PuzaTech/Fugue

package com.hongliangjie.fugue.utils;

/**
 * Created by liangjie on 10/30/14.
 */
public class LogGamma {

    // From libbow, dirichlet.c
    // Written by Tom Minka <minka@stat.cmu.edu>
    public static final double logGamma (double x)
    {
        double result;
        double y;
        double xnum;
        double xden;
        int i;
        final double d1 = -5.772156649015328605195174e-1;
        final double p1[] = {
                4.945235359296727046734888e0, 2.018112620856775083915565e2,
                2.290838373831346393026739e3, 1.131967205903380828685045e4,
                2.855724635671635335736389e4, 3.848496228443793359990269e4,
                2.637748787624195437963534e4, 7.225813979700288197698961e3
        };
        final double q1[] = {
                6.748212550303777196073036e1, 1.113332393857199323513008e3,
                7.738757056935398733233834e3, 2.763987074403340708898585e4,
                5.499310206226157329794414e4, 6.161122180066002127833352e4,
                3.635127591501940507276287e4, 8.785536302431013170870835e3
        };
        final double d2 = 4.227843350984671393993777e-1;
        final double p2[] = {
                4.974607845568932035012064e0, 5.424138599891070494101986e2,
                1.550693864978364947665077e4, 1.847932904445632425417223e5,
                1.088204769468828767498470e6, 3.338152967987029735917223e6,
                5.106661678927352456275255e6, 3.074109054850539556250927e6
        };
        final double q2[] = {
                1.830328399370592604055942e2, 7.765049321445005871323047e3,
                1.331903827966074194402448e5, 1.136705821321969608938755e6,
                5.267964117437946917577538e6, 1.346701454311101692290052e7,
                1.782736530353274213975932e7, 9.533095591844353613395747e6
        };
        final double d4 = 1.791759469228055000094023e0;
        final double p4[] = {
                1.474502166059939948905062e4, 2.426813369486704502836312e6,
                1.214755574045093227939592e8, 2.663432449630976949898078e9,
                2.940378956634553899906876e10, 1.702665737765398868392998e11,
                4.926125793377430887588120e11, 5.606251856223951465078242e11
        };
        final double q4[] = {
                2.690530175870899333379843e3, 6.393885654300092398984238e5,
                4.135599930241388052042842e7, 1.120872109616147941376570e9,
                1.488613728678813811542398e10, 1.016803586272438228077304e11,
                3.417476345507377132798597e11, 4.463158187419713286462081e11
        };
        final double c[] = {
                -1.910444077728e-03, 8.4171387781295e-04,
                -5.952379913043012e-04, 7.93650793500350248e-04,
                -2.777777777777681622553e-03, 8.333333333333333331554247e-02,
                5.7083835261e-03
        };
        final double a = 0.6796875;

        if((x <= 0.5) || ((x > a) && (x <= 1.5))) {
            if(x <= 0.5) {
                result = -Math.log(x);
                /*  Test whether X < machine epsilon. */
                if(x+1 == 1) {
                    return result;
                }
            }
            else {
                result = 0;
                x = (x - 0.5) - 0.5;
            }
            xnum = 0;
            xden = 1;
            for(i=0;i<8;i++) {
                xnum = xnum * x + p1[i];
                xden = xden * x + q1[i];
            }
            result += x*(d1 + x*(xnum/xden));
        }
        else if((x <= a) || ((x > 1.5) && (x <= 4))) {
            if(x <= a) {
                result = -Math.log(x);
                x = (x - 0.5) - 0.5;
            }
            else {
                result = 0;
                x -= 2;
            }
            xnum = 0;
            xden = 1;
            for(i=0;i<8;i++) {
                xnum = xnum * x + p2[i];
                xden = xden * x + q2[i];
            }
            result += x*(d2 + x*(xnum/xden));
        }
        else if(x <= 12) {
            x -= 4;
            xnum = 0;
            xden = -1;
            for(i=0;i<8;i++) {
                xnum = xnum * x + p4[i];
                xden = xden * x + q4[i];
            }
            result = d4 + x*(xnum/xden);
        }
        /*  X > 12  */
        else {
            y = Math.log(x);
            result = x*(y - 1) - y*0.5 + .9189385332046727417803297;
            x = 1/x;
            y = x*x;
            xnum = c[6];
            for(i=0;i<6;i++) {
                xnum = xnum * y + c[i];
            }
            xnum *= x;
            result += xnum;
        }
        return result;
    }
}