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math: Use lgammaf from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance to the generic lgammaf. The code was adapted to glibc style, to use the definition of math_config.h, to remove errno handling, to use math_narrow_eval on overflow usage, and to adapt to make it reentrant. Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (M1, gcc 13.2.1), and powerpc (POWER10, gcc 13.2.1): latency master patched improvement x86_64 86.5609 70.3278 18.75% x86_64v2 78.3030 69.9709 10.64% x86_64v3 74.7470 59.8457 19.94% i686 387.355 229.761 40.68% aarch64 40.8341 33.7563 17.33% power10 26.5520 16.1672 39.11% powerpc 28.3145 17.0625 39.74% reciprocal-throughput master patched improvement x86_64 68.0461 48.3098 29.00% x86_64v2 55.3256 47.2476 14.60% x86_64v3 52.3015 38.9028 25.62% i686 340.848 195.707 42.58% aarch64 36.8000 30.5234 17.06% power10 20.4043 12.6268 38.12% powerpc 22.6588 13.8866 38.71% 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
baa495f231
commit
d846f4c12d
@ -280,3 +280,11 @@ sysdeps/ieee754/flt-32/s_erfcf.c
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(file src/binary32/erfc/erfcf.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_lgammaf_r.c:
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(file src/binary32/lgamma/lgammaf.c in CORE-MATH)
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- change the function name from cr_lgammaf to __ieee754_lgammaf_r
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- add "int *signgamp" as 2nd argument and add at the beginning:
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if (signgamp != NULL) *signgamp = 1;
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- remove the errno stuff (this is done by the wrapper)
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- replace 0x1p127f * 0x1p127f by math_narrow_eval (x * 0x1p127f)
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- add libm_alias_finite (__ieee754_lgammaf_r, __lgammaf_r) at the end
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@ -1288,22 +1288,18 @@ ldouble: 7
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Function: "lgamma":
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double: 3
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float: 4
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ldouble: 5
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Function: "lgamma_downward":
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double: 4
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float: 4
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ldouble: 8
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Function: "lgamma_towardzero":
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double: 4
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float: 3
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ldouble: 5
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Function: "lgamma_upward":
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double: 4
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float: 5
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ldouble: 8
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Function: "log":
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@ -1134,22 +1134,18 @@ ldouble: 7
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Function: "lgamma":
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double: 4
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float: 7
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ldouble: 5
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Function: "lgamma_downward":
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double: 5
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float: 7
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ldouble: 8
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Function: "lgamma_towardzero":
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double: 5
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float: 6
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ldouble: 5
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Function: "lgamma_upward":
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double: 5
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float: 6
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ldouble: 8
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Function: "log":
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@ -917,19 +917,15 @@ float: 9
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Function: "lgamma":
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double: 7
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float: 6
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Function: "lgamma_downward":
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double: 6
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float: 5
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Function: "lgamma_towardzero":
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double: 7
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float: 6
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Function: "lgamma_upward":
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double: 7
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float: 6
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Function: "log":
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double: 1
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@ -223,7 +223,6 @@ float: 4
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Function: "lgamma":
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double: 4
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float: 7
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Function: "log10":
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double: 2
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@ -911,19 +911,15 @@ float: 5
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Function: "lgamma":
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double: 4
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float: 7
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Function: "lgamma_downward":
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double: 5
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float: 7
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Function: "lgamma_towardzero":
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double: 5
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float: 6
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Function: "lgamma_upward":
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double: 5
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float: 6
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Function: "log":
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float: 1
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@ -875,19 +875,15 @@ float: 5
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Function: "lgamma":
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double: 4
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float: 7
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Function: "lgamma_downward":
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double: 5
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float: 7
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Function: "lgamma_towardzero":
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double: 5
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float: 6
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Function: "lgamma_upward":
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double: 5
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float: 6
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Function: "log10":
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double: 2
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@ -873,19 +873,15 @@ float: 5
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Function: "lgamma":
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double: 4
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float: 7
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Function: "lgamma_downward":
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double: 5
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float: 4
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Function: "lgamma_towardzero":
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double: 5
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float: 4
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Function: "lgamma_upward":
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double: 5
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float: 5
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Function: "log":
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float: 1
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@ -934,20 +934,16 @@ float: 5
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Function: "lgamma":
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double: 4
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float: 7
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ldouble: 1
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Function: "lgamma_downward":
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double: 5
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float: 7
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Function: "lgamma_towardzero":
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double: 5
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float: 6
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Function: "lgamma_upward":
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double: 5
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float: 6
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Function: "log":
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double: 1
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@ -1354,25 +1354,21 @@ ldouble: 5
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Function: "lgamma":
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double: 4
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float: 5
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float128: 5
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ldouble: 4
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Function: "lgamma_downward":
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double: 5
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float: 5
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float128: 8
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ldouble: 7
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Function: "lgamma_towardzero":
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double: 5
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float: 6
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float128: 5
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ldouble: 7
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Function: "lgamma_upward":
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double: 5
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float: 6
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float128: 8
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ldouble: 6
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@ -1357,7 +1357,6 @@ ldouble: 5
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Function: "lgamma":
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double: 4
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float: 5
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float128: 5
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ldouble: 4
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@ -1,247 +1,367 @@
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/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
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*/
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/* Correctly-rounded logarithm of the absolute value of the gamma function
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for binary32 value.
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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Copyright (c) 2023, 2024 Alexei Sibidanov.
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This file is part of the CORE-MATH project
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project (file src/binary32/lgamma/lgammaf.c, revision bc385c2).
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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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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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/* Changes with respect to the original CORE-MATH code:
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- removed the dealing with errno
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(this is done in the wrapper math/w_lgammaf_compat2.c).
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- usage of math_narrow_eval to deal with underflow/overflow.
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- deal with signamp. */
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#include <array_length.h>
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#include <stdint.h>
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <libc-diag.h>
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#include <libm-alias-finite.h>
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#include <limits.h>
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#include <math-narrow-eval.h>
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#include "math_config.h"
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static const float
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two23= 8.3886080000e+06, /* 0x4b000000 */
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half= 5.0000000000e-01, /* 0x3f000000 */
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one = 1.0000000000e+00, /* 0x3f800000 */
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pi = 3.1415927410e+00, /* 0x40490fdb */
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a0 = 7.7215664089e-02, /* 0x3d9e233f */
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a1 = 3.2246702909e-01, /* 0x3ea51a66 */
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a2 = 6.7352302372e-02, /* 0x3d89f001 */
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a3 = 2.0580807701e-02, /* 0x3ca89915 */
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a4 = 7.3855509982e-03, /* 0x3bf2027e */
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a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
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a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
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a7 = 5.1006977446e-04, /* 0x3a05b634 */
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a8 = 2.2086278477e-04, /* 0x39679767 */
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a9 = 1.0801156895e-04, /* 0x38e28445 */
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a10 = 2.5214456400e-05, /* 0x37d383a2 */
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a11 = 4.4864096708e-05, /* 0x383c2c75 */
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tc = 1.4616321325e+00, /* 0x3fbb16c3 */
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tf = -1.2148628384e-01, /* 0xbdf8cdcd */
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/* tt = -(tail of tf) */
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tt = 6.6971006518e-09, /* 0x31e61c52 */
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t0 = 4.8383611441e-01, /* 0x3ef7b95e */
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t1 = -1.4758771658e-01, /* 0xbe17213c */
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t2 = 6.4624942839e-02, /* 0x3d845a15 */
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t3 = -3.2788541168e-02, /* 0xbd064d47 */
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t4 = 1.7970675603e-02, /* 0x3c93373d */
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t5 = -1.0314224288e-02, /* 0xbc28fcfe */
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t6 = 6.1005386524e-03, /* 0x3bc7e707 */
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t7 = -3.6845202558e-03, /* 0xbb7177fe */
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t8 = 2.2596477065e-03, /* 0x3b141699 */
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t9 = -1.4034647029e-03, /* 0xbab7f476 */
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t10 = 8.8108185446e-04, /* 0x3a66f867 */
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t11 = -5.3859531181e-04, /* 0xba0d3085 */
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t12 = 3.1563205994e-04, /* 0x39a57b6b */
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t13 = -3.1275415677e-04, /* 0xb9a3f927 */
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t14 = 3.3552918467e-04, /* 0x39afe9f7 */
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u0 = -7.7215664089e-02, /* 0xbd9e233f */
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u1 = 6.3282704353e-01, /* 0x3f2200f4 */
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u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
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u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
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u4 = 2.2896373272e-01, /* 0x3e6a7578 */
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u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
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v1 = 2.4559779167e+00, /* 0x401d2ebe */
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v2 = 2.1284897327e+00, /* 0x4008392d */
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v3 = 7.6928514242e-01, /* 0x3f44efdf */
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v4 = 1.0422264785e-01, /* 0x3dd572af */
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v5 = 3.2170924824e-03, /* 0x3b52d5db */
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s0 = -7.7215664089e-02, /* 0xbd9e233f */
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s1 = 2.1498242021e-01, /* 0x3e5c245a */
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s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
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s3 = 1.4635047317e-01, /* 0x3e15dce6 */
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s4 = 2.6642270386e-02, /* 0x3cda40e4 */
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s5 = 1.8402845599e-03, /* 0x3af135b4 */
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s6 = 3.1947532989e-05, /* 0x3805ff67 */
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r1 = 1.3920053244e+00, /* 0x3fb22d3b */
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r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
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r3 = 1.7193385959e-01, /* 0x3e300f6e */
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r4 = 1.8645919859e-02, /* 0x3c98bf54 */
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r5 = 7.7794247773e-04, /* 0x3a4beed6 */
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r6 = 7.3266842264e-06, /* 0x36f5d7bd */
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w0 = 4.1893854737e-01, /* 0x3ed67f1d */
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w1 = 8.3333335817e-02, /* 0x3daaaaab */
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w2 = -2.7777778450e-03, /* 0xbb360b61 */
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w3 = 7.9365057172e-04, /* 0x3a500cfd */
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w4 = -5.9518753551e-04, /* 0xba1c065c */
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w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
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w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
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static const float zero= 0.0000000000e+00;
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static float
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sin_pif(float x)
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static double
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as_r7 (double x, const double *c)
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{
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float y,z;
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int n,ix;
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GET_FLOAT_WORD(ix,x);
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ix &= 0x7fffffff;
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if(ix<0x3e800000) return __sinf (pi*x);
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y = -x; /* x is assume negative */
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/*
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* argument reduction, make sure inexact flag not raised if input
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* is an integer
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*/
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z = floorf(y);
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if(z!=y) { /* inexact anyway */
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y *= (float)0.5;
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y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
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n = (int) (y*(float)4.0);
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} else {
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if(ix>=0x4b800000) {
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y = zero; n = 0; /* y must be even */
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} else {
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if(ix<0x4b000000) z = y+two23; /* exact */
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GET_FLOAT_WORD(n,z);
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n &= 1;
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y = n;
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n<<= 2;
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}
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}
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switch (n) {
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case 0: y = __sinf (pi*y); break;
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case 1:
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case 2: y = __cosf (pi*((float)0.5-y)); break;
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case 3:
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case 4: y = __sinf (pi*(one-y)); break;
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case 5:
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case 6: y = -__cosf (pi*(y-(float)1.5)); break;
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default: y = __sinf (pi*(y-(float)2.0)); break;
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}
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return -y;
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return (((x - c[0]) * (x - c[1])) * ((x - c[2]) * (x - c[3])))
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* (((x - c[4]) * (x - c[5])) * ((x - c[6])));
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}
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static double
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as_r8 (double x, const double *c)
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{
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return (((x - c[0]) * (x - c[1])) * ((x - c[2]) * (x - c[3])))
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* (((x - c[4]) * (x - c[5])) * ((x - c[6]) * (x - c[7])));
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}
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static double
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as_sinpi (double x)
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{
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static const double c[] =
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{
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0x1p+2, -0x1.de9e64df22ea4p+1, 0x1.472be122401f8p+0,
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-0x1.d4fcd82df91bp-3, 0x1.9f05c97e0aab2p-6, -0x1.f3091c427b611p-10,
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0x1.b22c9bfdca547p-14, -0x1.15484325ef569p-18
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};
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x -= 0.5;
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double x2 = x * x, x4 = x2 * x2, x8 = x4 * x4;
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return (0.25 - x2)
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* ((c[0] + x2 * c[1]) + x4 * (c[2] + x2 * c[3])
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+ x8 * ((c[4] + x2 * c[5]) + x4 * (c[6] + x2 * c[7])));
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}
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static double
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as_ln (double x)
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{
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uint64_t t = asuint64 (x);
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int e = (t >> 52) - 0x3ff;
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static const double c[] =
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{
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0x1.fffffffffff24p-1, -0x1.ffffffffd1d67p-2, 0x1.55555537802dep-2,
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-0x1.ffffeca81b866p-3, 0x1.999611761d772p-3, -0x1.54f3e581b61bfp-3,
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0x1.1e642b4cb5143p-3, -0x1.9115a5af1e1edp-4
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};
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static const double il[] =
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{
|
||||
0x1.59caeec280116p-57, 0x1.f0a30c01162aap-5, 0x1.e27076e2af2ebp-4,
|
||||
0x1.5ff3070a793d6p-3, 0x1.c8ff7c79a9a2p-3, 0x1.1675cababa60fp-2,
|
||||
0x1.4618bc21c5ec2p-2, 0x1.739d7f6bbd007p-2, 0x1.9f323ecbf984dp-2,
|
||||
0x1.c8ff7c79a9a21p-2, 0x1.f128f5faf06ecp-2, 0x1.0be72e4252a83p-1,
|
||||
0x1.1e85f5e7040d1p-1, 0x1.307d7334f10bep-1, 0x1.41d8fe84672afp-1,
|
||||
0x1.52a2d265bc5abp-1
|
||||
};
|
||||
static const double ix[] =
|
||||
{
|
||||
0x1p+0, 0x1.e1e1e1e1e1e1ep-1, 0x1.c71c71c71c71cp-1,
|
||||
0x1.af286bca1af28p-1, 0x1.999999999999ap-1, 0x1.8618618618618p-1,
|
||||
0x1.745d1745d1746p-1, 0x1.642c8590b2164p-1, 0x1.5555555555555p-1,
|
||||
0x1.47ae147ae147bp-1, 0x1.3b13b13b13b14p-1, 0x1.2f684bda12f68p-1,
|
||||
0x1.2492492492492p-1, 0x1.1a7b9611a7b96p-1, 0x1.1111111111111p-1,
|
||||
0x1.0842108421084p-1
|
||||
};
|
||||
int i = (t >> 48) & 0xf;
|
||||
t = (t & (~UINT64_C(0) >> 12)) | (INT64_C(0x3ff) << 52);
|
||||
double z = ix[i] * asdouble (t) - 1;
|
||||
double z2 = z * z, z4 = z2 * z2;
|
||||
return e * 0x1.62e42fefa39efp-1 + il[i]
|
||||
+ z * ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])
|
||||
+ z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])));
|
||||
}
|
||||
|
||||
float
|
||||
__ieee754_lgammaf_r(float x, int *signgamp)
|
||||
__ieee754_lgammaf_r (float x, int *signgamp)
|
||||
{
|
||||
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,ix;
|
||||
static const struct
|
||||
{
|
||||
float x;
|
||||
float f;
|
||||
float df;
|
||||
} tb[] = {
|
||||
{ -0x1.efc2a2p+14, -0x1.222dbcp+18, -0x1p-7 },
|
||||
{ -0x1.627346p+7, -0x1.73235ep+9, -0x1p-16 },
|
||||
{ -0x1.08b14p+4, -0x1.f0cbe6p+4, -0x1p-21 },
|
||||
{ -0x1.69d628p+3, -0x1.0eac2ap+4, -0x1p-21 },
|
||||
{ -0x1.904902p+2, -0x1.65532cp+2, 0x1p-23 },
|
||||
{ -0x1.9272d2p+1, -0x1.170b98p-8, 0x1p-33 },
|
||||
{ -0x1.625edap+1, 0x1.6a6c4ap-5, -0x1p-30 },
|
||||
{ -0x1.5fc2aep+1, 0x1.c0a484p-11, -0x1p-36 },
|
||||
{ -0x1.5fb43ep+1, 0x1.5b697p-17, 0x1p-42 },
|
||||
{ -0x1.5fa20cp+1, -0x1.132f7ap-10, 0x1p-35 },
|
||||
{ -0x1.580c1ep+1, -0x1.5787c6p-4, 0x1p-29 },
|
||||
{ -0x1.3a7fcap+1, -0x1.e4cf24p-24, -0x1p-49 },
|
||||
{ -0x1.c2f04p-30, 0x1.43a6f6p+4, 0x1p-21 },
|
||||
{ -0x1.ade594p-30, 0x1.446ab2p+4, -0x1p-21 },
|
||||
{ -0x1.437e74p-40, 0x1.b7dec2p+4, -0x1p-21 },
|
||||
{ -0x1.d85bfep-43, 0x1.d31592p+4, -0x1p-21 },
|
||||
{ -0x1.f51c8ep-49, 0x1.0a572ap+5, -0x1p-20 },
|
||||
{ -0x1.108a5ap-66, 0x1.6d7b18p+5, -0x1p-20 },
|
||||
{ -0x1.ecf3fep-73, 0x1.8f8e5ap+5, -0x1p-20 },
|
||||
{ -0x1.25cb66p-123, 0x1.547a44p+6, -0x1p-19 },
|
||||
{ 0x1.ecf3fep-73, 0x1.8f8e5ap+5, -0x1p-20 },
|
||||
{ 0x1.108a5ap-66, 0x1.6d7b18p+5, -0x1p-20 },
|
||||
{ 0x1.a68bbcp-42, 0x1.c9c6e8p+4, 0x1p-21 },
|
||||
{ 0x1.ddfd06p-12, 0x1.ec5ba8p+2, -0x1p-23 },
|
||||
{ 0x1.f8a754p-9, 0x1.63acc2p+2, 0x1p-23 },
|
||||
{ 0x1.8d16b2p+5, 0x1.1e4b4ep+7, 0x1p-18 },
|
||||
{ 0x1.359e0ep+10, 0x1.d9ad02p+12, -0x1p-13 },
|
||||
{ 0x1.a82a2cp+13, 0x1.c38036p+16, 0x1p-9 },
|
||||
{ 0x1.62c646p+14, 0x1.9075bep+17, -0x1p-8 },
|
||||
{ 0x1.7f298p+31, 0x1.f44946p+35, -0x1p+10 },
|
||||
{ 0x1.a45ea4p+33, 0x1.25dcbcp+38, -0x1p+13 },
|
||||
{ 0x1.f9413ep+76, 0x1.9d5ab4p+82, -0x1p+57 },
|
||||
{ 0x1.dcbbaap+99, 0x1.fc5772p+105, 0x1p+80 },
|
||||
{ 0x1.58ace8p+112, 0x1.9e4f66p+118, -0x1p+93 },
|
||||
{ 0x1.87bdfp+115, 0x1.e465aep+121, 0x1p+96 },
|
||||
};
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(__builtin_expect(ix>=0x7f800000, 0)) return x*x;
|
||||
if(__builtin_expect(ix==0, 0))
|
||||
{
|
||||
if (hx < 0)
|
||||
*signgamp = -1;
|
||||
return one/fabsf(x);
|
||||
}
|
||||
if(__builtin_expect(ix<0x30800000, 0)) {
|
||||
/* |x|<2**-30, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_logf(-x);
|
||||
} else return -__ieee754_logf(x);
|
||||
float fx = floor (x);
|
||||
float ax = fabsf (x);
|
||||
uint32_t t = asuint (ax);
|
||||
if (__glibc_unlikely (t >= (0xffu << 23)))
|
||||
{
|
||||
*signgamp = 1;
|
||||
if (t == (0xffu << 23))
|
||||
return INFINITY;
|
||||
return x + x; /* nan */
|
||||
}
|
||||
if (__glibc_unlikely (fx == x))
|
||||
{
|
||||
if (x <= 0.0f)
|
||||
{
|
||||
*signgamp = asuint (x) >> 31 ? -1 : 1;
|
||||
return 1.0f / 0.0f;
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
|
||||
return fabsf (x)/zero;
|
||||
if (ix > 0x40000000 /* X < 2.0f. */
|
||||
&& ix < 0x41700000 /* X > -15.0f. */)
|
||||
return __lgamma_negf (x, signgamp);
|
||||
t = sin_pif(x);
|
||||
if(t==zero) return one/fabsf(t); /* -integer */
|
||||
nadj = __ieee754_logf(pi/fabsf(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
if (x == 1.0f || x == 2.0f)
|
||||
{
|
||||
*signgamp = 1;
|
||||
return 0.0f;
|
||||
}
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if (ix==0x3f800000||ix==0x40000000) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_logf(x);
|
||||
if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
/* Check the value of fx to avoid a spurious invalid exception.
|
||||
Note that for a binary32 |x| >= 2^23, x is necessarily an integer,
|
||||
and we already dealed with negative integers, thus now:
|
||||
-2^23 < x < +Inf and x is not a negative integer nor 0, 1, 2. */
|
||||
int k;
|
||||
if (__builtin_expect (fx >= 0x1p31f, 0))
|
||||
k = INT_MAX;
|
||||
else
|
||||
k = fx;
|
||||
*signgamp = 1 - (((k & (k >> 31)) & 1) << 1);
|
||||
|
||||
double z = ax, f;
|
||||
if (__glibc_unlikely (ax < 0x1.52p-1f))
|
||||
{
|
||||
static const double rn[] =
|
||||
{
|
||||
-0x1.505bdf4b65acp+4, -0x1.51c80eb47e068p+2,
|
||||
0x1.0000000007cb8p+0, -0x1.4ac529250a1fcp+1,
|
||||
-0x1.a8c99dbe1621ap+0, -0x1.4abdcc74115eap+0,
|
||||
-0x1.1b87fe5a5b923p+0, -0x1.05b8a4d47ff64p+0
|
||||
};
|
||||
const double c0 = 0x1.0fc0fad268c4dp+2;
|
||||
static const double rd[] =
|
||||
{
|
||||
-0x1.4db2cfe9a5265p+5, -0x1.062e99d1c4f27p+3,
|
||||
-0x1.c81bc2ecf25f6p+1, -0x1.108e55c10091bp+1,
|
||||
-0x1.7dd25af0b83d4p+0, -0x1.36bf1880125fcp+0,
|
||||
-0x1.1379fc8023d9cp+0, -0x1.03712e41525d2p+0
|
||||
};
|
||||
double s = x;
|
||||
f = (c0 * s) * as_r8 (s, rn) / as_r8 (s, rd) - as_ln (z);
|
||||
}
|
||||
else
|
||||
{
|
||||
if (ax > 0x1.afc1ap+1f)
|
||||
{
|
||||
if (__glibc_unlikely (x > 0x1.895f1cp+121f))
|
||||
return math_narrow_eval (0x1p127f * 0x1p127f);
|
||||
/* |x|>=2**23, must be -integer */
|
||||
if (__glibc_unlikely (x < 0.0f && ax > 0x1p+23))
|
||||
return ax / 0.0f;
|
||||
double lz = as_ln (z);
|
||||
f = (z - 0.5) * (lz - 1) + 0x1.acfe390c97d69p-2;
|
||||
if (ax < 0x1.0p+20f)
|
||||
{
|
||||
double iz = 1.0 / z, iz2 = iz * iz;
|
||||
if (ax > 1198.0f)
|
||||
f += iz * (1. / 12.);
|
||||
else if (ax > 0x1.279a7p+6f)
|
||||
{
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.555555547fbadp-4, -0x1.6c0fd270c465p-9
|
||||
};
|
||||
f += iz * (c[0] + iz2 * c[1]);
|
||||
}
|
||||
else if (ax > 0x1.555556p+3f)
|
||||
{
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.555555554de0bp-4, -0x1.6c16bdc45944fp-9,
|
||||
0x1.a0077f300ecb3p-11, -0x1.2e9cfff3b29c2p-11
|
||||
};
|
||||
double iz4 = iz2 * iz2;
|
||||
f += iz * ((c[0] + iz2 * c[1]) + iz4 * (c[2] + iz2 * c[3]));
|
||||
}
|
||||
else
|
||||
{
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.5555555551286p-4, -0x1.6c16c0e7c4cf4p-9,
|
||||
0x1.a0193267fe6f2p-11, -0x1.37e87ec19cb45p-11,
|
||||
0x1.b40011dfff081p-11, -0x1.c16c8946b19b6p-10,
|
||||
0x1.e9f47ace150d8p-9, -0x1.4f5843a71a338p-8
|
||||
};
|
||||
double iz4 = iz2 * iz2, iz8 = iz4 * iz4;
|
||||
double p = ((c[0] + iz2 * c[1]) + iz4 * (c[2] + iz2 * c[3]))
|
||||
+ iz8 * ((c[4] + iz2 * c[5])
|
||||
+ iz4 * (c[6] + iz2 * c[7]));
|
||||
f += iz * p;
|
||||
}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-(float)0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-(float)0.5*y + p1/p2);
|
||||
if (x < 0.0f)
|
||||
{
|
||||
f = 0x1.250d048e7a1bdp+0 - f - lz;
|
||||
double lp = as_ln (as_sinpi (x - fx));
|
||||
f -= lp;
|
||||
}
|
||||
}
|
||||
else if(ix<0x41000000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(float)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+(float)6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+(float)5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+(float)4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+(float)3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+(float)2.0); /* FALLTHRU */
|
||||
r += __ieee754_logf(z); break;
|
||||
else
|
||||
{
|
||||
static const double rn[] =
|
||||
{
|
||||
-0x1.667923ff14df7p+5, -0x1.2d35f25ad8f64p+3,
|
||||
-0x1.b8c9eab9d5bd3p+1, -0x1.7a4a97f494127p+0,
|
||||
-0x1.3a6c8295b4445p-1, -0x1.da44e8b810024p-3,
|
||||
-0x1.9061e81c77e4ap-5
|
||||
};
|
||||
if (x < 0.0f)
|
||||
{
|
||||
int ni = floorf (-2 * x);
|
||||
if ((ni & 1) == 0 && ni == -2 * x)
|
||||
return 1.0f / 0.0f;
|
||||
}
|
||||
/* 8.0 <= x < 2**26 */
|
||||
} else if (ix < 0x4c800000) {
|
||||
t = __ieee754_logf(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**26 <= x <= inf */
|
||||
r = math_narrow_eval (x*(__ieee754_logf(x)-one));
|
||||
/* NADJ is set for negative arguments but not otherwise,
|
||||
resulting in warnings that it may be used uninitialized
|
||||
although in the cases where it is used it has always been
|
||||
set. */
|
||||
DIAG_PUSH_NEEDS_COMMENT;
|
||||
DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized");
|
||||
if(hx<0) r = nadj - r;
|
||||
DIAG_POP_NEEDS_COMMENT;
|
||||
return r;
|
||||
const double c0 = 0x1.3cc0e6a0106b3p+2;
|
||||
static const double rd[] =
|
||||
{
|
||||
-0x1.491a899e84c52p+6, -0x1.d202961b9e098p+3,
|
||||
-0x1.4ced68c631ed6p+2, -0x1.2589eedf40738p+1,
|
||||
-0x1.1302e3337271p+0, -0x1.c36b802f26dffp-2,
|
||||
-0x1.3ded448acc39dp-3, -0x1.bffc491078eafp-6
|
||||
};
|
||||
f = (z - 1) * (z - 2) * c0 * as_r7 (z, rn) / as_r8 (z, rd);
|
||||
if (x < 0.0f)
|
||||
{
|
||||
if (__glibc_unlikely (t < 0x40301b93u && t > 0x402f95c2u))
|
||||
{
|
||||
double h = (x + 0x1.5fb410a1bd901p+1)
|
||||
- 0x1.a19a96d2e6f85p-54;
|
||||
double h2 = h * h;
|
||||
double h4 = h2 * h2;
|
||||
static const double c[] =
|
||||
{
|
||||
-0x1.ea12da904b18cp+0, 0x1.3267f3c265a54p+3,
|
||||
-0x1.4185ac30cadb3p+4, 0x1.f504accc3f2e4p+5,
|
||||
-0x1.8588444c679b4p+7, 0x1.43740491dc22p+9,
|
||||
-0x1.12400ea23f9e6p+11, 0x1.dac829f365795p+12
|
||||
};
|
||||
f = h * ((c[0] + h * c[1]) + h2 * (c[2] + h * c[3])
|
||||
+ h4 * ((c[4] + h * c[5]) + h2 * (c[6] + h * c[7])));
|
||||
}
|
||||
else if (__glibc_unlikely (t > 0x401ceccbu && t < 0x401d95cau))
|
||||
{
|
||||
double h = (x + 0x1.3a7fc9600f86cp+1)
|
||||
+ 0x1.55f64f98af8dp-55;
|
||||
double h2 = h * h;
|
||||
double h4 = h2 * h2;
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.83fe966af535fp+0, 0x1.36eebb002f61ap+2,
|
||||
0x1.694a60589a0b3p+0, 0x1.1718d7aedb0b5p+3,
|
||||
0x1.733a045eca0d3p+2, 0x1.8d4297421205bp+4,
|
||||
0x1.7feea5fb29965p+4
|
||||
};
|
||||
f = h
|
||||
* ((c[0] + h * c[1]) + h2 * (c[2] + h * c[3])
|
||||
+ h4 * ((c[4] + h * c[5]) + h2 * (c[6])));
|
||||
}
|
||||
else if (__glibc_unlikely (t > 0x40492009u && t < 0x404940efu))
|
||||
{
|
||||
double h = (x + 0x1.9260dbc9e59afp+1)
|
||||
+ 0x1.f717cd335a7b3p-53;
|
||||
double h2 = h * h;
|
||||
double h4 = h2 * h2;
|
||||
static const double c[] =
|
||||
{
|
||||
0x1.f20a65f2fac55p+2, 0x1.9d4d297715105p+4,
|
||||
0x1.c1137124d5b21p+6, 0x1.267203d24de38p+9,
|
||||
0x1.99a63399a0b44p+11, 0x1.2941214faaf0cp+14,
|
||||
0x1.bb912c0c9cdd1p+16
|
||||
};
|
||||
f = h * ((c[0] + h * c[1]) + h2 * (c[2] + h * c[3])
|
||||
+ h4 * ((c[4] + h * c[5]) + h2 * (c[6])));
|
||||
}
|
||||
else
|
||||
{
|
||||
f = 0x1.250d048e7a1bdp+0 - f;
|
||||
double lp = as_ln (as_sinpi (x - fx) * z);
|
||||
f -= lp;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
uint64_t tl = (asuint64 (f) + 5) & 0xfffffff;
|
||||
float r = f;
|
||||
if (__glibc_unlikely (tl <= 31u))
|
||||
{
|
||||
t = asuint (x);
|
||||
for (unsigned i = 0; i < array_length (tb); i++)
|
||||
{
|
||||
if (t == asuint (tb[i].x))
|
||||
return tb[i].f + tb[i].df;
|
||||
}
|
||||
}
|
||||
return r;
|
||||
}
|
||||
libm_alias_finite (__ieee754_lgammaf_r, __lgammaf_r)
|
||||
|
||||
@ -1,282 +1 @@
|
||||
/* lgammaf expanding around zeros.
|
||||
Copyright (C) 2015-2024 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 <float.h>
|
||||
#include <math.h>
|
||||
#include <math-narrow-eval.h>
|
||||
#include <math_private.h>
|
||||
#include <fenv_private.h>
|
||||
|
||||
static const float lgamma_zeros[][2] =
|
||||
{
|
||||
{ -0x2.74ff94p+0f, 0x1.3fe0f2p-24f },
|
||||
{ -0x2.bf682p+0f, -0x1.437b2p-24f },
|
||||
{ -0x3.24c1b8p+0f, 0x6.c34cap-28f },
|
||||
{ -0x3.f48e2cp+0f, 0x1.707a04p-24f },
|
||||
{ -0x4.0a13ap+0f, 0x1.e99aap-24f },
|
||||
{ -0x4.fdd5ep+0f, 0x1.64454p-24f },
|
||||
{ -0x5.021a98p+0f, 0x2.03d248p-24f },
|
||||
{ -0x5.ffa4cp+0f, 0x2.9b82fcp-24f },
|
||||
{ -0x6.005ac8p+0f, -0x1.625f24p-24f },
|
||||
{ -0x6.fff3p+0f, 0x2.251e44p-24f },
|
||||
{ -0x7.000dp+0f, 0x8.48078p-28f },
|
||||
{ -0x7.fffe6p+0f, 0x1.fa98c4p-28f },
|
||||
{ -0x8.0001ap+0f, -0x1.459fcap-28f },
|
||||
{ -0x8.ffffdp+0f, -0x1.c425e8p-24f },
|
||||
{ -0x9.00003p+0f, 0x1.c44b82p-24f },
|
||||
{ -0xap+0f, 0x4.9f942p-24f },
|
||||
{ -0xap+0f, -0x4.9f93b8p-24f },
|
||||
{ -0xbp+0f, 0x6.b9916p-28f },
|
||||
{ -0xbp+0f, -0x6.b9915p-28f },
|
||||
{ -0xcp+0f, 0x8.f76c8p-32f },
|
||||
{ -0xcp+0f, -0x8.f76c7p-32f },
|
||||
{ -0xdp+0f, 0xb.09231p-36f },
|
||||
{ -0xdp+0f, -0xb.09231p-36f },
|
||||
{ -0xep+0f, 0xc.9cba5p-40f },
|
||||
{ -0xep+0f, -0xc.9cba5p-40f },
|
||||
{ -0xfp+0f, 0xd.73f9fp-44f },
|
||||
};
|
||||
|
||||
static const float e_hi = 0x2.b7e15p+0f, e_lo = 0x1.628aeep-24f;
|
||||
|
||||
/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's
|
||||
approximation to lgamma function. */
|
||||
|
||||
static const float lgamma_coeff[] =
|
||||
{
|
||||
0x1.555556p-4f,
|
||||
-0xb.60b61p-12f,
|
||||
0x3.403404p-12f,
|
||||
};
|
||||
|
||||
#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0]))
|
||||
|
||||
/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is
|
||||
the integer end-point of the half-integer interval containing x and
|
||||
x0 is the zero of lgamma in that half-integer interval. Each
|
||||
polynomial is expressed in terms of x-xm, where xm is the midpoint
|
||||
of the interval for which the polynomial applies. */
|
||||
|
||||
static const float poly_coeff[] =
|
||||
{
|
||||
/* Interval [-2.125, -2] (polynomial degree 5). */
|
||||
-0x1.0b71c6p+0f,
|
||||
-0xc.73a1ep-4f,
|
||||
-0x1.ec8462p-4f,
|
||||
-0xe.37b93p-4f,
|
||||
-0x1.02ed36p-4f,
|
||||
-0xe.cbe26p-4f,
|
||||
/* Interval [-2.25, -2.125] (polynomial degree 5). */
|
||||
-0xf.29309p-4f,
|
||||
-0xc.a5cfep-4f,
|
||||
0x3.9c93fcp-4f,
|
||||
-0x1.02a2fp+0f,
|
||||
0x9.896bep-4f,
|
||||
-0x1.519704p+0f,
|
||||
/* Interval [-2.375, -2.25] (polynomial degree 5). */
|
||||
-0xd.7d28dp-4f,
|
||||
-0xe.6964cp-4f,
|
||||
0xb.0d4f1p-4f,
|
||||
-0x1.9240aep+0f,
|
||||
0x1.dadabap+0f,
|
||||
-0x3.1778c4p+0f,
|
||||
/* Interval [-2.5, -2.375] (polynomial degree 6). */
|
||||
-0xb.74ea2p-4f,
|
||||
-0x1.2a82cp+0f,
|
||||
0x1.880234p+0f,
|
||||
-0x3.320c4p+0f,
|
||||
0x5.572a38p+0f,
|
||||
-0x9.f92bap+0f,
|
||||
0x1.1c347ep+4f,
|
||||
/* Interval [-2.625, -2.5] (polynomial degree 6). */
|
||||
-0x3.d10108p-4f,
|
||||
0x1.cd5584p+0f,
|
||||
0x3.819c24p+0f,
|
||||
0x6.84cbb8p+0f,
|
||||
0xb.bf269p+0f,
|
||||
0x1.57fb12p+4f,
|
||||
0x2.7b9854p+4f,
|
||||
/* Interval [-2.75, -2.625] (polynomial degree 6). */
|
||||
-0x6.b5d25p-4f,
|
||||
0x1.28d604p+0f,
|
||||
0x1.db6526p+0f,
|
||||
0x2.e20b38p+0f,
|
||||
0x4.44c378p+0f,
|
||||
0x6.62a08p+0f,
|
||||
0x9.6db3ap+0f,
|
||||
/* Interval [-2.875, -2.75] (polynomial degree 5). */
|
||||
-0x8.a41b2p-4f,
|
||||
0xc.da87fp-4f,
|
||||
0x1.147312p+0f,
|
||||
0x1.7617dap+0f,
|
||||
0x1.d6c13p+0f,
|
||||
0x2.57a358p+0f,
|
||||
/* Interval [-3, -2.875] (polynomial degree 5). */
|
||||
-0xa.046d6p-4f,
|
||||
0x9.70b89p-4f,
|
||||
0xa.a89a6p-4f,
|
||||
0xd.2f2d8p-4f,
|
||||
0xd.e32b4p-4f,
|
||||
0xf.fb741p-4f,
|
||||
};
|
||||
|
||||
static const size_t poly_deg[] =
|
||||
{
|
||||
5,
|
||||
5,
|
||||
5,
|
||||
6,
|
||||
6,
|
||||
6,
|
||||
5,
|
||||
5,
|
||||
};
|
||||
|
||||
static const size_t poly_end[] =
|
||||
{
|
||||
5,
|
||||
11,
|
||||
17,
|
||||
24,
|
||||
31,
|
||||
38,
|
||||
44,
|
||||
50,
|
||||
};
|
||||
|
||||
/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */
|
||||
|
||||
static float
|
||||
lg_sinpi (float x)
|
||||
{
|
||||
if (x <= 0.25f)
|
||||
return __sinf (M_PIf * x);
|
||||
else
|
||||
return __cosf (M_PIf * (0.5f - x));
|
||||
}
|
||||
|
||||
/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */
|
||||
|
||||
static float
|
||||
lg_cospi (float x)
|
||||
{
|
||||
if (x <= 0.25f)
|
||||
return __cosf (M_PIf * x);
|
||||
else
|
||||
return __sinf (M_PIf * (0.5f - x));
|
||||
}
|
||||
|
||||
/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */
|
||||
|
||||
static float
|
||||
lg_cotpi (float x)
|
||||
{
|
||||
return lg_cospi (x) / lg_sinpi (x);
|
||||
}
|
||||
|
||||
/* Compute lgamma of a negative argument -15 < X < -2, setting
|
||||
*SIGNGAMP accordingly. */
|
||||
|
||||
float
|
||||
__lgamma_negf (float x, int *signgamp)
|
||||
{
|
||||
/* Determine the half-integer region X lies in, handle exact
|
||||
integers and determine the sign of the result. */
|
||||
int i = floorf (-2 * x);
|
||||
if ((i & 1) == 0 && i == -2 * x)
|
||||
return 1.0f / 0.0f;
|
||||
float xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2);
|
||||
i -= 4;
|
||||
*signgamp = ((i & 2) == 0 ? -1 : 1);
|
||||
|
||||
SET_RESTORE_ROUNDF (FE_TONEAREST);
|
||||
|
||||
/* Expand around the zero X0 = X0_HI + X0_LO. */
|
||||
float x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1];
|
||||
float xdiff = x - x0_hi - x0_lo;
|
||||
|
||||
/* For arguments in the range -3 to -2, use polynomial
|
||||
approximations to an adjusted version of the gamma function. */
|
||||
if (i < 2)
|
||||
{
|
||||
int j = floorf (-8 * x) - 16;
|
||||
float xm = (-33 - 2 * j) * 0.0625f;
|
||||
float x_adj = x - xm;
|
||||
size_t deg = poly_deg[j];
|
||||
size_t end = poly_end[j];
|
||||
float g = poly_coeff[end];
|
||||
for (size_t j = 1; j <= deg; j++)
|
||||
g = g * x_adj + poly_coeff[end - j];
|
||||
return __log1pf (g * xdiff / (x - xn));
|
||||
}
|
||||
|
||||
/* The result we want is log (sinpi (X0) / sinpi (X))
|
||||
+ log (gamma (1 - X0) / gamma (1 - X)). */
|
||||
float x_idiff = fabsf (xn - x), x0_idiff = fabsf (xn - x0_hi - x0_lo);
|
||||
float log_sinpi_ratio;
|
||||
if (x0_idiff < x_idiff * 0.5f)
|
||||
/* Use log not log1p to avoid inaccuracy from log1p of arguments
|
||||
close to -1. */
|
||||
log_sinpi_ratio = __ieee754_logf (lg_sinpi (x0_idiff)
|
||||
/ lg_sinpi (x_idiff));
|
||||
else
|
||||
{
|
||||
/* Use log1p not log to avoid inaccuracy from log of arguments
|
||||
close to 1. X0DIFF2 has positive sign if X0 is further from
|
||||
XN than X is from XN, negative sign otherwise. */
|
||||
float x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5f;
|
||||
float sx0d2 = lg_sinpi (x0diff2);
|
||||
float cx0d2 = lg_cospi (x0diff2);
|
||||
log_sinpi_ratio = __log1pf (2 * sx0d2
|
||||
* (-sx0d2 + cx0d2 * lg_cotpi (x_idiff)));
|
||||
}
|
||||
|
||||
float log_gamma_ratio;
|
||||
float y0 = math_narrow_eval (1 - x0_hi);
|
||||
float y0_eps = -x0_hi + (1 - y0) - x0_lo;
|
||||
float y = math_narrow_eval (1 - x);
|
||||
float y_eps = -x + (1 - y);
|
||||
/* We now wish to compute LOG_GAMMA_RATIO
|
||||
= log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF
|
||||
accurately approximates the difference Y0 + Y0_EPS - Y -
|
||||
Y_EPS. Use Stirling's approximation. */
|
||||
float log_gamma_high
|
||||
= (xdiff * __log1pf ((y0 - e_hi - e_lo + y0_eps) / e_hi)
|
||||
+ (y - 0.5f + y_eps) * __log1pf (xdiff / y));
|
||||
/* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */
|
||||
float y0r = 1 / y0, yr = 1 / y;
|
||||
float y0r2 = y0r * y0r, yr2 = yr * yr;
|
||||
float rdiff = -xdiff / (y * y0);
|
||||
float bterm[NCOEFF];
|
||||
float dlast = rdiff, elast = rdiff * yr * (yr + y0r);
|
||||
bterm[0] = dlast * lgamma_coeff[0];
|
||||
for (size_t j = 1; j < NCOEFF; j++)
|
||||
{
|
||||
float dnext = dlast * y0r2 + elast;
|
||||
float enext = elast * yr2;
|
||||
bterm[j] = dnext * lgamma_coeff[j];
|
||||
dlast = dnext;
|
||||
elast = enext;
|
||||
}
|
||||
float log_gamma_low = 0;
|
||||
for (size_t j = 0; j < NCOEFF; j++)
|
||||
log_gamma_low += bterm[NCOEFF - 1 - j];
|
||||
log_gamma_ratio = log_gamma_high + log_gamma_low;
|
||||
|
||||
return log_sinpi_ratio + log_gamma_ratio;
|
||||
}
|
||||
/* Not needed. */
|
||||
|
||||
@ -1140,22 +1140,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -125,7 +125,6 @@ float: 4
|
||||
|
||||
Function: "lgamma":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "log10":
|
||||
double: 1
|
||||
|
||||
@ -1017,22 +1017,18 @@ ldouble: 5
|
||||
|
||||
Function: "lgamma":
|
||||
double: 3
|
||||
float: 7
|
||||
ldouble: 2
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 3
|
||||
float: 7
|
||||
ldouble: 3
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 4
|
||||
float: 6
|
||||
ldouble: 3
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 4
|
||||
float: 6
|
||||
ldouble: 2
|
||||
|
||||
Function: "log10_downward":
|
||||
|
||||
@ -210,7 +210,6 @@ float: 4
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 4
|
||||
|
||||
Function: "log":
|
||||
float: 1
|
||||
|
||||
@ -908,19 +908,15 @@ float: 5
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
|
||||
Function: "log":
|
||||
float: 1
|
||||
|
||||
@ -1143,22 +1143,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -216,7 +216,6 @@ float: 4
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
|
||||
Function: "log":
|
||||
float: 1
|
||||
|
||||
@ -881,19 +881,15 @@ float: 9
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 7
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 7
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
|
||||
Function: "log10":
|
||||
double: 2
|
||||
|
||||
@ -879,19 +879,15 @@ float: 9
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 7
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 7
|
||||
float: 7
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
|
||||
Function: "log10":
|
||||
double: 2
|
||||
|
||||
@ -1431,25 +1431,21 @@ ldouble: 5
|
||||
|
||||
Function: "lgamma":
|
||||
double: 3
|
||||
float: 4
|
||||
float128: 5
|
||||
ldouble: 3
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 4
|
||||
float: 4
|
||||
float128: 8
|
||||
ldouble: 15
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 4
|
||||
float: 3
|
||||
float128: 5
|
||||
ldouble: 16
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 4
|
||||
float: 5
|
||||
float128: 8
|
||||
ldouble: 11
|
||||
|
||||
|
||||
@ -1201,22 +1201,18 @@ ldouble: 1
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
ldouble: 3
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
ldouble: 15
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 16
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 11
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -1112,22 +1112,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 4
|
||||
float: 3
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 4
|
||||
float: 5
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -1139,22 +1139,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 4
|
||||
float: 3
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 4
|
||||
float: 5
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -1141,22 +1141,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 4
|
||||
float: 3
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 4
|
||||
float: 5
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -435,11 +435,9 @@ float: 5
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 3
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 3
|
||||
|
||||
Function: "log":
|
||||
float: 1
|
||||
|
||||
@ -1143,22 +1143,18 @@ ldouble: 7
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
ldouble: 8
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 5
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
ldouble: 8
|
||||
|
||||
Function: "log":
|
||||
|
||||
@ -1712,25 +1712,21 @@ ldouble: 5
|
||||
|
||||
Function: "lgamma":
|
||||
double: 4
|
||||
float: 7
|
||||
float128: 5
|
||||
ldouble: 4
|
||||
|
||||
Function: "lgamma_downward":
|
||||
double: 5
|
||||
float: 7
|
||||
float128: 8
|
||||
ldouble: 7
|
||||
|
||||
Function: "lgamma_towardzero":
|
||||
double: 5
|
||||
float: 6
|
||||
float128: 5
|
||||
ldouble: 7
|
||||
|
||||
Function: "lgamma_upward":
|
||||
double: 5
|
||||
float: 6
|
||||
float128: 8
|
||||
ldouble: 6
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user