__lgamma.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/*
* double __k_lgamma(double x, int *signgamp);
*
* K.C. Ng, March, 1989.
*
* Part of the algorithm is based on W. Cody's lgamma function.
*/
#include "libm.h"
static const double
one = 1.0,
zero = 0.0,
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;
/*
* Return sin(pi*x). We assume x is finite and negative, and if it
* is an integer, then the sign of the zero returned doesn't matter.
*/
static double
sin_pi(double x) {
double y, z;
int n;
y = -x;
if (y <= 0.25)
if (y >= two52)
return (zero);
z = floor(y);
if (y == z)
return (zero);
/* argument reduction: set y = |x| mod 2 */
y *= 0.5;
y = 2.0 * (y - floor(y));
/* now floor(y * 4) tells which octant y is in */
n = (int)(y * 4.0);
switch (n) {
case 0:
break;
case 1:
case 2:
break;
case 3:
case 4:
break;
case 5:
case 6:
break;
default:
break;
}
return (-y);
}
static double
double t, p;
/*
* written by K.C. Ng, Feb 2, 1989.
*
* Since
* we have
* G(-z) = -pi/(sin(pi*z)*G(z)*z)
* = pi/(sin(pi*(-z))*G(z)*z)
* Algorithm
* z = |z|
* t = sin_pi(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) *signgamp = -1; else t= -t;
* if (z+1.0 == 1.0) ...tiny z
* return -log(z);
* else
* return log(pi/(t*z))-__k_lgamma(z, signgamp);
*/
t = sin_pi(z); /* t := sin(pi*z) */
if (t == zero) /* return 1.0/0.0 = +INF */
z = -z;
p = z + one;
if (p == one)
p = -log(z);
else
if (t < zero)
*signgamp = -1;
return (p);
}
double
__k_lgamma(double x, int *signgamp) {
double t, p, q, cr, y;
/* purge off +-inf, NaN and negative arguments */
if (!finite(x))
return (x * x);
*signgamp = 1;
if (signbit(x))
/* lgamma(x) ~ log(1/x) for really tiny x */
t = one + x;
if (t == one) {
if (x == zero)
return (one / x);
return (-log(x));
}
/* for tiny < x < inf */
if (x <= 1.5) {
if (x < 0.6796875) {
y = x;
} else {
y = x - one;
}
if (x <= 0.5 || x >= 0.6796875) {
if (x == one)
return (zero);
(q7+y)))))));
} else {
y = x - one;
(h7+y)))))));
}
} else if (x <= 4.0) {
if (x == 2.0)
return (zero);
y = x - 2.0;
return (y*(D2+y*(p/q)));
} else if (x <= 12.0) {
y = x - 4.0;
return (D4+y*(p/q));
} else if (x <= 1.0e17) { /* x ~< 2**(prec+3) */
t = one / x;
y = t * t;
q = log(x);
return (x*(q-one)-(0.5*q-p));
} else { /* may overflow */
return (x * (log(x) - 1.0));
}
}