Java BigDecimal exp(BigDecimal x, int scale)

Description

Compute e^x to a given scale.

License

Apache License

Parameter

Parameter	Description
x	the value of x
scale	the desired scale of the result

Return

the result value

Declaration

public static BigDecimal exp(BigDecimal x, int scale) 

Method Source Code

//package com.java2s;
//License from project: Apache License 

import java.math.BigDecimal;

public class Main {
    /**/*from  w w w  .  j  a va2 s  .c  o m*/
     * 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(BigDecimal x, 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.
        BigDecimal xFraction = x.subtract(xWhole);

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

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

        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 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
     */
    private static BigDecimal expTaylor(BigDecimal x, 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!
            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 x^exponent to a given scale.  Uses the same
      * algorithm as class numbercruncher.mathutils.IntPower.
      * @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, 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;
    }
}

Related

1. cuberoot(BigDecimal b)
2. currencyFormat(BigDecimal value, char decimalDelimiter)
3. decimalDigits(BigDecimal d)
4. deserializeBigDecimalFromString(String decimal)
5. exp(BigDecimal power)
6. exponentialFormatBigDecimal(BigDecimal bd)
7. expTaylor(BigDecimal x, int scale)
8. extractBigDecimal(String value)
9. firstNonZero(final BigDecimal... values)