Rev 1618 | Details | Compare with Previous | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 2 | pj | 1 | /* e_lgammaf_r.c -- float version of e_lgamma_r.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
||
| 3 | */ |
||
| 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 | #ifndef lint |
||
| 17 | static char rcsid[] = "$\Id: e_lgammaf_r.c,v 1.2 1995/05/30 05:48:29 rgrimes Exp $"; |
||
| 18 | #endif |
||
| 19 | |||
| 20 | #include "math.h" |
||
| 21 | #include "math_private.h" |
||
| 22 | |||
| 23 | #ifdef __STDC__ |
||
| 24 | static const float |
||
| 25 | #else |
||
| 26 | static float |
||
| 27 | #endif |
||
| 28 | two23= 8.3886080000e+06, /* 0x4b000000 */ |
||
| 29 | half= 5.0000000000e-01, /* 0x3f000000 */ |
||
| 30 | one = 1.0000000000e+00, /* 0x3f800000 */ |
||
| 31 | pi = 3.1415927410e+00, /* 0x40490fdb */ |
||
| 32 | a0 = 7.7215664089e-02, /* 0x3d9e233f */ |
||
| 33 | a1 = 3.2246702909e-01, /* 0x3ea51a66 */ |
||
| 34 | a2 = 6.7352302372e-02, /* 0x3d89f001 */ |
||
| 35 | a3 = 2.0580807701e-02, /* 0x3ca89915 */ |
||
| 36 | a4 = 7.3855509982e-03, /* 0x3bf2027e */ |
||
| 37 | a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ |
||
| 38 | a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ |
||
| 39 | a7 = 5.1006977446e-04, /* 0x3a05b634 */ |
||
| 40 | a8 = 2.2086278477e-04, /* 0x39679767 */ |
||
| 41 | a9 = 1.0801156895e-04, /* 0x38e28445 */ |
||
| 42 | a10 = 2.5214456400e-05, /* 0x37d383a2 */ |
||
| 43 | a11 = 4.4864096708e-05, /* 0x383c2c75 */ |
||
| 44 | tc = 1.4616321325e+00, /* 0x3fbb16c3 */ |
||
| 45 | tf = -1.2148628384e-01, /* 0xbdf8cdcd */ |
||
| 46 | /* tt = -(tail of tf) */ |
||
| 47 | tt = 6.6971006518e-09, /* 0x31e61c52 */ |
||
| 48 | t0 = 4.8383611441e-01, /* 0x3ef7b95e */ |
||
| 49 | t1 = -1.4758771658e-01, /* 0xbe17213c */ |
||
| 50 | t2 = 6.4624942839e-02, /* 0x3d845a15 */ |
||
| 51 | t3 = -3.2788541168e-02, /* 0xbd064d47 */ |
||
| 52 | t4 = 1.7970675603e-02, /* 0x3c93373d */ |
||
| 53 | t5 = -1.0314224288e-02, /* 0xbc28fcfe */ |
||
| 54 | t6 = 6.1005386524e-03, /* 0x3bc7e707 */ |
||
| 55 | t7 = -3.6845202558e-03, /* 0xbb7177fe */ |
||
| 56 | t8 = 2.2596477065e-03, /* 0x3b141699 */ |
||
| 57 | t9 = -1.4034647029e-03, /* 0xbab7f476 */ |
||
| 58 | t10 = 8.8108185446e-04, /* 0x3a66f867 */ |
||
| 59 | t11 = -5.3859531181e-04, /* 0xba0d3085 */ |
||
| 60 | t12 = 3.1563205994e-04, /* 0x39a57b6b */ |
||
| 61 | t13 = -3.1275415677e-04, /* 0xb9a3f927 */ |
||
| 62 | t14 = 3.3552918467e-04, /* 0x39afe9f7 */ |
||
| 63 | u0 = -7.7215664089e-02, /* 0xbd9e233f */ |
||
| 64 | u1 = 6.3282704353e-01, /* 0x3f2200f4 */ |
||
| 65 | u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ |
||
| 66 | u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ |
||
| 67 | u4 = 2.2896373272e-01, /* 0x3e6a7578 */ |
||
| 68 | u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ |
||
| 69 | v1 = 2.4559779167e+00, /* 0x401d2ebe */ |
||
| 70 | v2 = 2.1284897327e+00, /* 0x4008392d */ |
||
| 71 | v3 = 7.6928514242e-01, /* 0x3f44efdf */ |
||
| 72 | v4 = 1.0422264785e-01, /* 0x3dd572af */ |
||
| 73 | v5 = 3.2170924824e-03, /* 0x3b52d5db */ |
||
| 74 | s0 = -7.7215664089e-02, /* 0xbd9e233f */ |
||
| 75 | s1 = 2.1498242021e-01, /* 0x3e5c245a */ |
||
| 76 | s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ |
||
| 77 | s3 = 1.4635047317e-01, /* 0x3e15dce6 */ |
||
| 78 | s4 = 2.6642270386e-02, /* 0x3cda40e4 */ |
||
| 79 | s5 = 1.8402845599e-03, /* 0x3af135b4 */ |
||
| 80 | s6 = 3.1947532989e-05, /* 0x3805ff67 */ |
||
| 81 | r1 = 1.3920053244e+00, /* 0x3fb22d3b */ |
||
| 82 | r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ |
||
| 83 | r3 = 1.7193385959e-01, /* 0x3e300f6e */ |
||
| 84 | r4 = 1.8645919859e-02, /* 0x3c98bf54 */ |
||
| 85 | r5 = 7.7794247773e-04, /* 0x3a4beed6 */ |
||
| 86 | r6 = 7.3266842264e-06, /* 0x36f5d7bd */ |
||
| 87 | w0 = 4.1893854737e-01, /* 0x3ed67f1d */ |
||
| 88 | w1 = 8.3333335817e-02, /* 0x3daaaaab */ |
||
| 89 | w2 = -2.7777778450e-03, /* 0xbb360b61 */ |
||
| 90 | w3 = 7.9365057172e-04, /* 0x3a500cfd */ |
||
| 91 | w4 = -5.9518753551e-04, /* 0xba1c065c */ |
||
| 92 | w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ |
||
| 93 | w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ |
||
| 94 | |||
| 95 | #ifdef __STDC__ |
||
| 96 | static const float zero= 0.0000000000e+00; |
||
| 97 | #else |
||
| 98 | static float zero= 0.0000000000e+00; |
||
| 99 | #endif |
||
| 100 | |||
| 101 | #ifdef __STDC__ |
||
| 102 | static float sin_pif(float x) |
||
| 103 | #else |
||
| 104 | static float sin_pif(x) |
||
| 105 | float x; |
||
| 106 | #endif |
||
| 107 | { |
||
| 108 | float y,z; |
||
| 109 | int n,ix; |
||
| 110 | |||
| 111 | GET_FLOAT_WORD(ix,x); |
||
| 112 | ix &= 0x7fffffff; |
||
| 113 | |||
| 114 | if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); |
||
| 115 | y = -x; /* x is assume negative */ |
||
| 116 | |||
| 117 | /* |
||
| 118 | * argument reduction, make sure inexact flag not raised if input |
||
| 119 | * is an integer |
||
| 120 | */ |
||
| 121 | z = floorf(y); |
||
| 122 | if(z!=y) { /* inexact anyway */ |
||
| 123 | y *= (float)0.5; |
||
| 124 | y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ |
||
| 125 | n = (int) (y*(float)4.0); |
||
| 126 | } else { |
||
| 127 | if(ix>=0x4b800000) { |
||
| 128 | y = zero; n = 0; /* y must be even */ |
||
| 129 | } else { |
||
| 130 | if(ix<0x4b000000) z = y+two23; /* exact */ |
||
| 131 | GET_FLOAT_WORD(n,z); |
||
| 132 | n &= 1; |
||
| 133 | y = n; |
||
| 134 | n<<= 2; |
||
| 135 | } |
||
| 136 | } |
||
| 137 | switch (n) { |
||
| 138 | case 0: y = __kernel_sinf(pi*y,zero,0); break; |
||
| 139 | case 1: |
||
| 140 | case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; |
||
| 141 | case 3: |
||
| 142 | case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; |
||
| 143 | case 5: |
||
| 144 | case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; |
||
| 145 | default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; |
||
| 146 | } |
||
| 147 | return -y; |
||
| 148 | } |
||
| 149 | |||
| 150 | |||
| 151 | #ifdef __STDC__ |
||
| 152 | float __ieee754_lgammaf_r(float x, int *signgamp) |
||
| 153 | #else |
||
| 154 | float __ieee754_lgammaf_r(x,signgamp) |
||
| 155 | float x; int *signgamp; |
||
| 156 | #endif |
||
| 157 | { |
||
| 158 | float t,y,z,nadj,p,p1,p2,p3,q,r,w; |
||
| 159 | int i,hx,ix; |
||
| 160 | |||
| 161 | GET_FLOAT_WORD(hx,x); |
||
| 162 | |||
| 163 | /* purge off +-inf, NaN, +-0, and negative arguments */ |
||
| 164 | *signgamp = 1; |
||
| 165 | ix = hx&0x7fffffff; |
||
| 166 | if(ix>=0x7f800000) return x*x; |
||
| 167 | if(ix==0) return one/zero; |
||
| 168 | if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ |
||
| 169 | if(hx<0) { |
||
| 170 | *signgamp = -1; |
||
| 171 | return -__ieee754_logf(-x); |
||
| 172 | } else return -__ieee754_logf(x); |
||
| 173 | } |
||
| 174 | if(hx<0) { |
||
| 175 | if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ |
||
| 176 | return one/zero; |
||
| 177 | t = sin_pif(x); |
||
| 178 | if(t==zero) return one/zero; /* -integer */ |
||
| 179 | nadj = __ieee754_logf(pi/fabsf(t*x)); |
||
| 180 | if(t<zero) *signgamp = -1; |
||
| 181 | x = -x; |
||
| 182 | } |
||
| 183 | |||
| 184 | /* purge off 1 and 2 */ |
||
| 185 | if (ix==0x3f800000||ix==0x40000000) r = 0; |
||
| 186 | /* for x < 2.0 */ |
||
| 187 | else if(ix<0x40000000) { |
||
| 188 | if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ |
||
| 189 | r = -__ieee754_logf(x); |
||
| 190 | if(ix>=0x3f3b4a20) {y = one-x; i= 0;} |
||
| 191 | else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} |
||
| 192 | else {y = x; i=2;} |
||
| 193 | } else { |
||
| 194 | r = zero; |
||
| 195 | if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ |
||
| 196 | else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ |
||
| 197 | else {y=x-one;i=2;} |
||
| 198 | } |
||
| 199 | switch(i) { |
||
| 200 | case 0: |
||
| 201 | z = y*y; |
||
| 202 | p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); |
||
| 203 | p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); |
||
| 204 | p = y*p1+p2; |
||
| 205 | r += (p-(float)0.5*y); break; |
||
| 206 | case 1: |
||
| 207 | z = y*y; |
||
| 208 | w = z*y; |
||
| 209 | p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ |
||
| 210 | p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); |
||
| 211 | p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); |
||
| 212 | p = z*p1-(tt-w*(p2+y*p3)); |
||
| 213 | r += (tf + p); break; |
||
| 214 | case 2: |
||
| 215 | p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); |
||
| 216 | p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); |
||
| 217 | r += (-(float)0.5*y + p1/p2); |
||
| 218 | } |
||
| 219 | } |
||
| 220 | else if(ix<0x41000000) { /* x < 8.0 */ |
||
| 221 | i = (int)x; |
||
| 222 | t = zero; |
||
| 223 | y = x-(float)i; |
||
| 224 | p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); |
||
| 225 | q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); |
||
| 226 | r = half*y+p/q; |
||
| 227 | z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ |
||
| 228 | switch(i) { |
||
| 229 | case 7: z *= (y+(float)6.0); /* FALLTHRU */ |
||
| 230 | case 6: z *= (y+(float)5.0); /* FALLTHRU */ |
||
| 231 | case 5: z *= (y+(float)4.0); /* FALLTHRU */ |
||
| 232 | case 4: z *= (y+(float)3.0); /* FALLTHRU */ |
||
| 233 | case 3: z *= (y+(float)2.0); /* FALLTHRU */ |
||
| 234 | r += __ieee754_logf(z); break; |
||
| 235 | } |
||
| 236 | /* 8.0 <= x < 2**58 */ |
||
| 237 | } else if (ix < 0x5c800000) { |
||
| 238 | t = __ieee754_logf(x); |
||
| 239 | z = one/x; |
||
| 240 | y = z*z; |
||
| 241 | w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); |
||
| 242 | r = (x-half)*(t-one)+w; |
||
| 243 | } else |
||
| 244 | /* 2**58 <= x <= inf */ |
||
| 245 | r = x*(__ieee754_logf(x)-one); |
||
| 246 | if(hx<0) r = nadj - r; |
||
| 247 | return r; |
||
| 248 | } |