely (t <= 0x39ddb3d7u)) + { + if (__glibc_unlikely (t == 0)) + return x; + return fmaf (x, -0x1p-25f, x); } - if(__builtin_expect(ix>0x47000000, 0)) { /* |x| > 2**14 */ - if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ - w = __ieee754_logf(fabsf(x))+ln2; - } else { - float xa = fabsf(x); - if (ix>0x40000000) { /* 2**14 > |x| > 2.0 */ - w = __ieee754_logf(2.0f*xa+one/(sqrtf(xa*xa+one)+xa)); - } else { /* 2.0 > |x| > 2**-14 */ - float t = xa*xa; - w =__log1pf(xa+t/(one+sqrtf(one+t))); + static const double c[] = + { + 0x1.5555555555553p-3, -0x1.3333333330e9dp-4, 0x1.6db6db67cb37ap-5, + -0x1.f1c71699375dp-6, 0x1.6e8a374c39ff9p-6, -0x1.1c1e98f9d01e1p-6, + 0x1.c277e96d84026p-7, -0x1.329ff5faf02abp-7 + }; + double x2 = xs * xs; + double x4 = x2 * x2; + double x8 = x4 * x4; + double f = x2 * (((c[0] + x2 * c[1]) + x4 * (c[2] + x2 * c[3])) + + x8 * ((c[4] + x2 * c[5]) + x4 * (c[6] + x2 * c[7]))); + double r = xs - xs * f; + return r; + } + else + { + if (__glibc_unlikely (t >= 0x7f800000u)) + return x + x; /* +-inf or nan */ + double xd = fabs (xs); + double x2 = xd * xd; + uint64_t tp = asuint64 (xd + sqrt (x2 + 1)); + uint64_t m = tp & (~UINT64_C(0) >> 12); + int j = (m + (UINT64_C(1) << (52 - 8))) >> (52 - 7); + int e = (tp >> 52) - 0x3ff; + double w = asdouble (m | UINT64_C(0x3ff) << 52); + double z = w * ix[j] - 1.0; + static const double c[] = + { + 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 + }; + double z2 = z * z; + double r = ((lix[128] * e + lix[j]) + z * c[0]) + z2 * (c[1] + z * c[2]); + if (__glibc_unlikely (((asuint64 (r) + 259000) & INT64_C(0xfffffff)) + < 260000)) /* accurate path */ + { + static const double cp[] = + { + 0x1p+0, -0x1p-1, + 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, + 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 + }; + z2 = z * z; + double c0 = cp[0] + z * cp[1]; + double c2 = cp[2] + z * cp[3]; + double c4 = cp[4] + z * cp[5]; + c0 += z2 * (c2 + z2 * c4); + const double ln2l = 0x1.7f7d1cf79abcap-20; + const double ln2h = 0x1.62e4p-1; + double Lh = ln2h * e; + double Ll = ln2l * e; + r = fma (z, c0, Ll + lix[j]) + Lh; + if (__glibc_unlikely ((asuint64 (r) & INT64_C(0xfffffff)) == 0)) + { + double h = fma (z, c0, Ll + lix[j]) + (Lh - r); + r = r + 64 * h; } } - return copysignf(w, x); + return copysign (r, xs); + } } libm_alias_float (__asinh, asinh) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index 67beca8ff6..b24bc582ea 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps index 73019999e0..7b3e67efaf 100644 --- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps +++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps @@ -34,22 +34,18 @@ float: 1 Function: "asinh": double: 1 -float: 1 ldouble: 1 Function: "asinh_downward": double: 2 -float: 2 ldouble: 2 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 2 -float: 2 ldouble: 3 Function: "atan2": diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps index a0e8b5bd50..b7e73db063 100644 --- a/sysdeps/microblaze/libm-test-ulps +++ b/sysdeps/microblaze/libm-test-ulps @@ -10,7 +10,6 @@ Function: "asin": Function: "asinh": double: 1 -float: 1 Function: "atan": float: 1 diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps index 7eca3dc8df..ca4eac5090 100644 --- a/sysdeps/mips/mips32/libm-test-ulps +++ b/sysdeps/mips/mips32/libm-test-ulps @@ -39,19 +39,15 @@ double: 2 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "atan": double: 1 diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index 4cabe88af1..30e8d46c68 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index f95e138864..dd972b3063 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -39,19 +39,15 @@ double: 2 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "atan": double: 1 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index 5ec5b1f3f3..d5d1c8dc80 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -43,19 +43,15 @@ double: 1 Function: "asinh": double: 2 -float: 2 Function: "asinh_downward": double: 3 -float: 3 Function: "asinh_towardzero": double: 2 -float: 2 Function: "asinh_upward": double: 3 -float: 3 Function: "asinpi": double: 1 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index a11a5894e0..edb6678fdb 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -91,25 +91,21 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 float128: 4 ldouble: 2 Function: "asinh_downward": double: 3 -float: 3 float128: 4 ldouble: 5 Function: "asinh_towardzero": double: 2 -float: 2 float128: 2 ldouble: 5 Function: "asinh_upward": double: 3 -float: 3 float128: 4 ldouble: 7 diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps index d03d25e54a..939468399c 100644 --- a/sysdeps/powerpc/nofpu/libm-test-ulps +++ b/sysdeps/powerpc/nofpu/libm-test-ulps @@ -55,22 +55,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 2 Function: "asinh_downward": double: 3 -float: 3 ldouble: 5 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 5 Function: "asinh_upward": double: 3 -float: 3 ldouble: 7 Function: "atan": diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index edaa91a4c1..7c89f7915b 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index 4db2d0231b..e1c1a6aee5 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index 22dfe60294..038e3eb9d7 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps index e225f78936..4bd1ff1f98 100644 --- a/sysdeps/sh/libm-test-ulps +++ b/sysdeps/sh/libm-test-ulps @@ -19,11 +19,9 @@ double: 1 Function: "asinh": double: 2 -float: 2 Function: "asinh_towardzero": double: 2 -float: 2 Function: "atan": float: 1 diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index f24b64a944..a4d678da03 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -51,22 +51,18 @@ ldouble: 2 Function: "asinh": double: 2 -float: 2 ldouble: 4 Function: "asinh_downward": double: 3 -float: 3 ldouble: 4 Function: "asinh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "asinh_upward": double: 3 -float: 3 ldouble: 4 Function: "atan": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index ec2b3629ac..23c40d0590 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -147,25 +147,21 @@ float: 1 Function: "asinh": double: 2 -float: 2 float128: 4 ldouble: 3 Function: "asinh_downward": double: 3 -float: 3 float128: 4 ldouble: 5 Function: "asinh_towardzero": double: 2 -float: 2 float128: 2 ldouble: 4 Function: "asinh_upward": double: 3 -float: 3 float128: 4 ldouble: 5