pi_bigdecimal.js (2124B)
1 /* 2 * PI computation in Javascript using the QuickJS bigdecimal type 3 * (decimal floating point) 4 */ 5 "use strict"; 6 7 /* compute PI with a precision of 'prec' digits */ 8 function calc_pi(prec) { 9 const CHUD_A = 13591409m; 10 const CHUD_B = 545140134m; 11 const CHUD_C = 640320m; 12 const CHUD_C3 = 10939058860032000m; /* C^3/24 */ 13 const CHUD_DIGITS_PER_TERM = 14.18164746272548; /* log10(C/12)*3 */ 14 15 /* return [P, Q, G] */ 16 function chud_bs(a, b, need_G) { 17 var c, P, Q, G, P1, Q1, G1, P2, Q2, G2, b1; 18 if (a == (b - 1n)) { 19 b1 = BigDecimal(b); 20 G = (2m * b1 - 1m) * (6m * b1 - 1m) * (6m * b1 - 5m); 21 P = G * (CHUD_B * b1 + CHUD_A); 22 if (b & 1n) 23 P = -P; 24 G = G; 25 Q = b1 * b1 * b1 * CHUD_C3; 26 } else { 27 c = (a + b) >> 1n; 28 [P1, Q1, G1] = chud_bs(a, c, true); 29 [P2, Q2, G2] = chud_bs(c, b, need_G); 30 P = P1 * Q2 + P2 * G1; 31 Q = Q1 * Q2; 32 if (need_G) 33 G = G1 * G2; 34 else 35 G = 0m; 36 } 37 return [P, Q, G]; 38 } 39 40 var n, P, Q, G; 41 /* number of serie terms */ 42 n = BigInt(Math.ceil(prec / CHUD_DIGITS_PER_TERM)) + 10n; 43 [P, Q, G] = chud_bs(0n, n, false); 44 Q = BigDecimal.div(Q, (P + Q * CHUD_A), 45 { roundingMode: "half-even", 46 maximumSignificantDigits: prec }); 47 G = (CHUD_C / 12m) * BigDecimal.sqrt(CHUD_C, 48 { roundingMode: "half-even", 49 maximumSignificantDigits: prec }); 50 return Q * G; 51 } 52 53 (function() { 54 var r, n_digits, n_bits; 55 if (typeof scriptArgs != "undefined") { 56 if (scriptArgs.length < 2) { 57 print("usage: pi n_digits"); 58 return; 59 } 60 n_digits = scriptArgs[1] | 0; 61 } else { 62 n_digits = 1000; 63 } 64 /* we add more digits to reduce the probability of bad rounding for 65 the last digits */ 66 r = calc_pi(n_digits + 20); 67 print(r.toFixed(n_digits, "down")); 68 })();