nsz Git - musl/blob - 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 two23= 8.3886080000e+06, /* 0x4b000000 */
  20 half=  5.0000000000e-01, /* 0x3f000000 */
  21 one =  1.0000000000e+00, /* 0x3f800000 */
  22 pi  =  3.1415927410e+00, /* 0x40490fdb */
  23 a0  =  7.7215664089e-02, /* 0x3d9e233f */
  24 a1  =  3.2246702909e-01, /* 0x3ea51a66 */
  25 a2  =  6.7352302372e-02, /* 0x3d89f001 */
  26 a3  =  2.0580807701e-02, /* 0x3ca89915 */
  27 a4  =  7.3855509982e-03, /* 0x3bf2027e */
  28 a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
  29 a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
  30 a7  =  5.1006977446e-04, /* 0x3a05b634 */
  31 a8  =  2.2086278477e-04, /* 0x39679767 */
  32 a9  =  1.0801156895e-04, /* 0x38e28445 */
  33 a10 =  2.5214456400e-05, /* 0x37d383a2 */
  34 a11 =  4.4864096708e-05, /* 0x383c2c75 */
  35 tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
  36 tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
  37 /* tt = -(tail of tf) */
  38 tt  =  6.6971006518e-09, /* 0x31e61c52 */
  39 t0  =  4.8383611441e-01, /* 0x3ef7b95e */
  40 t1  = -1.4758771658e-01, /* 0xbe17213c */
  41 t2  =  6.4624942839e-02, /* 0x3d845a15 */
  42 t3  = -3.2788541168e-02, /* 0xbd064d47 */
  43 t4  =  1.7970675603e-02, /* 0x3c93373d */
  44 t5  = -1.0314224288e-02, /* 0xbc28fcfe */
  45 t6  =  6.1005386524e-03, /* 0x3bc7e707 */
  46 t7  = -3.6845202558e-03, /* 0xbb7177fe */
  47 t8  =  2.2596477065e-03, /* 0x3b141699 */
  48 t9  = -1.4034647029e-03, /* 0xbab7f476 */
  49 t10 =  8.8108185446e-04, /* 0x3a66f867 */
  50 t11 = -5.3859531181e-04, /* 0xba0d3085 */
  51 t12 =  3.1563205994e-04, /* 0x39a57b6b */
  52 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
  53 t14 =  3.3552918467e-04, /* 0x39afe9f7 */
  54 u0  = -7.7215664089e-02, /* 0xbd9e233f */
  55 u1  =  6.3282704353e-01, /* 0x3f2200f4 */
  56 u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
  57 u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
  58 u4  =  2.2896373272e-01, /* 0x3e6a7578 */
  59 u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
  60 v1  =  2.4559779167e+00, /* 0x401d2ebe */
  61 v2  =  2.1284897327e+00, /* 0x4008392d */
  62 v3  =  7.6928514242e-01, /* 0x3f44efdf */
  63 v4  =  1.0422264785e-01, /* 0x3dd572af */
  64 v5  =  3.2170924824e-03, /* 0x3b52d5db */
  65 s0  = -7.7215664089e-02, /* 0xbd9e233f */
  66 s1  =  2.1498242021e-01, /* 0x3e5c245a */
  67 s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
  68 s3  =  1.4635047317e-01, /* 0x3e15dce6 */
  69 s4  =  2.6642270386e-02, /* 0x3cda40e4 */
  70 s5  =  1.8402845599e-03, /* 0x3af135b4 */
  71 s6  =  3.1947532989e-05, /* 0x3805ff67 */
  72 r1  =  1.3920053244e+00, /* 0x3fb22d3b */
  73 r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
  74 r3  =  1.7193385959e-01, /* 0x3e300f6e */
  75 r4  =  1.8645919859e-02, /* 0x3c98bf54 */
  76 r5  =  7.7794247773e-04, /* 0x3a4beed6 */
  77 r6  =  7.3266842264e-06, /* 0x36f5d7bd */
  78 w0  =  4.1893854737e-01, /* 0x3ed67f1d */
  79 w1  =  8.3333335817e-02, /* 0x3daaaaab */
  80 w2  = -2.7777778450e-03, /* 0xbb360b61 */
  81 w3  =  7.9365057172e-04, /* 0x3a500cfd */
  82 w4  = -5.9518753551e-04, /* 0xba1c065c */
  83 w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
  84 w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
  85
  86 static const float zero = 0.0000000000e+00;
  87
  88 static float sin_pif(float x)
  89 {
  90         float y,z;
  91         int n,ix;
  92
  93         GET_FLOAT_WORD(ix, x);
  94         ix &= 0x7fffffff;
  95
  96         if(ix < 0x3e800000)
  97                 return __sindf(pi*x);
  98
  99         y = -x;  /* negative x is assumed */
 100
 101         /*
 102          * argument reduction, make sure inexact flag not raised if input
 103          * is an integer
 104          */
 105         z = floorf(y);
 106         if (z != y) {   /* inexact anyway */
 107                 y *= 0.5f;
 108                 y  = 2.0f*(y - floorf(y));   /* y = |x| mod 2.0 */
 109                 n  = (int)(y*4.0f);
 110         } else {
 111                 if (ix >= 0x4b800000) {
 112                         y = zero;  /* y must be even */
 113                         n = 0;
 114                 } else {
 115                         if (ix < 0x4b000000)
 116                                 z = y + two23;  /* exact */
 117                         GET_FLOAT_WORD(n, z);
 118                         n &= 1;
 119                         y = n;
 120                         n <<= 2;
 121                 }
 122         }
 123         switch (n) {
 124         case 0:  y =  __sindf(pi*y); break;
 125         case 1:
 126         case 2:  y =  __cosdf(pi*(0.5f - y)); break;
 127         case 3:
 128         case 4:  y =  __sindf(pi*(one - y)); break;
 129         case 5:
 130         case 6:  y = -__cosdf(pi*(y - 1.5f)); break;
 131         default: y =  __sindf(pi*(y - 2.0f)); break;
 132         }
 133         return -y;
 134 }
 135
 136
 137 float __lgammaf_r(float x, int *signgamp)
 138 {
 139         float t,y,z,nadj,p,p1,p2,p3,q,r,w;
 140         int32_t hx;
 141         int i,ix;
 142
 143         GET_FLOAT_WORD(hx, x);
 144
 145         /* purge off +-inf, NaN, +-0, tiny and negative arguments */
 146         *signgamp = 1;
 147         ix = hx & 0x7fffffff;
 148         if (ix >= 0x7f800000)
 149                 return x*x;
 150         if (ix == 0)
 151                 return one/zero;
 152         if (ix < 0x35000000) {  /* |x| < 2**-21, return -log(|x|) */
 153                 if (hx < 0) {
 154                         *signgamp = -1;
 155                         return -logf(-x);
 156                 }
 157                 return -logf(x);
 158         }
 159         if (hx < 0) {
 160                 if (ix >= 0x4b000000)  /* |x| >= 2**23, must be -integer */
 161                         return one/zero;
 162                 t = sin_pif(x);
 163                 if (t == zero) /* -integer */
 164                         return one/zero;
 165                 nadj = logf(pi/fabsf(t*x));
 166                 if (t < zero)
 167                         *signgamp = -1;
 168                 x = -x;
 169         }
 170
 171         /* purge off 1 and 2 */
 172         if (ix == 0x3f800000 || ix == 0x40000000)
 173                 r = 0;
 174         /* for x < 2.0 */
 175         else if (ix < 0x40000000) {
 176                 if (ix <= 0x3f666666) {  /* lgamma(x) = lgamma(x+1)-log(x) */
 177                         r = -logf(x);
 178                         if (ix >= 0x3f3b4a20) {
 179                                 y = one - x;
 180                                 i = 0;
 181                         } else if (ix >= 0x3e6d3308) {
 182                                 y = x - (tc-one);
 183                                 i = 1;
 184                         } else {
 185                                 y = x;
 186                                 i = 2;
 187                         }
 188                 } else {
 189                         r = zero;
 190                         if (ix >= 0x3fdda618) {  /* [1.7316,2] */
 191                                 y = 2.0f - x;
 192                                 i = 0;
 193                         } else if (ix >= 0x3F9da620) {  /* [1.23,1.73] */
 194                                 y = x - tc;
 195                                 i = 1;
 196                         } else {
 197                                 y = x - one;
 198                                 i = 2;
 199                         }
 200                 }
 201                 switch(i) {
 202                 case 0:
 203                         z = y*y;
 204                         p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
 205                         p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
 206                         p = y*p1+p2;
 207                         r += p - 0.5f*y;
 208                         break;
 209                 case 1:
 210                         z = y*y;
 211                         w = z*y;
 212                         p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));    /* parallel comp */
 213                         p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
 214                         p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
 215                         p = z*p1-(tt-w*(p2+y*p3));
 216                         r += (tf + p);
 217                         break;
 218                 case 2:
 219                         p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
 220                         p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
 221                         r += -0.5f*y + p1/p2;
 222                 }
 223         } else if (ix < 0x41000000) {  /* x < 8.0 */
 224                 i = (int)x;
 225                 y = x - (float)i;
 226                 p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
 227                 q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
 228                 r = half*y+p/q;
 229                 z = one;    /* lgamma(1+s) = log(s) + lgamma(s) */
 230                 switch (i) {
 231                 case 7: z *= y + 6.0f;  /* FALLTHRU */
 232                 case 6: z *= y + 5.0f;  /* FALLTHRU */
 233                 case 5: z *= y + 4.0f;  /* FALLTHRU */
 234                 case 4: z *= y + 3.0f;  /* FALLTHRU */
 235                 case 3: z *= y + 2.0f;  /* FALLTHRU */
 236                         r += logf(z);
 237                         break;
 238                 }
 239         } else if (ix < 0x5c800000) {  /* 8.0 <= x < 2**58 */
 240                 t = logf(x);
 241                 z = one/x;
 242                 y = z*z;
 243                 w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
 244                 r = (x-half)*(t-one)+w;
 245         } else                         /* 2**58 <= x <= inf */
 246                 r =  x*(logf(x)-one);
 247         if (hx < 0)
 248                 r = nadj - r;
 249         return r;
 250 }
 251
 252 weak_alias(__lgammaf_r, lgammaf_r);