package username.analysis;

import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Random;
import java.util.Vector;

/**
 * A class that supports various kinds of mathematical computations.
 *
 * @author Samuel A. Rebelsky
 * @version 1.0 of April 2006
 */
public class Mathematician
{

  // +--------+--------------------------------------------------
  // | Fields |
  // +--------+

  /** The analyst that helps determine running time. */
  Analyst a;


  // +--------------+--------------------------------------------
  // | Constructors |
  // +--------------+

  /**
   * Build a new searcher that records information using 
   * an analyst.
   */
  public Mathematician(Analyst _a)
  {
    this.a = _a;
  } // Mathematician(Analyst)


  // +-----------------+-----------------------------------------
  // | Primary Methods |
  // +-----------------+

  /**
   * Compute x^n using a straightforward for loop.
   *
   * @pre
   *   n >= 0
   * @post
   *   result = x * x * x * ... * x, with n x's.
   */
  public BigDecimal exptFor(BigDecimal x, int n)
  {
    BigDecimal result = new BigDecimal(1.0);
    for (int i = 0; i < n ; i++) {
      a.step();
      result = result.multiply(x);
    }
    return result;
  } // exptFor(BigDecimal, int)

  /**
   * Compute x^n using a clever algorithm.
   *
   * @pre
   *   n >= 0
   * @post
   *   result = x * x * x * ... * x, with n x's.
   */
  public BigDecimal exptWhile(BigDecimal x, int n)
  {
    BigDecimal accumulator = new BigDecimal(1);
    // need to repeatedly reduce the power.  Idea:
    // currentx^currentn * accumulator = originalx^originaln
    while (n > 0) {
      a.step();
      // If n is even, divide it by two and multiply x by
      // itself, using the amazing rule that
      // (x^n = (x^2)^(n/2))
      if ((n % 2) == 0) {
        n = n/2;
	    x = x.multiply(x);
      } // n is even
      // If n is odd, subtract 1 from it and ..
      else {
        n = n - 1;
	    accumulator = x.multiply(accumulator);
      } // n is odd
    } // while
    return accumulator;
  } // exptWhile(BigDecimal, int)

} // class Mathematician