Compute BigDecimal e^x to a given scale.

Description

Demo Code

/*/*from w  ww . j a  va  2s  .co m*/
 * Copyright 2013 Valentyn Kolesnikov
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
//package com.java2s;
import java.math.BigDecimal;

public class Main {
    /**
     * 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;
    }
}
Compute BigDecimal e^x to a given scale. - Java java.math

Description

Demo Code

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