Java Factorial factorial(int x)

Here you can find the source of factorial(int x)

Description

factorial

License

Open Source License

Declaration

public static double factorial(int x) 

Method Source Code

//package com.java2s;
/*//from  w  w  w .  j  a va2 s  . co  m
 * Copyright (c) 2010 The Broad Institute
 *
 * Permission is hereby granted, free of charge, to any person
 * obtaining a copy of this software and associated documentation
 * files (the "Software"), to deal in the Software without
 * restriction, including without limitation the rights to use,
 * copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following
 * conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR
 * THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

public class Main {
    /**
     * Constants to simplify the log gamma function calculation.
     */
    private static final double zero = 0.0, one = 1.0, half = .5, a0 = 7.72156649015328655494e-02,
            a1 = 3.22467033424113591611e-01, a2 = 6.73523010531292681824e-02, a3 = 2.05808084325167332806e-02,
            a4 = 7.38555086081402883957e-03, a5 = 2.89051383673415629091e-03, a6 = 1.19270763183362067845e-03,
            a7 = 5.10069792153511336608e-04, a8 = 2.20862790713908385557e-04, a9 = 1.08011567247583939954e-04,
            a10 = 2.52144565451257326939e-05, a11 = 4.48640949618915160150e-05, tc = 1.46163214496836224576e+00,
            tf = -1.21486290535849611461e-01, tt = -3.63867699703950536541e-18, t0 = 4.83836122723810047042e-01,
            t1 = -1.47587722994593911752e-01, t2 = 6.46249402391333854778e-02, t3 = -3.27885410759859649565e-02,
            t4 = 1.79706750811820387126e-02, t5 = -1.03142241298341437450e-02, t6 = 6.10053870246291332635e-03,
            t7 = -3.68452016781138256760e-03, t8 = 2.25964780900612472250e-03, t9 = -1.40346469989232843813e-03,
            t10 = 8.81081882437654011382e-04, t11 = -5.38595305356740546715e-04, t12 = 3.15632070903625950361e-04,
            t13 = -3.12754168375120860518e-04, t14 = 3.35529192635519073543e-04, u0 = -7.72156649015328655494e-02,
            u1 = 6.32827064025093366517e-01, u2 = 1.45492250137234768737e+00, u3 = 9.77717527963372745603e-01,
            u4 = 2.28963728064692451092e-01, u5 = 1.33810918536787660377e-02, v1 = 2.45597793713041134822e+00,
            v2 = 2.12848976379893395361e+00, v3 = 7.69285150456672783825e-01, v4 = 1.04222645593369134254e-01,
            v5 = 3.21709242282423911810e-03, s0 = -7.72156649015328655494e-02, s1 = 2.14982415960608852501e-01,
            s2 = 3.25778796408930981787e-01, s3 = 1.46350472652464452805e-01, s4 = 2.66422703033638609560e-02,
            s5 = 1.84028451407337715652e-03, s6 = 3.19475326584100867617e-05, r1 = 1.39200533467621045958e+00,
            r2 = 7.21935547567138069525e-01, r3 = 1.71933865632803078993e-01, r4 = 1.86459191715652901344e-02,
            r5 = 7.77942496381893596434e-04, r6 = 7.32668430744625636189e-06, w0 = 4.18938533204672725052e-01,
            w1 = 8.33333333333329678849e-02, w2 = -2.77777777728775536470e-03, w3 = 7.93650558643019558500e-04,
            w4 = -5.95187557450339963135e-04, w5 = 8.36339918996282139126e-04, w6 = -1.63092934096575273989e-03;

    public static double factorial(int x) {
        return Math.pow(10, log10Gamma(x + 1));
    }

    /**
     * Calculates the log10 of the gamma function for x using the efficient FDLIBM
     * implementation to avoid overflows and guarantees high accuracy even for large
     * numbers.
     *
     * @param x the x parameter
     * @return the log10 of the gamma function at x.
     */
    public static double log10Gamma(double x) {
        return lnToLog10(lnGamma(x));
    }

    /**
     * Converts LN to LOG10
     *
     * @param ln log(x)
     * @return log10(x)
     */
    public static double lnToLog10(double ln) {
        return ln * Math.log10(Math.exp(1));
    }

    /**
     * Most efficent implementation of the lnGamma (FDLIBM)
     * Use via the log10Gamma wrapper method.
     */
    private static double lnGamma(double x) {
        double t, y, z, p, p1, p2, p3, q, r, w;
        int i;

        int hx = HI(x);
        int lx = LO(x);

        /* purge off +-inf, NaN, +-0, and negative arguments */
        int ix = hx & 0x7fffffff;
        if (ix >= 0x7ff00000)
            return Double.POSITIVE_INFINITY;
        if ((ix | lx) == 0 || hx < 0)
            return Double.NaN;
        if (ix < 0x3b900000) { /* |x|<2**-70, return -log(|x|) */
            return -Math.log(x);
        }

        /* purge off 1 and 2 */
        if ((((ix - 0x3ff00000) | lx) == 0) || (((ix - 0x40000000) | lx) == 0))
            r = 0;
        /* for x < 2.0 */
        else if (ix < 0x40000000) {
            if (ix <= 0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
                r = -Math.log(x);
                if (ix >= 0x3FE76944) {
                    y = one - x;
                    i = 0;
                } else if (ix >= 0x3FCDA661) {
                    y = x - (tc - one);
                    i = 1;
                } else {
                    y = x;
                    i = 2;
                }
            } else {
                r = zero;
                if (ix >= 0x3FFBB4C3) {
                    y = 2.0 - x;
                    i = 0;
                } /* [1.7316,2] */
                else if (ix >= 0x3FF3B4C4) {
                    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 - 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 += (-0.5 * y + p1 / p2);
            }
        } else if (ix < 0x40200000) { /* x < 8.0 */
            i = (int) x;
            t = zero;
            y = x - (double) 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 + 6.0); /* FALLTHRU */
            case 6:
                z *= (y + 5.0); /* FALLTHRU */
            case 5:
                z *= (y + 4.0); /* FALLTHRU */
            case 4:
                z *= (y + 3.0); /* FALLTHRU */
            case 3:
                z *= (y + 2.0); /* FALLTHRU */
                r += Math.log(z);
                break;
            }
            /* 8.0 <= x < 2**58 */
        } else if (ix < 0x43900000) {
            t = Math.log(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 * (Math.log(x) - one);
        return r;
    }

    /**
     * Efficient rounding functions to simplify the log gamma function calculation
     * double to long with 32 bit shift
     */
    private static final int HI(double x) {
        return (int) (Double.doubleToLongBits(x) >> 32);
    }

    /**
     * Efficient rounding functions to simplify the log gamma function calculation
     * double to long without shift
     */
    private static final int LO(double x) {
        return (int) Double.doubleToLongBits(x);
    }
}

Related

  1. factorial(int n)
  2. factorial(int n)
  3. factorial(int n)
  4. factorial(int number)
  5. factorial(int value)
  6. Factorial(int x)
  7. factorial(int x)
  8. factorial(long l)
  9. factorial(long n)