gonzui

    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 "math.h"
   17: #include "math_private.h"
   18: 
   19: static const float 
   20: two23=  8.3886080000e+06, /* 0x4b000000 */
   21: half=  5.0000000000e-01, /* 0x3f000000 */
   22: one =  1.0000000000e+00, /* 0x3f800000 */
   23: pi  =  3.1415927410e+00, /* 0x40490fdb */
   24: a0  =  7.7215664089e-02, /* 0x3d9e233f */
   25: a1  =  3.2246702909e-01, /* 0x3ea51a66 */
   26: a2  =  6.7352302372e-02, /* 0x3d89f001 */
   27: a3  =  2.0580807701e-02, /* 0x3ca89915 */
   28: a4  =  7.3855509982e-03, /* 0x3bf2027e */
   29: a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
   30: a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
   31: a7  =  5.1006977446e-04, /* 0x3a05b634 */
   32: a8  =  2.2086278477e-04, /* 0x39679767 */
   33: a9  =  1.0801156895e-04, /* 0x38e28445 */
   34: a10 =  2.5214456400e-05, /* 0x37d383a2 */
   35: a11 =  4.4864096708e-05, /* 0x383c2c75 */
   36: tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
   37: tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
   38: /* tt = -(tail of tf) */
   39: tt  =  6.6971006518e-09, /* 0x31e61c52 */
   40: t0  =  4.8383611441e-01, /* 0x3ef7b95e */
   41: t1  = -1.4758771658e-01, /* 0xbe17213c */
   42: t2  =  6.4624942839e-02, /* 0x3d845a15 */
   43: t3  = -3.2788541168e-02, /* 0xbd064d47 */
   44: t4  =  1.7970675603e-02, /* 0x3c93373d */
   45: t5  = -1.0314224288e-02, /* 0xbc28fcfe */
   46: t6  =  6.1005386524e-03, /* 0x3bc7e707 */
   47: t7  = -3.6845202558e-03, /* 0xbb7177fe */
   48: t8  =  2.2596477065e-03, /* 0x3b141699 */
   49: t9  = -1.4034647029e-03, /* 0xbab7f476 */
   50: t10 =  8.8108185446e-04, /* 0x3a66f867 */
   51: t11 = -5.3859531181e-04, /* 0xba0d3085 */
   52: t12 =  3.1563205994e-04, /* 0x39a57b6b */
   53: t13 = -3.1275415677e-04, /* 0xb9a3f927 */
   54: t14 =  3.3552918467e-04, /* 0x39afe9f7 */
   55: u0  = -7.7215664089e-02, /* 0xbd9e233f */
   56: u1  =  6.3282704353e-01, /* 0x3f2200f4 */
   57: u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
   58: u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
   59: u4  =  2.2896373272e-01, /* 0x3e6a7578 */
   60: u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
   61: v1  =  2.4559779167e+00, /* 0x401d2ebe */
   62: v2  =  2.1284897327e+00, /* 0x4008392d */
   63: v3  =  7.6928514242e-01, /* 0x3f44efdf */
   64: v4  =  1.0422264785e-01, /* 0x3dd572af */
   65: v5  =  3.2170924824e-03, /* 0x3b52d5db */
   66: s0  = -7.7215664089e-02, /* 0xbd9e233f */
   67: s1  =  2.1498242021e-01, /* 0x3e5c245a */
   68: s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
   69: s3  =  1.4635047317e-01, /* 0x3e15dce6 */
   70: s4  =  2.6642270386e-02, /* 0x3cda40e4 */
   71: s5  =  1.8402845599e-03, /* 0x3af135b4 */
   72: s6  =  3.1947532989e-05, /* 0x3805ff67 */
   73: r1  =  1.3920053244e+00, /* 0x3fb22d3b */
   74: r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
   75: r3  =  1.7193385959e-01, /* 0x3e300f6e */
   76: r4  =  1.8645919859e-02, /* 0x3c98bf54 */
   77: r5  =  7.7794247773e-04, /* 0x3a4beed6 */
   78: r6  =  7.3266842264e-06, /* 0x36f5d7bd */
   79: w0  =  4.1893854737e-01, /* 0x3ed67f1d */
   80: w1  =  8.3333335817e-02, /* 0x3daaaaab */
   81: w2  = -2.7777778450e-03, /* 0xbb360b61 */
   82: w3  =  7.9365057172e-04, /* 0x3a500cfd */
   83: w4  = -5.9518753551e-04, /* 0xba1c065c */
   84: w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
   85: w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
   86: 
   87: static const float zero=  0.0000000000e+00;
   88: 
   89: static float
   90: sin_pif(float x)
   91: {
   92:         float y,z;
   93:         int n,ix;
   94: 
   95:         GET_FLOAT_WORD(ix,x);
   96:         ix &= 0x7fffffff;
   97: 
   98:         if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
   99:         y = -x;                /* x is assume negative */
  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  *= (float)0.5;
  108:             y   = (float)2.0*(y - floorf(y));  /* y = |x| mod 2.0 */
  109:             n   = (int) (y*(float)4.0);
  110:         } else {
  111:             if(ix>=0x4b800000) {
  112:                 y = zero; n = 0;                 /* y must be even */
  113:             } else {
  114:                 if(ix<0x4b000000) z = y+two23;  /* exact */
  115:                 GET_FLOAT_WORD(n,z);
  116:                 n &= 1;
  117:                 y  = n;
  118:                 n<<= 2;
  119:             }
  120:         }
  121:         switch (n) {
  122:             case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
  123:             case 1:   
  124:             case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
  125:             case 3:  
  126:             case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
  127:             case 5:
  128:             case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
  129:             default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
  130:             }
  131:         return -y;
  132: }
  133: 
  134: 
  135: float
  136: lgammaf_r(float x, int *signgamp)
  137: {
  138:         float t,y,z,nadj,p,p1,p2,p3,q,r,w;
  139:         int i,hx,ix;
  140: 
  141:         GET_FLOAT_WORD(hx,x);
  142: 
  143:     /* purge off +-inf, NaN, +-0, and negative arguments */
  144:         *signgamp = 1;
  145:         ix = hx&0x7fffffff;
  146:         if(ix>=0x7f800000) return x*x;
  147:         if(ix==0) {
  148:             if(hx<0)
  149:                 *signgamp = -1;
  150:             return one/zero;
  151:         }
  152:         if(ix<0x1c800000) {    /* |x|<2**-70, return -log(|x|) */
  153:             if(hx<0) {
  154:                 *signgamp = -1;
  155:                 return - logf(-x);
  156:             } else return - logf(x);
  157:         }
  158:         if(hx<0) {
  159:             if(ix>=0x4b000000)         /* |x|>=2**23, must be -integer */
  160:                 return one/zero;
  161:             t = sin_pif(x);
  162:             if(t==zero) return one/zero; /* -integer */
  163:             nadj = logf(pi/fabsf(t*x));
  164:             if(t<zero) *signgamp = -1;
  165:             x = -x;
  166:         }
  167: 
  168:     /* purge off 1 and 2 */
  169:         if (ix==0x3f800000||ix==0x40000000) r = 0;
  170:     /* for x < 2.0 */
  171:         else if(ix<0x40000000) {
  172:             if(ix<=0x3f666666) {       /* lgamma(x) = lgamma(x+1)-log(x) */
  173:                 r = - logf(x);
  174:                 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
  175:                 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
  176:                else {y = x; i=2;}
  177:             } else {
  178:                r = zero;
  179:                 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
  180:                 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
  181:                 else {y=x-one;i=2;}
  182:             }
  183:             switch(i) {
  184:               case 0:
  185:                 z = y*y;
  186:                 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
  187:                 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
  188:                 p  = y*p1+p2;
  189:                 r  += (p-(float)0.5*y); break;
  190:               case 1:
  191:                 z = y*y;
  192:                 w = z*y;
  193:                 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));  /* parallel comp */
  194:                 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
  195:                 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
  196:                 p  = z*p1-(tt-w*(p2+y*p3));
  197:                 r += (tf + p); break;
  198:               case 2:  
  199:                 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
  200:                 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
  201:                 r += (-(float)0.5*y + p1/p2);
  202:             }
  203:         }
  204:         else if(ix<0x41000000) {                       /* x < 8.0 */
  205:             i = (int)x;
  206:             t = zero;
  207:             y = x-(float)i;
  208:             p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
  209:             q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
  210:             r = half*y+p/q;
  211:             z = one;   /* lgamma(1+s) = log(s) + lgamma(s) */
  212:             switch(i) {
  213:             case 7: z *= (y+(float)6.0);       /* FALLTHRU */
  214:             case 6: z *= (y+(float)5.0);       /* FALLTHRU */
  215:             case 5: z *= (y+(float)4.0);       /* FALLTHRU */
  216:             case 4: z *= (y+(float)3.0);       /* FALLTHRU */
  217:             case 3: z *= (y+(float)2.0);       /* FALLTHRU */
  218:                     r += logf(z); break;
  219:             }
  220:     /* 8.0 <= x < 2**58 */
  221:         } else if (ix < 0x5c800000) {
  222:             t = logf(x);
  223:             z = one/x;
  224:             y = z*z;
  225:             w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
  226:             r = (x-half)*(t-one)+w;
  227:         } else 
  228:     /* 2**58 <= x <= inf */
  229:             r =  x*(logf(x)-one);
  230:         if(hx<0) r = nadj - r;
  231:         return r;
  232: }