From 673e6fe11083760f77001285790b1117b09b2283 Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Mon, 21 Oct 2024 10:51:09 -0300 Subject: [PATCH] math: Use acoshf from CORE-MATH The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic acoshf. 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 61.2471 58.7742 4.04% x86_64-v2 62.6519 59.0523 5.75% x86_64-v3 58.7408 50.1393 14.64% aarch64 24.8580 21.3317 14.19% power10 17.0469 13.1345 22.95% reciprocal-throughput master patched improvement x86_64 16.1618 15.1864 6.04% x86_64-v2 15.7729 14.7563 6.45% x86_64-v3 14.1669 11.9568 15.60% aarch64 10.911 9.5486 12.49% power10 6.38196 5.06734 20.60% 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/e_acoshf.S | 101 ----------- sysdeps/ieee754/flt-32/e_acoshf.c | 230 ++++++++++++++++++++----- 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 - 26 files changed, 195 insertions(+), 224 deletions(-) delete mode 100644 sysdeps/i386/fpu/e_acoshf.S diff --git a/SHARED-FILES b/SHARED-FILES index 3d32f0f3b6..c29c1c8106 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -298,3 +298,7 @@ sysdeps/ieee754/flt-32/e_acosf.c: (src/binary32/acos/acosf.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/e_acoshf.c: + (src/binary32/acosh/acoshf.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 a925a3834c..8ab673c4b7 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -27,7 +27,6 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_advsimd": @@ -36,7 +35,6 @@ float: 2 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_sve": @@ -45,12 +43,10 @@ float: 2 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "acospi": diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps index aac2e31951..d26fcb40c9 100644 --- a/sysdeps/alpha/fpu/libm-test-ulps +++ b/sysdeps/alpha/fpu/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index b80f97b5ed..0057716df0 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 3 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 3 -float: 3 Function: "asin": double: 1 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index de1fdd9b1e..2fa0c82346 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -6,7 +6,6 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "asin": double: 1 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index 25c06306cd..d6c56fd5b5 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "acospi": double: 1 diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps index 3e7b07e81a..ebde72f4d7 100644 --- a/sysdeps/csky/fpu/libm-test-ulps +++ b/sysdeps/csky/fpu/libm-test-ulps @@ -14,19 +14,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "asin": float: 1 diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps index 58bd5eaa15..73b6a2042a 100644 --- a/sysdeps/csky/nofpu/libm-test-ulps +++ b/sysdeps/csky/nofpu/libm-test-ulps @@ -14,19 +14,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "asin": float: 1 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index 629fb5b414..f7f5d6b1b7 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "acospi": double: 1 diff --git a/sysdeps/i386/fpu/e_acoshf.S b/sysdeps/i386/fpu/e_acoshf.S deleted file mode 100644 index 6eda9dc584..0000000000 --- a/sysdeps/i386/fpu/e_acoshf.S +++ /dev/null @@ -1,101 +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.cst8,"aM",@progbits,8 - - .p2align 3 - .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(__ieee754_acoshf) - movl 4(%esp), %ecx - cmpl $0x3f800000, %ecx - jl 5f // < 1 => invalid - fldln2 // log(2) - flds 4(%esp) // x : log(2) - cmpl $0x47000000, %ecx - ja 3f // x > 2^14 -#ifdef PIC - LOAD_PIC_REG (dx) -#endif - cmpl $0x40000000, %ecx - ja 4f // x > 2 - - // 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2)) - fsubl MO(one) // x-1 : log(2) - fabs // acosh(1) is +0 in all rounding modes - fld %st // x-1 : x-1 : log(2) - fmul %st(1) // (x-1)^2 : x-1 : log(2) - fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2) - fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2) - fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2) - faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2) - fcoml MO(limit) - fnstsw - sahf - ja 2f - fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2)) - ret - -2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2) - fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2)) - ret - - // x > 2^14 => y = log(x) + log(2) - .align ALIGNARG(4) -3: fyl2x // log(x) - fldln2 // log(2) : log(x) - faddp // log(x)+log(2) - ret - - // 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1))) - .align ALIGNARG(4) -4: 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) - fsubl MO(one) // x^2-1 : x : 2*x : log(2) - fsqrt // sqrt(x^2-1) : x : 2*x : log(2) - faddp // x+sqrt(x^2-1) : 2*x : log(2) - fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2) - fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2) - fyl2x // log(2*x+1/(x+sqrt(x^2-1))) - ret - - // x < 1 (or -NaN) => NaN - .align ALIGNARG(4) -5: flds 4(%esp) - fsub %st - fdiv %st, %st(0) - ret -END(__ieee754_acoshf) -libm_alias_finite (__ieee754_acoshf, __acoshf) diff --git a/sysdeps/ieee754/flt-32/e_acoshf.c b/sysdeps/ieee754/flt-32/e_acoshf.c index 2237af4ba4..a0a0abc2dd 100644 --- a/sysdeps/ieee754/flt-32/e_acoshf.c +++ b/sysdeps/ieee754/flt-32/e_acoshf.c @@ -1,49 +1,201 @@ -/* e_acoshf.c -- float version of e_acosh.c. - */ +/* Correctly-rounded inverse hyperbolic cosine 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. -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_acoshf.c,v 1.5 1995/05/12 04:57:20 jtc Exp $"; -#endif +The original version of this file was copied from the CORE-MATH +project (file src/binary32/acosh/acoshf.c, revision d0b9ddd). + +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 "math_config.h" -static const float -one = 1.0, -ln2 = 6.9314718246e-01; /* 0x3f317218 */ - -float __ieee754_acoshf(float x) +static __attribute__ ((noinline)) float +as_special (float x) { - float t; - int32_t hx; - GET_FLOAT_WORD(hx,x); - if(hx<0x3f800000) { /* x < 1 */ - return (x-x)/(x-x); - } else if(hx >=0x4d800000) { /* x > 2**28 */ - if(hx >=0x7f800000) { /* x is inf of NaN */ - return x+x; - } else - return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ - } else if (hx==0x3f800000) { - return 0.0; /* acosh(1) = 0 */ - } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ - t=x*x; - return __ieee754_logf((float)2.0*x-one/(x+sqrtf(t-one))); - } else { /* 1 0xff000000u) + return x + x; /* nan */ + if (t == 0x7f800000u) + return x; /* inf */ + return __math_invalidf (x); +} + +float +__ieee754_acoshf (float x) +{ + 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); + if (__glibc_unlikely (t <= 0x3f800000u)) + return as_special (x); + else if (__glibc_unlikely (t <= 0x3f99db23u)) /* x <= 0x1.33b646p+0 */ + { + float zf = x - 1.0f; + double z = zf; + double a = sqrt (2.0 * z); + static const double c[] = + { + -0x1.555555555491ep-4, 0x1.333333319c2p-6, + -0x1.6db6da26e5e0ep-8, 0x1.f1c698b7100cep-10, + -0x1.6e7ca9e152dc2p-11, 0x1.1b4cf187158bdp-12, + -0x1.b5137f11a88e5p-14, 0x1.056c6c57152b2p-15 + }; + double z2 = z * z; + double z4 = z2 * z2; + double f = ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])) + + z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])); + double r = a + (a * z) * f; + return r; + } + else if (__glibc_likely (t < 0x7f800000u)) + { + double xd = x; + 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) & UINT64_C(0xfffffff)) == 0)) + { + double h = fma (z, c0, Ll + lix[j]) + (Lh - r); + r = r + 64.0 * h; + } } + return r; + } + else + return as_special (x); } libm_alias_finite (__ieee754_acoshf, __acoshf) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index 67bf2d2f9f..63fd07fbe0 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps index 50080f46b3..73019999e0 100644 --- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps +++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps @@ -3,22 +3,18 @@ # Maximal error of functions: Function: "acosh": double: 1 -float: 1 ldouble: 1 Function: "acosh_downward": double: 2 -float: 1 ldouble: 1 Function: "acosh_towardzero": double: 2 -float: 1 ldouble: 1 Function: "acosh_upward": double: 2 -float: 1 ldouble: 1 Function: "asin": diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps index c93ebfa21b..a9e3f3a318 100644 --- a/sysdeps/microblaze/libm-test-ulps +++ b/sysdeps/microblaze/libm-test-ulps @@ -5,7 +5,6 @@ Function: "acos": Function: "acosh": double: 2 -float: 2 Function: "asin": float: 1 diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps index d23762642b..fc0d001750 100644 --- a/sysdeps/mips/mips32/libm-test-ulps +++ b/sysdeps/mips/mips32/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "asin": double: 1 diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index aece335d6b..855b48e800 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index 862ab6b559..0cc7beccfc 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "asin": double: 1 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index 27ddaf0510..4e3928a325 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -15,19 +15,15 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_downward": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "acosh_upward": double: 2 -float: 2 Function: "acospi": double: 1 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index 6e0a9de7bb..0fc38f8e70 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -23,25 +23,21 @@ ldouble: 2 Function: "acosh": double: 2 -float: 2 float128: 4 ldouble: 2 Function: "acosh_downward": double: 2 -float: 2 float128: 3 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 float128: 2 ldouble: 5 Function: "acosh_upward": double: 2 -float: 2 float128: 3 ldouble: 4 diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps index 44cf9983dc..f553da0caa 100644 --- a/sysdeps/powerpc/nofpu/libm-test-ulps +++ b/sysdeps/powerpc/nofpu/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 2 Function: "acosh": double: 2 -float: 2 ldouble: 1 Function: "acosh_downward": double: 2 -float: 2 ldouble: 2 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 5 Function: "acosh_upward": double: 2 -float: 2 ldouble: 4 Function: "add_ldouble": diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index 8d3b048e84..3bf997c5d8 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 2 Function: "asin": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index a1d85be3b6..f85d9caf03 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index 0d47af49bc..9433370865 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps index d1e5b05531..d46c722ea1 100644 --- a/sysdeps/sh/libm-test-ulps +++ b/sysdeps/sh/libm-test-ulps @@ -8,11 +8,9 @@ double: 1 Function: "acosh": double: 2 -float: 2 Function: "acosh_towardzero": double: 2 -float: 2 Function: "asin": float: 1 diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index fe2d1dd34e..1fde571203 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -19,22 +19,18 @@ ldouble: 1 Function: "acosh": double: 2 -float: 2 ldouble: 4 Function: "acosh_downward": double: 2 -float: 2 ldouble: 3 Function: "acosh_towardzero": double: 2 -float: 2 ldouble: 2 Function: "acosh_upward": double: 2 -float: 2 ldouble: 3 Function: "asin": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index f6c19d309d..3ad52717e7 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -43,25 +43,21 @@ float: 1 Function: "acosh": double: 2 -float: 2 float128: 4 ldouble: 3 Function: "acosh_downward": double: 2 -float: 2 float128: 3 ldouble: 4 Function: "acosh_towardzero": double: 2 -float: 2 float128: 2 ldouble: 4 Function: "acosh_upward": double: 2 -float: 2 float128: 3 ldouble: 3