BigDecimalHelper.java

/*
    This file is part of Cyclos (www.cyclos.org).
    A project of the Social Trade Organisation (www.socialtrade.org).

    Cyclos is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    Cyclos is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with Cyclos; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

 */
package nl.strohalm.cyclos.utils;

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

import nl.strohalm.cyclos.entities.settings.LocalSettings;

/**
 * Helper class for handling <code>BigDecimal</code>s Contains several useful BigDecimal mathematical functions taken from:
 * "Java Number Cruncher, the java programmer's guide to numerical computing" by Ronald Mak, Prentice Hall PTR, 2003. pages 330 & 331
 * 
 * @author luis
 * @author Rinke
 * @author Ronald Mak
 */
public class BigDecimalHelper {

    public static final BigDecimal ONE_HUNDRED = new BigDecimal(100.0);

    /**
     * Compute the arctangent of x to a given scale, |x| < 1
     * @param x the value of x
     * @param scale the desired scale of the result
     * @return the result value
     */
    public static BigDecimal arctan(final BigDecimal x, final int scale) {
        // Check that |x| < 1.
        if (x.abs().compareTo(BigDecimal.valueOf(1)) >= 0) {
            throw new IllegalArgumentException("|x| >= 1");
        }

        // If x is negative, return -arctan(-x).
        if (x.signum() == -1) {
            return arctan(x.negate(), scale).negate();
        } else {
            return arctanTaylor(x, scale);
        }
    }

    /**
     * returns amount as a percentage of total. Example: if amount is 5 and total is 50, then BigDecimalHelper.asPercentageOf(amount, total) equals 10
     * (%).
     * @param amount the BigDecimal to be written as a percentage.
     * @param total the BigDecimal representing the total amount of which amount is a percentage.
     * @return amount as a BigDecimal percentage of total.
     */
    public static BigDecimal asPercentageOf(final BigDecimal amount, final BigDecimal total) {
        final MathContext mathContext = new MathContext(LocalSettings.MAX_PRECISION);
        final BigDecimal asFractionOf = amount.divide(total, mathContext);
        return asFractionOf.multiply(ONE_HUNDRED, mathContext);
    }

    /**
     * returns a nominal percentage (like 5.2%) as a fraction (0.052).
     * @return the BigDecimal divided by 100. In the above example this would be 0.052.
     */
    public static BigDecimal asPercentFraction(final BigDecimal bigDecimal) {
        final MathContext mathContext = new MathContext(LocalSettings.MAX_PRECISION);
        return bigDecimal.divide(ONE_HUNDRED, mathContext);
    }

    /**
     * Compute e^x to a given scale. Break x into its whole and fraction parts and compute (e^(1 + fraction/whole))^whole using Taylor's formula.
     * @param x the value of x
     * @param scale the desired scale of the result
     * @return the result value
     */
    public static BigDecimal exp(final BigDecimal x, final int scale) {
        // e^0 = 1
        if (x.signum() == 0) {
            return BigDecimal.valueOf(1);
        }

        // If x is negative, return 1/(e^-x).
        else if (x.signum() == -1) {
            return BigDecimal.valueOf(1).divide(exp(x.negate(), scale), scale, BigDecimal.ROUND_HALF_EVEN);
        }

        // Compute the whole part of x.
        BigDecimal xWhole = x.setScale(0, BigDecimal.ROUND_DOWN);

        // If there isn't a whole part, compute and return e^x.
        if (xWhole.signum() == 0) {
            return expTaylor(x, scale);
        }

        // Compute the fraction part of x.
        final BigDecimal xFraction = x.subtract(xWhole);

        // z = 1 + fraction/whole
        final BigDecimal z = BigDecimal.valueOf(1).add(xFraction.divide(xWhole, scale, BigDecimal.ROUND_HALF_EVEN));

        // t = e^z
        final BigDecimal t = expTaylor(z, scale);

        final BigDecimal maxLong = BigDecimal.valueOf(Long.MAX_VALUE);
        BigDecimal result = BigDecimal.valueOf(1);

        // Compute and return t^whole using intPower().
        // If whole > Long.MAX_VALUE, then first compute products
        // of e^Long.MAX_VALUE.
        while (xWhole.compareTo(maxLong) >= 0) {
            result = result.multiply(intPower(t, Long.MAX_VALUE, scale)).setScale(scale, BigDecimal.ROUND_HALF_EVEN);
            xWhole = xWhole.subtract(maxLong);

            Thread.yield();
        }
        return result.multiply(intPower(t, xWhole.longValue(), scale)).setScale(scale, BigDecimal.ROUND_HALF_EVEN);
    }

    /**
     * Compute x^exponent to a given scale.
     * @param x the value x
     * @param exponent the exponent value
     * @param scale the desired scale of the result
     * @return the result value
     */
    public static BigDecimal intPower(BigDecimal x, long exponent, final int scale) {
        // If the exponent is negative, compute 1/(x^-exponent).
        if (exponent < 0) {
            return BigDecimal.valueOf(1).divide(intPower(x, -exponent, scale), scale, BigDecimal.ROUND_HALF_EVEN);
        }

        BigDecimal power = BigDecimal.valueOf(1);

        // Loop to compute value^exponent.
        while (exponent > 0) {

            // Is the rightmost bit a 1?
            if ((exponent & 1) == 1) {
                power = power.multiply(x).setScale(scale, BigDecimal.ROUND_HALF_EVEN);
            }

            // Square x and shift exponent 1 bit to the right.
            x = x.multiply(x).setScale(scale, BigDecimal.ROUND_HALF_EVEN);
            exponent >>= 1;

            Thread.yield();
        }

        return power;
    }

    /**
     * Compute the integral root of x to a given scale, x >= 0. Use Newton's algorithm.
     * @param x the value of x
     * @param index the integral root value
     * @param scale the desired scale of the result
     * @return the result value
     */
    public static BigDecimal intRoot(BigDecimal x, final long index, final int scale) {
        // Check that x >= 0.
        if (x.signum() < 0) {
            throw new IllegalArgumentException("x < 0");
        }

        final int sp1 = scale + 1;
        final BigDecimal n = x;
        final BigDecimal i = BigDecimal.valueOf(index);
        final BigDecimal im1 = BigDecimal.valueOf(index - 1);
        final BigDecimal tolerance = BigDecimal.valueOf(5).movePointLeft(sp1);
        BigDecimal xPrev;

        // The initial approximation is x/index.
        x = x.divide(i, scale, BigDecimal.ROUND_HALF_EVEN);

        // Loop until the approximations converge
        // (two successive approximations are equal after rounding).
        do {
            // x^(index-1)
            final BigDecimal xToIm1 = intPower(x, index - 1, sp1);

            // x^index
            final BigDecimal xToI = x.multiply(xToIm1).setScale(sp1, BigDecimal.ROUND_HALF_EVEN);

            // n + (index-1)*(x^index)
            final BigDecimal numerator = n.add(im1.multiply(xToI)).setScale(sp1, BigDecimal.ROUND_HALF_EVEN);

            // (index*(x^(index-1))
            final BigDecimal denominator = i.multiply(xToIm1).setScale(sp1, BigDecimal.ROUND_HALF_EVEN);

            // x = (n + (index-1)*(x^index)) / (index*(x^(index-1)))
            xPrev = x;
            x = numerator.divide(denominator, sp1, BigDecimal.ROUND_DOWN);

            Thread.yield();
        } while (x.subtract(xPrev).abs().compareTo(tolerance) > 0);

        return x;
    }

    /**
     * Compute the natural logarithm of x to a given scale, x > 0.
     */
    public static BigDecimal ln(final BigDecimal x, final int scale) {
        // Check that x > 0.
        if (x.signum() <= 0) {
            throw new IllegalArgumentException("x <= 0");
        }

        // The number of digits to the left of the decimal point.
        final int magnitude = x.toString().length() - x.scale() - 1;

        if (magnitude < 3) {
            return lnNewton(x, scale);
        }

        // Compute magnitude*ln(x^(1/magnitude)).
        else {

            // x^(1/magnitude)
            final BigDecimal root = intRoot(x, magnitude, scale);

            // ln(x^(1/magnitude))
            final BigDecimal lnRoot = lnNewton(root, scale);

            // magnitude*ln(x^(1/magnitude))
            return BigDecimal.valueOf(magnitude).multiply(lnRoot).setScale(scale, BigDecimal.ROUND_HALF_EVEN);
        }
    }

    /**
     * Returns zero when the given BigDecimal is null
     */
    public static BigDecimal nvl(final BigDecimal bigDecimal) {
        return bigDecimal == null ? BigDecimal.ZERO : bigDecimal;
    }

    /**
     * calculates x^exponent, that is, raise x to the poser of exponent. (by Rinke)
     * @param x the BigDecimal to be "powered".
     * @param scale the desired scale of the result
     * @param exponent the double which will be used to raise x to its power.
     * @return the result value
     */
    public static BigDecimal pow(final BigDecimal x, final int scale, final BigDecimal exponent) {
        final BigDecimal lnX = BigDecimalHelper.ln(x, scale);
        final BigDecimal newExponent = lnX.multiply(exponent);
        return BigDecimalHelper.exp(newExponent, scale);
    }

    /**
     * extremely simple version natural logarithm, using no algorith tricks, but just via doubles and recreating BigDecimal Might give less accurate
     * results, but this is to be tested. As long as this hasn't happened it is deprecated.
     */
    @Deprecated
    public static BigDecimal simpleLn(final BigDecimal x, final int scale) {
        final long unscaledValue = x.unscaledValue().longValue();
        final int scalevalue = x.scale();
        final double result = Math.log(unscaledValue) - (scalevalue * Math.log(10.0));
        return new BigDecimal(result, new MathContext(scale));
    }

    /**
     * Compute the square root of x to a given scale, x >= 0. Use Newton's algorithm.
     * @param x the value of x
     * @param scale the desired scale of the result
     * @return the result value
     */
    public static BigDecimal sqrt(final BigDecimal x, final int scale) {
        // Check that x >= 0.
        if (x.signum() < 0) {
            throw new IllegalArgumentException("x < 0");
        }

        // n = x*(10^(2*scale))
        final BigInteger n = x.movePointRight(scale << 1).toBigInteger();

        // The first approximation is the upper half of n.
        final int bits = (n.bitLength() + 1) >> 1;
        BigInteger ix = n.shiftRight(bits);
        BigInteger ixPrev;

        // Loop until the approximations converge
        // (two successive approximations are equal after rounding).
        do {
            ixPrev = ix;

            // x = (x + n/x)/2
            ix = ix.add(n.divide(ix)).shiftRight(1);

            Thread.yield();
        } while (ix.compareTo(ixPrev) != 0);

        return new BigDecimal(ix, scale);
    }

    /**
     * Compute the arctangent of x to a given scale by the Taylor series, |x| < 1
     * @param x the value of x
     * @param scale the desired scale of the result
     * @return the result value
     * @author Ronald Mak: "Java Number Cruncher, the java programmer's guide to numerical computing" Prentice Hall PTR, 2003. pages 330 & 331
     */
    private static BigDecimal arctanTaylor(final BigDecimal x, final int scale) {
        final int sp1 = scale + 1;
        int i = 3;
        boolean addFlag = false;

        BigDecimal power = x;
        BigDecimal sum = x;
        BigDecimal term;

        // Convergence tolerance = 5*(10^-(scale+1))
        final BigDecimal tolerance = BigDecimal.valueOf(5).movePointLeft(sp1);

        // Loop until the approximations converge
        // (two successive approximations are within the tolerance).
        do {
            // x^i
            power = power.multiply(x).multiply(x).setScale(sp1, BigDecimal.ROUND_HALF_EVEN);

            // (x^i)/i
            term = power.divide(BigDecimal.valueOf(i), sp1, BigDecimal.ROUND_HALF_EVEN);

            // sum = sum +- (x^i)/i
            sum = addFlag ? sum.add(term) : sum.subtract(term);

            i += 2;
            addFlag = !addFlag;

            Thread.yield();
        } while (term.compareTo(tolerance) > 0);

        return sum;
    }

    /**
     * Compute e^x to a given scale by the Taylor series.
     * @param x the value of x
     * @param scale the desired scale of the result
     * @return the result value
     * @author Ronald Mak: "Java Number Cruncher, the java programmer's guide to numerical computing" Prentice Hall PTR, 2003. pages 330 & 331
     */
    private static BigDecimal expTaylor(final BigDecimal x, final int scale) {
        BigDecimal factorial = BigDecimal.valueOf(1);
        BigDecimal xPower = x;
        BigDecimal sumPrev;

        // 1 + x
        BigDecimal sum = x.add(BigDecimal.valueOf(1));

        // Loop until the sums converge
        // (two successive sums are equal after rounding).
        int i = 2;
        do {
            // x^i
            xPower = xPower.multiply(x).setScale(scale, BigDecimal.ROUND_HALF_EVEN);

            // i!
            factorial = factorial.multiply(BigDecimal.valueOf(i));

            // x^i/i!
            final BigDecimal term = xPower.divide(factorial, scale, BigDecimal.ROUND_HALF_EVEN);

            // sum = sum + x^i/i!
            sumPrev = sum;
            sum = sum.add(term);

            ++i;
            Thread.yield();
        } while (sum.compareTo(sumPrev) != 0);

        return sum;
    }

    /**
     * Compute the natural logarithm of x to a given scale, x > 0. Use Newton's algorithm.
     * @author Ronald Mak: "Java Number Cruncher, the java programmer's guide to numerical computing" Prentice Hall PTR, 2003. pages 330 & 331
     */
    private static BigDecimal lnNewton(BigDecimal x, final int scale) {
        final int sp1 = scale + 1;
        final BigDecimal n = x;
        BigDecimal term;

        // Convergence tolerance = 5*(10^-(scale+1))
        final BigDecimal tolerance = BigDecimal.valueOf(5).movePointLeft(sp1);

        // Loop until the approximations converge
        // (two successive approximations are within the tolerance).
        do {

            // e^x
            final BigDecimal eToX = exp(x, sp1);

            // (e^x - n)/e^x
            term = eToX.subtract(n).divide(eToX, sp1, BigDecimal.ROUND_DOWN);

            // x - (e^x - n)/e^x
            x = x.subtract(term);

            Thread.yield();
        } while (term.compareTo(tolerance) > 0);

        return x.setScale(scale, BigDecimal.ROUND_HALF_EVEN);
    }

}