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