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Annotation of src/lib/libm/src/e_lgammaf_r.c, Revision 1.6

1.1       jtc         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
1.5       simonb     11:  * software is freely granted, provided that this notice
1.1       jtc        12:  * is preserved.
                     13:  * ====================================================
                     14:  */
                     15:
1.4       lukem      16: #include <sys/cdefs.h>
1.2       jtc        17: #if defined(LIBM_SCCS) && !defined(lint)
1.6     ! wiz        18: __RCSID("$NetBSD: e_lgammaf_r.c,v 1.5 1999/07/02 15:37:40 simonb Exp $");
1.1       jtc        19: #endif
                     20:
                     21: #include "math.h"
                     22: #include "math_private.h"
                     23:
1.5       simonb     24: static const float
1.1       jtc        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:
1.6     ! wiz        94: static float
        !            95: sin_pif(float x)
1.1       jtc        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;
1.5       simonb    128:            case 1:
1.1       jtc       129:            case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
1.5       simonb    130:            case 3:
1.1       jtc       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:
1.6     ! wiz       140: float
        !           141: __ieee754_lgammaf_r(float x, int *signgamp)
1.1       jtc       142: {
                    143:        float t,y,z,nadj,p,p1,p2,p3,q,r,w;
                    144:        int i,hx,ix;
                    145:
1.4       lukem     146:        nadj = 0;
1.1       jtc       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;
1.5       simonb    200:              case 2:
1.1       jtc       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;
1.5       simonb    229:        } else
1.1       jtc       230:     /* 2**58 <= x <= inf */
                    231:            r =  x*(__ieee754_logf(x)-one);
                    232:        if(hx<0) r = nadj - r;
                    233:        return r;
                    234: }

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