Initial data commit

Task/Almkvist-Giullera-formula-for-pi/Java/almkvist-giullera-formula-for-pi.java

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+import java.math.BigDecimal;
+import java.math.BigInteger;
+import java.math.MathContext;
+import java.math.RoundingMode;
+
+public final class AlmkvistGiulleraFormula {
+
+	public static void main(String[] aArgs) {
+		System.out.println("n                                   Integer part");
+		System.out.println("================================================");
+		for ( int n = 0; n <= 9; n++ ) {
+			System.out.println(String.format("%d%47s", n, almkvistGiullera(n).toString()));
+		}
+		
+		final int decimalPlaces = 70;
+		final MathContext mathContext = new MathContext(decimalPlaces + 1, RoundingMode.HALF_EVEN);
+		final BigDecimal epsilon = BigDecimal.ONE.divide(BigDecimal.TEN.pow(decimalPlaces));		
+		BigDecimal previous = BigDecimal.ONE;		
+		BigDecimal sum = BigDecimal.ZERO;
+		BigDecimal pi = BigDecimal.ZERO;
+		int n = 0;
+		
+		while ( pi.subtract(previous).abs().compareTo(epsilon) >= 0 ) {
+			BigDecimal nextTerm = new BigDecimal(almkvistGiullera(n)).divide(BigDecimal.TEN.pow(6 * n + 3));			
+			sum = sum.add(nextTerm);			
+			previous = pi;
+			n += 1;
+			pi = BigDecimal.ONE.divide(sum, mathContext).sqrt(mathContext);
+		}
+		
+		System.out.println(System.lineSeparator() + "pi to " + decimalPlaces + " decimal places:");
+		System.out.println(pi);
+	}	
+	
+	// The integer part of the n'th term of Almkvist-Giullera series.
+	private static BigInteger almkvistGiullera(int aN) {
+	    BigInteger term1 = factorial(6 * aN).multiply(BigInteger.valueOf(32));
+	    BigInteger term2 = BigInteger.valueOf(532 * aN * aN + 126 * aN + 9);
+	    BigInteger term3 = factorial(aN).pow(6).multiply(BigInteger.valueOf(3));
+	    return term1.multiply(term2).divide(term3);
+	}
+
+	private static BigInteger factorial(int aNumber) {
+	    BigInteger result = BigInteger.ONE;
+	    for ( int i = 2; i <= aNumber; i++ ) {
+	    	result = result.multiply(BigInteger.valueOf(i));
+	    }
+	    return result;
+	}
+	
+}