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Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/lgammal.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/lgammal.c | 361 |
1 files changed, 0 insertions, 361 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/lgammal.c b/lib/mlibc/options/ansi/musl-generic-math/lgammal.c deleted file mode 100644 index f0bea36..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/lgammal.c +++ /dev/null @@ -1,361 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_lgammal.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * 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. - */ -/* lgammal(x) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: - * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may - * reduce x to a number in [1.5,2.5] by - * lgamma(1+s) = log(s) + lgamma(s) - * for example, - * lgamma(7.3) = log(6.3) + lgamma(6.3) - * = log(6.3*5.3) + lgamma(5.3) - * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) - * 2. Polynomial approximation of lgamma around its - * minimun ymin=1.461632144968362245 to maintain monotonicity. - * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use - * Let z = x-ymin; - * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) - * 2. Rational approximation in the primary interval [2,3] - * We use the following approximation: - * s = x-2.0; - * lgamma(x) = 0.5*s + s*P(s)/Q(s) - * Our algorithms are based on the following observation - * - * zeta(2)-1 2 zeta(3)-1 3 - * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... - * 2 3 - * - * where Euler = 0.5771... is the Euler constant, which is very - * close to 0.5. - * - * 3. For x>=8, we have - * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... - * (better formula: - * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) - * Let z = 1/x, then we approximation - * f(z) = lgamma(x) - (x-0.5)(log(x)-1) - * by - * 3 5 11 - * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * - * 4. For negative x, since (G is gamma function) - * -x*G(-x)*G(x) = pi/sin(pi*x), - * we have - * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) - * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and - * lgamma(x) = log(|Gamma(x)|) - * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the - * computation of sin(pi*(-x)). - * - * 5. Special Cases - * lgamma(2+s) ~ s*(1-Euler) for tiny s - * lgamma(1)=lgamma(2)=0 - * lgamma(x) ~ -log(x) for tiny x - * lgamma(0) = lgamma(inf) = inf - * lgamma(-integer) = +-inf - * - */ - -#define _GNU_SOURCE -#include "libm.h" -#include "weak_alias.h" -//#include "libc.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -double __lgamma_r(double x, int *sg); - -long double __lgammal_r(long double x, int *sg) -{ - return __lgamma_r(x, sg); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double -pi = 3.14159265358979323846264L, - -/* lgam(1+x) = 0.5 x + x a(x)/b(x) - -0.268402099609375 <= x <= 0 - peak relative error 6.6e-22 */ -a0 = -6.343246574721079391729402781192128239938E2L, -a1 = 1.856560238672465796768677717168371401378E3L, -a2 = 2.404733102163746263689288466865843408429E3L, -a3 = 8.804188795790383497379532868917517596322E2L, -a4 = 1.135361354097447729740103745999661157426E2L, -a5 = 3.766956539107615557608581581190400021285E0L, - -b0 = 8.214973713960928795704317259806842490498E3L, -b1 = 1.026343508841367384879065363925870888012E4L, -b2 = 4.553337477045763320522762343132210919277E3L, -b3 = 8.506975785032585797446253359230031874803E2L, -b4 = 6.042447899703295436820744186992189445813E1L, -/* b5 = 1.000000000000000000000000000000000000000E0 */ - - -tc = 1.4616321449683623412626595423257213284682E0L, -tf = -1.2148629053584961146050602565082954242826E-1, /* double precision */ -/* tt = (tail of tf), i.e. tf + tt has extended precision. */ -tt = 3.3649914684731379602768989080467587736363E-18L, -/* lgam ( 1.4616321449683623412626595423257213284682E0 ) = --1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ - -/* lgam (x + tc) = tf + tt + x g(x)/h(x) - -0.230003726999612341262659542325721328468 <= x - <= 0.2699962730003876587373404576742786715318 - peak relative error 2.1e-21 */ -g0 = 3.645529916721223331888305293534095553827E-18L, -g1 = 5.126654642791082497002594216163574795690E3L, -g2 = 8.828603575854624811911631336122070070327E3L, -g3 = 5.464186426932117031234820886525701595203E3L, -g4 = 1.455427403530884193180776558102868592293E3L, -g5 = 1.541735456969245924860307497029155838446E2L, -g6 = 4.335498275274822298341872707453445815118E0L, - -h0 = 1.059584930106085509696730443974495979641E4L, -h1 = 2.147921653490043010629481226937850618860E4L, -h2 = 1.643014770044524804175197151958100656728E4L, -h3 = 5.869021995186925517228323497501767586078E3L, -h4 = 9.764244777714344488787381271643502742293E2L, -h5 = 6.442485441570592541741092969581997002349E1L, -/* h6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam (x+1) = -0.5 x + x u(x)/v(x) - -0.100006103515625 <= x <= 0.231639862060546875 - peak relative error 1.3e-21 */ -u0 = -8.886217500092090678492242071879342025627E1L, -u1 = 6.840109978129177639438792958320783599310E2L, -u2 = 2.042626104514127267855588786511809932433E3L, -u3 = 1.911723903442667422201651063009856064275E3L, -u4 = 7.447065275665887457628865263491667767695E2L, -u5 = 1.132256494121790736268471016493103952637E2L, -u6 = 4.484398885516614191003094714505960972894E0L, - -v0 = 1.150830924194461522996462401210374632929E3L, -v1 = 3.399692260848747447377972081399737098610E3L, -v2 = 3.786631705644460255229513563657226008015E3L, -v3 = 1.966450123004478374557778781564114347876E3L, -v4 = 4.741359068914069299837355438370682773122E2L, -v5 = 4.508989649747184050907206782117647852364E1L, -/* v6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam (x+2) = .5 x + x s(x)/r(x) - 0 <= x <= 1 - peak relative error 7.2e-22 */ -s0 = 1.454726263410661942989109455292824853344E6L, -s1 = -3.901428390086348447890408306153378922752E6L, -s2 = -6.573568698209374121847873064292963089438E6L, -s3 = -3.319055881485044417245964508099095984643E6L, -s4 = -7.094891568758439227560184618114707107977E5L, -s5 = -6.263426646464505837422314539808112478303E4L, -s6 = -1.684926520999477529949915657519454051529E3L, - -r0 = -1.883978160734303518163008696712983134698E7L, -r1 = -2.815206082812062064902202753264922306830E7L, -r2 = -1.600245495251915899081846093343626358398E7L, -r3 = -4.310526301881305003489257052083370058799E6L, -r4 = -5.563807682263923279438235987186184968542E5L, -r5 = -3.027734654434169996032905158145259713083E4L, -r6 = -4.501995652861105629217250715790764371267E2L, -/* r6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) - x >= 8 - Peak relative error 1.51e-21 -w0 = LS2PI - 0.5 */ -w0 = 4.189385332046727417803e-1L, -w1 = 8.333333333333331447505E-2L, -w2 = -2.777777777750349603440E-3L, -w3 = 7.936507795855070755671E-4L, -w4 = -5.952345851765688514613E-4L, -w5 = 8.412723297322498080632E-4L, -w6 = -1.880801938119376907179E-3L, -w7 = 4.885026142432270781165E-3L; - -/* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */ -static long double sin_pi(long double x) -{ - int n; - - /* spurious inexact if odd int */ - x *= 0.5; - x = 2.0*(x - floorl(x)); /* x mod 2.0 */ - - n = (int)(x*4.0); - n = (n+1)/2; - x -= n*0.5f; - x *= pi; - - switch (n) { - default: /* case 4: */ - case 0: return __sinl(x, 0.0, 0); - case 1: return __cosl(x, 0.0); - case 2: return __sinl(-x, 0.0, 0); - case 3: return -__cosl(x, 0.0); - } -} - -long double __lgammal_r(long double x, int *sg) { - long double t, y, z, nadj, p, p1, p2, q, r, w; - union ldshape u = {x}; - uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48; - int sign = u.i.se >> 15; - int i; - - *sg = 1; - - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ - if (ix >= 0x7fff0000) - return x * x; - if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */ - if (sign) { - *sg = -1; - x = -x; - } - return -logl(x); - } - if (sign) { - x = -x; - t = sin_pi(x); - if (t == 0.0) - return 1.0 / (x-x); /* -integer */ - if (t > 0.0) - *sg = -1; - else - t = -t; - nadj = logl(pi / (t * x)); - } - - /* purge off 1 and 2 (so the sign is ok with downward rounding) */ - if ((ix == 0x3fff8000 || ix == 0x40008000) && u.i.m == 0) { - r = 0; - } else if (ix < 0x40008000) { /* x < 2.0 */ - if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */ - /* lgamma(x) = lgamma(x+1) - log(x) */ - r = -logl(x); - if (ix >= 0x3ffebb4a) { /* 7.31597900390625e-1 */ - y = x - 1.0; - i = 0; - } else if (ix >= 0x3ffced33) { /* 2.31639862060546875e-1 */ - y = x - (tc - 1.0); - i = 1; - } else { /* x < 0.23 */ - y = x; - i = 2; - } - } else { - r = 0.0; - if (ix >= 0x3fffdda6) { /* 1.73162841796875 */ - /* [1.7316,2] */ - y = x - 2.0; - i = 0; - } else if (ix >= 0x3fff9da6) { /* 1.23162841796875 */ - /* [1.23,1.73] */ - y = x - tc; - i = 1; - } else { - /* [0.9, 1.23] */ - y = x - 1.0; - i = 2; - } - } - switch (i) { - case 0: - p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); - p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); - r += 0.5 * y + y * p1/p2; - break; - case 1: - p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); - p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); - p = tt + y * p1/p2; - r += (tf + p); - break; - case 2: - p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); - p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); - r += (-0.5 * y + p1 / p2); - } - } else if (ix < 0x40028000) { /* 8.0 */ - /* x < 8.0 */ - i = (int)x; - y = x - (double)i; - p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); - q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); - r = 0.5 * y + p / q; - z = 1.0; - /* lgamma(1+s) = log(s) + lgamma(s) */ - switch (i) { - case 7: - z *= (y + 6.0); /* FALLTHRU */ - case 6: - z *= (y + 5.0); /* FALLTHRU */ - case 5: - z *= (y + 4.0); /* FALLTHRU */ - case 4: - z *= (y + 3.0); /* FALLTHRU */ - case 3: - z *= (y + 2.0); /* FALLTHRU */ - r += logl(z); - break; - } - } else if (ix < 0x40418000) { /* 2^66 */ - /* 8.0 <= x < 2**66 */ - t = logl(x); - z = 1.0 / x; - y = z * z; - w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); - r = (x - 0.5) * (t - 1.0) + w; - } else /* 2**66 <= x <= inf */ - r = x * (logl(x) - 1.0); - if (sign) - r = nadj - r; - return r; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -double __lgamma_r(double x, int *sg); - -long double __lgammal_r(long double x, int *sg) -{ - return __lgamma_r(x, sg); -} -#endif - -extern int __signgam; - -long double lgammal(long double x) -{ - return __lgammal_r(x, &__signgam); -} - -weak_alias(__lgammal_r, lgammal_r); |