Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 1 | /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_lgammal.c */ |
| 2 | /* |
| 3 | * ==================================================== |
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 5 | * |
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 7 | * Permission to use, copy, modify, and distribute this |
| 8 | * software is freely granted, provided that this notice |
| 9 | * is preserved. |
| 10 | * ==================================================== |
| 11 | */ |
| 12 | /* |
| 13 | * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
| 14 | * |
| 15 | * Permission to use, copy, modify, and distribute this software for any |
| 16 | * purpose with or without fee is hereby granted, provided that the above |
| 17 | * copyright notice and this permission notice appear in all copies. |
| 18 | * |
| 19 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 20 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 21 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
| 22 | * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 23 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
| 24 | * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
| 25 | * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
| 26 | */ |
| 27 | /* lgammal(x) |
| 28 | * Reentrant version of the logarithm of the Gamma function |
| 29 | * with user provide pointer for the sign of Gamma(x). |
| 30 | * |
| 31 | * Method: |
| 32 | * 1. Argument Reduction for 0 < x <= 8 |
| 33 | * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may |
| 34 | * reduce x to a number in [1.5,2.5] by |
| 35 | * lgamma(1+s) = log(s) + lgamma(s) |
| 36 | * for example, |
| 37 | * lgamma(7.3) = log(6.3) + lgamma(6.3) |
| 38 | * = log(6.3*5.3) + lgamma(5.3) |
| 39 | * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) |
| 40 | * 2. Polynomial approximation of lgamma around its |
| 41 | * minimun ymin=1.461632144968362245 to maintain monotonicity. |
| 42 | * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use |
| 43 | * Let z = x-ymin; |
| 44 | * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) |
| 45 | * 2. Rational approximation in the primary interval [2,3] |
| 46 | * We use the following approximation: |
| 47 | * s = x-2.0; |
| 48 | * lgamma(x) = 0.5*s + s*P(s)/Q(s) |
| 49 | * Our algorithms are based on the following observation |
| 50 | * |
| 51 | * zeta(2)-1 2 zeta(3)-1 3 |
| 52 | * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... |
| 53 | * 2 3 |
| 54 | * |
| 55 | * where Euler = 0.5771... is the Euler constant, which is very |
| 56 | * close to 0.5. |
| 57 | * |
| 58 | * 3. For x>=8, we have |
| 59 | * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... |
| 60 | * (better formula: |
| 61 | * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) |
| 62 | * Let z = 1/x, then we approximation |
| 63 | * f(z) = lgamma(x) - (x-0.5)(log(x)-1) |
| 64 | * by |
| 65 | * 3 5 11 |
| 66 | * w = w0 + w1*z + w2*z + w3*z + ... + w6*z |
| 67 | * |
| 68 | * 4. For negative x, since (G is gamma function) |
| 69 | * -x*G(-x)*G(x) = pi/sin(pi*x), |
| 70 | * we have |
| 71 | * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) |
| 72 | * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 |
| 73 | * Hence, for x<0, signgam = sign(sin(pi*x)) and |
| 74 | * lgamma(x) = log(|Gamma(x)|) |
| 75 | * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); |
| 76 | * Note: one should avoid compute pi*(-x) directly in the |
| 77 | * computation of sin(pi*(-x)). |
| 78 | * |
| 79 | * 5. Special Cases |
| 80 | * lgamma(2+s) ~ s*(1-Euler) for tiny s |
| 81 | * lgamma(1)=lgamma(2)=0 |
| 82 | * lgamma(x) ~ -log(x) for tiny x |
| 83 | * lgamma(0) = lgamma(inf) = inf |
| 84 | * lgamma(-integer) = +-inf |
| 85 | * |
| 86 | */ |
| 87 | |
nsz | 40305f7 | 2012-03-15 09:29:53 +0100 | [diff] [blame] | 88 | #define _GNU_SOURCE |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 89 | #include "libm.h" |
Szabolcs Nagy | afa2aac | 2013-09-05 14:03:10 +0000 | [diff] [blame] | 90 | #include "libc.h" |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 91 | |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 92 | #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
nsz | 1b229a2 | 2012-03-27 22:12:20 +0200 | [diff] [blame] | 93 | double __lgamma_r(double x, int *sg); |
| 94 | |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 95 | long double __lgammal_r(long double x, int *sg) |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 96 | { |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 97 | return __lgamma_r(x, sg); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 98 | } |
| 99 | #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 |
| 100 | static const long double |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 101 | pi = 3.14159265358979323846264L, |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 102 | |
| 103 | /* lgam(1+x) = 0.5 x + x a(x)/b(x) |
| 104 | -0.268402099609375 <= x <= 0 |
| 105 | peak relative error 6.6e-22 */ |
| 106 | a0 = -6.343246574721079391729402781192128239938E2L, |
| 107 | a1 = 1.856560238672465796768677717168371401378E3L, |
| 108 | a2 = 2.404733102163746263689288466865843408429E3L, |
| 109 | a3 = 8.804188795790383497379532868917517596322E2L, |
| 110 | a4 = 1.135361354097447729740103745999661157426E2L, |
| 111 | a5 = 3.766956539107615557608581581190400021285E0L, |
| 112 | |
| 113 | b0 = 8.214973713960928795704317259806842490498E3L, |
| 114 | b1 = 1.026343508841367384879065363925870888012E4L, |
| 115 | b2 = 4.553337477045763320522762343132210919277E3L, |
| 116 | b3 = 8.506975785032585797446253359230031874803E2L, |
| 117 | b4 = 6.042447899703295436820744186992189445813E1L, |
| 118 | /* b5 = 1.000000000000000000000000000000000000000E0 */ |
| 119 | |
| 120 | |
| 121 | tc = 1.4616321449683623412626595423257213284682E0L, |
| 122 | tf = -1.2148629053584961146050602565082954242826E-1, /* double precision */ |
| 123 | /* tt = (tail of tf), i.e. tf + tt has extended precision. */ |
| 124 | tt = 3.3649914684731379602768989080467587736363E-18L, |
| 125 | /* lgam ( 1.4616321449683623412626595423257213284682E0 ) = |
| 126 | -1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ |
| 127 | |
| 128 | /* lgam (x + tc) = tf + tt + x g(x)/h(x) |
| 129 | -0.230003726999612341262659542325721328468 <= x |
| 130 | <= 0.2699962730003876587373404576742786715318 |
| 131 | peak relative error 2.1e-21 */ |
| 132 | g0 = 3.645529916721223331888305293534095553827E-18L, |
| 133 | g1 = 5.126654642791082497002594216163574795690E3L, |
| 134 | g2 = 8.828603575854624811911631336122070070327E3L, |
| 135 | g3 = 5.464186426932117031234820886525701595203E3L, |
| 136 | g4 = 1.455427403530884193180776558102868592293E3L, |
| 137 | g5 = 1.541735456969245924860307497029155838446E2L, |
| 138 | g6 = 4.335498275274822298341872707453445815118E0L, |
| 139 | |
| 140 | h0 = 1.059584930106085509696730443974495979641E4L, |
| 141 | h1 = 2.147921653490043010629481226937850618860E4L, |
| 142 | h2 = 1.643014770044524804175197151958100656728E4L, |
| 143 | h3 = 5.869021995186925517228323497501767586078E3L, |
| 144 | h4 = 9.764244777714344488787381271643502742293E2L, |
| 145 | h5 = 6.442485441570592541741092969581997002349E1L, |
| 146 | /* h6 = 1.000000000000000000000000000000000000000E0 */ |
| 147 | |
| 148 | |
| 149 | /* lgam (x+1) = -0.5 x + x u(x)/v(x) |
| 150 | -0.100006103515625 <= x <= 0.231639862060546875 |
| 151 | peak relative error 1.3e-21 */ |
| 152 | u0 = -8.886217500092090678492242071879342025627E1L, |
| 153 | u1 = 6.840109978129177639438792958320783599310E2L, |
| 154 | u2 = 2.042626104514127267855588786511809932433E3L, |
| 155 | u3 = 1.911723903442667422201651063009856064275E3L, |
| 156 | u4 = 7.447065275665887457628865263491667767695E2L, |
| 157 | u5 = 1.132256494121790736268471016493103952637E2L, |
| 158 | u6 = 4.484398885516614191003094714505960972894E0L, |
| 159 | |
| 160 | v0 = 1.150830924194461522996462401210374632929E3L, |
| 161 | v1 = 3.399692260848747447377972081399737098610E3L, |
| 162 | v2 = 3.786631705644460255229513563657226008015E3L, |
| 163 | v3 = 1.966450123004478374557778781564114347876E3L, |
| 164 | v4 = 4.741359068914069299837355438370682773122E2L, |
| 165 | v5 = 4.508989649747184050907206782117647852364E1L, |
| 166 | /* v6 = 1.000000000000000000000000000000000000000E0 */ |
| 167 | |
| 168 | |
| 169 | /* lgam (x+2) = .5 x + x s(x)/r(x) |
| 170 | 0 <= x <= 1 |
| 171 | peak relative error 7.2e-22 */ |
| 172 | s0 = 1.454726263410661942989109455292824853344E6L, |
| 173 | s1 = -3.901428390086348447890408306153378922752E6L, |
| 174 | s2 = -6.573568698209374121847873064292963089438E6L, |
| 175 | s3 = -3.319055881485044417245964508099095984643E6L, |
| 176 | s4 = -7.094891568758439227560184618114707107977E5L, |
| 177 | s5 = -6.263426646464505837422314539808112478303E4L, |
| 178 | s6 = -1.684926520999477529949915657519454051529E3L, |
| 179 | |
| 180 | r0 = -1.883978160734303518163008696712983134698E7L, |
| 181 | r1 = -2.815206082812062064902202753264922306830E7L, |
| 182 | r2 = -1.600245495251915899081846093343626358398E7L, |
| 183 | r3 = -4.310526301881305003489257052083370058799E6L, |
| 184 | r4 = -5.563807682263923279438235987186184968542E5L, |
| 185 | r5 = -3.027734654434169996032905158145259713083E4L, |
| 186 | r6 = -4.501995652861105629217250715790764371267E2L, |
| 187 | /* r6 = 1.000000000000000000000000000000000000000E0 */ |
| 188 | |
| 189 | |
| 190 | /* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) |
| 191 | x >= 8 |
| 192 | Peak relative error 1.51e-21 |
| 193 | w0 = LS2PI - 0.5 */ |
| 194 | w0 = 4.189385332046727417803e-1L, |
| 195 | w1 = 8.333333333333331447505E-2L, |
| 196 | w2 = -2.777777777750349603440E-3L, |
| 197 | w3 = 7.936507795855070755671E-4L, |
| 198 | w4 = -5.952345851765688514613E-4L, |
| 199 | w5 = 8.412723297322498080632E-4L, |
| 200 | w6 = -1.880801938119376907179E-3L, |
| 201 | w7 = 4.885026142432270781165E-3L; |
| 202 | |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 203 | /* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */ |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 204 | static long double sin_pi(long double x) |
| 205 | { |
Szabolcs Nagy | 34660d7 | 2013-09-04 15:52:23 +0000 | [diff] [blame] | 206 | int n; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 207 | |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 208 | /* spurious inexact if odd int */ |
| 209 | x *= 0.5; |
| 210 | x = 2.0*(x - floorl(x)); /* x mod 2.0 */ |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 211 | |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 212 | n = (int)(x*4.0); |
| 213 | n = (n+1)/2; |
| 214 | x -= n*0.5f; |
| 215 | x *= pi; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 216 | |
| 217 | switch (n) { |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 218 | default: /* case 4: */ |
| 219 | case 0: return __sinl(x, 0.0, 0); |
| 220 | case 1: return __cosl(x, 0.0); |
| 221 | case 2: return __sinl(-x, 0.0, 0); |
| 222 | case 3: return -__cosl(x, 0.0); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 223 | } |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 224 | } |
| 225 | |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 226 | long double __lgammal_r(long double x, int *sg) { |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 227 | long double t, y, z, nadj, p, p1, p2, q, r, w; |
Szabolcs Nagy | 34660d7 | 2013-09-04 15:52:23 +0000 | [diff] [blame] | 228 | union ldshape u = {x}; |
| 229 | uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48; |
| 230 | int sign = u.i.se >> 15; |
| 231 | int i; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 232 | |
| 233 | *sg = 1; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 234 | |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 235 | /* purge off +-inf, NaN, +-0, tiny and negative arguments */ |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 236 | if (ix >= 0x7fff0000) |
| 237 | return x * x; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 238 | if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */ |
Szabolcs Nagy | 34660d7 | 2013-09-04 15:52:23 +0000 | [diff] [blame] | 239 | if (sign) { |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 240 | *sg = -1; |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 241 | x = -x; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 242 | } |
| 243 | return -logl(x); |
| 244 | } |
Szabolcs Nagy | 34660d7 | 2013-09-04 15:52:23 +0000 | [diff] [blame] | 245 | if (sign) { |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 246 | x = -x; |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 247 | t = sin_pi(x); |
| 248 | if (t == 0.0) |
| 249 | return 1.0 / (x-x); /* -integer */ |
| 250 | if (t > 0.0) |
| 251 | *sg = -1; |
| 252 | else |
| 253 | t = -t; |
| 254 | nadj = logl(pi / (t * x)); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 255 | } |
| 256 | |
Szabolcs Nagy | ebbaf21 | 2013-11-21 01:01:57 +0000 | [diff] [blame] | 257 | /* purge off 1 and 2 (so the sign is ok with downward rounding) */ |
| 258 | if ((ix == 0x3fff8000 || ix == 0x40008000) && u.i.m == 0) { |
| 259 | r = 0; |
| 260 | } else if (ix < 0x40008000) { /* x < 2.0 */ |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 261 | if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */ |
| 262 | /* lgamma(x) = lgamma(x+1) - log(x) */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 263 | r = -logl(x); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 264 | if (ix >= 0x3ffebb4a) { /* 7.31597900390625e-1 */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 265 | y = x - 1.0; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 266 | i = 0; |
| 267 | } else if (ix >= 0x3ffced33) { /* 2.31639862060546875e-1 */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 268 | y = x - (tc - 1.0); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 269 | i = 1; |
| 270 | } else { /* x < 0.23 */ |
| 271 | y = x; |
| 272 | i = 2; |
| 273 | } |
| 274 | } else { |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 275 | r = 0.0; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 276 | if (ix >= 0x3fffdda6) { /* 1.73162841796875 */ |
| 277 | /* [1.7316,2] */ |
| 278 | y = x - 2.0; |
| 279 | i = 0; |
| 280 | } else if (ix >= 0x3fff9da6) { /* 1.23162841796875 */ |
| 281 | /* [1.23,1.73] */ |
| 282 | y = x - tc; |
| 283 | i = 1; |
| 284 | } else { |
| 285 | /* [0.9, 1.23] */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 286 | y = x - 1.0; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 287 | i = 2; |
| 288 | } |
| 289 | } |
| 290 | switch (i) { |
| 291 | case 0: |
| 292 | p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); |
| 293 | p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 294 | r += 0.5 * y + y * p1/p2; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 295 | break; |
| 296 | case 1: |
| 297 | p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); |
| 298 | p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); |
| 299 | p = tt + y * p1/p2; |
| 300 | r += (tf + p); |
| 301 | break; |
| 302 | case 2: |
| 303 | p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); |
| 304 | p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 305 | r += (-0.5 * y + p1 / p2); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 306 | } |
| 307 | } else if (ix < 0x40028000) { /* 8.0 */ |
| 308 | /* x < 8.0 */ |
| 309 | i = (int)x; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 310 | y = x - (double)i; |
| 311 | p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); |
| 312 | q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 313 | r = 0.5 * y + p / q; |
Szabolcs Nagy | e71981a | 2013-10-04 18:08:16 +0000 | [diff] [blame] | 314 | z = 1.0; |
| 315 | /* lgamma(1+s) = log(s) + lgamma(s) */ |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 316 | switch (i) { |
| 317 | case 7: |
| 318 | z *= (y + 6.0); /* FALLTHRU */ |
| 319 | case 6: |
| 320 | z *= (y + 5.0); /* FALLTHRU */ |
| 321 | case 5: |
| 322 | z *= (y + 4.0); /* FALLTHRU */ |
| 323 | case 4: |
| 324 | z *= (y + 3.0); /* FALLTHRU */ |
| 325 | case 3: |
| 326 | z *= (y + 2.0); /* FALLTHRU */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 327 | r += logl(z); |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 328 | break; |
| 329 | } |
| 330 | } else if (ix < 0x40418000) { /* 2^66 */ |
| 331 | /* 8.0 <= x < 2**66 */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 332 | t = logl(x); |
| 333 | z = 1.0 / x; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 334 | y = z * z; |
| 335 | w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 336 | r = (x - 0.5) * (t - 1.0) + w; |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 337 | } else /* 2**66 <= x <= inf */ |
nsz | 0cbb654 | 2012-03-19 23:41:19 +0100 | [diff] [blame] | 338 | r = x * (logl(x) - 1.0); |
Szabolcs Nagy | 34660d7 | 2013-09-04 15:52:23 +0000 | [diff] [blame] | 339 | if (sign) |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 340 | r = nadj - r; |
| 341 | return r; |
| 342 | } |
Szabolcs Nagy | f4e4632 | 2015-03-10 20:01:20 +0000 | [diff] [blame] | 343 | #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 |
| 344 | // TODO: broken implementation to make things compile |
| 345 | double __lgamma_r(double x, int *sg); |
| 346 | |
| 347 | long double __lgammal_r(long double x, int *sg) |
| 348 | { |
| 349 | return __lgamma_r(x, sg); |
| 350 | } |
Rich Felker | b69f695 | 2012-03-13 01:17:53 -0400 | [diff] [blame] | 351 | #endif |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 352 | |
Rich Felker | 8c071f8 | 2012-03-16 21:20:53 -0400 | [diff] [blame] | 353 | extern int __signgam; |
| 354 | |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 355 | long double lgammal(long double x) |
| 356 | { |
Rich Felker | 8c071f8 | 2012-03-16 21:20:53 -0400 | [diff] [blame] | 357 | return __lgammal_r(x, &__signgam); |
Rich Felker | de7db6e | 2012-03-16 21:16:32 -0400 | [diff] [blame] | 358 | } |
| 359 | |
| 360 | weak_alias(__lgammal_r, lgammal_r); |