simple-squiggle

A restricted subset of Squiggle
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probability.js (1645B)

      1 /* eslint-disable no-loss-of-precision */
      2 import { isInteger } from '../../utils/number.js';
      3 import { product } from '../../utils/product.js';
      4 export function gammaNumber(n) {
      5   var x;
      6 
      7   if (isInteger(n)) {
      8     if (n <= 0) {
      9       return isFinite(n) ? Infinity : NaN;
     10     }
     11 
     12     if (n > 171) {
     13       return Infinity; // Will overflow
     14     }
     15 
     16     return product(1, n - 1);
     17   }
     18 
     19   if (n < 0.5) {
     20     return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n));
     21   }
     22 
     23   if (n >= 171.35) {
     24     return Infinity; // will overflow
     25   }
     26 
     27   if (n > 85.0) {
     28     // Extended Stirling Approx
     29     var twoN = n * n;
     30     var threeN = twoN * n;
     31     var fourN = threeN * n;
     32     var fiveN = fourN * n;
     33     return Math.sqrt(2 * Math.PI / n) * Math.pow(n / Math.E, n) * (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) - 571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) + 5246819 / (75246796800 * fiveN * n));
     34   }
     35 
     36   --n;
     37   x = gammaP[0];
     38 
     39   for (var i = 1; i < gammaP.length; ++i) {
     40     x += gammaP[i] / (n + i);
     41   }
     42 
     43   var t = n + gammaG + 0.5;
     44   return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x;
     45 }
     46 gammaNumber.signature = 'number'; // TODO: comment on the variables g and p
     47 
     48 export var gammaG = 4.7421875;
     49 export var gammaP = [0.99999999999999709182, 57.156235665862923517, -59.597960355475491248, 14.136097974741747174, -0.49191381609762019978, 0.33994649984811888699e-4, 0.46523628927048575665e-4, -0.98374475304879564677e-4, 0.15808870322491248884e-3, -0.21026444172410488319e-3, 0.21743961811521264320e-3, -0.16431810653676389022e-3, 0.84418223983852743293e-4, -0.26190838401581408670e-4, 0.36899182659531622704e-5];