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Ramanujan's constant: Difference between revisions
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=={{header|Java}}==
Very interesting. Compute Pi, E, and square root to arbitrary precision.
<lang java>
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.Arrays;
import java.util.List;
public class RamanujanConstant {
public static void main(String[] args) {
System.out.printf("Ramanujan's Constant to 100 digits = %s%n%n", ramanujanConstant(163, 100));
System.out.printf("Heegner numbers yielding 'almost' integers:%n");
List<Integer> heegnerNumbers = Arrays.asList(19, 43, 67, 163);
List<Integer> heegnerVals = Arrays.asList(96, 960, 5280, 640320);
for ( int i = 0 ; i < heegnerNumbers.size() ; i++ ) {
int heegnerNumber = heegnerNumbers.get(i);
int heegnerVal = heegnerVals.get(i);
BigDecimal integer = BigDecimal.valueOf(heegnerVal).pow(3).add(BigDecimal.valueOf(744));
BigDecimal compute = ramanujanConstant(heegnerNumber, 50);
System.out.printf("%3d : %50s ~ %18s (diff ~ %s)%n", heegnerNumber, compute, integer, integer.subtract(compute, new MathContext(30)).toPlainString());
}
}
public static BigDecimal ramanujanConstant(int sqrt, int digits) {
// For accuracy on lat digit, computations with a few extra digits
MathContext mc = new MathContext(digits + 5);
return bigE(bigPi(mc).multiply(bigSquareRoot(BigDecimal.valueOf(sqrt), mc), mc), mc).round(new MathContext(digits));
}
// e = 1 + x/1! + x^2/2! + x^3/3! + ...
public static BigDecimal bigE(BigDecimal exponent, MathContext mc) {
BigDecimal e = BigDecimal.ONE;
BigDecimal ak = e;
int k = 0;
BigDecimal min = BigDecimal.ONE.divide(BigDecimal.TEN.pow(mc.getPrecision()));
while ( true ) {
k++;
ak = ak.multiply(exponent).divide(BigDecimal.valueOf(k), mc);
e = e.add(ak, mc);
if ( ak.compareTo(min) < 0 ) {
break;
}
}
return e;
}
// See : https://www.craig-wood.com/nick/articles/pi-chudnovsky/
public static BigDecimal bigPi(MathContext mc) {
int k = 0;
BigDecimal ak = BigDecimal.ONE;
BigDecimal a = ak;
BigDecimal b = BigDecimal.ZERO;
BigDecimal c = BigDecimal.valueOf(640320);
BigDecimal c3 = c.pow(3);
double digitePerTerm = Math.log10(c.pow(3).divide(BigDecimal.valueOf(24), mc).doubleValue()) - Math.log10(72);
double digits = 0;
while ( digits < mc.getPrecision() ) {
k++;
digits += digitePerTerm;
BigDecimal top = BigDecimal.valueOf(-24).multiply(BigDecimal.valueOf(6*k-5)).multiply(BigDecimal.valueOf(2*k-1)).multiply(BigDecimal.valueOf(6*k-1));
BigDecimal term = top.divide(BigDecimal.valueOf(k*k*k).multiply(c3), mc);
ak = ak.multiply(term, mc);
a = a.add(ak, mc);
b = b.add(BigDecimal.valueOf(k).multiply(ak, mc), mc);
}
BigDecimal total = BigDecimal.valueOf(13591409).multiply(a, mc).add(BigDecimal.valueOf(545140134).multiply(b, mc), mc);
return BigDecimal.valueOf(426880).multiply(bigSquareRoot(BigDecimal.valueOf(10005), mc), mc).divide(total, mc);
}
// See : https://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
public static BigDecimal bigSquareRoot(BigDecimal squareDecimal, MathContext mc) {
// Estimate
double sqrt = Math.sqrt(squareDecimal.doubleValue());
BigDecimal x0 = new BigDecimal(sqrt, mc);
BigDecimal two = BigDecimal.valueOf(2);
while ( true ) {
BigDecimal x1 = x0.subtract(x0.multiply(x0, mc).subtract(squareDecimal).divide(two.multiply(x0, mc), mc), mc);
String x1String = x1.toPlainString();
String x0String = x0.toPlainString();
if ( x1String.substring(0, x1String.length()-1).compareTo(x0String.substring(0, x0String.length()-1)) == 0 ) {
break;
}
x0 = x1;
}
return x0;
}
}
</lang>
{{out}}
<pre>
Ramanujan's Constant to 100 digits = 262537412640768743.9999999999992500725971981856888793538563373369908627075374103782106479101186073130
Heegner numbers yielding 'almost' integers:
19 : 885479.77768015431949753789348171962682071428650186 ~ 885480 (diff ~ 0.222319845680502462106518280373)
43 : 884736743.99977746603490666193746207858537684739913 ~ 884736744 (diff ~ 0.000222533965093338062537921414623)
67 : 147197952743.99999866245422450682926131257862850818 ~ 147197952744 (diff ~ 0.00000133754577549317073868742137149)
163 : 262537412640768743.99999999999925007259719818568888 ~ 262537412640768744 (diff ~ 0.00000000000074992740280181431112)
</pre>
=={{header|Julia}}==
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