/* * PI computation in Javascript using the BigInt type */"use strict"; /* return floor(log2(a)) for a > 0 and 0 for a = 0 */function floor_log2(a){ var k_max, a1, k, i; k_max = 0n; while ((a >> (2n ** k_max)) != 0n) { k_max++; } k = 0n; a1 = a; for(i = k_max - 1n; i >= 0n; i--) { a1 = a >> (2n ** i); if (a1 != 0n) { a = a1; k |= (1n << i); } } return k;} /* return ceil(log2(a)) for a > 0 */function ceil_log2(a){ return floor_log2(a - 1n) + 1n;} /* return floor(sqrt(a)) (not efficient but simple) */function int_sqrt(a){ var l, u, s; if (a == 0n) return a; l = ceil_log2(a); u = 1n << ((l + 1n) / 2n); /* u >= floor(sqrt(a)) */ for(;;) { s = u; u = ((a / s) + s) / 2n; if (u >= s) break; } return s;} /* return pi * 2**prec */function calc_pi(prec) { const CHUD_A = 13591409n; const CHUD_B = 545140134n; const CHUD_C = 640320n; const CHUD_C3 = 10939058860032000n; /* C^3/24 */ const CHUD_BITS_PER_TERM = 47.11041313821584202247; /* log2(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; if (a == (b - 1n)) { G = (2n * b - 1n) * (6n * b - 1n) * (6n * b - 5n); P = G * (CHUD_B * b + CHUD_A); if (b & 1n) P = -P; Q = b * b * b * 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 = 0n; } return [P, Q, G]; } var n, P, Q, G; /* number of serie terms */ n = BigInt(Math.ceil(Number(prec) / CHUD_BITS_PER_TERM)) + 10n; [P, Q, G] = chud_bs(0n, n, false); Q = (CHUD_C / 12n) * (Q << prec) / (P + Q * CHUD_A); G = int_sqrt(CHUD_C << (2n * prec)); return (Q * G) >> prec;} function main(args) { var r, n_digits, n_bits, out; if (args.length < 1) { print("usage: pi n_digits"); return; } n_digits = args[0] | 0; /* we add more bits to reduce the probability of bad rounding for the last digits */ n_bits = BigInt(Math.ceil(n_digits * Math.log2(10))) + 32n; r = calc_pi(n_bits); r = ((10n ** BigInt(n_digits)) * r) >> n_bits; out = r.toString(); print(out[0] + "." + out.slice(1));} var args;if (typeof scriptArgs != "undefined") { args = scriptArgs; args.shift();} else if (typeof arguments != "undefined") { args = arguments;} else { /* default: 1000 digits */ args=[1000];} main(args);
/*
* PI computation in Javascript using the BigInt type
*/
"use strict";
/* return floor(log2(a)) for a > 0 and 0 for a = 0 */
function floor_log2(a)
{
var k_max, a1, k, i;
k_max = 0n;
while ((a >> (2n ** k_max)) != 0n) {
k_max++;
}
k = 0n;
a1 = a;
for(i = k_max - 1n; i >= 0n; i--) {
a1 = a >> (2n ** i);
if (a1 != 0n) {
a = a1;
k |= (1n << i);
}
}
return k;
}
/* return ceil(log2(a)) for a > 0 */
function ceil_log2(a)
{
return floor_log2(a - 1n) + 1n;
}
/* return floor(sqrt(a)) (not efficient but simple) */
function int_sqrt(a)
{
var l, u, s;
if (a == 0n)
return a;
l = ceil_log2(a);
u = 1n << ((l + 1n) / 2n);
/* u >= floor(sqrt(a)) */
for(;;) {
s = u;
u = ((a / s) + s) / 2n;
if (u >= s)
break;
}
return s;
}
/* return pi * 2**prec */
function calc_pi(prec) {
const CHUD_A = 13591409n;
const CHUD_B = 545140134n;
const CHUD_C = 640320n;
const CHUD_C3 = 10939058860032000n; /* C^3/24 */
const CHUD_BITS_PER_TERM = 47.11041313821584202247; /* log2(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;
if (a == (b - 1n)) {
G = (2n * b - 1n) * (6n * b - 1n) * (6n * b - 5n);
P = G * (CHUD_B * b + CHUD_A);
if (b & 1n)
P = -P;
Q = b * b * b * 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 = 0n;
}
return [P, Q, G];
}
var n, P, Q, G;
/* number of serie terms */
n = BigInt(Math.ceil(Number(prec) / CHUD_BITS_PER_TERM)) + 10n;
[P, Q, G] = chud_bs(0n, n, false);
Q = (CHUD_C / 12n) * (Q << prec) / (P + Q * CHUD_A);
G = int_sqrt(CHUD_C << (2n * prec));
return (Q * G) >> prec;
}
function main(args) {
var r, n_digits, n_bits, out;
if (args.length < 1) {
print("usage: pi n_digits");
return;
}
n_digits = args[0] | 0;
/* we add more bits to reduce the probability of bad rounding for
the last digits */
n_bits = BigInt(Math.ceil(n_digits * Math.log2(10))) + 32n;
r = calc_pi(n_bits);
r = ((10n ** BigInt(n_digits)) * r) >> n_bits;
out = r.toString();
print(out[0] + "." + out.slice(1));
}
var args;
if (typeof scriptArgs != "undefined") {
args = scriptArgs;
args.shift();
} else if (typeof arguments != "undefined") {
args = arguments;
} else {
/* default: 1000 digits */
args=[1000];
}
main(args);