BigSquareRoot.java :  » Math » algebra » util » Java Open Source

/**
 * Ariel
 * BigSquareRoot.java
 *
 * finds square roots of BigDecimals
 * @version  Jan 31, 2009
 */

package util;

import java.math.BigDecimal;
import java.math.BigInteger;

// ----------------------------------------------------------
// Compute square root of large numbers using Heron's method
// ----------------------------------------------------------

public class BigSquareRoot {
  private static BigDecimal ZERO = new BigDecimal("0");
  private static BigDecimal ONE = new BigDecimal("1");
  private static BigDecimal TWO = new BigDecimal("2");
  public static final int DEFAULT_MAX_ITERATIONS = 50;
  public static final int DEFAULT_SCALE = 10;
  private BigDecimal error;
  private int iterations;
  private boolean traceFlag;
  private int scale = DEFAULT_SCALE;
  private int maxIterations = DEFAULT_MAX_ITERATIONS;

  // ---------------------------------------
  // The error is the original number minus
  // (sqrt * sqrt). If the original number
  // was a perfect square, the error is 0.
  // ---------------------------------------

  public BigDecimal getError() {
    return error;
  }

  // -------------------------------------------------------------
  // Number of iterations performed when square root was computed
  // -------------------------------------------------------------

  public int getIterations() {
    return iterations;
  }

  // -----------
  // Trace flag
  // -----------

  public boolean getTraceFlag() {
    return traceFlag;
  }

  public void setTraceFlag(boolean flag) {
    traceFlag = flag;
  }

  // ------
  // Scale
  // ------

  public int getScale() {
    return scale;
  }

  public void setScale(int scale) {
    this.scale = scale;
  }

  // -------------------
  // Maximum iterations
  // -------------------

  public int getMaxIterations() {
    return maxIterations;
  }

  public void setMaxIterations(int maxIterations) {
    this.maxIterations = maxIterations;
  }

  // --------------------------
  // Get initial approximation
  // --------------------------

  private static BigDecimal getInitialApproximation(BigDecimal n) {
    BigInteger integerPart = n.toBigInteger();
    int length = integerPart.toString().length();
    if ((length % 2) == 0) {
      length--;
    }
    length /= 2;
    BigDecimal guess = ONE.movePointRight(length);
    return guess;
  }

  // ----------------
  // Get square root
  // ----------------

  public BigDecimal get(BigInteger n) {
    // make sure n is a positive number
    return get(new BigDecimal(n));
  }

  public BigDecimal get(BigDecimal n) {
    // make sure n is a positive number
    if (n.compareTo(ZERO) <= 0)
      throw new IllegalArgumentException(n + " is negative");

    BigDecimal initialGuess = getInitialApproximation(n);
    trace("Initial guess " + initialGuess.toString());
    BigDecimal lastGuess = ZERO;
    BigDecimal guess = new BigDecimal(initialGuess.toString());

    // iterate
    iterations = 0;
    boolean more = true;
    while (more) {
      lastGuess = guess;
      guess = n.divide(guess, scale, BigDecimal.ROUND_HALF_UP);
      guess = guess.add(lastGuess);
      guess = guess.divide(TWO, scale, BigDecimal.ROUND_HALF_UP);
      trace("Next guess " + guess.toString());
      error = n.subtract(guess.multiply(guess));
      if (++iterations >= maxIterations) {
        more = false;
      } else if (lastGuess.equals(guess)) {
        more = error.abs().compareTo(ONE) >= 0;
      }
    }
    return guess;

  }

  // ------
  // Trace
  // ------

  private void trace(String s) {
    if (traceFlag) {
      System.out.println(s);
    }
  }

  // ----------------------
  // Get random BigInteger
  // ----------------------

  public static BigInteger getRandomBigInteger(int nDigits) {
    StringBuffer sb = new StringBuffer();
    java.util.Random r = new java.util.Random();
    for (int i = 0; i < nDigits; i++) {
      sb.append(r.nextInt(10));
    }
    return new BigInteger(sb.toString());
  }

}