68 lines
2.1 KiB
JavaScript
68 lines
2.1 KiB
JavaScript
/*
|
|
* PI computation in Javascript using the QuickJS bigdecimal type
|
|
* (decimal floating point)
|
|
*/
|
|
"use strict";
|
|
|
|
/* compute PI with a precision of 'prec' digits */
|
|
function calc_pi(prec) {
|
|
const CHUD_A = 13591409m;
|
|
const CHUD_B = 545140134m;
|
|
const CHUD_C = 640320m;
|
|
const CHUD_C3 = 10939058860032000m; /* C^3/24 */
|
|
const CHUD_DIGITS_PER_TERM = 14.18164746272548; /* log10(C/12)*3 */
|
|
|
|
/* return [P, Q, G] */
|
|
function chud_bs(a, b, need_G) {
|
|
var c, P, Q, G, P1, Q1, G1, P2, Q2, G2, b1;
|
|
if (a == (b - 1n)) {
|
|
b1 = BigDecimal(b);
|
|
G = (2m * b1 - 1m) * (6m * b1 - 1m) * (6m * b1 - 5m);
|
|
P = G * (CHUD_B * b1 + CHUD_A);
|
|
if (b & 1n)
|
|
P = -P;
|
|
G = G;
|
|
Q = b1 * b1 * b1 * CHUD_C3;
|
|
} else {
|
|
c = (a + b) >> 1n;
|
|
[P1, Q1, G1] = chud_bs(a, c, true);
|
|
[P2, Q2, G2] = chud_bs(c, b, need_G);
|
|
P = P1 * Q2 + P2 * G1;
|
|
Q = Q1 * Q2;
|
|
if (need_G)
|
|
G = G1 * G2;
|
|
else
|
|
G = 0m;
|
|
}
|
|
return [P, Q, G];
|
|
}
|
|
|
|
var n, P, Q, G;
|
|
/* number of serie terms */
|
|
n = BigInt(Math.ceil(prec / CHUD_DIGITS_PER_TERM)) + 10n;
|
|
[P, Q, G] = chud_bs(0n, n, false);
|
|
Q = BigDecimal.div(Q, (P + Q * CHUD_A),
|
|
{ roundingMode: "half-even",
|
|
maximumSignificantDigits: prec });
|
|
G = (CHUD_C / 12m) * BigDecimal.sqrt(CHUD_C,
|
|
{ roundingMode: "half-even",
|
|
maximumSignificantDigits: prec });
|
|
return Q * G;
|
|
}
|
|
|
|
(function() {
|
|
var r, n_digits, n_bits;
|
|
if (typeof scriptArgs != "undefined") {
|
|
if (scriptArgs.length < 2) {
|
|
print("usage: pi n_digits");
|
|
return;
|
|
}
|
|
n_digits = scriptArgs[1] | 0;
|
|
} else {
|
|
n_digits = 1000;
|
|
}
|
|
/* we add more digits to reduce the probability of bad rounding for
|
|
the last digits */
|
|
r = calc_pi(n_digits + 20);
|
|
print(r.toFixed(n_digits, "down"));
|
|
})();
|