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glibc  2.9
e_lgammaf_r.c
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00001 /* e_lgammaf_r.c -- float version of e_lgamma_r.c.
00002  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
00003  */
00004 
00005 /*
00006  * ====================================================
00007  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00008  *
00009  * Developed at SunPro, a Sun Microsystems, Inc. business.
00010  * Permission to use, copy, modify, and distribute this
00011  * software is freely granted, provided that this notice
00012  * is preserved.
00013  * ====================================================
00014  */
00015 
00016 #if defined(LIBM_SCCS) && !defined(lint)
00017 static char rcsid[] = "$NetBSD: e_lgammaf_r.c,v 1.3 1995/05/10 20:45:47 jtc Exp $";
00018 #endif
00019 
00020 #include "math.h"
00021 #include "math_private.h"
00022 
00023 #ifdef __STDC__
00024 static const float
00025 #else
00026 static float
00027 #endif
00028 two23=  8.3886080000e+06, /* 0x4b000000 */
00029 half=  5.0000000000e-01, /* 0x3f000000 */
00030 one =  1.0000000000e+00, /* 0x3f800000 */
00031 pi  =  3.1415927410e+00, /* 0x40490fdb */
00032 a0  =  7.7215664089e-02, /* 0x3d9e233f */
00033 a1  =  3.2246702909e-01, /* 0x3ea51a66 */
00034 a2  =  6.7352302372e-02, /* 0x3d89f001 */
00035 a3  =  2.0580807701e-02, /* 0x3ca89915 */
00036 a4  =  7.3855509982e-03, /* 0x3bf2027e */
00037 a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
00038 a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
00039 a7  =  5.1006977446e-04, /* 0x3a05b634 */
00040 a8  =  2.2086278477e-04, /* 0x39679767 */
00041 a9  =  1.0801156895e-04, /* 0x38e28445 */
00042 a10 =  2.5214456400e-05, /* 0x37d383a2 */
00043 a11 =  4.4864096708e-05, /* 0x383c2c75 */
00044 tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
00045 tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
00046 /* tt = -(tail of tf) */
00047 tt  =  6.6971006518e-09, /* 0x31e61c52 */
00048 t0  =  4.8383611441e-01, /* 0x3ef7b95e */
00049 t1  = -1.4758771658e-01, /* 0xbe17213c */
00050 t2  =  6.4624942839e-02, /* 0x3d845a15 */
00051 t3  = -3.2788541168e-02, /* 0xbd064d47 */
00052 t4  =  1.7970675603e-02, /* 0x3c93373d */
00053 t5  = -1.0314224288e-02, /* 0xbc28fcfe */
00054 t6  =  6.1005386524e-03, /* 0x3bc7e707 */
00055 t7  = -3.6845202558e-03, /* 0xbb7177fe */
00056 t8  =  2.2596477065e-03, /* 0x3b141699 */
00057 t9  = -1.4034647029e-03, /* 0xbab7f476 */
00058 t10 =  8.8108185446e-04, /* 0x3a66f867 */
00059 t11 = -5.3859531181e-04, /* 0xba0d3085 */
00060 t12 =  3.1563205994e-04, /* 0x39a57b6b */
00061 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
00062 t14 =  3.3552918467e-04, /* 0x39afe9f7 */
00063 u0  = -7.7215664089e-02, /* 0xbd9e233f */
00064 u1  =  6.3282704353e-01, /* 0x3f2200f4 */
00065 u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
00066 u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
00067 u4  =  2.2896373272e-01, /* 0x3e6a7578 */
00068 u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
00069 v1  =  2.4559779167e+00, /* 0x401d2ebe */
00070 v2  =  2.1284897327e+00, /* 0x4008392d */
00071 v3  =  7.6928514242e-01, /* 0x3f44efdf */
00072 v4  =  1.0422264785e-01, /* 0x3dd572af */
00073 v5  =  3.2170924824e-03, /* 0x3b52d5db */
00074 s0  = -7.7215664089e-02, /* 0xbd9e233f */
00075 s1  =  2.1498242021e-01, /* 0x3e5c245a */
00076 s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
00077 s3  =  1.4635047317e-01, /* 0x3e15dce6 */
00078 s4  =  2.6642270386e-02, /* 0x3cda40e4 */
00079 s5  =  1.8402845599e-03, /* 0x3af135b4 */
00080 s6  =  3.1947532989e-05, /* 0x3805ff67 */
00081 r1  =  1.3920053244e+00, /* 0x3fb22d3b */
00082 r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
00083 r3  =  1.7193385959e-01, /* 0x3e300f6e */
00084 r4  =  1.8645919859e-02, /* 0x3c98bf54 */
00085 r5  =  7.7794247773e-04, /* 0x3a4beed6 */
00086 r6  =  7.3266842264e-06, /* 0x36f5d7bd */
00087 w0  =  4.1893854737e-01, /* 0x3ed67f1d */
00088 w1  =  8.3333335817e-02, /* 0x3daaaaab */
00089 w2  = -2.7777778450e-03, /* 0xbb360b61 */
00090 w3  =  7.9365057172e-04, /* 0x3a500cfd */
00091 w4  = -5.9518753551e-04, /* 0xba1c065c */
00092 w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
00093 w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
00094 
00095 #ifdef __STDC__
00096 static const float zero=  0.0000000000e+00;
00097 #else
00098 static float zero=  0.0000000000e+00;
00099 #endif
00100 
00101 #ifdef __STDC__
00102        static float sin_pif(float x)
00103 #else
00104        static float sin_pif(x)
00105        float x;
00106 #endif
00107 {
00108        float y,z;
00109        int n,ix;
00110 
00111        GET_FLOAT_WORD(ix,x);
00112        ix &= 0x7fffffff;
00113 
00114        if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
00115        y = -x;              /* x is assume negative */
00116 
00117     /*
00118      * argument reduction, make sure inexact flag not raised if input
00119      * is an integer
00120      */
00121        z = __floorf(y);
00122        if(z!=y) {                         /* inexact anyway */
00123            y  *= (float)0.5;
00124            y   = (float)2.0*(y - __floorf(y));   /* y = |x| mod 2.0 */
00125            n   = (int) (y*(float)4.0);
00126        } else {
00127             if(ix>=0x4b800000) {
00128                 y = zero; n = 0;                 /* y must be even */
00129             } else {
00130                 if(ix<0x4b000000) z = y+two23;   /* exact */
00131               GET_FLOAT_WORD(n,z);
00132               n &= 1;
00133                 y  = n;
00134                 n<<= 2;
00135             }
00136         }
00137        switch (n) {
00138            case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
00139            case 1:
00140            case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
00141            case 3:
00142            case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
00143            case 5:
00144            case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
00145            default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
00146            }
00147        return -y;
00148 }
00149 
00150 
00151 #ifdef __STDC__
00152        float __ieee754_lgammaf_r(float x, int *signgamp)
00153 #else
00154        float __ieee754_lgammaf_r(x,signgamp)
00155        float x; int *signgamp;
00156 #endif
00157 {
00158        float t,y,z,nadj,p,p1,p2,p3,q,r,w;
00159        int i,hx,ix;
00160 
00161        GET_FLOAT_WORD(hx,x);
00162 
00163     /* purge off +-inf, NaN, +-0, and negative arguments */
00164        *signgamp = 1;
00165        ix = hx&0x7fffffff;
00166        if(ix>=0x7f800000) return x*x;
00167        if(ix==0)
00168          {
00169            if (hx < 0)
00170              *signgamp = -1;
00171            return one/fabsf(x);
00172          }
00173        if(ix<0x1c800000) {  /* |x|<2**-70, return -log(|x|) */
00174            if(hx<0) {
00175                *signgamp = -1;
00176                return -__ieee754_logf(-x);
00177            } else return -__ieee754_logf(x);
00178        }
00179        if(hx<0) {
00180            if(ix>=0x4b000000)      /* |x|>=2**23, must be -integer */
00181               return x/zero;
00182            t = sin_pif(x);
00183            if(t==zero) return one/fabsf(t); /* -integer */
00184            nadj = __ieee754_logf(pi/fabsf(t*x));
00185            if(t<zero) *signgamp = -1;
00186            x = -x;
00187        }
00188 
00189     /* purge off 1 and 2 */
00190        if (ix==0x3f800000||ix==0x40000000) r = 0;
00191     /* for x < 2.0 */
00192        else if(ix<0x40000000) {
00193            if(ix<=0x3f666666) {    /* lgamma(x) = lgamma(x+1)-log(x) */
00194               r = -__ieee754_logf(x);
00195               if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
00196               else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
00197               else {y = x; i=2;}
00198            } else {
00199               r = zero;
00200                if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
00201                else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
00202               else {y=x-one;i=2;}
00203            }
00204            switch(i) {
00205              case 0:
00206               z = y*y;
00207               p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
00208               p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
00209               p  = y*p1+p2;
00210               r  += (p-(float)0.5*y); break;
00211              case 1:
00212               z = y*y;
00213               w = z*y;
00214               p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));      /* parallel comp */
00215               p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
00216               p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
00217               p  = z*p1-(tt-w*(p2+y*p3));
00218               r += (tf + p); break;
00219              case 2:
00220               p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
00221               p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
00222               r += (-(float)0.5*y + p1/p2);
00223            }
00224        }
00225        else if(ix<0x41000000) {                  /* x < 8.0 */
00226            i = (int)x;
00227            t = zero;
00228            y = x-(float)i;
00229            p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
00230            q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
00231            r = half*y+p/q;
00232            z = one;  /* lgamma(1+s) = log(s) + lgamma(s) */
00233            switch(i) {
00234            case 7: z *= (y+(float)6.0);   /* FALLTHRU */
00235            case 6: z *= (y+(float)5.0);   /* FALLTHRU */
00236            case 5: z *= (y+(float)4.0);   /* FALLTHRU */
00237            case 4: z *= (y+(float)3.0);   /* FALLTHRU */
00238            case 3: z *= (y+(float)2.0);   /* FALLTHRU */
00239                   r += __ieee754_logf(z); break;
00240            }
00241     /* 8.0 <= x < 2**58 */
00242        } else if (ix < 0x5c800000) {
00243            t = __ieee754_logf(x);
00244            z = one/x;
00245            y = z*z;
00246            w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
00247            r = (x-half)*(t-one)+w;
00248        } else
00249     /* 2**58 <= x <= inf */
00250            r =  x*(__ieee754_logf(x)-one);
00251        if(hx<0) r = nadj - r;
00252        return r;
00253 }