| 1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
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| 2 | /*
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| 3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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| 4 | */
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| 5 | /*
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| 6 | * ====================================================
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 8 | *
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 10 | * Permission to use, copy, modify, and distribute this
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| 11 | * software is freely granted, provided that this notice
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| 12 | * is preserved.
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| 13 | * ====================================================
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| 14 | */
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| 15 |
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| 16 | #include "libm.h"
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| 17 | #include "libc.h"
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| 18 |
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| 19 | static const float
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| 20 | pi = 3.1415927410e+00, /* 0x40490fdb */
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| 21 | a0 = 7.7215664089e-02, /* 0x3d9e233f */
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| 22 | a1 = 3.2246702909e-01, /* 0x3ea51a66 */
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| 23 | a2 = 6.7352302372e-02, /* 0x3d89f001 */
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| 24 | a3 = 2.0580807701e-02, /* 0x3ca89915 */
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| 25 | a4 = 7.3855509982e-03, /* 0x3bf2027e */
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| 26 | a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
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| 27 | a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
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| 28 | a7 = 5.1006977446e-04, /* 0x3a05b634 */
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| 29 | a8 = 2.2086278477e-04, /* 0x39679767 */
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| 30 | a9 = 1.0801156895e-04, /* 0x38e28445 */
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| 31 | a10 = 2.5214456400e-05, /* 0x37d383a2 */
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| 32 | a11 = 4.4864096708e-05, /* 0x383c2c75 */
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| 33 | tc = 1.4616321325e+00, /* 0x3fbb16c3 */
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| 34 | tf = -1.2148628384e-01, /* 0xbdf8cdcd */
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| 35 | /* tt = -(tail of tf) */
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| 36 | tt = 6.6971006518e-09, /* 0x31e61c52 */
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| 37 | t0 = 4.8383611441e-01, /* 0x3ef7b95e */
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| 38 | t1 = -1.4758771658e-01, /* 0xbe17213c */
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| 39 | t2 = 6.4624942839e-02, /* 0x3d845a15 */
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| 40 | t3 = -3.2788541168e-02, /* 0xbd064d47 */
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| 41 | t4 = 1.7970675603e-02, /* 0x3c93373d */
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| 42 | t5 = -1.0314224288e-02, /* 0xbc28fcfe */
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| 43 | t6 = 6.1005386524e-03, /* 0x3bc7e707 */
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| 44 | t7 = -3.6845202558e-03, /* 0xbb7177fe */
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| 45 | t8 = 2.2596477065e-03, /* 0x3b141699 */
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| 46 | t9 = -1.4034647029e-03, /* 0xbab7f476 */
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| 47 | t10 = 8.8108185446e-04, /* 0x3a66f867 */
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| 48 | t11 = -5.3859531181e-04, /* 0xba0d3085 */
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| 49 | t12 = 3.1563205994e-04, /* 0x39a57b6b */
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| 50 | t13 = -3.1275415677e-04, /* 0xb9a3f927 */
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| 51 | t14 = 3.3552918467e-04, /* 0x39afe9f7 */
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| 52 | u0 = -7.7215664089e-02, /* 0xbd9e233f */
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| 53 | u1 = 6.3282704353e-01, /* 0x3f2200f4 */
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| 54 | u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
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| 55 | u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
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| 56 | u4 = 2.2896373272e-01, /* 0x3e6a7578 */
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| 57 | u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
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| 58 | v1 = 2.4559779167e+00, /* 0x401d2ebe */
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| 59 | v2 = 2.1284897327e+00, /* 0x4008392d */
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| 60 | v3 = 7.6928514242e-01, /* 0x3f44efdf */
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| 61 | v4 = 1.0422264785e-01, /* 0x3dd572af */
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| 62 | v5 = 3.2170924824e-03, /* 0x3b52d5db */
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| 63 | s0 = -7.7215664089e-02, /* 0xbd9e233f */
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| 64 | s1 = 2.1498242021e-01, /* 0x3e5c245a */
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| 65 | s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
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| 66 | s3 = 1.4635047317e-01, /* 0x3e15dce6 */
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| 67 | s4 = 2.6642270386e-02, /* 0x3cda40e4 */
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| 68 | s5 = 1.8402845599e-03, /* 0x3af135b4 */
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| 69 | s6 = 3.1947532989e-05, /* 0x3805ff67 */
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| 70 | r1 = 1.3920053244e+00, /* 0x3fb22d3b */
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| 71 | r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
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| 72 | r3 = 1.7193385959e-01, /* 0x3e300f6e */
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| 73 | r4 = 1.8645919859e-02, /* 0x3c98bf54 */
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| 74 | r5 = 7.7794247773e-04, /* 0x3a4beed6 */
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| 75 | r6 = 7.3266842264e-06, /* 0x36f5d7bd */
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| 76 | w0 = 4.1893854737e-01, /* 0x3ed67f1d */
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| 77 | w1 = 8.3333335817e-02, /* 0x3daaaaab */
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| 78 | w2 = -2.7777778450e-03, /* 0xbb360b61 */
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| 79 | w3 = 7.9365057172e-04, /* 0x3a500cfd */
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| 80 | w4 = -5.9518753551e-04, /* 0xba1c065c */
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| 81 | w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
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| 82 | w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
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| 83 |
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| 84 | /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
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| 85 | static float sin_pi(float x)
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| 86 | {
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| 87 | double_t y;
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| 88 | int n;
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| 89 |
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| 90 | /* spurious inexact if odd int */
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| 91 | x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */
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| 92 |
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| 93 | n = (int)(x*4);
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| 94 | n = (n+1)/2;
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| 95 | y = x - n*0.5f;
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| 96 | y *= 3.14159265358979323846;
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| 97 | switch (n) {
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| 98 | default: /* case 4: */
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| 99 | case 0: return __sindf(y);
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| 100 | case 1: return __cosdf(y);
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| 101 | case 2: return __sindf(-y);
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| 102 | case 3: return -__cosdf(y);
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| 103 | }
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| 104 | }
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| 105 |
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| 106 | float __lgammaf_r(float x, int *signgamp)
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| 107 | {
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| 108 | union {float f; uint32_t i;} u = {x};
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| 109 | float t,y,z,nadj,p,p1,p2,p3,q,r,w;
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| 110 | uint32_t ix;
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| 111 | int i,sign;
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| 112 |
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| 113 | /* purge off +-inf, NaN, +-0, tiny and negative arguments */
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| 114 | *signgamp = 1;
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| 115 | sign = u.i>>31;
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| 116 | ix = u.i & 0x7fffffff;
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| 117 | if (ix >= 0x7f800000)
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| 118 | return x*x;
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| 119 | if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
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| 120 | if (sign) {
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| 121 | *signgamp = -1;
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| 122 | x = -x;
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| 123 | }
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| 124 | return -logf(x);
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| 125 | }
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| 126 | if (sign) {
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| 127 | x = -x;
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| 128 | t = sin_pi(x);
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| 129 | if (t == 0.0f) /* -integer */
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| 130 | return 1.0f/(x-x);
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| 131 | if (t > 0.0f)
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| 132 | *signgamp = -1;
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| 133 | else
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| 134 | t = -t;
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| 135 | nadj = logf(pi/(t*x));
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| 136 | }
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| 137 |
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| 138 | /* purge off 1 and 2 */
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| 139 | if (ix == 0x3f800000 || ix == 0x40000000)
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| 140 | r = 0;
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| 141 | /* for x < 2.0 */
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| 142 | else if (ix < 0x40000000) {
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| 143 | if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
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| 144 | r = -logf(x);
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| 145 | if (ix >= 0x3f3b4a20) {
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| 146 | y = 1.0f - x;
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| 147 | i = 0;
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| 148 | } else if (ix >= 0x3e6d3308) {
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| 149 | y = x - (tc-1.0f);
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| 150 | i = 1;
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| 151 | } else {
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| 152 | y = x;
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| 153 | i = 2;
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| 154 | }
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| 155 | } else {
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| 156 | r = 0.0f;
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| 157 | if (ix >= 0x3fdda618) { /* [1.7316,2] */
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| 158 | y = 2.0f - x;
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| 159 | i = 0;
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| 160 | } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
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| 161 | y = x - tc;
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| 162 | i = 1;
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| 163 | } else {
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| 164 | y = x - 1.0f;
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| 165 | i = 2;
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| 166 | }
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| 167 | }
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| 168 | switch(i) {
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| 169 | case 0:
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| 170 | z = y*y;
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| 171 | p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
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| 172 | p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
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| 173 | p = y*p1+p2;
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| 174 | r += p - 0.5f*y;
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| 175 | break;
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| 176 | case 1:
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| 177 | z = y*y;
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| 178 | w = z*y;
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| 179 | p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
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| 180 | p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
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| 181 | p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
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| 182 | p = z*p1-(tt-w*(p2+y*p3));
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| 183 | r += (tf + p);
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| 184 | break;
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| 185 | case 2:
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| 186 | p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
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| 187 | p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
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| 188 | r += -0.5f*y + p1/p2;
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| 189 | }
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| 190 | } else if (ix < 0x41000000) { /* x < 8.0 */
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| 191 | i = (int)x;
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| 192 | y = x - (float)i;
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| 193 | p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
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| 194 | q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
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| 195 | r = 0.5f*y+p/q;
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| 196 | z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
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| 197 | switch (i) {
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| 198 | case 7: z *= y + 6.0f; /* FALLTHRU */
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| 199 | case 6: z *= y + 5.0f; /* FALLTHRU */
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| 200 | case 5: z *= y + 4.0f; /* FALLTHRU */
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| 201 | case 4: z *= y + 3.0f; /* FALLTHRU */
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| 202 | case 3: z *= y + 2.0f; /* FALLTHRU */
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| 203 | r += logf(z);
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| 204 | break;
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| 205 | }
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| 206 | } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
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| 207 | t = logf(x);
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| 208 | z = 1.0f/x;
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| 209 | y = z*z;
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| 210 | w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
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| 211 | r = (x-0.5f)*(t-1.0f)+w;
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| 212 | } else /* 2**58 <= x <= inf */
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| 213 | r = x*(logf(x)-1.0f);
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| 214 | if (sign)
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| 215 | r = nadj - r;
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| 216 | return r;
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| 217 | }
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| 218 |
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| 219 | weak_alias(__lgammaf_r, lgammaf_r);
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