diff options
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/tgammal.c')
-rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/tgammal.c | 281 |
1 files changed, 0 insertions, 281 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/tgammal.c b/lib/mlibc/options/ansi/musl-generic-math/tgammal.c deleted file mode 100644 index 5336c5b..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/tgammal.c +++ /dev/null @@ -1,281 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_tgammal.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Gamma function - * - * - * SYNOPSIS: - * - * long double x, y, tgammal(); - * - * y = tgammal( x ); - * - * - * DESCRIPTION: - * - * Returns gamma function of the argument. The result is - * correctly signed. - * - * Arguments |x| <= 13 are reduced by recurrence and the function - * approximated by a rational function of degree 7/8 in the - * interval (2,3). Large arguments are handled by Stirling's - * formula. Large negative arguments are made positive using - * a reflection formula. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -40,+40 10000 3.6e-19 7.9e-20 - * IEEE -1755,+1755 10000 4.8e-18 6.5e-19 - * - * Accuracy for large arguments is dominated by error in powl(). - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double tgammal(long double x) -{ - return tgamma(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* -tgamma(x+2) = tgamma(x+2) P(x)/Q(x) -0 <= x <= 1 -Relative error -n=7, d=8 -Peak error = 1.83e-20 -Relative error spread = 8.4e-23 -*/ -static const long double P[8] = { - 4.212760487471622013093E-5L, - 4.542931960608009155600E-4L, - 4.092666828394035500949E-3L, - 2.385363243461108252554E-2L, - 1.113062816019361559013E-1L, - 3.629515436640239168939E-1L, - 8.378004301573126728826E-1L, - 1.000000000000000000009E0L, -}; -static const long double Q[9] = { --1.397148517476170440917E-5L, - 2.346584059160635244282E-4L, --1.237799246653152231188E-3L, --7.955933682494738320586E-4L, - 2.773706565840072979165E-2L, --4.633887671244534213831E-2L, --2.243510905670329164562E-1L, - 4.150160950588455434583E-1L, - 9.999999999999999999908E-1L, -}; - -/* -static const long double P[] = { --3.01525602666895735709e0L, --3.25157411956062339893e1L, --2.92929976820724030353e2L, --1.70730828800510297666e3L, --7.96667499622741999770e3L, --2.59780216007146401957e4L, --5.99650230220855581642e4L, --7.15743521530849602425e4L -}; -static const long double Q[] = { - 1.00000000000000000000e0L, --1.67955233807178858919e1L, - 8.85946791747759881659e1L, - 5.69440799097468430177e1L, --1.98526250512761318471e3L, - 3.31667508019495079814e3L, - 1.60577839621734713377e4L, --2.97045081369399940529e4L, --7.15743521530849602412e4L -}; -*/ -#define MAXGAML 1755.455L -/*static const long double LOGPI = 1.14472988584940017414L;*/ - -/* Stirling's formula for the gamma function -tgamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x)) -z(x) = x -13 <= x <= 1024 -Relative error -n=8, d=0 -Peak error = 9.44e-21 -Relative error spread = 8.8e-4 -*/ -static const long double STIR[9] = { - 7.147391378143610789273E-4L, --2.363848809501759061727E-5L, --5.950237554056330156018E-4L, - 6.989332260623193171870E-5L, - 7.840334842744753003862E-4L, --2.294719747873185405699E-4L, --2.681327161876304418288E-3L, - 3.472222222230075327854E-3L, - 8.333333333333331800504E-2L, -}; - -#define MAXSTIR 1024.0L -static const long double SQTPI = 2.50662827463100050242E0L; - -/* 1/tgamma(x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 4.2e-23 - */ -static const long double S[9] = { --1.193945051381510095614E-3L, - 7.220599478036909672331E-3L, --9.622023360406271645744E-3L, --4.219773360705915470089E-2L, - 1.665386113720805206758E-1L, --4.200263503403344054473E-2L, --6.558780715202540684668E-1L, - 5.772156649015328608253E-1L, - 1.000000000000000000000E0L, -}; - -/* 1/tgamma(-x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 5.16e-23 - * Relative error spread = 2.5e-24 - */ -static const long double SN[9] = { - 1.133374167243894382010E-3L, - 7.220837261893170325704E-3L, - 9.621911155035976733706E-3L, --4.219773343731191721664E-2L, --1.665386113944413519335E-1L, --4.200263503402112910504E-2L, - 6.558780715202536547116E-1L, - 5.772156649015328608727E-1L, --1.000000000000000000000E0L, -}; - -static const long double PIL = 3.1415926535897932384626L; - -/* Gamma function computed by Stirling's formula. - */ -static long double stirf(long double x) -{ - long double y, w, v; - - w = 1.0/x; - /* For large x, use rational coefficients from the analytical expansion. */ - if (x > 1024.0) - w = (((((6.97281375836585777429E-5L * w - + 7.84039221720066627474E-4L) * w - - 2.29472093621399176955E-4L) * w - - 2.68132716049382716049E-3L) * w - + 3.47222222222222222222E-3L) * w - + 8.33333333333333333333E-2L) * w - + 1.0; - else - w = 1.0 + w * __polevll(w, STIR, 8); - y = expl(x); - if (x > MAXSTIR) { /* Avoid overflow in pow() */ - v = powl(x, 0.5L * x - 0.25L); - y = v * (v / y); - } else { - y = powl(x, x - 0.5L) / y; - } - y = SQTPI * y * w; - return y; -} - -long double tgammal(long double x) -{ - long double p, q, z; - - if (!isfinite(x)) - return x + INFINITY; - - q = fabsl(x); - if (q > 13.0) { - if (x < 0.0) { - p = floorl(q); - z = q - p; - if (z == 0) - return 0 / z; - if (q > MAXGAML) { - z = 0; - } else { - if (z > 0.5) { - p += 1.0; - z = q - p; - } - z = q * sinl(PIL * z); - z = fabsl(z) * stirf(q); - z = PIL/z; - } - if (0.5 * p == floorl(q * 0.5)) - z = -z; - } else if (x > MAXGAML) { - z = x * 0x1p16383L; - } else { - z = stirf(x); - } - return z; - } - - z = 1.0; - while (x >= 3.0) { - x -= 1.0; - z *= x; - } - while (x < -0.03125L) { - z /= x; - x += 1.0; - } - if (x <= 0.03125L) - goto small; - while (x < 2.0) { - z /= x; - x += 1.0; - } - if (x == 2.0) - return z; - - x -= 2.0; - p = __polevll(x, P, 7); - q = __polevll(x, Q, 8); - z = z * p / q; - return z; - -small: - /* z==1 if x was originally +-0 */ - if (x == 0 && z != 1) - return x / x; - if (x < 0.0) { - x = -x; - q = z / (x * __polevll(x, SN, 8)); - } else - q = z / (x * __polevll(x, S, 8)); - return q; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double tgammal(long double x) -{ - return tgamma(x); -} -#endif |