8/07/2011

Example of expensive computation

Sometimes I need to simulate some expensive computation, or long-running task, without using Thread.sleep or Object.wait. A real busy waiting. The following example of computing PI is adapted from this RMI tutorial:

package test;
import java.math.BigDecimal;

public class Pi implements java.io.Serializable {
private static final long serialVersionUID = 227L;
private static final BigDecimal FOUR = BigDecimal.valueOf(4);
private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;
public static void main(String[] args) {
BigDecimal result = computePi(Integer.parseInt(args[0]));
System.out.println("Pi is " + result);
}

/**
* 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 = BigDecimal.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(BigDecimal.ZERO) != 0);
return result;
}
}
To run and time the task:
$ time java test.Pi 50000
Pi is 3.14159265358979323846264338327950288419716939937510 ...
9.263u 0.187s 0:09.22 102.3% 0+0k 0+6io 8pf+0w
It takes about 10 seconds to compute PI with 5000 digits after the decimal point.

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