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Introduce lgammal, tgammal, erfl, and erfcl
git://git.musl-libc.org/musl 79bdacff83a6bd5b70ff5ae5eb8b6de82c2f7c30
This commit is contained in:
Justine Tunney
parent
b4084dd6c6
commit
3b791d2f44
8 changed files with 1100 additions and 319 deletions
314
libc/tinymath/tgammal.c
Normal file
314
libc/tinymath/tgammal.c
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@ -0,0 +1,314 @@
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/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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#include "libc/tinymath/internal.h"
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#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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asm(".ident\t\"\\n\\n\
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OpenBSD libm (ISC License)\\n\
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Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_tgammal.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Gamma function
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, tgammal();
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*
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* y = tgammal( x );
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*
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*
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* DESCRIPTION:
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*
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* Returns gamma function of the argument. The result is
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* correctly signed.
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*
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* Arguments |x| <= 13 are reduced by recurrence and the function
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* approximated by a rational function of degree 7/8 in the
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* interval (2,3). Large arguments are handled by Stirling's
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* formula. Large negative arguments are made positive using
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* a reflection formula.
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -40,+40 10000 3.6e-19 7.9e-20
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* IEEE -1755,+1755 10000 4.8e-18 6.5e-19
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*
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* Accuracy for large arguments is dominated by error in powl().
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*
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*/
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/*
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tgamma(x+2) = tgamma(x+2) P(x)/Q(x)
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0 <= x <= 1
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Relative error
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n=7, d=8
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Peak error = 1.83e-20
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Relative error spread = 8.4e-23
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*/
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static const long double P[8] = {
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4.212760487471622013093E-5L,
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4.542931960608009155600E-4L,
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4.092666828394035500949E-3L,
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2.385363243461108252554E-2L,
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1.113062816019361559013E-1L,
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3.629515436640239168939E-1L,
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8.378004301573126728826E-1L,
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1.000000000000000000009E0L,
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};
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static const long double Q[9] = {
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-1.397148517476170440917E-5L,
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2.346584059160635244282E-4L,
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-1.237799246653152231188E-3L,
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-7.955933682494738320586E-4L,
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2.773706565840072979165E-2L,
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-4.633887671244534213831E-2L,
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-2.243510905670329164562E-1L,
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4.150160950588455434583E-1L,
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9.999999999999999999908E-1L,
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};
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/*
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static const long double P[] = {
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-3.01525602666895735709e0L,
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-3.25157411956062339893e1L,
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-2.92929976820724030353e2L,
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-1.70730828800510297666e3L,
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-7.96667499622741999770e3L,
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-2.59780216007146401957e4L,
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-5.99650230220855581642e4L,
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-7.15743521530849602425e4L
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};
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static const long double Q[] = {
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1.00000000000000000000e0L,
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-1.67955233807178858919e1L,
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8.85946791747759881659e1L,
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5.69440799097468430177e1L,
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-1.98526250512761318471e3L,
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3.31667508019495079814e3L,
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1.60577839621734713377e4L,
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-2.97045081369399940529e4L,
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-7.15743521530849602412e4L
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};
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*/
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#define MAXGAML 1755.455L
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/*static const long double LOGPI = 1.14472988584940017414L;*/
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/* Stirling's formula for the gamma function
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tgamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
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z(x) = x
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13 <= x <= 1024
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Relative error
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n=8, d=0
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Peak error = 9.44e-21
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Relative error spread = 8.8e-4
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*/
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static const long double STIR[9] = {
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7.147391378143610789273E-4L,
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-2.363848809501759061727E-5L,
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-5.950237554056330156018E-4L,
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6.989332260623193171870E-5L,
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7.840334842744753003862E-4L,
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-2.294719747873185405699E-4L,
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-2.681327161876304418288E-3L,
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3.472222222230075327854E-3L,
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8.333333333333331800504E-2L,
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};
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#define MAXSTIR 1024.0L
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static const long double SQTPI = 2.50662827463100050242E0L;
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/* 1/tgamma(x) = z P(z)
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* z(x) = 1/x
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* 0 < x < 0.03125
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* Peak relative error 4.2e-23
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*/
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static const long double S[9] = {
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-1.193945051381510095614E-3L,
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7.220599478036909672331E-3L,
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-9.622023360406271645744E-3L,
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-4.219773360705915470089E-2L,
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1.665386113720805206758E-1L,
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-4.200263503403344054473E-2L,
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-6.558780715202540684668E-1L,
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5.772156649015328608253E-1L,
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1.000000000000000000000E0L,
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};
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/* 1/tgamma(-x) = z P(z)
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* z(x) = 1/x
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* 0 < x < 0.03125
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* Peak relative error 5.16e-23
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* Relative error spread = 2.5e-24
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*/
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static const long double SN[9] = {
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1.133374167243894382010E-3L,
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7.220837261893170325704E-3L,
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9.621911155035976733706E-3L,
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-4.219773343731191721664E-2L,
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-1.665386113944413519335E-1L,
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-4.200263503402112910504E-2L,
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6.558780715202536547116E-1L,
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5.772156649015328608727E-1L,
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-1.000000000000000000000E0L,
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};
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static const long double PIL = 3.1415926535897932384626L;
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/* Gamma function computed by Stirling's formula.
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*/
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static long double stirf(long double x)
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{
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long double y, w, v;
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w = 1.0/x;
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/* For large x, use rational coefficients from the analytical expansion. */
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if (x > 1024.0)
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w = (((((6.97281375836585777429E-5L * w
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+ 7.84039221720066627474E-4L) * w
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- 2.29472093621399176955E-4L) * w
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- 2.68132716049382716049E-3L) * w
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+ 3.47222222222222222222E-3L) * w
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+ 8.33333333333333333333E-2L) * w
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+ 1.0;
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else
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w = 1.0 + w * __polevll(w, STIR, 8);
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y = expl(x);
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if (x > MAXSTIR) { /* Avoid overflow in pow() */
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v = powl(x, 0.5L * x - 0.25L);
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y = v * (v / y);
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} else {
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y = powl(x, x - 0.5L) / y;
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}
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y = SQTPI * y * w;
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return y;
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}
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long double tgammal(long double x)
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{
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long double p, q, z;
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if (!isfinite(x))
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return x + INFINITY;
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q = fabsl(x);
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if (q > 13.0) {
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if (x < 0.0) {
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p = floorl(q);
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z = q - p;
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if (z == 0)
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return 0 / z;
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if (q > MAXGAML) {
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z = 0;
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} else {
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if (z > 0.5) {
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p += 1.0;
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z = q - p;
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}
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z = q * sinl(PIL * z);
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z = fabsl(z) * stirf(q);
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z = PIL/z;
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}
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if (0.5 * p == floorl(q * 0.5))
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z = -z;
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} else if (x > MAXGAML) {
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z = x * 0x1p16383L;
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} else {
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z = stirf(x);
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}
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return z;
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}
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z = 1.0;
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while (x >= 3.0) {
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x -= 1.0;
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z *= x;
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}
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while (x < -0.03125L) {
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z /= x;
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x += 1.0;
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}
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if (x <= 0.03125L)
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goto small;
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while (x < 2.0) {
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z /= x;
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x += 1.0;
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}
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if (x == 2.0)
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return z;
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x -= 2.0;
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p = __polevll(x, P, 7);
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q = __polevll(x, Q, 8);
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z = z * p / q;
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return z;
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small:
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/* z==1 if x was originally +-0 */
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if (x == 0 && z != 1)
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return x / x;
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if (x < 0.0) {
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x = -x;
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q = z / (x * __polevll(x, SN, 8));
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} else
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q = z / (x * __polevll(x, S, 8));
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return q;
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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// TODO: broken implementation to make things compile
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long double tgammal(long double x)
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{
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return tgamma(x);
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}
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#endif /* long double is long */
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