lgamma.c

操作系统SunOS 4.1.3版本的源码

#ifndef lint
static	char sccsid[] = "@(#)lgamma.c 1.1 92/07/30 SMI";
#endif

/*
 * Copyright (c) 1989 by Sun Microsystems, Inc.
 */

/* double lgamma(double x)
 * K.C. Ng, March, 1989.
 *
 * Part of the algorithm is based on cody's lgamma function.
 */

extern	double SVID_libm_err(),log(),sinpi(),lgamma(),fabs();

int	signgam = 0;

static double 
one  =	 1.0,
zero =	 0.0,
hln2pi = 0.9189385332046727417803297,	/* log(2*pi)/2 */
pi     = 3.1415926535897932384626434,
/*
 * Numerator and denominator coefficients for rational minimax Approximation
 * P/Q over (0.5,1.5).
 */
D1 = 	-5.772156649015328605195174e-1,
p7 =	 4.945235359296727046734888e0,
p6 =	 2.018112620856775083915565e2,
p5 =	 2.290838373831346393026739e3,
p4 =	 1.131967205903380828685045e4,
p3 =	 2.855724635671635335736389e4,
p2 =	 3.848496228443793359990269e4,
p1 =	 2.637748787624195437963534e4,
p0 =	 7.225813979700288197698961e3,
q7 =	 6.748212550303777196073036e1,
q6 =	 1.113332393857199323513008e3,
q5 =	 7.738757056935398733233834e3,
q4 =	 2.763987074403340708898585e4,
q3 =	 5.499310206226157329794414e4,
q2 =	 6.161122180066002127833352e4,
q1 =	 3.635127591501940507276287e4,
q0 =	 8.785536302431013170870835e3,
/*
 * Numerator and denominator coefficients for rational minimax Approximation
 * G/H over (1.5,4.0).
 */
D2 =	 4.227843350984671393993777e-1,
g7 =	 4.974607845568932035012064e0,
g6 =	 5.424138599891070494101986e2,
g5 =	 1.550693864978364947665077e4,
g4 =	 1.847932904445632425417223e5,
g3 =	 1.088204769468828767498470e6,
g2 =	 3.338152967987029735917223e6,
g1 =	 5.106661678927352456275255e6,
g0 =	 3.074109054850539556250927e6,
h7 =	 1.830328399370592604055942e2,
h6 =	 7.765049321445005871323047e3,
h5 =	 1.331903827966074194402448e5,
h4 =	 1.136705821321969608938755e6,
h3 =	 5.267964117437946917577538e6,
h2 =	 1.346701454311101692290052e7,
h1 =	 1.782736530353274213975932e7,
h0 =	 9.533095591844353613395747e6,
/*
 * Numerator and denominator coefficients for rational minimax Approximation
 * U/V over (4.0,12.0).
 */
D4 = 	 1.791759469228055000094023e0,
u7 =	 1.474502166059939948905062e4,
u6 =	 2.426813369486704502836312e6,
u5 =	 1.214755574045093227939592e8,
u4 =	 2.663432449630976949898078e9,
u3 =	 2.940378956634553899906876e10,
u2 =	 1.702665737765398868392998e11,
u1 =	 4.926125793377430887588120e11,
u0 =	 5.606251856223951465078242e11,
v7 =	 2.690530175870899333379843e3,
v6 =	 6.393885654300092398984238e5,
v5 =	 4.135599930241388052042842e7,
v4 =	 1.120872109616147941376570e9,
v3 =	 1.488613728678813811542398e10,
v2 =	 1.016803586272438228077304e11,
v1 =	 3.417476345507377132798597e11,
v0 =	 4.463158187419713286462081e11,
/*
 * Coefficients for minimax approximation over (12, INF).
 */
c5 =	-1.910444077728e-03,
c4 =	 8.4171387781295e-04,
c3 =	-5.952379913043012e-04,
c2 =	 7.93650793500350248e-04,
c1 =	-2.777777777777681622553e-03,
c0 =	 8.333333333333333331554247e-02,
c6 =	 5.7083835261e-03;

double lgamma(x)
double x;
{
	double neg();
	double t,p,q,cr,y;

    /* purge off +-inf, NaN and negative arguments */
	if(!finite(x)) return x*x;
	signgam = 1;
	if(signbit(x)) return(neg(x));

    /* lgamma(x) ~ log(1/x) for really tiny x */
	t = one+x;
	if(t==one) return -log(x);

    /* for tiny < x < inf */
	if(x<=1.5) {
	    if(x<0.6796875) 
		{cr = -log(x); y=x;}
	    else
		{cr = zero; y = x-one;}

	    if(x<=0.5||x>=0.6796875) {
		if(x==one) return zero;
		p = p0+y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7))))));
		q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*(q7+y)))))));
		return cr+y*(D1+y*(p/q));
	    } else {
		y = x-one;
		p = g0+y*(g1+y*(g2+y*(g3+y*(g4+y*(g5+y*(g6+y*g7))))));
		q = h0+y*(h1+y*(h2+y*(h3+y*(h4+y*(h5+y*(h6+y*(h7+y)))))));
		return cr+y*(D2+y*(p/q));
	    }
	} else if (x<=4.0) {
	    if(x==2.0) return zero;
	    y = x-2.0;
	    p = g0+y*(g1+y*(g2+y*(g3+y*(g4+y*(g5+y*(g6+y*g7))))));
	    q = h0+y*(h1+y*(h2+y*(h3+y*(h4+y*(h5+y*(h6+y*(h7+y)))))));
	    return y*(D2+y*(p/q));
	} else if (x<=12.0) {
	    y = x-4.0;
	    p = u0+y*(u1+y*(u2+y*(u3+y*(u4+y*(u5+y*(u6+y*u7))))));
	    q = v0+y*(v1+y*(v2+y*(v3+y*(v4+y*(v5+y*(v6+y*(v7-y)))))));
	    return D4+y*(p/q);
	} else if (x<=1.0e17) {		/* x ~< 2**(prec+3) */
	    t = one/x;
	    y = t*t;
	    p = hln2pi+t*(c0+y*(c1+y*(c2+y*(c3+y*(c4+y*(c5+y*c6))))));
	    q = log(x);
	    return x*(q-one)-(0.5*q-p);
	} else {			/* may overflow */
	    t = x*log(x)-x;
	    if(!finite(t)) t = SVID_libm_err(x,x,14);
	    return t;
	}
}

static double neg(z)
double z;
{
	double t,p;

     /* 
      * written by K.C. Ng,  Feb 2, 1989.
      *
      * Since  
      *		-z*G(-z)*G(z) = pi/sin(pi*z),
      * we have
      * 	G(-z) = -pi/(sin(pi*z)*G(z)*z)
      * 	      =  pi/(sin(pi*(-z))*G(z)*z)
      * Algorithm 
      *		z = |z|
      *		t = sinpi(z); ...note that when z>2**52, z is an int
      *		and hence t=0.
      *
      *		if(t==0.0) return 1.0/0.0;
      *		if(t< 0.0) signgam = -1; else t= -t;
      *		if(z+1.0==1.0)	...tiny z
      *		    return -log(z);
      *		else
      *		    return log(pi/(t*z))-lgamma(z);
      *		
      */		

	t = sinpi(z);			/* t := sin(pi*z) */
	if (t==zero) { 			/* return   1.0/0.0 =  +INF */
	    return SVID_libm_err(z,z,15);
	}
	z = -z;
	p = z+one;
	if(p==one) 
	    p = -log(z);
	else
      	    p = log(pi/(fabs(t)*z))-lgamma(z);
	if(t<zero) signgam = -1;
	return p;
}

double gamma(x)
double x ;
{
	return(lgamma(x));
}