libpok-refman-current-html/html/e__lgammaf__r_8c_source.html

00001 /*
00002  *                               POK header
00003  *
00004  * The following file is a part of the POK project. Any modification should
00005  * made according to the POK licence. You CANNOT use this file or a part of
00006  * this file is this part of a file for your own project
00007  *
00008  * For more information on the POK licence, please see our LICENCE FILE
00009  *
00010  * Please follow the coding guidelines described in doc/CODING_GUIDELINES
00011  *
00012  *                                      Copyright (c) 2007-2009 POK team
00013  *
00014  * Created by julien on Fri Jan 30 14:41:34 2009
00015  */
00016
00017 /* e_lgammaf_r.c -- float version of e_lgamma_r.c.
00018  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
00019  */
00020
00021 /*
00022  * ====================================================
00023  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00024  *
00025  * Developed at SunPro, a Sun Microsystems, Inc. business.
00026  * Permission to use, copy, modify, and distribute this
00027  * software is freely granted, provided that this notice
00028  * is preserved.
00029  * ====================================================
00030  */
00031
00032 #ifdef POK_NEEDS_LIBMATH
00033
00034 #include <libm.h>
00035 #include "math_private.h"
00036
00037 static const float
00038 two23=  8.3886080000e+06, /* 0x4b000000 */
00039 half=  5.0000000000e-01, /* 0x3f000000 */
00040 one =  1.0000000000e+00, /* 0x3f800000 */
00041 pi  =  3.1415927410e+00, /* 0x40490fdb */
00042 a0  =  7.7215664089e-02, /* 0x3d9e233f */
00043 a1  =  3.2246702909e-01, /* 0x3ea51a66 */
00044 a2  =  6.7352302372e-02, /* 0x3d89f001 */
00045 a3  =  2.0580807701e-02, /* 0x3ca89915 */
00046 a4  =  7.3855509982e-03, /* 0x3bf2027e */
00047 a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
00048 a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
00049 a7  =  5.1006977446e-04, /* 0x3a05b634 */
00050 a8  =  2.2086278477e-04, /* 0x39679767 */
00051 a9  =  1.0801156895e-04, /* 0x38e28445 */
00052 a10 =  2.5214456400e-05, /* 0x37d383a2 */
00053 a11 =  4.4864096708e-05, /* 0x383c2c75 */
00054 tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
00055 tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
00056 /* tt = -(tail of tf) */
00057 tt  =  6.6971006518e-09, /* 0x31e61c52 */
00058 t0  =  4.8383611441e-01, /* 0x3ef7b95e */
00059 t1  = -1.4758771658e-01, /* 0xbe17213c */
00060 t2  =  6.4624942839e-02, /* 0x3d845a15 */
00061 t3  = -3.2788541168e-02, /* 0xbd064d47 */
00062 t4  =  1.7970675603e-02, /* 0x3c93373d */
00063 t5  = -1.0314224288e-02, /* 0xbc28fcfe */
00064 t6  =  6.1005386524e-03, /* 0x3bc7e707 */
00065 t7  = -3.6845202558e-03, /* 0xbb7177fe */
00066 t8  =  2.2596477065e-03, /* 0x3b141699 */
00067 t9  = -1.4034647029e-03, /* 0xbab7f476 */
00068 t10 =  8.8108185446e-04, /* 0x3a66f867 */
00069 t11 = -5.3859531181e-04, /* 0xba0d3085 */
00070 t12 =  3.1563205994e-04, /* 0x39a57b6b */
00071 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
00072 t14 =  3.3552918467e-04, /* 0x39afe9f7 */
00073 u0  = -7.7215664089e-02, /* 0xbd9e233f */
00074 u1  =  6.3282704353e-01, /* 0x3f2200f4 */
00075 u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
00076 u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
00077 u4  =  2.2896373272e-01, /* 0x3e6a7578 */
00078 u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
00079 v1  =  2.4559779167e+00, /* 0x401d2ebe */
00080 v2  =  2.1284897327e+00, /* 0x4008392d */
00081 v3  =  7.6928514242e-01, /* 0x3f44efdf */
00082 v4  =  1.0422264785e-01, /* 0x3dd572af */
00083 v5  =  3.2170924824e-03, /* 0x3b52d5db */
00084 s0  = -7.7215664089e-02, /* 0xbd9e233f */
00085 s1  =  2.1498242021e-01, /* 0x3e5c245a */
00086 s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
00087 s3  =  1.4635047317e-01, /* 0x3e15dce6 */
00088 s4  =  2.6642270386e-02, /* 0x3cda40e4 */
00089 s5  =  1.8402845599e-03, /* 0x3af135b4 */
00090 s6  =  3.1947532989e-05, /* 0x3805ff67 */
00091 r1  =  1.3920053244e+00, /* 0x3fb22d3b */
00092 r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
00093 r3  =  1.7193385959e-01, /* 0x3e300f6e */
00094 r4  =  1.8645919859e-02, /* 0x3c98bf54 */
00095 r5  =  7.7794247773e-04, /* 0x3a4beed6 */
00096 r6  =  7.3266842264e-06, /* 0x36f5d7bd */
00097 w0  =  4.1893854737e-01, /* 0x3ed67f1d */
00098 w1  =  8.3333335817e-02, /* 0x3daaaaab */
00099 w2  = -2.7777778450e-03, /* 0xbb360b61 */
00100 w3  =  7.9365057172e-04, /* 0x3a500cfd */
00101 w4  = -5.9518753551e-04, /* 0xba1c065c */
00102 w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
00103 w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
00104
00105 static const float zero=  0.0000000000e+00;
00106
00107 static float
00108 sin_pif(float x)
00109 {
00110         float y,z;
00111         int n,ix;
00112
00113         GET_FLOAT_WORD(ix,x);
00114         ix &= 0x7fffffff;
00115
00116         if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
00117         y = -x;         /* x is assume negative */
00118
00119     /*
00120      * argument reduction, make sure inexact flag not raised if input
00121      * is an integer
00122      */
00123         z = floorf(y);
00124         if(z!=y) {                              /* inexact anyway */
00125             y  *= (float)0.5;
00126             y   = (float)2.0*(y - floorf(y));   /* y = |x| mod 2.0 */
00127             n   = (int) (y*(float)4.0);
00128         } else {
00129             if(ix>=0x4b800000) {
00130                 y = zero; n = 0;                 /* y must be even */
00131             } else {
00132                 if(ix<0x4b000000) z = y+two23;  /* exact */
00133                 GET_FLOAT_WORD(n,z);
00134                 n &= 1;
00135                 y  = n;
00136                 n<<= 2;
00137             }
00138         }
00139         switch (n) {
00140             case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
00141             case 1:
00142             case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
00143             case 3:
00144             case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
00145             case 5:
00146             case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
00147             default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
00148             }
00149         return -y;
00150 }
00151
00152
00153 float
00154 __ieee754_lgammaf_r(float x, int *signgamp)
00155 {
00156         float t,y,z,nadj,p,p1,p2,p3,q,r,w;
00157         int i,hx,ix;
00158
00159         nadj = 0;
00160         GET_FLOAT_WORD(hx,x);
00161
00162     /* purge off +-inf, NaN, +-0, and negative arguments */
00163         *signgamp = 1;
00164         ix = hx&0x7fffffff;
00165         if(ix>=0x7f800000) return x*x;
00166         if(ix==0) return one/zero;
00167         if(ix<0x1c800000) {     /* |x|<2**-70, return -log(|x|) */
00168             if(hx<0) {
00169                 *signgamp = -1;
00170                 return -__ieee754_logf(-x);
00171             } else return -__ieee754_logf(x);
00172         }
00173         if(hx<0) {
00174             if(ix>=0x4b000000)  /* |x|>=2**23, must be -integer */
00175                 return one/zero;
00176             t = sin_pif(x);
00177             if(t==zero) return one/zero; /* -integer */
00178             nadj = __ieee754_logf(pi/fabsf(t*x));
00179             if(t<zero) *signgamp = -1;
00180             x = -x;
00181         }
00182
00183     /* purge off 1 and 2 */
00184         if (ix==0x3f800000||ix==0x40000000) r = 0;
00185     /* for x < 2.0 */
00186         else if(ix<0x40000000) {
00187             if(ix<=0x3f666666) {        /* lgamma(x) = lgamma(x+1)-log(x) */
00188                 r = -__ieee754_logf(x);
00189                 if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
00190                 else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
00191                 else {y = x; i=2;}
00192             } else {
00193                 r = zero;
00194                 if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
00195                 else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
00196                 else {y=x-one;i=2;}
00197             }
00198             switch(i) {
00199               case 0:
00200                 z = y*y;
00201                 p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
00202                 p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
00203                 p  = y*p1+p2;
00204                 r  += (p-(float)0.5*y); break;
00205               case 1:
00206                 z = y*y;
00207                 w = z*y;
00208                 p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));    /* parallel comp */
00209                 p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
00210                 p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
00211                 p  = z*p1-(tt-w*(p2+y*p3));
00212                 r += (tf + p); break;
00213               case 2:
00214                 p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
00215                 p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
00216                 r += (-(float)0.5*y + p1/p2);
00217             }
00218         }
00219         else if(ix<0x41000000) {                        /* x < 8.0 */
00220             i = (int)x;
00221             t = zero;
00222             y = x-(float)i;
00223             p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
00224             q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
00225             r = half*y+p/q;
00226             z = one;    /* lgamma(1+s) = log(s) + lgamma(s) */
00227             switch(i) {
00228             case 7: z *= (y+(float)6.0);        /* FALLTHRU */
00229             case 6: z *= (y+(float)5.0);        /* FALLTHRU */
00230             case 5: z *= (y+(float)4.0);        /* FALLTHRU */
00231             case 4: z *= (y+(float)3.0);        /* FALLTHRU */
00232             case 3: z *= (y+(float)2.0);        /* FALLTHRU */
00233                     r += __ieee754_logf(z); break;
00234             }
00235     /* 8.0 <= x < 2**58 */
00236         } else if (ix < 0x5c800000) {
00237             t = __ieee754_logf(x);
00238             z = one/x;
00239             y = z*z;
00240             w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
00241             r = (x-half)*(t-one)+w;
00242         } else
00243     /* 2**58 <= x <= inf */
00244             r =  x*(__ieee754_logf(x)-one);
00245         if(hx<0) r = nadj - r;
00246         return r;
00247 }
00248
00249 #endif
00250