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