Compute the arctangent of x to a given scale by the Taylor series, |x| < 1 - Java java.lang

Java examples for java.lang:Math Trigonometric Function

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Description

Compute the arctangent of x to a given scale by the Taylor series, |x| < 1

Demo Code

/*// ww w.j a v a 2s.  co m
 Anders H?fft, note: This class was downloaded as a quick, and temprory, way of getting a BigDecimal ln() method. 
 The code belongs to Cyclos. See comment below:

 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 com.java2s;
import java.math.BigDecimal;

public class Main {
    public static void main(String[] argv) throws Exception {
        BigDecimal x = new BigDecimal("1234");
        int scale = 2;
        System.out.println(arctanTaylor(x, 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;
    }
}

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