119 lines
2.8 KiB
JavaScript
119 lines
2.8 KiB
JavaScript
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/*
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* PI computation in Javascript using the BigInt type
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*/
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"use strict";
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/* return floor(log2(a)) for a > 0 and 0 for a = 0 */
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function floor_log2(a)
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{
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var k_max, a1, k, i;
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k_max = 0n;
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while ((a >> (2n ** k_max)) != 0n) {
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k_max++;
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}
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k = 0n;
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a1 = a;
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for(i = k_max - 1n; i >= 0n; i--) {
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a1 = a >> (2n ** i);
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if (a1 != 0n) {
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a = a1;
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k |= (1n << i);
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}
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}
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return k;
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}
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/* return ceil(log2(a)) for a > 0 */
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function ceil_log2(a)
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{
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return floor_log2(a - 1n) + 1n;
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}
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/* return floor(sqrt(a)) (not efficient but simple) */
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function int_sqrt(a)
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{
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var l, u, s;
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if (a == 0n)
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return a;
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l = ceil_log2(a);
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u = 1n << ((l + 1n) / 2n);
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/* u >= floor(sqrt(a)) */
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for(;;) {
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s = u;
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u = ((a / s) + s) / 2n;
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if (u >= s)
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break;
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}
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return s;
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}
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/* return pi * 2**prec */
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function calc_pi(prec) {
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const CHUD_A = 13591409n;
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const CHUD_B = 545140134n;
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const CHUD_C = 640320n;
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const CHUD_C3 = 10939058860032000n; /* C^3/24 */
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const CHUD_BITS_PER_TERM = 47.11041313821584202247; /* log2(C/12)*3 */
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/* return [P, Q, G] */
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function chud_bs(a, b, need_G) {
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var c, P, Q, G, P1, Q1, G1, P2, Q2, G2;
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if (a == (b - 1n)) {
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G = (2n * b - 1n) * (6n * b - 1n) * (6n * b - 5n);
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P = G * (CHUD_B * b + CHUD_A);
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if (b & 1n)
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P = -P;
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Q = b * b * b * CHUD_C3;
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} else {
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c = (a + b) >> 1n;
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[P1, Q1, G1] = chud_bs(a, c, true);
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[P2, Q2, G2] = chud_bs(c, b, need_G);
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P = P1 * Q2 + P2 * G1;
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Q = Q1 * Q2;
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if (need_G)
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G = G1 * G2;
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else
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G = 0n;
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}
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return [P, Q, G];
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}
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var n, P, Q, G;
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/* number of serie terms */
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n = BigInt(Math.ceil(Number(prec) / CHUD_BITS_PER_TERM)) + 10n;
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[P, Q, G] = chud_bs(0n, n, false);
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Q = (CHUD_C / 12n) * (Q << prec) / (P + Q * CHUD_A);
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G = int_sqrt(CHUD_C << (2n * prec));
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return (Q * G) >> prec;
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}
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function main(args) {
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var r, n_digits, n_bits, out;
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if (args.length < 1) {
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print("usage: pi n_digits");
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return;
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}
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n_digits = args[0] | 0;
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/* we add more bits to reduce the probability of bad rounding for
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the last digits */
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n_bits = BigInt(Math.ceil(n_digits * Math.log2(10))) + 32n;
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r = calc_pi(n_bits);
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r = ((10n ** BigInt(n_digits)) * r) >> n_bits;
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out = r.toString();
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print(out[0] + "." + out.slice(1));
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}
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var args;
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if (typeof scriptArgs != "undefined") {
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args = scriptArgs;
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args.shift();
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} else if (typeof arguments != "undefined") {
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args = arguments;
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} else {
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/* default: 1000 digits */
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args=[1000];
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}
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main(args);
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