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math: Use acoshf from CORE-MATH

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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 <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 2024-10-21 10:51:09 -03:00
parent 66fa7ad437
commit 673e6fe110
26 changed files with 195 additions and 224 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
SHARED-FILES
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@ -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.

4
sysdeps/aarch64/libm-test-ulps
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@ -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":

4
sysdeps/alpha/fpu/libm-test-ulps
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@ -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":

4
sysdeps/arc/fpu/libm-test-ulps
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@ -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

1
sysdeps/arc/nofpu/libm-test-ulps
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@ -6,7 +6,6 @@ double: 1
Function: "acosh":
double: 2
float: 2
Function: "asin":
double: 1

4
sysdeps/arm/libm-test-ulps
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@ -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

4
sysdeps/csky/fpu/libm-test-ulps
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@ -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

4
sysdeps/csky/nofpu/libm-test-ulps
View File

@ -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

4
sysdeps/hppa/fpu/libm-test-ulps
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@ -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

101
sysdeps/i386/fpu/e_acoshf.S
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@ -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
<https://www.gnu.org/licenses/>. */
#include <machine/asm.h>
#include <libm-alias-finite.h>
.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)

230
sysdeps/ieee754/flt-32/e_acoshf.c
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@ -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 <math.h>
#include <math_private.h>
#include <stdint.h>
#include <libm-alias-finite.h>
#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<x<2 */
t = x-one;
return __log1pf(t+sqrtf((float)2.0*t+t*t));
uint32_t t = asuint (x);
if (t == 0x3f800000u)
return 0.0f;
if ((t << 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)

4
sysdeps/loongarch/lp64/libm-test-ulps
View File

@ -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":

4
sysdeps/m68k/m680x0/fpu/libm-test-ulps
View File

@ -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":

1
sysdeps/microblaze/libm-test-ulps
View File

@ -5,7 +5,6 @@ Function: "acos":
Function: "acosh":
double: 2
float: 2
Function: "asin":
float: 1

4
sysdeps/mips/mips32/libm-test-ulps
View File

@ -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

4
sysdeps/mips/mips64/libm-test-ulps
View File

@ -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":

4
sysdeps/or1k/fpu/libm-test-ulps
View File

@ -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

4
sysdeps/or1k/nofpu/libm-test-ulps
View File

@ -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

4
sysdeps/powerpc/fpu/libm-test-ulps
View File

@ -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

4
sysdeps/powerpc/nofpu/libm-test-ulps
View File

@ -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":

4
sysdeps/riscv/nofpu/libm-test-ulps
View File

@ -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":

4
sysdeps/riscv/rvd/libm-test-ulps
View File

@ -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":

4
sysdeps/s390/fpu/libm-test-ulps
View File

@ -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":

2
sysdeps/sh/libm-test-ulps
View File

@ -8,11 +8,9 @@ double: 1
Function: "acosh":
double: 2
float: 2
Function: "acosh_towardzero":
double: 2
float: 2
Function: "asin":
float: 1

4
sysdeps/sparc/fpu/libm-test-ulps
View File

@ -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":

4
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -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