package elte.java2_utikalauz5.math;

import java.math.*;

/**
pi értékének Gauss-Legendre algoritmussal való kiszámolása fixpontos műveletekkel.

@link.forrásfájl {@docRoot}/../data/math/src PiJava2.java
@link.letöltés {@docRoot}/../data/math PiJava2.jar
@since Java 2 Útikalauz programozóknak
*/
class PiJava2 {
    private static final BigDecimal ONE = new BigDecimal(1);
    private static final BigDecimal TWO = new BigDecimal(2);
    private static final BigDecimal FOUR = new BigDecimal(4);

    public static void main(String[] args) {
        System.out.println(pi(Integer.parseInt(args[0])));
    }

    // Gauss-Legendre algoritmus
    public static BigDecimal pi(final int SCALE) {
        BigDecimal a = ONE;
        BigDecimal b = ONE.divide(sqrt(TWO, SCALE), SCALE, BigDecimal.ROUND_HALF_UP);
        BigDecimal t = new BigDecimal(0.25);
        BigDecimal x = ONE;
        BigDecimal y;

        while (!a.equals(b)) {
            y = a;
            a = a.add(b).divide(TWO, SCALE, BigDecimal.ROUND_HALF_UP);
            b = sqrt(b.multiply(y), SCALE);
            t = t.subtract(x.multiply(y.subtract(a).multiply(y.subtract(a))));
            x = x.multiply(TWO);
        }

        return a.add(b).multiply(a.add(b)).divide(t.multiply(FOUR), SCALE, BigDecimal.ROUND_HALF_UP);
    }

    // Newton módszer
    public static BigDecimal sqrt(BigDecimal A, final int SCALE) {
        BigDecimal x0 = new BigDecimal("0");
        BigDecimal x1 = new BigDecimal(Math.sqrt(A.doubleValue()));

        while (!x0.equals(x1)) {
            x0 = x1;
            x1 = A.divide(x0, SCALE, BigDecimal.ROUND_HALF_UP);
            x1 = x1.add(x0);
            x1 = x1.divide(TWO, SCALE, BigDecimal.ROUND_HALF_UP);
        }
        return x1;
    }
}