Almkvist-Giullera formula for pi: Difference between revisions
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Pi after 52 iterations:
3.1415926535897932384626433832795028841971693993751058209749445923078164</pre>
=={{header|JavaScript}}==
{{trans|Common Lisp}}
{{works with|Node.js|13+}}
{{libheader|bigfloat-esnext}}
{{libheader|es-main}} to support use of module as main code
<lang javascript>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();
</lang>
{{Out}}
<pre>N. Integral part of Nth term ×10^ =Actual value of Nth term
0. 96 -3 0.096
1. 5122560 -9 0.00512256
2. 190722470400 -15 0.0001907224704
3. 7574824857600000 -21 0.0000075748248576
4. 312546150372456000000 -27 0.000000312546150372456
5. 13207874703225491420651520 -33 0.00000001320787470322549142065152
6. 567273919793089083292259942400 -39 0.0000000005672739197930890832922599424
7. 24650600248172987140112763715584000 -45 0.000000000024650600248172987140112763715584
8. 1080657854354639453670407474439566400000 -51 0.0000000000010806578543546394536704074744395664
9. 47701779391594966287470570490839978880000000 -57 0.00000000000004770177939159496628747057049083997888
Pi after 52 iterations: 3.1415926535897932384626433832795028841971693993751058209749445923078164</pre>
=={{header|Julia}}==
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