DDComputeTest.java

package com.revolsys.geometry.test.old.math;

import com.revolsys.geometry.math.DD;

import junit.framework.TestCase;
import junit.textui.TestRunner;

/**
 * Various tests involving computing known mathematical quantities
 * using the basic {@link DD} arithmetic operations.
 *
 * @author Martin Davis
 *
 */
public class DDComputeTest extends TestCase {
  public static void main(final String args[]) {
    TestRunner.run(DDComputeTest.class);
  }

  public DDComputeTest(final String name) {
    super(name);
  }

  /**
   * Computes the arctangent based on the Taylor series expansion
   *
   *    arctan(x) = x - x^3 / 3 + x^5 / 5 - x^7 / 7 + ...
   *
   * @param x the argument
   * @return an approximation to the arctangent of the input
   */
  private DD arctan(final DD x) {
    DD t = x;
    final DD t2 = t.sqr();
    DD at = new DD(0.0);
    final DD two = new DD(2.0);
    int k = 0;
    DD d = new DD(1.0);
    int sign = 1;
    while (t.doubleValue() > DD.EPS) {
      k++;
      if (sign < 0) {
        at = at.subtract(t.divide(d));
      } else {
        at = at.add(t.divide(d));
      }

      d = d.add(two);
      t = t.multiply(t2);
      sign = -sign;
    }
    // System.out.println("Computed DD.atan(): " + at + " Math.atan = "
    // + Math.atan(x.doubleValue()));
    return at;
  }

  /**
   * Uses Taylor series to compute e
   *
   * e = 1 + 1 + 1/2! + 1/3! + 1/4! + ...
   *
   * @return an approximation to e
   */
  private DD computeEByTaylorSeries() {
    DD s = DD.valueOf(2.0);
    DD t = DD.valueOf(1.0);
    double n = 1.0;
    int i = 0;

    while (t.doubleValue() > DD.EPS) {
      i++;
      n += 1.0;
      t = t.divide(DD.valueOf(n));
      s = s.add(t);
      // System.out.println(i + ": " + s);
    }
    return s;
  }

  /**
   * Uses Machin's arctangent formula to compute Pi:
   *
   *    Pi / 4  =  4 arctan(1/5) - arctan(1/239)
   *
   * @return an approximation to Pi
   */
  private DD computePiByMachin() {
    final DD t1 = DD.valueOf(1.0).divide(DD.valueOf(5.0));
    final DD t2 = DD.valueOf(1.0).divide(DD.valueOf(239.0));

    final DD pi4 = DD.valueOf(4.0).multiply(arctan(t1)).subtract(arctan(t2));
    final DD pi = DD.valueOf(4.0).multiply(pi4);
    // System.out.println("Computed value = " + pi);
    return pi;
  }

  public void testEByTaylorSeries() {
    // System.out.println("--------------------------------");
    // System.out.println("Computing e by Taylor series");
    final DD testE = computeEByTaylorSeries();
    final double err = Math.abs(testE.subtract(DD.E).doubleValue());
    // System.out.println("Difference from DoubleDouble.E = " + err);
    assertTrue(err < 64 * DD.EPS);
  }

  public void testPiByMachin() {
    // System.out.println("--------------------------------");
    // System.out.println("Computing Pi by Machin's rule");
    final DD testE = computePiByMachin();
    final double err = Math.abs(testE.subtract(DD.PI).doubleValue());
    // System.out.println("Difference from DoubleDouble.PI = " + err);
    assertTrue(err < 8 * DD.EPS);
  }

}