[PATCH 20/23] math: Use atanhf from CORE-MATH
Adhemerval Zanella
adhemerval.zanella@linaro.org
Fri Nov 29 13:17:44 GMT 2024
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows slight better performance to the generic atanhf.
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 59.4930 45.8568 22.92%
x86_64v2 59.5705 45.5804 23.48%
x86_64v3 53.1838 37.7155 29.08%
i686 169.354 133.5940 21.12%
aarch64 (Neoverse) 26.0781 16.9829 34.88%
power10 15.6591 10.7623 31.27%
reciprocal-throughput master patched improvement
x86_64 23.5903 18.5766 21.25%
x86_64v2 22.6489 18.2683 19.34%
x86_64v3 19.0401 13.9474 26.75%
i686 97.6034 107.3260 -9.96%
aarch64 (Neoverse) 15.3664 9.57846 37.67%
power10 6.8877 4.6242 32.86%
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>
---
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_atanhf.S | 110 ---------
sysdeps/i386/fpu/libm-test-ulps | 3 -
.../i386/i686/fpu/multiarch/libm-test-ulps | 3 -
sysdeps/ieee754/flt-32/e_atanhf.c | 210 +++++++++++++-----
sysdeps/loongarch/lp64/libm-test-ulps | 4 -
sysdeps/m68k/coldfire/fpu/libm-test-ulps | 1 -
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, 159 insertions(+), 252 deletions(-)
delete mode 100644 sysdeps/i386/fpu/e_atanhf.S
diff --git a/SHARED-FILES b/SHARED-FILES
index 99f8554393..d32c837b46 100644
--- a/SHARED-FILES
+++ b/SHARED-FILES
@@ -318,3 +318,7 @@ sysdeps/ieee754/flt-32/e_atan2f.c:
(src/binary32/atan2/atan2f.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_atanhf.c:
+ (src/binary32/atanh/atanhf.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 f48a4d2e76..0c686221d2 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -146,7 +146,6 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_advsimd":
@@ -155,7 +154,6 @@ float: 1
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_sve":
@@ -164,12 +162,10 @@ float: 1
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps
index 860da75a86..e108b2543c 100644
--- a/sysdeps/alpha/fpu/libm-test-ulps
+++ b/sysdeps/alpha/fpu/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index 7b5208e2f8..a0d6e89b49 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -75,19 +75,15 @@ double: 2
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index a46825b0c1..1a6b37a728 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -20,7 +20,6 @@ Function: "atan2":
Function: "atanh":
double: 2
-float: 2
Function: "cabs":
double: 1
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index 5c1046b9f5..ea2f3a22b0 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -74,19 +74,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps
index 0a18d51742..f8ab682f84 100644
--- a/sysdeps/csky/fpu/libm-test-ulps
+++ b/sysdeps/csky/fpu/libm-test-ulps
@@ -71,19 +71,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps
index 55be0213ec..f8b888ea9d 100644
--- a/sysdeps/csky/nofpu/libm-test-ulps
+++ b/sysdeps/csky/nofpu/libm-test-ulps
@@ -71,19 +71,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index c92f46cc15..c8d4423ae0 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -74,19 +74,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/i386/fpu/e_atanhf.S b/sysdeps/i386/fpu/e_atanhf.S
deleted file mode 100644
index c94dc7ba51..0000000000
--- a/sysdeps/i386/fpu/e_atanhf.S
+++ /dev/null
@@ -1,110 +0,0 @@
-/* ix87 specific implementation of arctanh function.
- 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 <i386-math-asm.h>
-#include <libm-alias-finite.h>
-
- .section .rodata
-
- .align ALIGNARG(4)
- .type half,@object
-half: .double 0.5
- ASM_SIZE_DIRECTIVE(half)
- .type one,@object
-one: .double 1.0
- ASM_SIZE_DIRECTIVE(one)
- .type limit,@object
-limit: .double 0.29
- ASM_SIZE_DIRECTIVE(limit)
- .align ALIGNARG(4)
- .type ln2_2,@object
-ln2_2: .quad 0xb17217f7d1cf79ac /* 0.3465735902799726547086160 */
- .short 0x3ffd
- ASM_SIZE_DIRECTIVE(ln2_2)
-
-DEFINE_FLT_MIN
-
-#ifdef PIC
-#define MO(op) op##@GOTOFF(%edx)
-#else
-#define MO(op) op
-#endif
-
- .text
-ENTRY(__ieee754_atanhf)
- movl 4(%esp), %ecx
-
- movl %ecx, %eax
- andl $0x7fffffff, %eax
- cmpl $0x7f800000, %eax
- ja 5f
-
-#ifdef PIC
- LOAD_PIC_REG (dx)
-#endif
-
- andl $0x80000000, %ecx // ECX == 0 iff X >= 0
-
- fldt MO(ln2_2) // 0.5*ln2
- xorl %ecx, 4(%esp)
- flds 4(%esp) // |x| : 0.5*ln2
- fcoml MO(half) // |x| : 0.5*ln2
- fld %st(0) // |x| : |x| : 0.5*ln2
- fnstsw // |x| : |x| : 0.5*ln2
- sahf
- jae 2f
- fadd %st, %st(1) // |x| : 2*|x| : 0.5*ln2
- fld %st // |x| : |x| : 2*|x| : 0.5*ln2
- fsubrl MO(one) // 1-|x| : |x| : 2*|x| : 0.5*ln2
- fxch // |x| : 1-|x| : 2*|x| : 0.5*ln2
- fmul %st(2) // 2*|x|^2 : 1-|x| : 2*|x| : 0.5*ln2
- fdivp // (2*|x|^2)/(1-|x|) : 2*|x| : 0.5*ln2
- faddp // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
- fcoml MO(limit) // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
- fnstsw // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
- sahf
- jae 4f
- fyl2xp1 // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
- FLT_CHECK_FORCE_UFLOW_NONNEG
- jecxz 3f
- fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
-3: ret
-
- .align ALIGNARG(4)
-4: faddl MO(one) // 1+2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
- fyl2x // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
- jecxz 3f
- fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
-3: ret
-
- .align ALIGNARG(4)
-2: faddl MO(one) // 1+|x| : |x| : 0.5*ln2
- fxch // |x| : 1+|x| : 0.5*ln2
- fsubrl MO(one) // 1-|x| : 1+|x| : 0.5*ln2
- fdivrp // (1+|x|)/(1-|x|) : 0.5*ln2
- fyl2x // 0.5*ln2*ld((1+|x|)/(1-|x|))
- jecxz 3f
- fchs // 0.5*ln2*ld((1+x)/(1-x))
-3: ret
-
- // x == NaN
-5: flds 4(%esp)
- ret
-END(__ieee754_atanhf)
-libm_alias_finite (__ieee754_atanhf, __atanhf)
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index b1f5b5f900..f0cc6594af 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -126,19 +126,16 @@ ldouble: 3
Function: "atanh_downward":
double: 1
-float: 1
float128: 4
ldouble: 4
Function: "atanh_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 3
Function: "atanh_upward":
double: 1
-float: 1
float128: 4
ldouble: 5
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index b651fd4fbf..8a56f383a9 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -126,19 +126,16 @@ ldouble: 3
Function: "atanh_downward":
double: 1
-float: 1
float128: 4
ldouble: 4
Function: "atanh_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 3
Function: "atanh_upward":
double: 1
-float: 1
float128: 4
ldouble: 5
diff --git a/sysdeps/ieee754/flt-32/e_atanhf.c b/sysdeps/ieee754/flt-32/e_atanhf.c
index d36eb15160..f6de5281ca 100644
--- a/sysdeps/ieee754/flt-32/e_atanhf.c
+++ b/sysdeps/ieee754/flt-32/e_atanhf.c
@@ -1,76 +1,176 @@
-/* Copyright (C) 2011-2024 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
+/* Correctly-rounded inverse hyperbolic tangent function for binary32 value.
- 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.
+Copyright (c) 2023-2024 Alexei Sibidanov.
- 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.
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/acosh/acoshf.c, revision bc385c2).
- 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/>. */
+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.
-/* __ieee754_atanh(x)
- Method :
- 1.Reduced x to positive by atanh(-x) = -atanh(x)
- 2.For x>=0.5
- 1 2x x
- atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
- 2 1 - x 1 - x
+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.
+*/
- For x<0.5
- atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
-
- Special cases:
- atanh(x) is NaN if |x| > 1 with signal;
- atanh(NaN) is that NaN with no signal;
- atanh(+-1) is +-INF with signal.
-
- */
-
-#include <float.h>
-#include <inttypes.h>
#include <math.h>
-#include <math-barriers.h>
-#include <math_private.h>
-#include <math-underflow.h>
+#include <stdint.h>
#include <libm-alias-finite.h>
+#include "math_config.h"
-static const float huge = 1e30;
+static __attribute__((noinline)) float
+as_special (float x)
+{
+ uint32_t ix = asuint (x);
+ uint32_t ax = ix << 1;
+ if (ax == 0x7f000000u) /* +-1 */
+ return __math_divzerof (ix >> 31);
+ if (ax > 0xff000000u)
+ return x + x; /* nan */
+ return __math_invalidf (x);
+}
float
__ieee754_atanhf (float x)
{
- float xa = fabsf (x);
- float t;
- if (isless (xa, 0.5f))
+ /* Calculate atanh(x) using the difference of two logarithms -- atanh(x) =
+ (ln(1+x) - ln(1-x))/2 */
+ static const double tr[] =
+ {
+ 0x1.fc07f02p-1, 0x1.f44659ep-1, 0x1.ecc07b3p-1, 0x1.e573ac9p-1,
+ 0x1.de5d6e4p-1, 0x1.d77b655p-1, 0x1.d0cb58fp-1, 0x1.ca4b305p-1,
+ 0x1.c3f8f02p-1, 0x1.bdd2b8ap-1, 0x1.b7d6c3ep-1, 0x1.b20364p-1,
+ 0x1.ac5701bp-1, 0x1.a6d01a7p-1, 0x1.a16d3f9p-1, 0x1.9c2d14fp-1,
+ 0x1.970e4f8p-1, 0x1.920fb4ap-1, 0x1.8d3018dp-1, 0x1.886e5f1p-1,
+ 0x1.83c977bp-1, 0x1.7f405fdp-1, 0x1.7ad2209p-1, 0x1.767dce4p-1,
+ 0x1.724287fp-1, 0x1.6e1f76bp-1, 0x1.6a13cd1p-1, 0x1.661ec6ap-1,
+ 0x1.623fa77p-1, 0x1.5e75bb9p-1, 0x1.5ac056bp-1, 0x1.571ed3cp-1,
+ 0x1.5390949p-1, 0x1.5015015p-1, 0x1.4cab887p-1, 0x1.49539e4p-1,
+ 0x1.460cbc8p-1, 0x1.42d6626p-1, 0x1.3fb014p-1, 0x1.3c995a4p-1,
+ 0x1.3991c2cp-1, 0x1.3698df4p-1, 0x1.33ae45bp-1, 0x1.30d1901p-1,
+ 0x1.2e025cp-1, 0x1.2b404adp-1, 0x1.288b013p-1, 0x1.25e2271p-1,
+ 0x1.2345679p-1, 0x1.20b470cp-1, 0x1.1e2ef3bp-1, 0x1.1bb4a4p-1,
+ 0x1.1945381p-1, 0x1.16e0689p-1, 0x1.1485f0ep-1, 0x1.12358e7p-1,
+ 0x1.0fef011p-1, 0x1.0db20a9p-1, 0x1.0b7e6ecp-1, 0x1.0953f39p-1,
+ 0x1.073260ap-1, 0x1.05197f8p-1, 0x1.03091b5p-1, 0x1.010101p-1
+ };
+ static const double tl[] =
+ {
+ 0x1.fe02a69106789p-9, 0x1.7b91b1155b11bp-7, 0x1.39e87ba1ebd6p-6,
+ 0x1.b42dd713971bfp-6, 0x1.16536ee637ae1p-5, 0x1.51b073c96183fp-5,
+ 0x1.8c345da019b21p-5, 0x1.c5e5492abc743p-5, 0x1.fec912fbbeabbp-5,
+ 0x1.1b72ad33f67ap-4, 0x1.371fc1f6e8f74p-4, 0x1.526e5e5a1b438p-4,
+ 0x1.6d60fe601d21dp-4, 0x1.87fa06438c911p-4, 0x1.a23bc223ab563p-4,
+ 0x1.bc28673a58cd6p-4, 0x1.d5c216b8fbb91p-4, 0x1.ef0adcaec5936p-4,
+ 0x1.040259530d041p-3, 0x1.1058bf8d24ad5p-3, 0x1.1c898c09d99fbp-3,
+ 0x1.2895a13e286a3p-3, 0x1.347dd9a447d55p-3, 0x1.404308716a7e4p-3,
+ 0x1.4be5f963b78a1p-3, 0x1.5767718015a6cp-3, 0x1.62c82f3a5c795p-3,
+ 0x1.6e08eab13a1e4p-3, 0x1.792a55fe147a2p-3, 0x1.842d1d9928b17p-3,
+ 0x1.8f11e873a62c7p-3, 0x1.99d958207e08bp-3, 0x1.a484090c1bb0ap-3,
+ 0x1.af129324b786bp-3, 0x1.b9858970710fbp-3, 0x1.c3dd7a6ddad4dp-3,
+ 0x1.ce1af0b65f3ebp-3, 0x1.d83e725022f3ep-3, 0x1.e2488197c6c26p-3,
+ 0x1.ec399d3d68ccp-3, 0x1.f6123fac028acp-3, 0x1.ffd2e07e7f498p-3,
+ 0x1.04bdf9e3b26d2p-2, 0x1.0986f4fa93521p-2, 0x1.0e4498651cc8cp-2,
+ 0x1.12f719595efbcp-2, 0x1.179eabb0a99a1p-2, 0x1.1c3b81e933c25p-2,
+ 0x1.20cdcd0e0ab6ep-2, 0x1.2555bcf50f7cbp-2, 0x1.29d37ff34b08bp-2,
+ 0x1.2e47437640268p-2, 0x1.32b1338401d71p-2, 0x1.37117b5c147b6p-2,
+ 0x1.3b6844a13fc23p-2, 0x1.3fb5b857f6f42p-2, 0x1.43f9fe2f7ce67p-2,
+ 0x1.48353d11488dfp-2, 0x1.4c679b014ee3ap-2, 0x1.50913cc03686bp-2,
+ 0x1.54b2468259498p-2, 0x1.58cadb57d7989p-2, 0x1.5cdb1dcaa1765p-2,
+ 0x1.60e32f46788d9p-2
+ };
+ static const double ln2n[] =
+ {
+ 0x1.62e42fedb2a44p-2, 0x1.62e42feeab21ap-1, 0x1.0a2b23f33e789p+0,
+ 0x1.62e42fef27604p+0, 0x1.bb9d3beb1048p+0, 0x1.0a2b23f37c97ep+1,
+ 0x1.3687a9f1710bcp+1, 0x1.62e42fef657fap+1, 0x1.8f40b5ed59f38p+1,
+ 0x1.bb9d3beb4e676p+1, 0x1.e7f9c1e942db4p+1, 0x1.0a2b23f39ba79p+2,
+ 0x1.205966f295e18p+2, 0x1.3687a9f1901b7p+2, 0x1.4cb5ecf08a556p+2,
+ 0x1.62e42fef848f5p+2, 0x1.791272ee7ec93p+2, 0x1.8f40b5ed79032p+2,
+ 0x1.a56ef8ec733d1p+2, 0x1.bb9d3beb6d77p+2, 0x1.d1cb7eea67b0fp+2,
+ 0x1.e7f9c1e961eaep+2, 0x1.fe2804e85c24dp+2, 0x1.0a2b23f3ab2f6p+3
+ };
+ static const double b[] =
{
- if (__glibc_unlikely (xa < 0x1.0p-28f))
+ 0x1.fffffffce5a6ap-2, -0x1.0001f81ec0ab8p-2, 0x1.555a0f53d79a5p-3
+ };
+ static const double s[] = { 1, -1 };
+
+ uint32_t ux = asuint (x);
+ uint32_t ax = ux << 1;
+ if (__glibc_unlikely (ax < 0x7a300000u || ax >= 0x7f000000u))
+ {
+ if (__glibc_unlikely (ax >= 0x7f000000u))
+ return as_special (x);
+ if (__glibc_unlikely (ax < 0x73713744u))
{
- math_force_eval (huge + x);
- math_check_force_underflow (x);
- return x;
+ if (ax == 0)
+ return x; /* x = +-0 */
+ return fmaf (x, 0x1p-25f, x); /* |x| < 0.000352112(0x1.713744p-12) */
+ }
+ else
+ { /* |x| < 0x1.3p-5 */
+ static const double c[] =
+ {
+ 0x1.5555555555527p-2, 0x1.9999999ba4ee8p-3,
+ 0x1.24922c280990ap-3, 0x1.c8236aae809c6p-4
+ };
+ double z = x;
+ double z2 = z * z;
+ double z4 = z2 * z2;
+ double r = c[0] + z2 * c[1] + z4 * (c[2] + z2 * c[3]);
+ return z + (z * z2) * r;
}
-
- t = xa + xa;
- t = 0.5f * __log1pf (t + t * xa / (1.0f - xa));
}
- else if (__glibc_likely (isless (xa, 1.0f)))
- t = 0.5f * __log1pf ((xa + xa) / (1.0f - xa));
- else
+ double sgn = s[ux >> 31];
+ unsigned int e = ax >> 24;
+ unsigned int md = ((ux << 8) | 1 << 31) >> (126 - e);
+ unsigned int mn = -md;
+ int nz = __builtin_clz (mn) + 1;
+ mn <<= nz;
+ unsigned jn = mn >> 26, jd = md >> 26;
+ double tn = asdouble (((int64_t) mn << 20) | (INT64_C(1023) << 52));
+ double td = asdouble (((int64_t) md << 20) | (INT64_C(1023) << 52));
+ double zn = tn * tr[jn] - 1;
+ double zd = td * tr[jd] - 1;
+ double zn2 = zn * zn;
+ double zd2 = zd * zd;
+ double rn = ((tl[jn] - ln2n[nz - 1]) + zn * b[0]) + zn2 * (b[1] + zn * b[2]);
+ double rd = (tl[jd] + zd * b[0]) + zd2 * (b[1] + zd * b[2]);
+ double r = sgn * (rd - rn);
+ float ub = r;
+ float lb = r + sgn * 0.226e-9;
+ if (__glibc_unlikely (ub != lb))
{
- if (isgreater (xa, 1.0f))
- return (x - x) / (x - x);
-
- return x / 0.0f;
+ static const double c[] =
+ {
+ 0x1p-1, -0x1.000000000001bp-2, 0x1.55555555555bap-3,
+ -0x1.fffffff26d72ep-4, 0x1.99999989035p-4, -0x1.555c39cb9ee8p-4,
+ 0x1.24992d8b014a1p-4
+ };
+ double zn4 = zn2 * zn2, zd4 = zd2 * zd2;
+ double fn = zn * (((c[0] + zn * c[1]) + zn2 * (c[2] + zn * c[3]))
+ + zn4 * ((c[4] + zn * c[5]) + zn2 * c[6]));
+ fn += 0x1.0ca86c3898dp-50 * nz;
+ fn += tl[jn];
+ double en = nz * 0x1.62e42fefa3ap-2;
+ double fd = zd * (((c[0] + zd * c[1]) + zd2 * (c[2] + zd * c[3]))
+ + zd4 * ((c[4] + zd * c[5]) + zd2 * c[6]));
+ fd += tl[jd];
+ r = fd - fn + en;
+ ub = sgn * r;
}
-
- return copysignf (t, x);
+ return ub;
}
libm_alias_finite (__ieee754_atanhf, __atanhf)
diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
index 2b726c95a9..08a3d63393 100644
--- a/sysdeps/loongarch/lp64/libm-test-ulps
+++ b/sysdeps/loongarch/lp64/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/m68k/coldfire/fpu/libm-test-ulps b/sysdeps/m68k/coldfire/fpu/libm-test-ulps
index 989015ff9a..998088f295 100644
--- a/sysdeps/m68k/coldfire/fpu/libm-test-ulps
+++ b/sysdeps/m68k/coldfire/fpu/libm-test-ulps
@@ -4,7 +4,6 @@
Function: "atan2":
Function: "atanh":
-float: 1
Function: Imaginary part of "cacosh":
float: 1
diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps
index 30eb8f1a0c..a6fa8376e1 100644
--- a/sysdeps/microblaze/libm-test-ulps
+++ b/sysdeps/microblaze/libm-test-ulps
@@ -17,7 +17,6 @@ Function: "atan2":
Function: "atanh":
double: 2
-float: 2
Function: "cabs":
double: 1
diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
index 6b0bf0e003..2487ffe183 100644
--- a/sysdeps/mips/mips32/libm-test-ulps
+++ b/sysdeps/mips/mips32/libm-test-ulps
@@ -74,19 +74,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
index 1ed68bb36d..0ce7c06b2b 100644
--- a/sysdeps/mips/mips64/libm-test-ulps
+++ b/sysdeps/mips/mips64/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
index 56485715bd..c673d62a62 100644
--- a/sysdeps/or1k/fpu/libm-test-ulps
+++ b/sysdeps/or1k/fpu/libm-test-ulps
@@ -74,19 +74,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
index 7ece256112..8e4801fe24 100644
--- a/sysdeps/or1k/nofpu/libm-test-ulps
+++ b/sysdeps/or1k/nofpu/libm-test-ulps
@@ -74,19 +74,15 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_downward":
double: 3
-float: 3
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "atanh_upward":
double: 3
-float: 3
Function: "cabs":
double: 1
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index 95e4d049ac..e394159703 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -126,25 +126,21 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
float128: 4
ldouble: 2
Function: "atanh_downward":
double: 3
-float: 3
float128: 4
ldouble: 3
Function: "atanh_towardzero":
double: 2
-float: 2
float128: 2
ldouble: 4
Function: "atanh_upward":
double: 3
-float: 3
float128: 4
ldouble: 4
diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
index 5d6a34115e..deec711353 100644
--- a/sysdeps/powerpc/nofpu/libm-test-ulps
+++ b/sysdeps/powerpc/nofpu/libm-test-ulps
@@ -102,22 +102,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 2
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 3
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 4
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
index ff1e792986..3a551201e7 100644
--- a/sysdeps/riscv/nofpu/libm-test-ulps
+++ b/sysdeps/riscv/nofpu/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
index 1a4577cd5c..2f89c82811 100644
--- a/sysdeps/riscv/rvd/libm-test-ulps
+++ b/sysdeps/riscv/rvd/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
index 4ff845bc0a..54a42a8c51 100644
--- a/sysdeps/s390/fpu/libm-test-ulps
+++ b/sysdeps/s390/fpu/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps
index d87533a5cc..3694110fc1 100644
--- a/sysdeps/sh/libm-test-ulps
+++ b/sysdeps/sh/libm-test-ulps
@@ -35,11 +35,9 @@ double: 1
Function: "atanh":
double: 2
-float: 2
Function: "atanh_towardzero":
double: 2
-float: 2
Function: "cabs":
double: 1
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 01e9cd360a..56a7a04480 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -98,22 +98,18 @@ ldouble: 2
Function: "atanh":
double: 2
-float: 2
ldouble: 4
Function: "atanh_downward":
double: 3
-float: 3
ldouble: 4
Function: "atanh_towardzero":
double: 2
-float: 2
ldouble: 2
Function: "atanh_upward":
double: 3
-float: 3
ldouble: 4
Function: "cabs":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 2a4b3bcfc6..74192a4c77 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -239,25 +239,21 @@ float: 1
Function: "atanh":
double: 2
-float: 2
float128: 4
ldouble: 3
Function: "atanh_downward":
double: 3
-float: 3
float128: 4
ldouble: 5
Function: "atanh_towardzero":
double: 2
-float: 2
float128: 2
ldouble: 4
Function: "atanh_upward":
double: 3
-float: 3
float128: 4
ldouble: 5
--
2.43.0
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