1/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */ 2/* 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 4 */ 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16#include "libm.h" 17#include "libc.h" 18 19static const float 20pi = 3.1415927410e+00, /* 0x40490fdb */ 21a0 = 7.7215664089e-02, /* 0x3d9e233f */ 22a1 = 3.2246702909e-01, /* 0x3ea51a66 */ 23a2 = 6.7352302372e-02, /* 0x3d89f001 */ 24a3 = 2.0580807701e-02, /* 0x3ca89915 */ 25a4 = 7.3855509982e-03, /* 0x3bf2027e */ 26a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ 27a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ 28a7 = 5.1006977446e-04, /* 0x3a05b634 */ 29a8 = 2.2086278477e-04, /* 0x39679767 */ 30a9 = 1.0801156895e-04, /* 0x38e28445 */ 31a10 = 2.5214456400e-05, /* 0x37d383a2 */ 32a11 = 4.4864096708e-05, /* 0x383c2c75 */ 33tc = 1.4616321325e+00, /* 0x3fbb16c3 */ 34tf = -1.2148628384e-01, /* 0xbdf8cdcd */ 35/* tt = -(tail of tf) */ 36tt = 6.6971006518e-09, /* 0x31e61c52 */ 37t0 = 4.8383611441e-01, /* 0x3ef7b95e */ 38t1 = -1.4758771658e-01, /* 0xbe17213c */ 39t2 = 6.4624942839e-02, /* 0x3d845a15 */ 40t3 = -3.2788541168e-02, /* 0xbd064d47 */ 41t4 = 1.7970675603e-02, /* 0x3c93373d */ 42t5 = -1.0314224288e-02, /* 0xbc28fcfe */ 43t6 = 6.1005386524e-03, /* 0x3bc7e707 */ 44t7 = -3.6845202558e-03, /* 0xbb7177fe */ 45t8 = 2.2596477065e-03, /* 0x3b141699 */ 46t9 = -1.4034647029e-03, /* 0xbab7f476 */ 47t10 = 8.8108185446e-04, /* 0x3a66f867 */ 48t11 = -5.3859531181e-04, /* 0xba0d3085 */ 49t12 = 3.1563205994e-04, /* 0x39a57b6b */ 50t13 = -3.1275415677e-04, /* 0xb9a3f927 */ 51t14 = 3.3552918467e-04, /* 0x39afe9f7 */ 52u0 = -7.7215664089e-02, /* 0xbd9e233f */ 53u1 = 6.3282704353e-01, /* 0x3f2200f4 */ 54u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ 55u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ 56u4 = 2.2896373272e-01, /* 0x3e6a7578 */ 57u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ 58v1 = 2.4559779167e+00, /* 0x401d2ebe */ 59v2 = 2.1284897327e+00, /* 0x4008392d */ 60v3 = 7.6928514242e-01, /* 0x3f44efdf */ 61v4 = 1.0422264785e-01, /* 0x3dd572af */ 62v5 = 3.2170924824e-03, /* 0x3b52d5db */ 63s0 = -7.7215664089e-02, /* 0xbd9e233f */ 64s1 = 2.1498242021e-01, /* 0x3e5c245a */ 65s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ 66s3 = 1.4635047317e-01, /* 0x3e15dce6 */ 67s4 = 2.6642270386e-02, /* 0x3cda40e4 */ 68s5 = 1.8402845599e-03, /* 0x3af135b4 */ 69s6 = 3.1947532989e-05, /* 0x3805ff67 */ 70r1 = 1.3920053244e+00, /* 0x3fb22d3b */ 71r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ 72r3 = 1.7193385959e-01, /* 0x3e300f6e */ 73r4 = 1.8645919859e-02, /* 0x3c98bf54 */ 74r5 = 7.7794247773e-04, /* 0x3a4beed6 */ 75r6 = 7.3266842264e-06, /* 0x36f5d7bd */ 76w0 = 4.1893854737e-01, /* 0x3ed67f1d */ 77w1 = 8.3333335817e-02, /* 0x3daaaaab */ 78w2 = -2.7777778450e-03, /* 0xbb360b61 */ 79w3 = 7.9365057172e-04, /* 0x3a500cfd */ 80w4 = -5.9518753551e-04, /* 0xba1c065c */ 81w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ 82w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ 83 84/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ 85static float sin_pi(float x) 86{ 87 double_t y; 88 int n; 89 90 /* spurious inexact if odd int */ 91 x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */ 92 93 n = (int)(x*4); 94 n = (n+1)/2; 95 y = x - n*0.5f; 96 y *= 3.14159265358979323846; 97 switch (n) { 98 default: /* case 4: */ 99 case 0: return __sindf(y); 100 case 1: return __cosdf(y); 101 case 2: return __sindf(-y); 102 case 3: return -__cosdf(y); 103 } 104} 105 106float __lgammaf_r(float x, int *signgamp) 107{ 108 union {float f; uint32_t i;} u = {x}; 109 float t,y,z,nadj,p,p1,p2,p3,q,r,w; 110 uint32_t ix; 111 int i,sign; 112 113 /* purge off +-inf, NaN, +-0, tiny and negative arguments */ 114 *signgamp = 1; 115 sign = u.i>>31; 116 ix = u.i & 0x7fffffff; 117 if (ix >= 0x7f800000) 118 return x*x; 119 if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */ 120 if (sign) { 121 *signgamp = -1; 122 x = -x; 123 } 124 return -logf(x); 125 } 126 if (sign) { 127 x = -x; 128 t = sin_pi(x); 129 if (t == 0.0f) /* -integer */ 130 return 1.0f/(x-x); 131 if (t > 0.0f) 132 *signgamp = -1; 133 else 134 t = -t; 135 nadj = logf(pi/(t*x)); 136 } 137 138 /* purge off 1 and 2 */ 139 if (ix == 0x3f800000 || ix == 0x40000000) 140 r = 0; 141 /* for x < 2.0 */ 142 else if (ix < 0x40000000) { 143 if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ 144 r = -logf(x); 145 if (ix >= 0x3f3b4a20) { 146 y = 1.0f - x; 147 i = 0; 148 } else if (ix >= 0x3e6d3308) { 149 y = x - (tc-1.0f); 150 i = 1; 151 } else { 152 y = x; 153 i = 2; 154 } 155 } else { 156 r = 0.0f; 157 if (ix >= 0x3fdda618) { /* [1.7316,2] */ 158 y = 2.0f - x; 159 i = 0; 160 } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */ 161 y = x - tc; 162 i = 1; 163 } else { 164 y = x - 1.0f; 165 i = 2; 166 } 167 } 168 switch(i) { 169 case 0: 170 z = y*y; 171 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 172 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 173 p = y*p1+p2; 174 r += p - 0.5f*y; 175 break; 176 case 1: 177 z = y*y; 178 w = z*y; 179 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 180 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 181 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 182 p = z*p1-(tt-w*(p2+y*p3)); 183 r += (tf + p); 184 break; 185 case 2: 186 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 187 p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 188 r += -0.5f*y + p1/p2; 189 } 190 } else if (ix < 0x41000000) { /* x < 8.0 */ 191 i = (int)x; 192 y = x - (float)i; 193 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 194 q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 195 r = 0.5f*y+p/q; 196 z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */ 197 switch (i) { 198 case 7: z *= y + 6.0f; /* FALLTHRU */ 199 case 6: z *= y + 5.0f; /* FALLTHRU */ 200 case 5: z *= y + 4.0f; /* FALLTHRU */ 201 case 4: z *= y + 3.0f; /* FALLTHRU */ 202 case 3: z *= y + 2.0f; /* FALLTHRU */ 203 r += logf(z); 204 break; 205 } 206 } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */ 207 t = logf(x); 208 z = 1.0f/x; 209 y = z*z; 210 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 211 r = (x-0.5f)*(t-1.0f)+w; 212 } else /* 2**58 <= x <= inf */ 213 r = x*(logf(x)-1.0f); 214 if (sign) 215 r = nadj - r; 216 return r; 217} 218 219weak_alias(__lgammaf_r, lgammaf_r); 220