Implementation of Fourier Transform as described on SMBC

smbcFourierTransform.ts

'use strict';

/*
 * Documentation: http://www.smbc-comics.com/?id=2874
 * Copyright 2016 Arran Schlosberg (https://arranschlosberg.com)
 * License: MIT
 * Written in honour of the Viking sitting in the corner.
 */

interface fourierTransform {
  (base10: number) => fourierRepresentation;
}

interface fourierRepresentation {
  base:number;
  fours:number;
  representation:string;
}

var fourier:fourierTransform = (base10: number): fourierRepresentation => {
  var chars:string[] = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+/'.split('');
  
  base10 = base10|0; // force integer
  
  var fouriest: fourierRepresentation = {
    'base': 10,
    'fours': 0, // assume 0 and this will update if necessary
    'representation': base10.toString()
  };
  
  for(var base:number = 5; base<=chars.length; base++){ // technically this could go to base<=base10 but then we can't ensure enough characters for a representation
    var BaseX:string = '', // any similarity to the rocketry is purely coincidental
        remains:number = base10,
        digit:number,
        fours:number = 0;
    
    for(var rounds:number = 0; rounds<64 && remains>0; rounds++){ // avoid an infinite loop when I make a mistake
      digit = remains % base;
      if(digit==4){
        fours++;
      }
      BaseX = chars[digit] + BaseX;
      remains = (remains / base)|0;
    }
    
    console.debug('Base %d: %s has %d four(s)', base, BaseX, fours);
    if(fours > fouriest.fours){
      console.debug('More fours in base %d', base);
      fouriest.base = base;
      fouriest.fours = fours;
      fouriest.representation = BaseX;
    }
  }
  return fouriest;
}

console.debug(fourier(624)); // See documentation
exports = fourier;