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MathematicalFunctions.java (1st part) (mathematical functions Java source code file) Print E-mail
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//
// Creator:    http://www.dicelocksecurity.com
// Version:    vers.6.0.0.1
//
// Copyright (C) 2011-2012 DiceLock Security, LLC. All rights reserved.
//
//                               DISCLAIMER
//
// THIS SOFTWARE IS PROVIDED "AS IS" AND ANY EXPRESSED OR IMPLIED WARRANTIES,
// INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
// AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
// REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// DICELOCK IS A REGISTERED TRADEMARK OR TRADEMARK OF THE OWNERS.
//
// Environment:
// java version "1.6.0_29"
// Java(TM) SE Runtime Environment (build 1.6.0_29-b11)
// Java HotSpot(TM) Server VM (build 20.4-b02, mixed mode)
//
 
package com.dicelocksecurity.jdicelock.RandomTest;
 
/**
 * mathematica funcions used by random number tests implemented
 *
 * @author      Angel Ferré @ DiceLock Security
 * @version     6.0.0.1
 * @since       2011-09-29
 */
public class MathematicalFunctions {
 
    /**
     * 2**-53
     */
    private static final double MACHEP = 1.11022302462515654042E-16;
 
    /**
     * 2**1024 * (1-MACHEP)
     */
    private static final double MAXNUM = 1.79769313486231570815E308;
 
    /**
     * log(MAXNUM)
     */
    private static final double MAXLOG = 7.09782712893383996732E2;
 
    /**
     * pi number
     */
    private static final double PI = 3.14159265358979323846;
 
    /**
     * log(pi)
     */
    private static final double LOGPI = 1.14472988584940017414;
 
    /**
     * log( sqrt( 2*pi )
     */
    private static final double LS2PI = 0.91893853320467274178;
 
    /**
     * BIG number
     */
    private static final double BIG = 4.503599627370496e15;
 
    /**
     * inverse BIG number
     */
    private static final double BIGINV = 2.22044604925031308085e-16;
 
    /**
     * A[]: Stirling's formula expansion of log gamma
     */
    double A_LGAM[] =
    { 8.11614167470508450300E-4, -5.95061904284301438324E-4, 7.93650340457716943945E-4, -2.77777777730099687205E-3,
      8.33333333333331927722E-2 };
 
    /**
     * B[], C[]: log gamma function between 2 and 3
     */
    double B_LGAM[] =
    { -1.37825152569120859100E3, -3.88016315134637840924E4, -3.31612992738871184744E5, -1.16237097492762307383E6,
      -1.72173700820839662146E6, -8.53555664245765465627E5 };
 
    /**
     * B[], C[]: log gamma function between 2 and 3
     */
    double C_LGAM[] =
    { -3.51815701436523470549E2, -1.70642106651881159223E4, -2.20528590553854454839E5, -1.13933444367982507207E6,
      -2.53252307177582951285E6, -2.01889141433532773231E6 };
    private static final double MAXLGM = 2.556348e305;
 
    /**
     * boolean "error" result indicating if an error has been produced while operating
     * true:    an error has been produced
     * false:   no error has been produced
     */
    protected boolean error;
    protected MathematicalErrors mathError;
 
    /**
     * Constructor, default
     */
    public MathematicalFunctions() {
 
        super();
    }
 
    /**
     * Logarithm of gamma function
     *
     * @param     x         x value to evaluate logarithm of gamma function
     * @return    double:   logarithm of gamma of value "x"
     */
    public double LGamma(double x) {
        double p, q, u, w, z;
        int i;
        int sgngam;
        boolean loverf;
 
        sgngam = 1;
        this.error = false;
        this.mathError = MathematicalErrors.None;
        loverf = false;
        if (x < -34.0) {
            q = -x;
            w = this.LGamma(q); /* note this modifies sgngam! */
            p = Math.floor(q);
            if (p == q) {
                loverf = true;
            } else {
                i = (int)p;
                if ((i & 1) == 0)
                    sgngam = -1;
                else
                    sgngam = 1;
                z = q - p;
                if (z > 0.5) {
                    p += 1.0;
                    z = p - q;
                }
                z = q * Math.sin(MathematicalFunctions.PI * z);
                if (z == 0.0) {
                    loverf = true;
                } else {
                    z = MathematicalFunctions.LOGPI - Math.log(z) - w;
                    return (z);
                }
            }
        }
        if (x < 13.0) {
            z = 1.0;
            p = 0.0;
            u = x;
            while (u >= 3.0) {
                p -= 1.0;
                u = x + p;
                z *= u;
            }
            while ((u < 2.0) && !loverf) {
                if (u == 0.0) {
                    loverf = true;
                } else {
                    z /= u;
                    p += 1.0;
                    u = x + p;
                }
            }
            if (!loverf) {
                if (z < 0.0) {
                    sgngam = -1;
                    z = -z;
                } else
                    sgngam = 1;
                if (u == 2.0)
                    return (Math.log(z));
                p -= 2.0;
                x = x + p;
                p = x * this.PolEvl(x, this.B_LGAM, 5) / this.P1Evl(x, this.C_LGAM, 6);
                return (Math.log(z) + p);
            }
        }
        if ((x > MathematicalFunctions.MAXLGM) || loverf) {
            this.error = true;
            this.mathError = MathematicalErrors.Overflow;
            return (sgngam * MathematicalFunctions.MAXNUM);
        }
        q = (x - 0.5) * Math.log(x) - x + MathematicalFunctions.LS2PI;
        if (x > 1.0e8)
            return (q);
        p = 1.0 / (x * x);
        if (x >= 1000.0)
            q += ((7.9365079365079365079365e-4 * p - 2.7777777777777777777778e-3) * p + 0.0833333333333333333333) / x;
        else
            q += this.PolEvl(p, this.A_LGAM, 4) / x;
        return (q);
    }
 
    /**
     * Incomplete gamma function
     *
     * @param     a         a value to evaluate incomplete gamma function
     * @param     x         x value to evaluate incomplete gamma function
     * @return    double:   incomplete gamma of values "a" and "x"
     */
    public double IGamma(double a, double x) {
        double ans, ax, c, r;
 
        this.error = false;
        this.mathError = MathematicalErrors.None;
        if ((x <= 0) || (a <= 0))
            return (0.0);
        if ((x > 1.0) && (x > a))
            return (1.e0 - this.IGammaC(a, x));
        ax = a * Math.log(x) - x - this.LGamma(a);
        if (ax < -(MathematicalFunctions.MAXLOG)) {
            this.error = true;
            this.mathError = MathematicalErrors.Underflow;
            return (0.0);
        }
        ax = Math.exp(ax);
        r = a;
        c = 1.0;
        ans = 1.0;
        do {
            r += 1.0;
            c *= x / r;
            ans += c;
        } while (c / ans > MathematicalFunctions.MACHEP);
        return (ans * ax / a);
    }
 
    /**
     * Complemented incomplete gamma integral
     *
     * @param     a         a value to evaluate complemented incomplete gamma integral
     * @param     x         x value to evaluate complemented incomplete gamma integral
     * @return    double:   complemented incomplete gamma integral of values "a" and "x"
     */
    public double IGammaC(double a, double x) {
        double ans, ax, c, yc, r, t, y, z;
        double pk, pkm1, pkm2, qk, qkm1, qkm2;
 
        this.error = false;
        this.mathError = MathematicalErrors.None;
        if ((x <= 0) || (a <= 0))
            return (1.0);
        if ((x < 1.0) || (x < a))
            return (1.e0 - this.IGamma(a, x));
        ax = a * Math.log(x) - x - this.LGamma(a);
        if (ax < -(MathematicalFunctions.MAXLOG)) {
            this.error = true;
            this.mathError = MathematicalErrors.Underflow;
            return (0.0);
        }
        ax = Math.exp(ax);
        y = 1.0 - a;
        z = x + y + 1.0;
        c = 0.0;
        pkm2 = 1.0;
        qkm2 = x;
        pkm1 = x + 1.0;
        qkm1 = z * x;
        ans = pkm1 / qkm1;
        do {
            c += 1.0;
            y += 1.0;
            z += 2.0;
            yc = y * c;
            pk = pkm1 * z - pkm2 * yc;
            qk = qkm1 * z - qkm2 * yc;
            if (qk != 0) {
                r = pk / qk;
                t = Math.abs((ans - r) / r);
                ans = r;
            } else
                t = 1.0;
            pkm2 = pkm1;
            pkm1 = pk;
            qkm2 = qkm1;
            qkm1 = qk;
            if (Math.abs(pk) > MathematicalFunctions.BIG) {
                pkm2 *= MathematicalFunctions.BIGINV;
                pkm1 *= MathematicalFunctions.BIGINV;
                qkm2 *= MathematicalFunctions.BIGINV;
                qkm1 *= MathematicalFunctions.BIGINV;
            }
        } while (t > MathematicalFunctions.MACHEP);
        return (ans * ax);
    }
 
    /**
     * Evaluate polynomial of degree N
     *
     * @param     x         x value to evaluate polynomial
     * @param     coef      coef array of double values to evaluate polynomial
     * @param     N         N degree to evaluate polynomial
     * @return    double:   polynomial of degree N of values "x" and "coef" array
     */
    public double PolEvl(double x, double[] coef, int N) {
        double ans;
        double p[];
        int i;
        int index;
 
        index = 0;
        p = coef;
        ans = p[index++];
        i = N;
        do
            ans = ans * x + p[index++];
        while ((--i) != 0);
        return (ans);
    }
 
    /**
     * Evaluate polynomial when coefficient of x  is 1.0.
     *
     * @param     x         x value to evaluate polynomial when it is 1.0
     * @param     coef      coef array of double values to evaluate polynomial when x value is 1.0
     * @param     N         N degree to evaluate polynomial when x value is 1.0
     * @return    double:   polynomial of degree N of values "x" and "coef" array when x value is 1.0
     */
    public double P1Evl(double x, double[] coef, int N) {
        double ans;
        double p[];
        int i;
        int index;
 
        index = 0;
        p = coef;
        ans = x + p[index++];
        i = N - 1;
        do
            ans = ans * x + p[index++];
        while ((--i) != 0);
        return (ans);
    }