src/math/lgammaf_r.c

   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);