compiler/stdc/math/e_lgammaf_r.c

   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[] = "$FreeBSD: src/lib/msun/src/e_lgammaf_r.c,v 1.12 2011/10/15 07:00:28 das Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const volatile float vzero __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) = 0.0;
  24
  25 static const float
  26 zero=  0,
  27 half=  0.5,
  28 one =  1,
  29 pi  =  3.1415927410e+00, /* 0x40490fdb */
  30 /*
  31  * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]:
  32  * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4
  33  */
  34 a0  =  7.72156641e-02, /* 0x3d9e233f */
  35 a1  =  3.22467119e-01, /* 0x3ea51a69 */
  36 a2  =  6.73484802e-02, /* 0x3d89ee00 */
  37 a3  =  2.06395667e-02, /* 0x3ca9144f */
  38 a4  =  6.98275631e-03, /* 0x3be4cf9b */
  39 a5  =  4.11768444e-03, /* 0x3b86eda4 */
  40 /*
  41  * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]:
  42  * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8.
  43  */
  44 tc  =  1.46163213e+00, /* 0x3fbb16c3 */
  45 tf  = -1.21486291e-01, /* 0xbdf8cdce */
  46 t0  = -2.94064460e-11, /* 0xae0154b7 */
  47 t1  = -2.35939837e-08, /* 0xb2caabb8 */
  48 t2  =  4.83836412e-01, /* 0x3ef7b968 */
  49 t3  = -1.47586212e-01, /* 0xbe1720d7 */
  50 t4  =  6.46013096e-02, /* 0x3d844db1 */
  51 t5  = -3.28450352e-02, /* 0xbd068884 */
  52 t6  =  1.86483748e-02, /* 0x3c98c47a */
  53 t7  = -9.89206228e-03, /* 0xbc221251 */
  54 /*
  55  * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]:
  56  * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2
  57  */
  58 u0  = -7.72156641e-02, /* 0xbd9e233f */
  59 u1  =  7.36789703e-01, /* 0x3f3c9e40 */
  60 u2  =  4.95649040e-01, /* 0x3efdc5b6 */
  61 v1  =  1.10958421e+00, /* 0x3f8e06db */
  62 v2  =  2.10598111e-01, /* 0x3e57a708 */
  63 v3  = -1.02995494e-02, /* 0xbc28bf71 */
  64 /*
  65  * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]:
  66  * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0
  67  * with y = x - 2.
  68  */
  69 s0 = -7.72156641e-02, /* 0xbd9e233f */
  70 s1 =  2.69987404e-01, /* 0x3e8a3bca */
  71 s2 =  1.42851010e-01, /* 0x3e124789 */
  72 s3 =  1.19389519e-02, /* 0x3c439b98 */
  73 r1 =  6.79650068e-01, /* 0x3f2dfd8c */
  74 r2 =  1.16058730e-01, /* 0x3dedb033 */
  75 r3 =  3.75673687e-03, /* 0x3b763396 */
  76 /*
  77  * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]:
  78  * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6.
  79  */
  80 w0 =  4.18938547e-01, /* 0x3ed67f1d */
  81 w1 =  8.33332464e-02, /* 0x3daaaa9f */
  82 w2 = -2.76129087e-03; /* 0xbb34f6c6 */
  83
  84 static float
  85 sin_pif(float x)
  86 {
  87         volatile float vz;
  88         float y,z;
  89         int n;
  90
  91         y = -x;
  92
  93         vz = y+0x1p23F;                 /* depend on 0 <= y < 0x1p23 */
  94         z = vz-0x1p23F;                 /* rintf(y) for the above range */
  95         if (z == y)
  96             return zero;
  97
  98         vz = y+0x1p21F;
  99         GET_FLOAT_WORD(n,vz);           /* bits for rounded y (units 0.25) */
 100         z = vz-0x1p21F;                 /* y rounded to a multiple of 0.25 */
 101         if (z > y) {
 102             z -= 0.25F;                 /* adjust to round down */
 103             n--;
 104         }
 105         n &= 7;                         /* octant of y mod 2 */
 106         y = y - z + n * 0.25F;          /* y mod 2 */
 107
 108         switch (n) {
 109             case 0:   y =  __kernel_sindf(pi*y); break;
 110             case 1:
 111             case 2:   y =  __kernel_cosdf(pi*((float)0.5-y)); break;
 112             case 3:
 113             case 4:   y =  __kernel_sindf(pi*(one-y)); break;
 114             case 5:
 115             case 6:   y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
 116             default:  y =  __kernel_sindf(pi*(y-(float)2.0)); break;
 117             }
 118         return -y;
 119 }
 120
 121
 122 float
 123 __ieee754_lgammaf_r(float x, int *signgamp)
 124 {
 125         float nadj,p,p1,p2,q,r,t,w,y,z;
 126         int32_t hx;
 127         int i,ix;
 128
 129         GET_FLOAT_WORD(hx,x);
 130
 131     /* purge +-Inf and NaNs */
 132         *signgamp = 1;
 133         ix = hx&0x7fffffff;
 134         if(ix>=0x7f800000) return x*x;
 135
 136     /* purge +-0 and tiny arguments */
 137         *signgamp = 1-2*((uint32_t)hx>>31);
 138         if(ix<0x32000000) {             /* |x|<2**-27, return -log(|x|) */
 139             if(ix==0)
 140                 return one/vzero;
 141             return -__ieee754_logf(fabsf(x));
 142         }
 143     /* purge negative integers and start evaluation for other x < 0 */
 144         if(hx<0) {
 145             *signgamp = 1;
 146             if(ix>=0x4b000000)  /* |x|>=2**23, must be -integer */
 147                 return one/vzero;
 148             t = sin_pif(x);
 149             if(t==zero) return one/vzero; /* -integer */
 150             nadj = __ieee754_logf(pi/fabsf(t*x));
 151             if(t<zero) *signgamp = -1;
 152             x = -x;
 153         }
 154
 155     /* purge 1 and 2 */
 156         if (ix==0x3f800000||ix==0x40000000) r = 0;
 157     /* for x < 2.0 */
 158         else if(ix<0x40000000) {
 159             if(ix<=0x3f666666) {        /* lgamma(x) = lgamma(x+1)-log(x) */
 160                 r = -__ieee754_logf(x);
 161                 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
 162                 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
 163                 else {y = x; i=2;}
 164             } else {
 165                 r = zero;
 166                 if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */
 167                 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
 168                 else {y=x-one;i=2;}
 169             }
 170             switch(i) {
 171               case 0:
 172                 z = y*y;
 173                 p1 = a0+z*(a2+z*a4);
 174                 p2 = z*(a1+z*(a3+z*a5));
 175                 p  = y*p1+p2;
 176                 r  += p-y/2; break;
 177               case 1:
 178                 p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7)))));
 179                 r += tf + p; break;
 180               case 2:
 181                 p1 = y*(u0+y*(u1+y*u2));
 182                 p2 = one+y*(v1+y*(v2+y*v3));
 183                 r += p1/p2-y/2;
 184             }
 185         }
 186     /* x < 8.0 */
 187         else if(ix<0x41000000) {
 188             i = x;
 189             y = x-i;
 190             p = y*(s0+y*(s1+y*(s2+y*s3)));
 191             q = one+y*(r1+y*(r2+y*r3));
 192             r = y/2+p/q;
 193             z = one;    /* lgamma(1+s) = log(s) + lgamma(s) */
 194             switch(i) {
 195             case 7: z *= (y+6);         /* FALLTHRU */
 196             case 6: z *= (y+5);         /* FALLTHRU */
 197             case 5: z *= (y+4);         /* FALLTHRU */
 198             case 4: z *= (y+3);         /* FALLTHRU */
 199             case 3: z *= (y+2);         /* FALLTHRU */
 200                     r += __ieee754_logf(z); break;
 201             }
 202     /* 8.0 <= x < 2**27 */
 203         } else if (ix < 0x4d000000) {
 204             t = __ieee754_logf(x);
 205             z = one/x;
 206             y = z*z;
 207             w = w0+z*(w1+y*w2);
 208             r = (x-half)*(t-one)+w;
 209         } else
 210     /* 2**27 <= x <= inf */
 211             r =  x*(__ieee754_logf(x)-one);
 212         if(hx<0) r = nadj - r;
 213         return r;
 214 }