Initial data commit

Task/Almkvist-Giullera-formula-for-pi/JavaScript/almkvist-giullera-formula-for-pi.js

@@ -0,0 +1,55 @@
+import esMain from 'es-main';
+import { BigFloat, set_precision as SetPrecision } from 'bigfloat-esnext';
+
+const Iterations = 52;
+
+export const demo = function() {
+  SetPrecision(-75);
+  console.log("N." + "Integral part of Nth term".padStart(45) + " ×10^ =Actual value of Nth term");
+  for (let i=0; i<10; i++) {
+    let line = `${i}. `;
+    line += `${integral(i)} `.padStart(45);
+    line += `${tenExponent(i)} `.padStart(5);
+    line += nthTerm(i);
+    console.log(line);
+  }
+
+  let pi = approximatePi(Iterations);
+  SetPrecision(-70);
+  pi = pi.dividedBy(100000).times(100000);
+  console.log(`\nPi after ${Iterations} iterations: ${pi}`)
+}
+
+export const bigFactorial = n => n <= 1n ? 1n : n * bigFactorial(n-1n);
+
+// the nth integer term
+export const integral = function(i) {
+  let n = BigInt(i);
+  const polynomial  = 532n * n * n + 126n * n + 9n;
+  const numerator   = 32n * bigFactorial(6n * n) * polynomial;
+  const denominator = 3n * bigFactorial(n) ** 6n;
+  return numerator / denominator;
+}
+
+// the exponent for 10 in the nth term of the series
+export const tenExponent = n => 3n - 6n * (BigInt(n) + 1n);
+
+// the nth term of the series
+export const nthTerm = n =>
+  new BigFloat(integral(n)).dividedBy(new BigFloat(10n ** -tenExponent(n)))
+
+// the sum of the first n terms
+export const sumThrough = function(n) {
+  let sum = new BigFloat(0);
+  for (let i=0; i<=n; ++i) {
+    sum = sum.plus(nthTerm(i));
+  }
+  return sum;
+}
+
+// the approximation to pi after n terms
+export const approximatePi  = n =>
+   new BigFloat(1).dividedBy(sumThrough(n)).sqrt();
+
+if (esMain(import.meta))
+   demo();