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math: Use atanhf from CORE-MATH
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> Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella
parent
6f9bacf36b
commit
7cfd8b5698
28 changed files with 161 additions and 252 deletions
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@ -318,3 +318,7 @@ sysdeps/ieee754/flt-32/e_atan2f.c:
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(src/binary32/atan2/atan2f.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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sysdeps/ieee754/flt-32/e_atanhf.c:
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(src/binary32/atanh/atanhf.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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@ -206,7 +206,6 @@ ldouble: 2
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Function: "atanh":
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double: 2
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float: 2
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ldouble: 4
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Function: "atanh_advsimd":
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@ -215,7 +214,6 @@ float: 1
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Function: "atanh_downward":
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double: 3
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float: 3
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ldouble: 4
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Function: "atanh_sve":
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@ -224,12 +222,10 @@ float: 1
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Function: "atanh_towardzero":
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double: 2
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float: 2
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ldouble: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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ldouble: 4
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Function: "atanpi":
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@ -98,22 +98,18 @@ ldouble: 2
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Function: "atanh":
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double: 2
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float: 2
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ldouble: 4
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Function: "atanh_downward":
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double: 3
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float: 3
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ldouble: 4
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Function: "atanh_towardzero":
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double: 2
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float: 2
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ldouble: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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ldouble: 4
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Function: "cabs":
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@ -75,19 +75,15 @@ double: 2
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Function: "atanh":
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double: 2
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float: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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Function: "cabs":
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double: 1
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@ -20,7 +20,6 @@ Function: "atan2":
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Function: "atanh":
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double: 2
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float: 2
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Function: "cabs":
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double: 1
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@ -122,19 +122,15 @@ double: 1
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Function: "atanh":
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double: 2
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float: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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Function: "atanpi":
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double: 1
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@ -71,19 +71,15 @@ double: 1
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Function: "atanh":
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double: 2
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float: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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Function: "cabs":
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double: 1
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@ -71,19 +71,15 @@ double: 1
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Function: "atanh":
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double: 2
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float: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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Function: "cabs":
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double: 1
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@ -122,19 +122,15 @@ double: 1
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Function: "atanh":
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double: 2
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float: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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Function: "atanpi":
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double: 1
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@ -1,110 +0,0 @@
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/* ix87 specific implementation of arctanh function.
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Copyright (C) 1996-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include <machine/asm.h>
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#include <i386-math-asm.h>
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#include <libm-alias-finite.h>
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.section .rodata
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.align ALIGNARG(4)
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.type half,@object
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half: .double 0.5
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ASM_SIZE_DIRECTIVE(half)
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.type one,@object
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one: .double 1.0
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ASM_SIZE_DIRECTIVE(one)
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.type limit,@object
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limit: .double 0.29
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ASM_SIZE_DIRECTIVE(limit)
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.align ALIGNARG(4)
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.type ln2_2,@object
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ln2_2: .quad 0xb17217f7d1cf79ac /* 0.3465735902799726547086160 */
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.short 0x3ffd
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ASM_SIZE_DIRECTIVE(ln2_2)
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DEFINE_FLT_MIN
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#ifdef PIC
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#define MO(op) op##@GOTOFF(%edx)
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#else
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#define MO(op) op
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#endif
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.text
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ENTRY(__ieee754_atanhf)
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movl 4(%esp), %ecx
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movl %ecx, %eax
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andl $0x7fffffff, %eax
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cmpl $0x7f800000, %eax
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ja 5f
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#ifdef PIC
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LOAD_PIC_REG (dx)
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#endif
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andl $0x80000000, %ecx // ECX == 0 iff X >= 0
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fldt MO(ln2_2) // 0.5*ln2
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xorl %ecx, 4(%esp)
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flds 4(%esp) // |x| : 0.5*ln2
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fcoml MO(half) // |x| : 0.5*ln2
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fld %st(0) // |x| : |x| : 0.5*ln2
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fnstsw // |x| : |x| : 0.5*ln2
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sahf
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jae 2f
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fadd %st, %st(1) // |x| : 2*|x| : 0.5*ln2
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fld %st // |x| : |x| : 2*|x| : 0.5*ln2
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fsubrl MO(one) // 1-|x| : |x| : 2*|x| : 0.5*ln2
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fxch // |x| : 1-|x| : 2*|x| : 0.5*ln2
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fmul %st(2) // 2*|x|^2 : 1-|x| : 2*|x| : 0.5*ln2
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fdivp // (2*|x|^2)/(1-|x|) : 2*|x| : 0.5*ln2
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faddp // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
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fcoml MO(limit) // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
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fnstsw // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
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sahf
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jae 4f
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fyl2xp1 // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
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FLT_CHECK_FORCE_UFLOW_NONNEG
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jecxz 3f
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fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
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3: ret
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.align ALIGNARG(4)
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4: faddl MO(one) // 1+2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
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fyl2x // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
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jecxz 3f
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fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
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3: ret
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.align ALIGNARG(4)
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2: faddl MO(one) // 1+|x| : |x| : 0.5*ln2
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fxch // |x| : 1+|x| : 0.5*ln2
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fsubrl MO(one) // 1-|x| : 1+|x| : 0.5*ln2
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fdivrp // (1+|x|)/(1-|x|) : 0.5*ln2
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fyl2x // 0.5*ln2*ld((1+|x|)/(1-|x|))
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jecxz 3f
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fchs // 0.5*ln2*ld((1+x)/(1-x))
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3: ret
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// x == NaN
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5: flds 4(%esp)
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ret
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END(__ieee754_atanhf)
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libm_alias_finite (__ieee754_atanhf, __atanhf)
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@ -198,19 +198,16 @@ ldouble: 3
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Function: "atanh_downward":
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double: 1
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float: 1
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float128: 4
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ldouble: 4
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Function: "atanh_towardzero":
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double: 1
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float: 1
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float128: 2
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ldouble: 3
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Function: "atanh_upward":
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double: 1
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float: 1
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float128: 4
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ldouble: 5
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@ -198,19 +198,16 @@ ldouble: 3
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Function: "atanh_downward":
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double: 1
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float: 1
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float128: 4
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ldouble: 4
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Function: "atanh_towardzero":
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double: 1
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float: 1
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float128: 2
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ldouble: 3
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Function: "atanh_upward":
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double: 1
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float: 1
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float128: 4
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ldouble: 5
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@ -1,76 +1,178 @@
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/* Copyright (C) 2011-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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/* Correctly-rounded inverse hyperbolic tangent function for binary32 value.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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Copyright (c) 2023-2024 Alexei Sibidanov.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/acosh/acoshf.c, revision bc385c2).
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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/* __ieee754_atanh(x)
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Method :
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1.Reduced x to positive by atanh(-x) = -atanh(x)
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2.For x>=0.5
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1 2x x
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atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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2 1 - x 1 - x
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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For x<0.5
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atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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Special cases:
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atanh(x) is NaN if |x| > 1 with signal;
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atanh(NaN) is that NaN with no signal;
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atanh(+-1) is +-INF with signal.
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*/
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#include <float.h>
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#include <inttypes.h>
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#include <math.h>
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#include <math-barriers.h>
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#include <math_private.h>
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#include <math-underflow.h>
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#include <stdint.h>
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#include <libm-alias-finite.h>
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#include "math_config.h"
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static const float huge = 1e30;
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static __attribute__((noinline)) float
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as_special (float x)
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{
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uint32_t ix = asuint (x);
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uint32_t ax = ix << 1;
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if (ax == 0x7f000000u) /* +-1 */
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return __math_divzerof (ix >> 31);
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if (ax > 0xff000000u)
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return x + x; /* nan */
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return __math_invalidf (x);
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}
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float
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__ieee754_atanhf (float x)
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{
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float xa = fabsf (x);
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float t;
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if (isless (xa, 0.5f))
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/* Calculate atanh(x) using the difference of two logarithms -- atanh(x) =
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(ln(1+x) - ln(1-x))/2 */
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static const double tr[] =
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{
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if (__glibc_unlikely (xa < 0x1.0p-28f))
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0x1.fc07f02p-1, 0x1.f44659ep-1, 0x1.ecc07b3p-1, 0x1.e573ac9p-1,
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0x1.de5d6e4p-1, 0x1.d77b655p-1, 0x1.d0cb58fp-1, 0x1.ca4b305p-1,
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0x1.c3f8f02p-1, 0x1.bdd2b8ap-1, 0x1.b7d6c3ep-1, 0x1.b20364p-1,
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0x1.ac5701bp-1, 0x1.a6d01a7p-1, 0x1.a16d3f9p-1, 0x1.9c2d14fp-1,
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0x1.970e4f8p-1, 0x1.920fb4ap-1, 0x1.8d3018dp-1, 0x1.886e5f1p-1,
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0x1.83c977bp-1, 0x1.7f405fdp-1, 0x1.7ad2209p-1, 0x1.767dce4p-1,
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0x1.724287fp-1, 0x1.6e1f76bp-1, 0x1.6a13cd1p-1, 0x1.661ec6ap-1,
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0x1.623fa77p-1, 0x1.5e75bb9p-1, 0x1.5ac056bp-1, 0x1.571ed3cp-1,
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0x1.5390949p-1, 0x1.5015015p-1, 0x1.4cab887p-1, 0x1.49539e4p-1,
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0x1.460cbc8p-1, 0x1.42d6626p-1, 0x1.3fb014p-1, 0x1.3c995a4p-1,
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0x1.3991c2cp-1, 0x1.3698df4p-1, 0x1.33ae45bp-1, 0x1.30d1901p-1,
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0x1.2e025cp-1, 0x1.2b404adp-1, 0x1.288b013p-1, 0x1.25e2271p-1,
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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[] =
|
||||
{
|
||||
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 int jn = mn >> 26;
|
||||
unsigned int 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;
|
||||
double 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)
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -4,7 +4,6 @@
|
|||
Function: "atan2":
|
||||
|
||||
Function: "atanh":
|
||||
float: 1
|
||||
|
||||
Function: Imaginary part of "cacosh":
|
||||
float: 1
|
||||
|
|
|
|||
|
|
@ -17,7 +17,6 @@ Function: "atan2":
|
|||
|
||||
Function: "atanh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cabs":
|
||||
double: 1
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -86,19 +86,15 @@ 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: "atanpi":
|
||||
double: 1
|
||||
|
|
|
|||
|
|
@ -198,25 +198,21 @@ 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
|
||||
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -35,11 +35,9 @@ double: 1
|
|||
|
||||
Function: "atanh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "atanh_towardzero":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cabs":
|
||||
double: 1
|
||||
|
|
|
|||
|
|
@ -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":
|
||||
|
|
|
|||
|
|
@ -311,25 +311,21 @@ 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
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue