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Revision 1.2, Thu Sep 22 16:39:52 1994 UTC (23 years, 8 months ago) by jtc
Branch: MAIN
Changes since 1.1: +2 -2 lines

LIBM_SCCS must be defined for the RCS ID to be defined.
This library will soon be used by DJGPP.  And since memory is often tight
on DOS machines, there is little benifit to be had from including RCS IDs.

/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$Id: e_lgammaf_r.c,v 1.2 1994/09/22 16:39:52 jtc Exp $";
#endif

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const float 
#else
static float 
#endif
two23=  8.3886080000e+06, /* 0x4b000000 */
half=  5.0000000000e-01, /* 0x3f000000 */
one =  1.0000000000e+00, /* 0x3f800000 */
pi  =  3.1415927410e+00, /* 0x40490fdb */
a0  =  7.7215664089e-02, /* 0x3d9e233f */
a1  =  3.2246702909e-01, /* 0x3ea51a66 */
a2  =  6.7352302372e-02, /* 0x3d89f001 */
a3  =  2.0580807701e-02, /* 0x3ca89915 */
a4  =  7.3855509982e-03, /* 0x3bf2027e */
a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
a7  =  5.1006977446e-04, /* 0x3a05b634 */
a8  =  2.2086278477e-04, /* 0x39679767 */
a9  =  1.0801156895e-04, /* 0x38e28445 */
a10 =  2.5214456400e-05, /* 0x37d383a2 */
a11 =  4.4864096708e-05, /* 0x383c2c75 */
tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
/* tt = -(tail of tf) */
tt  =  6.6971006518e-09, /* 0x31e61c52 */
t0  =  4.8383611441e-01, /* 0x3ef7b95e */
t1  = -1.4758771658e-01, /* 0xbe17213c */
t2  =  6.4624942839e-02, /* 0x3d845a15 */
t3  = -3.2788541168e-02, /* 0xbd064d47 */
t4  =  1.7970675603e-02, /* 0x3c93373d */
t5  = -1.0314224288e-02, /* 0xbc28fcfe */
t6  =  6.1005386524e-03, /* 0x3bc7e707 */
t7  = -3.6845202558e-03, /* 0xbb7177fe */
t8  =  2.2596477065e-03, /* 0x3b141699 */
t9  = -1.4034647029e-03, /* 0xbab7f476 */
t10 =  8.8108185446e-04, /* 0x3a66f867 */
t11 = -5.3859531181e-04, /* 0xba0d3085 */
t12 =  3.1563205994e-04, /* 0x39a57b6b */
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
t14 =  3.3552918467e-04, /* 0x39afe9f7 */
u0  = -7.7215664089e-02, /* 0xbd9e233f */
u1  =  6.3282704353e-01, /* 0x3f2200f4 */
u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
u4  =  2.2896373272e-01, /* 0x3e6a7578 */
u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
v1  =  2.4559779167e+00, /* 0x401d2ebe */
v2  =  2.1284897327e+00, /* 0x4008392d */
v3  =  7.6928514242e-01, /* 0x3f44efdf */
v4  =  1.0422264785e-01, /* 0x3dd572af */
v5  =  3.2170924824e-03, /* 0x3b52d5db */
s0  = -7.7215664089e-02, /* 0xbd9e233f */
s1  =  2.1498242021e-01, /* 0x3e5c245a */
s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
s3  =  1.4635047317e-01, /* 0x3e15dce6 */
s4  =  2.6642270386e-02, /* 0x3cda40e4 */
s5  =  1.8402845599e-03, /* 0x3af135b4 */
s6  =  3.1947532989e-05, /* 0x3805ff67 */
r1  =  1.3920053244e+00, /* 0x3fb22d3b */
r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
r3  =  1.7193385959e-01, /* 0x3e300f6e */
r4  =  1.8645919859e-02, /* 0x3c98bf54 */
r5  =  7.7794247773e-04, /* 0x3a4beed6 */
r6  =  7.3266842264e-06, /* 0x36f5d7bd */
w0  =  4.1893854737e-01, /* 0x3ed67f1d */
w1  =  8.3333335817e-02, /* 0x3daaaaab */
w2  = -2.7777778450e-03, /* 0xbb360b61 */
w3  =  7.9365057172e-04, /* 0x3a500cfd */
w4  = -5.9518753551e-04, /* 0xba1c065c */
w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
w6  = -1.6309292987e-03; /* 0xbad5c4e8 */

#ifdef __STDC__
static const float zero=  0.0000000000e+00;
#else
static float zero=  0.0000000000e+00;
#endif

#ifdef __STDC__
	static float sin_pif(float x)
#else
	static float sin_pif(x)
	float x;
#endif
{
	float y,z;
	int n,ix;

	GET_FLOAT_WORD(ix,x);
	ix &= 0x7fffffff;

	if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
	y = -x;		/* x is assume negative */

    /*
     * argument reduction, make sure inexact flag not raised if input
     * is an integer
     */
	z = floorf(y);
	if(z!=y) {				/* inexact anyway */
	    y  *= (float)0.5;
	    y   = (float)2.0*(y - floorf(y));	/* y = |x| mod 2.0 */
	    n   = (int) (y*(float)4.0);
	} else {
            if(ix>=0x4b800000) {
                y = zero; n = 0;                 /* y must be even */
            } else {
                if(ix<0x4b000000) z = y+two23;	/* exact */
		GET_FLOAT_WORD(n,z);
		n &= 1;
                y  = n;
                n<<= 2;
            }
        }
	switch (n) {
	    case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
	    case 1:   
	    case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
	    case 3:  
	    case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
	    case 5:
	    case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
	    default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
	    }
	return -y;
}


#ifdef __STDC__
	float __ieee754_lgammaf_r(float x, int *signgamp)
#else
	float __ieee754_lgammaf_r(x,signgamp)
	float x; int *signgamp;
#endif
{
	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
	int i,hx,ix;

	GET_FLOAT_WORD(hx,x);

    /* purge off +-inf, NaN, +-0, and negative arguments */
	*signgamp = 1;
	ix = hx&0x7fffffff;
	if(ix>=0x7f800000) return x*x;
	if(ix==0) return one/zero;
	if(ix<0x1c800000) {	/* |x|<2**-70, return -log(|x|) */
	    if(hx<0) {
	        *signgamp = -1;
	        return -__ieee754_logf(-x);
	    } else return -__ieee754_logf(x);
	}
	if(hx<0) {
	    if(ix>=0x4b000000) 	/* |x|>=2**23, must be -integer */
		return one/zero;
	    t = sin_pif(x);
	    if(t==zero) return one/zero; /* -integer */
	    nadj = __ieee754_logf(pi/fabsf(t*x));
	    if(t<zero) *signgamp = -1;
	    x = -x;
	}

    /* purge off 1 and 2 */
	if (ix==0x3f800000||ix==0x40000000) r = 0;
    /* for x < 2.0 */
	else if(ix<0x40000000) {
	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
		r = -__ieee754_logf(x);
		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
	  	else {y = x; i=2;}
	    } else {
	  	r = zero;
	        if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
		else {y=x-one;i=2;}
	    }
	    switch(i) {
	      case 0:
		z = y*y;
		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
		p  = y*p1+p2;
		r  += (p-(float)0.5*y); break;
	      case 1:
		z = y*y;
		w = z*y;
		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
		p  = z*p1-(tt-w*(p2+y*p3));
		r += (tf + p); break;
	      case 2:	
		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
		r += (-(float)0.5*y + p1/p2);
	    }
	}
	else if(ix<0x41000000) { 			/* x < 8.0 */
	    i = (int)x;
	    t = zero;
	    y = x-(float)i;
	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
	    r = half*y+p/q;
	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
	    switch(i) {
	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
		    r += __ieee754_logf(z); break;
	    }
    /* 8.0 <= x < 2**58 */
	} else if (ix < 0x5c800000) {
	    t = __ieee754_logf(x);
	    z = one/x;
	    y = z*z;
	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
	    r = (x-half)*(t-one)+w;
	} else 
    /* 2**58 <= x <= inf */
	    r =  x*(__ieee754_logf(x)-one);
	if(hx<0) r = nadj - r;
	return r;
}