lib/libm/src/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 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: e_lgammaf_r.c,v 1.6 2002/05/26 22:01:51 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float
  25 two23=  8.3886080000e+06, /* 0x4b000000 */
  26 half=  5.0000000000e-01, /* 0x3f000000 */
  27 one =  1.0000000000e+00, /* 0x3f800000 */
  28 pi  =  3.1415927410e+00, /* 0x40490fdb */
  29 a0  =  7.7215664089e-02, /* 0x3d9e233f */
  30 a1  =  3.2246702909e-01, /* 0x3ea51a66 */
  31 a2  =  6.7352302372e-02, /* 0x3d89f001 */
  32 a3  =  2.0580807701e-02, /* 0x3ca89915 */
  33 a4  =  7.3855509982e-03, /* 0x3bf2027e */
  34 a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
  35 a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
  36 a7  =  5.1006977446e-04, /* 0x3a05b634 */
  37 a8  =  2.2086278477e-04, /* 0x39679767 */
  38 a9  =  1.0801156895e-04, /* 0x38e28445 */
  39 a10 =  2.5214456400e-05, /* 0x37d383a2 */
  40 a11 =  4.4864096708e-05, /* 0x383c2c75 */
  41 tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
  42 tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
  43 /* tt = -(tail of tf) */
  44 tt  =  6.6971006518e-09, /* 0x31e61c52 */
  45 t0  =  4.8383611441e-01, /* 0x3ef7b95e */
  46 t1  = -1.4758771658e-01, /* 0xbe17213c */
  47 t2  =  6.4624942839e-02, /* 0x3d845a15 */
  48 t3  = -3.2788541168e-02, /* 0xbd064d47 */
  49 t4  =  1.7970675603e-02, /* 0x3c93373d */
  50 t5  = -1.0314224288e-02, /* 0xbc28fcfe */
  51 t6  =  6.1005386524e-03, /* 0x3bc7e707 */
  52 t7  = -3.6845202558e-03, /* 0xbb7177fe */
  53 t8  =  2.2596477065e-03, /* 0x3b141699 */
  54 t9  = -1.4034647029e-03, /* 0xbab7f476 */
  55 t10 =  8.8108185446e-04, /* 0x3a66f867 */
  56 t11 = -5.3859531181e-04, /* 0xba0d3085 */
  57 t12 =  3.1563205994e-04, /* 0x39a57b6b */
  58 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
  59 t14 =  3.3552918467e-04, /* 0x39afe9f7 */
  60 u0  = -7.7215664089e-02, /* 0xbd9e233f */
  61 u1  =  6.3282704353e-01, /* 0x3f2200f4 */
  62 u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
  63 u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
  64 u4  =  2.2896373272e-01, /* 0x3e6a7578 */
  65 u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
  66 v1  =  2.4559779167e+00, /* 0x401d2ebe */
  67 v2  =  2.1284897327e+00, /* 0x4008392d */
  68 v3  =  7.6928514242e-01, /* 0x3f44efdf */
  69 v4  =  1.0422264785e-01, /* 0x3dd572af */
  70 v5  =  3.2170924824e-03, /* 0x3b52d5db */
  71 s0  = -7.7215664089e-02, /* 0xbd9e233f */
  72 s1  =  2.1498242021e-01, /* 0x3e5c245a */
  73 s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
  74 s3  =  1.4635047317e-01, /* 0x3e15dce6 */
  75 s4  =  2.6642270386e-02, /* 0x3cda40e4 */
  76 s5  =  1.8402845599e-03, /* 0x3af135b4 */
  77 s6  =  3.1947532989e-05, /* 0x3805ff67 */
  78 r1  =  1.3920053244e+00, /* 0x3fb22d3b */
  79 r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
  80 r3  =  1.7193385959e-01, /* 0x3e300f6e */
  81 r4  =  1.8645919859e-02, /* 0x3c98bf54 */
  82 r5  =  7.7794247773e-04, /* 0x3a4beed6 */
  83 r6  =  7.3266842264e-06, /* 0x36f5d7bd */
  84 w0  =  4.1893854737e-01, /* 0x3ed67f1d */
  85 w1  =  8.3333335817e-02, /* 0x3daaaaab */
  86 w2  = -2.7777778450e-03, /* 0xbb360b61 */
  87 w3  =  7.9365057172e-04, /* 0x3a500cfd */
  88 w4  = -5.9518753551e-04, /* 0xba1c065c */
  89 w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
  90 w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
  91
  92 static const float zero=  0.0000000000e+00;
  93
  94 static float
  95 sin_pif(float x)
  96 {
  97         float y,z;
  98         int n,ix;
  99
 100         GET_FLOAT_WORD(ix,x);
 101         ix &= 0x7fffffff;
 102
 103         if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
 104         y = -x;         /* x is assume negative */
 105
 106     /*
 107      * argument reduction, make sure inexact flag not raised if input
 108      * is an integer
 109      */
 110         z = floorf(y);
 111         if(z!=y) {                              /* inexact anyway */
 112             y  *= (float)0.5;
 113             y   = (float)2.0*(y - floorf(y));   /* y = |x| mod 2.0 */
 114             n   = (int) (y*(float)4.0);
 115         } else {
 116             if(ix>=0x4b800000) {
 117                 y = zero; n = 0;                 /* y must be even */
 118             } else {
 119                 if(ix<0x4b000000) z = y+two23;  /* exact */
 120                 GET_FLOAT_WORD(n,z);
 121                 n &= 1;
 122                 y  = n;
 123                 n<<= 2;
 124             }
 125         }
 126         switch (n) {
 127             case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
 128             case 1:
 129             case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
 130             case 3:
 131             case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
 132             case 5:
 133             case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
 134             default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
 135             }
 136         return -y;
 137 }
 138
 139
 140 float
 141 __ieee754_lgammaf_r(float x, int *signgamp)
 142 {
 143         float t,y,z,nadj,p,p1,p2,p3,q,r,w;
 144         int i,hx,ix;
 145
 146         nadj = 0;
 147         GET_FLOAT_WORD(hx,x);
 148
 149     /* purge off +-inf, NaN, +-0, and negative arguments */
 150         *signgamp = 1;
 151         ix = hx&0x7fffffff;
 152         if(ix>=0x7f800000) return x*x;
 153         if(ix==0) return one/zero;
 154         if(ix<0x1c800000) {     /* |x|<2**-70, return -log(|x|) */
 155             if(hx<0) {
 156                 *signgamp = -1;
 157                 return -__ieee754_logf(-x);
 158             } else return -__ieee754_logf(x);
 159         }
 160         if(hx<0) {
 161             if(ix>=0x4b000000)  /* |x|>=2**23, must be -integer */
 162                 return one/zero;
 163             t = sin_pif(x);
 164             if(t==zero) return one/zero; /* -integer */
 165             nadj = __ieee754_logf(pi/fabsf(t*x));
 166             if(t<zero) *signgamp = -1;
 167             x = -x;
 168         }
 169
 170     /* purge off 1 and 2 */
 171         if (ix==0x3f800000||ix==0x40000000) r = 0;
 172     /* for x < 2.0 */
 173         else if(ix<0x40000000) {
 174             if(ix<=0x3f666666) {        /* lgamma(x) = lgamma(x+1)-log(x) */
 175                 r = -__ieee754_logf(x);
 176                 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
 177                 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
 178                 else {y = x; i=2;}
 179             } else {
 180                 r = zero;
 181                 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
 182                 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
 183                 else {y=x-one;i=2;}
 184             }
 185             switch(i) {
 186               case 0:
 187                 z = y*y;
 188                 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
 189                 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
 190                 p  = y*p1+p2;
 191                 r  += (p-(float)0.5*y); break;
 192               case 1:
 193                 z = y*y;
 194                 w = z*y;
 195                 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));    /* parallel comp */
 196                 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
 197                 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
 198                 p  = z*p1-(tt-w*(p2+y*p3));
 199                 r += (tf + p); break;
 200               case 2:
 201                 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
 202                 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
 203                 r += (-(float)0.5*y + p1/p2);
 204             }
 205         }
 206         else if(ix<0x41000000) {                        /* x < 8.0 */
 207             i = (int)x;
 208             t = zero;
 209             y = x-(float)i;
 210             p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
 211             q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
 212             r = half*y+p/q;
 213             z = one;    /* lgamma(1+s) = log(s) + lgamma(s) */
 214             switch(i) {
 215             case 7: z *= (y+(float)6.0);        /* FALLTHRU */
 216             case 6: z *= (y+(float)5.0);        /* FALLTHRU */
 217             case 5: z *= (y+(float)4.0);        /* FALLTHRU */
 218             case 4: z *= (y+(float)3.0);        /* FALLTHRU */
 219             case 3: z *= (y+(float)2.0);        /* FALLTHRU */
 220                     r += __ieee754_logf(z); break;
 221             }
 222     /* 8.0 <= x < 2**58 */
 223         } else if (ix < 0x5c800000) {
 224             t = __ieee754_logf(x);
 225             z = one/x;
 226             y = z*z;
 227             w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
 228             r = (x-half)*(t-one)+w;
 229         } else
 230     /* 2**58 <= x <= inf */
 231             r =  x*(__ieee754_logf(x)-one);
 232         if(hx<0) r = nadj - r;
 233         return r;
 234 }