Pi Day

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// Calculate PI with arbitrary precision

// ( source: http://java.sun.com/docs/books/tutorial/rmi/client.html )

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import java.math.BigDecimal;

BigDecimal FOUR = BigDecimal.valueOf(4);

int round = BigDecimal.ROUND_HALF_EVEN;

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// Machins Formula :  pi/4 = 4*arctan(1/5) - arctan(1/239) 

BigDecimal PI(int n) {

  int s = n + 5;

  BigDecimal atan5 = atan(5, s);

  BigDecimal atan239 = atan(239, s);

  BigDecimal pi = atan5.multiply(FOUR).subtract(atan239).multiply(FOUR);

  return pi.setScale(n, BigDecimal.ROUND_HALF_UP);

}

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// Power Series expansion : atan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 +  (x^9)/9 ...

BigDecimal atan(int invx, int s) {

  BigDecimal r, n, t, invx2 = BigDecimal.valueOf(invx * invx);

  r = n = BigDecimal.ONE.divide(BigDecimal.valueOf(invx) , s, round);

  int i = 1;

  do {

    n = n.divide(invx2, s, round);

    t = n.divide(BigDecimal.valueOf(2*i+1), s, round);

    r = (i%2 == 0) ? r.add(t) : r.subtract(t);

    i++;

  } while (t.compareTo(BigDecimal.ZERO) != 0);

  return r;

}

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