Java Fun and Games: Java Grab包的技术提示

// CalcPi.java
import java.awt.Toolkit;

import java.math.BigDecimal;

public class CalcPi
{
    /* constants used in pi computation */

    private static final BigDecimal ZERO = BigDecimal.valueOf (0);

    private static final BigDecimal ONE = BigDecimal.valueOf (1);

    private static final BigDecimal FOUR = BigDecimal.valueOf (4);

    /* rounding mode to use during pi computation */

    private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;

    /* digits of precision after the decimal point */

    private static int digits;

    public static void main (String [] args)
    {
       if (args.length != 1)
       {
           System.err.println ("usage: java CalcPi digits");
           return;
       }

       int digits = 0;

       try
       {
           digits = Integer.parseInt (args [0]);
       }
       catch (NumberFormatException e)
       {
           System.err.println (args [0] + " is not a valid integer");
           return;
       }

       System.out.println (computePi (digits));
       Toolkit.getDefaultToolkit ().beep ();
    }

    /*
     * Compute the value of pi to the specified number of 
     * digits after the decimal point.  The value is 
     * computed using Machin''s formula:
     *
     *          pi/4 = 4*arctan(1/5) - arctan(1/239)
     *
     * and a power series expansion of arctan(x) to 
     * sufficient precision.
     */

    public static BigDecimal computePi (int digits)
    {
       int scale = digits + 5;
       BigDecimal arctan1_5 = arctan (5, scale);
       BigDecimal arctan1_239 = arctan (239, scale);
       BigDecimal pi = arctan1_5.multiply (FOUR).
                       subtract (arctan1_239).multiply (FOUR);

       return pi.setScale (digits, BigDecimal.ROUND_HALF_UP);
    }

    /*
     * Compute the value, in radians, of the arctangent of 
     * the inverse of the supplied integer to the specified
     * number of digits after the decimal point.  The value
     * is computed using the power series expansion for the
     * arc tangent:
     *
     * arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + 
     *     (x^9)/9 ...
     */

    public static BigDecimal arctan (int inverseX, int scale) 
    {
       BigDecimal result, numer, term;
       BigDecimal invX = BigDecimal.valueOf (inverseX);
       BigDecimal invX2 = BigDecimal.valueOf (inverseX * inverseX);

       numer = ONE.divide (invX, scale, roundingMode);

       result = numer;
       int i = 1;

       do
       {
          numer = numer.divide (invX2, scale, roundingMode);
          int denom = 2 * i + 1;
          term = numer.divide (BigDecimal.valueOf (denom), scale, roundingMode);
          if ((i % 2) != 0)
              result = result.subtract (term);          else
              result = result.add (term);
          i++;
       }
       while (term.compareTo (ZERO) != 0);

       return result;
    }
}

列表 1 使用一种算法来计算 pi，该算法是早在 18 世纪初期由英国数学家 John Machin 发明的。 算法首先计算 pi/4 = 4*arctan(1/5)-arctan(1/239)，然后将结果乘以 4 得出 pi 的值。 由于 arc (inverse) tangent 是使用一系列庞大的 term 来计算的, term 的数量越大得出的 pi 值越准确（小数点后显示的位数）

注意
列表 1 的大部分代码引用自 Sun 的远程方法调用教程的“创建一个客户端程序”部分。