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