Compute BigDecimal the integral root of x to a given scale, x >= 0. - Java java.math

Java examples for java.math:BigDecimal Calculation

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Description

Compute BigDecimal the integral root of x to a given scale, x >= 0.

Demo Code

/*/*from w w  w.ja  va  2 s. com*/
 * 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 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, long index, int scale) {
        // Check that x >= 0.
        if (x.signum() < 0) {
            throw new IllegalArgumentException("x < 0");
        }

        int sp1 = scale + 1;
        BigDecimal n = x;
        BigDecimal i = BigDecimal.valueOf(index);
        BigDecimal im1 = BigDecimal.valueOf(index - 1);
        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)
            BigDecimal xToIm1 = intPower(x, index - 1, sp1);

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

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

            // (index*(x^(index-1))
            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 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;
    }
}

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