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      1 /* e_lgammaf_r.c -- float version of e_lgamma_r.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 <sys/cdefs.h>
     17 __FBSDID("$FreeBSD$");
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 static const float
     23 two23=  8.3886080000e+06, /* 0x4b000000 */
     24 half=  5.0000000000e-01, /* 0x3f000000 */
     25 one =  1.0000000000e+00, /* 0x3f800000 */
     26 pi  =  3.1415927410e+00, /* 0x40490fdb */
     27 a0  =  7.7215664089e-02, /* 0x3d9e233f */
     28 a1  =  3.2246702909e-01, /* 0x3ea51a66 */
     29 a2  =  6.7352302372e-02, /* 0x3d89f001 */
     30 a3  =  2.0580807701e-02, /* 0x3ca89915 */
     31 a4  =  7.3855509982e-03, /* 0x3bf2027e */
     32 a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
     33 a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
     34 a7  =  5.1006977446e-04, /* 0x3a05b634 */
     35 a8  =  2.2086278477e-04, /* 0x39679767 */
     36 a9  =  1.0801156895e-04, /* 0x38e28445 */
     37 a10 =  2.5214456400e-05, /* 0x37d383a2 */
     38 a11 =  4.4864096708e-05, /* 0x383c2c75 */
     39 tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
     40 tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
     41 /* tt = -(tail of tf) */
     42 tt  =  6.6971006518e-09, /* 0x31e61c52 */
     43 t0  =  4.8383611441e-01, /* 0x3ef7b95e */
     44 t1  = -1.4758771658e-01, /* 0xbe17213c */
     45 t2  =  6.4624942839e-02, /* 0x3d845a15 */
     46 t3  = -3.2788541168e-02, /* 0xbd064d47 */
     47 t4  =  1.7970675603e-02, /* 0x3c93373d */
     48 t5  = -1.0314224288e-02, /* 0xbc28fcfe */
     49 t6  =  6.1005386524e-03, /* 0x3bc7e707 */
     50 t7  = -3.6845202558e-03, /* 0xbb7177fe */
     51 t8  =  2.2596477065e-03, /* 0x3b141699 */
     52 t9  = -1.4034647029e-03, /* 0xbab7f476 */
     53 t10 =  8.8108185446e-04, /* 0x3a66f867 */
     54 t11 = -5.3859531181e-04, /* 0xba0d3085 */
     55 t12 =  3.1563205994e-04, /* 0x39a57b6b */
     56 t13 = -3.1275415677e-04, /* 0xb9a3f927 */
     57 t14 =  3.3552918467e-04, /* 0x39afe9f7 */
     58 u0  = -7.7215664089e-02, /* 0xbd9e233f */
     59 u1  =  6.3282704353e-01, /* 0x3f2200f4 */
     60 u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
     61 u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
     62 u4  =  2.2896373272e-01, /* 0x3e6a7578 */
     63 u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
     64 v1  =  2.4559779167e+00, /* 0x401d2ebe */
     65 v2  =  2.1284897327e+00, /* 0x4008392d */
     66 v3  =  7.6928514242e-01, /* 0x3f44efdf */
     67 v4  =  1.0422264785e-01, /* 0x3dd572af */
     68 v5  =  3.2170924824e-03, /* 0x3b52d5db */
     69 s0  = -7.7215664089e-02, /* 0xbd9e233f */
     70 s1  =  2.1498242021e-01, /* 0x3e5c245a */
     71 s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
     72 s3  =  1.4635047317e-01, /* 0x3e15dce6 */
     73 s4  =  2.6642270386e-02, /* 0x3cda40e4 */
     74 s5  =  1.8402845599e-03, /* 0x3af135b4 */
     75 s6  =  3.1947532989e-05, /* 0x3805ff67 */
     76 r1  =  1.3920053244e+00, /* 0x3fb22d3b */
     77 r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
     78 r3  =  1.7193385959e-01, /* 0x3e300f6e */
     79 r4  =  1.8645919859e-02, /* 0x3c98bf54 */
     80 r5  =  7.7794247773e-04, /* 0x3a4beed6 */
     81 r6  =  7.3266842264e-06, /* 0x36f5d7bd */
     82 w0  =  4.1893854737e-01, /* 0x3ed67f1d */
     83 w1  =  8.3333335817e-02, /* 0x3daaaaab */
     84 w2  = -2.7777778450e-03, /* 0xbb360b61 */
     85 w3  =  7.9365057172e-04, /* 0x3a500cfd */
     86 w4  = -5.9518753551e-04, /* 0xba1c065c */
     87 w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
     88 w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
     89 
     90 static const float zero=  0.0000000000e+00;
     91 
     92 	static float sin_pif(float x)
     93 {
     94 	float y,z;
     95 	int n,ix;
     96 
     97 	GET_FLOAT_WORD(ix,x);
     98 	ix &= 0x7fffffff;
     99 
    100 	if(ix<0x3e800000) return __kernel_sindf(pi*x);
    101 	y = -x;		/* x is assume negative */
    102 
    103     /*
    104      * argument reduction, make sure inexact flag not raised if input
    105      * is an integer
    106      */
    107 	z = floorf(y);
    108 	if(z!=y) {				/* inexact anyway */
    109 	    y  *= (float)0.5;
    110 	    y   = (float)2.0*(y - floorf(y));	/* y = |x| mod 2.0 */
    111 	    n   = (int) (y*(float)4.0);
    112 	} else {
    113             if(ix>=0x4b800000) {
    114                 y = zero; n = 0;                 /* y must be even */
    115             } else {
    116                 if(ix<0x4b000000) z = y+two23;	/* exact */
    117 		GET_FLOAT_WORD(n,z);
    118 		n &= 1;
    119                 y  = n;
    120                 n<<= 2;
    121             }
    122         }
    123 	switch (n) {
    124 	    case 0:   y =  __kernel_sindf(pi*y); break;
    125 	    case 1:
    126 	    case 2:   y =  __kernel_cosdf(pi*((float)0.5-y)); break;
    127 	    case 3:
    128 	    case 4:   y =  __kernel_sindf(pi*(one-y)); break;
    129 	    case 5:
    130 	    case 6:   y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
    131 	    default:  y =  __kernel_sindf(pi*(y-(float)2.0)); break;
    132 	    }
    133 	return -y;
    134 }
    135 
    136 
    137 float
    138 __ieee754_lgammaf_r(float x, int *signgamp)
    139 {
    140 	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
    141 	int32_t hx;
    142 	int i,ix;
    143 
    144 	GET_FLOAT_WORD(hx,x);
    145 
    146     /* purge off +-inf, NaN, +-0, tiny and negative arguments */
    147 	*signgamp = 1;
    148 	ix = hx&0x7fffffff;
    149 	if(ix>=0x7f800000) return x*x;
    150 	if(ix==0) return one/zero;
    151 	if(ix<0x35000000) {	/* |x|<2**-21, return -log(|x|) */
    152 	    if(hx<0) {
    153 	        *signgamp = -1;
    154 	        return -__ieee754_logf(-x);
    155 	    } else return -__ieee754_logf(x);
    156 	}
    157 	if(hx<0) {
    158 	    if(ix>=0x4b000000) 	/* |x|>=2**23, must be -integer */
    159 		return one/zero;
    160 	    t = sin_pif(x);
    161 	    if(t==zero) return one/zero; /* -integer */
    162 	    nadj = __ieee754_logf(pi/fabsf(t*x));
    163 	    if(t<zero) *signgamp = -1;
    164 	    x = -x;
    165 	}
    166 
    167     /* purge off 1 and 2 */
    168 	if (ix==0x3f800000||ix==0x40000000) r = 0;
    169     /* for x < 2.0 */
    170 	else if(ix<0x40000000) {
    171 	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
    172 		r = -__ieee754_logf(x);
    173 		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
    174 		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
    175 	  	else {y = x; i=2;}
    176 	    } else {
    177 	  	r = zero;
    178 	        if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
    179 	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
    180 		else {y=x-one;i=2;}
    181 	    }
    182 	    switch(i) {
    183 	      case 0:
    184 		z = y*y;
    185 		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
    186 		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
    187 		p  = y*p1+p2;
    188 		r  += (p-(float)0.5*y); break;
    189 	      case 1:
    190 		z = y*y;
    191 		w = z*y;
    192 		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
    193 		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
    194 		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
    195 		p  = z*p1-(tt-w*(p2+y*p3));
    196 		r += (tf + p); break;
    197 	      case 2:
    198 		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
    199 		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
    200 		r += (-(float)0.5*y + p1/p2);
    201 	    }
    202 	}
    203 	else if(ix<0x41000000) { 			/* x < 8.0 */
    204 	    i = (int)x;
    205 	    y = x-(float)i;
    206 	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
    207 	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
    208 	    r = half*y+p/q;
    209 	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
    210 	    switch(i) {
    211 	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
    212 	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
    213 	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
    214 	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
    215 	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
    216 		    r += __ieee754_logf(z); break;
    217 	    }
    218     /* 8.0 <= x < 2**58 */
    219 	} else if (ix < 0x5c800000) {
    220 	    t = __ieee754_logf(x);
    221 	    z = one/x;
    222 	    y = z*z;
    223 	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
    224 	    r = (x-half)*(t-one)+w;
    225 	} else
    226     /* 2**58 <= x <= inf */
    227 	    r =  x*(__ieee754_logf(x)-one);
    228 	if(hx<0) r = nadj - r;
    229 	return r;
    230 }
    231