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[/] [or1k/] [trunk/] [newlib-1.10.0/] [newlib/] [libm/] [math/] [erf_lgamma.c] - Blame information for rev 1765

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1 1010 ivang
/* erf_lgamma.c -- float version of er_lgamma.c.
2
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 */
4
 
5
/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 *
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 */
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#include "fdlibm.h"
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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two23=  8.3886080000e+06, /* 0x4b000000 */
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half=  5.0000000000e-01, /* 0x3f000000 */
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one =  1.0000000000e+00, /* 0x3f800000 */
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pi  =  3.1415927410e+00, /* 0x40490fdb */
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a0  =  7.7215664089e-02, /* 0x3d9e233f */
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a1  =  3.2246702909e-01, /* 0x3ea51a66 */
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a2  =  6.7352302372e-02, /* 0x3d89f001 */
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a3  =  2.0580807701e-02, /* 0x3ca89915 */
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a4  =  7.3855509982e-03, /* 0x3bf2027e */
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a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
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a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
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a7  =  5.1006977446e-04, /* 0x3a05b634 */
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a8  =  2.2086278477e-04, /* 0x39679767 */
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a9  =  1.0801156895e-04, /* 0x38e28445 */
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a10 =  2.5214456400e-05, /* 0x37d383a2 */
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a11 =  4.4864096708e-05, /* 0x383c2c75 */
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tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
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tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
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/* tt = -(tail of tf) */
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tt  =  6.6971006518e-09, /* 0x31e61c52 */
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t0  =  4.8383611441e-01, /* 0x3ef7b95e */
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t1  = -1.4758771658e-01, /* 0xbe17213c */
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t2  =  6.4624942839e-02, /* 0x3d845a15 */
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t3  = -3.2788541168e-02, /* 0xbd064d47 */
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t4  =  1.7970675603e-02, /* 0x3c93373d */
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t5  = -1.0314224288e-02, /* 0xbc28fcfe */
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t6  =  6.1005386524e-03, /* 0x3bc7e707 */
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t7  = -3.6845202558e-03, /* 0xbb7177fe */
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t8  =  2.2596477065e-03, /* 0x3b141699 */
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t9  = -1.4034647029e-03, /* 0xbab7f476 */
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t10 =  8.8108185446e-04, /* 0x3a66f867 */
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t11 = -5.3859531181e-04, /* 0xba0d3085 */
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t12 =  3.1563205994e-04, /* 0x39a57b6b */
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t13 = -3.1275415677e-04, /* 0xb9a3f927 */
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t14 =  3.3552918467e-04, /* 0x39afe9f7 */
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u0  = -7.7215664089e-02, /* 0xbd9e233f */
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u1  =  6.3282704353e-01, /* 0x3f2200f4 */
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u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
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u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
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u4  =  2.2896373272e-01, /* 0x3e6a7578 */
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u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
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v1  =  2.4559779167e+00, /* 0x401d2ebe */
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v2  =  2.1284897327e+00, /* 0x4008392d */
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v3  =  7.6928514242e-01, /* 0x3f44efdf */
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v4  =  1.0422264785e-01, /* 0x3dd572af */
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v5  =  3.2170924824e-03, /* 0x3b52d5db */
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s0  = -7.7215664089e-02, /* 0xbd9e233f */
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s1  =  2.1498242021e-01, /* 0x3e5c245a */
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s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
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s3  =  1.4635047317e-01, /* 0x3e15dce6 */
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s4  =  2.6642270386e-02, /* 0x3cda40e4 */
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s5  =  1.8402845599e-03, /* 0x3af135b4 */
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s6  =  3.1947532989e-05, /* 0x3805ff67 */
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r1  =  1.3920053244e+00, /* 0x3fb22d3b */
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r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
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r3  =  1.7193385959e-01, /* 0x3e300f6e */
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r4  =  1.8645919859e-02, /* 0x3c98bf54 */
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r5  =  7.7794247773e-04, /* 0x3a4beed6 */
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r6  =  7.3266842264e-06, /* 0x36f5d7bd */
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w0  =  4.1893854737e-01, /* 0x3ed67f1d */
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w1  =  8.3333335817e-02, /* 0x3daaaaab */
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w2  = -2.7777778450e-03, /* 0xbb360b61 */
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w3  =  7.9365057172e-04, /* 0x3a500cfd */
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w4  = -5.9518753551e-04, /* 0xba1c065c */
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w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
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w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
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#ifdef __STDC__
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static const float zero=  0.0000000000e+00;
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#else
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static float zero=  0.0000000000e+00;
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#endif
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#ifdef __STDC__
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        static float sin_pif(float x)
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#else
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        static float sin_pif(x)
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        float x;
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#endif
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{
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        float y,z;
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        __int32_t n,ix;
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        GET_FLOAT_WORD(ix,x);
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        ix &= 0x7fffffff;
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110
        if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
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        y = -x;         /* x is assume negative */
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113
    /*
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     * argument reduction, make sure inexact flag not raised if input
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     * is an integer
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     */
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        z = floorf(y);
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        if(z!=y) {                              /* inexact anyway */
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            y  *= (float)0.5;
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            y   = (float)2.0*(y - floorf(y));   /* y = |x| mod 2.0 */
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            n   = (__int32_t) (y*(float)4.0);
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        } else {
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            if(ix>=0x4b800000) {
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                y = zero; n = 0;                 /* y must be even */
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            } else {
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                if(ix<0x4b000000) z = y+two23;  /* exact */
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                GET_FLOAT_WORD(n,z);
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                n &= 1;
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                y  = n;
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                n<<= 2;
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            }
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        }
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        switch (n) {
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            case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
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            case 1:
136
            case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
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            case 3:
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            case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
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            case 5:
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            case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
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            default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
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            }
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        return -y;
144
}
145
 
146
 
147
#ifdef __STDC__
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        float __ieee754_lgammaf_r(float x, int *signgamp)
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#else
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        float __ieee754_lgammaf_r(x,signgamp)
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        float x; int *signgamp;
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#endif
153
{
154
        float t,y,z,nadj,p,p1,p2,p3,q,r,w;
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        __int32_t i,hx,ix;
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157
        GET_FLOAT_WORD(hx,x);
158
 
159
    /* purge off +-inf, NaN, +-0, and negative arguments */
160
        *signgamp = 1;
161
        ix = hx&0x7fffffff;
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        if(ix>=0x7f800000) return x*x;
163
        if(ix==0) return one/zero;
164
        if(ix<0x1c800000) {     /* |x|<2**-70, return -log(|x|) */
165
            if(hx<0) {
166
                *signgamp = -1;
167
                return -__ieee754_logf(-x);
168
            } else return -__ieee754_logf(x);
169
        }
170
        if(hx<0) {
171
            if(ix>=0x4b000000)  /* |x|>=2**23, must be -integer */
172
                return one/zero;
173
            t = sin_pif(x);
174
            if(t==zero) return one/zero; /* -integer */
175
            nadj = __ieee754_logf(pi/fabsf(t*x));
176
            if(t<zero) *signgamp = -1;
177
            x = -x;
178
        }
179
 
180
    /* purge off 1 and 2 */
181
        if (ix==0x3f800000||ix==0x40000000) r = 0;
182
    /* for x < 2.0 */
183
        else if(ix<0x40000000) {
184
            if(ix<=0x3f666666) {        /* lgamma(x) = lgamma(x+1)-log(x) */
185
                r = -__ieee754_logf(x);
186
                if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
187
                else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
188
                else {y = x; i=2;}
189
            } else {
190
                r = zero;
191
                if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
192
                else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
193
                else {y=x-one;i=2;}
194
            }
195
            switch(i) {
196
              case 0:
197
                z = y*y;
198
                p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
199
                p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
200
                p  = y*p1+p2;
201
                r  += (p-(float)0.5*y); break;
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              case 1:
203
                z = y*y;
204
                w = z*y;
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                p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));    /* parallel comp */
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                p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
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                p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
208
                p  = z*p1-(tt-w*(p2+y*p3));
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                r += (tf + p); break;
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              case 2:
211
                p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
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                p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
213
                r += (-(float)0.5*y + p1/p2);
214
            }
215
        }
216
        else if(ix<0x41000000) {                        /* x < 8.0 */
217
            i = (__int32_t)x;
218
            t = zero;
219
            y = x-(float)i;
220
            p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
221
            q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
222
            r = half*y+p/q;
223
            z = one;    /* lgamma(1+s) = log(s) + lgamma(s) */
224
            switch(i) {
225
            case 7: z *= (y+(float)6.0);        /* FALLTHRU */
226
            case 6: z *= (y+(float)5.0);        /* FALLTHRU */
227
            case 5: z *= (y+(float)4.0);        /* FALLTHRU */
228
            case 4: z *= (y+(float)3.0);        /* FALLTHRU */
229
            case 3: z *= (y+(float)2.0);        /* FALLTHRU */
230
                    r += __ieee754_logf(z); break;
231
            }
232
    /* 8.0 <= x < 2**58 */
233
        } else if (ix < 0x5c800000) {
234
            t = __ieee754_logf(x);
235
            z = one/x;
236
            y = z*z;
237
            w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
238
            r = (x-half)*(t-one)+w;
239
        } else
240
    /* 2**58 <= x <= inf */
241
            r =  x*(__ieee754_logf(x)-one);
242
        if(hx<0) r = nadj - r;
243
        return r;
244
}

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