How to create my own JavaScript Random Number generator that I can also set the seed

Question

The JavaScript Math.random() function returns a random value between 0 and 1 (automatically seeded based on the current time (similar to Java I believe)). However I'd like to make a more robust function that accepts a min, a max, and (optionally) a seed.

I found this code kicking around and it appears to work fine for getting a random number and then using the seed afterward but I'm not quite sure how the logic works (e.g. where the 2345678901, 48271 & 2147483647 numbers came from). Does anyone know what I need to do to be able to pass in the seed?

function nextRandomNumber(){
  var hi = this.seed / this.Q;
  var lo = this.seed % this.Q;
  var test = this.A * lo - this.R * hi;
  if(test > 0){
    this.seed = test;
  } else {
    this.seed = test + this.M;
  }
  return (this.seed * this.oneOverM);
}

function RandomNumberGenerator(){
  var d = new Date();
  this.seed = 2345678901 + (d.getSeconds() * 0xFFFFFF) + (d.getMinutes() * 0xFFFF);
  this.A = 48271;
  this.M = 2147483647;
  this.Q = this.M / this.A;
  this.R = this.M % this.A;
  this.oneOverM = 1.0 / this.M;
  this.next = nextRandomNumber;
  return this;
}

function createRandomNumber(Min, Max){
  var rand = new RandomNumberGenerator();
  return Math.round((Max-Min) * rand.next() + Min);
}

//Thus I can now do:
var letters = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'];
var numbers = ['1','2','3','4','5','6','7','8','9','10'];
var colors = ['red','orange','yellow','green','blue','indigo','violet'];
var first = createRandomNumber(0, letters.length);
var second = createRandomNumber(0, numbers.length);
var third = createRandomNumber(0, colors.length);

alert("Today's show was brought to you by the letter: " + first + ", the number " + second + ", and the color " + third + "!");

/*
  If I could pass my own seed into the createRandomNumber(min, max, seed);
  function then I could reproduce a random output later if desired.
*/

For the record, my real intentions are a bit more involved than this but I wanted a fairly straight forward example.

Answer 1

Just parameterize the constructor and set the seed:

function RandomNumberGenerator(Seed){
  var d = new Date();
  this.seed = Seed;
  this.A = 48271;
  this.M = 2147483647;
  this.Q = this.M / this.A;
  this.R = this.M % this.A;
  this.oneOverM = 1.0 / this.M;
  this.next = nextRandomNumber;
  return this;
}

And adjust your function that creates the random number generator like this:

function createRandomNumber(Seed, Min, Max){
  var rand = new RandomNumberGenerator(Seed);
  return Math.round((Max-Min) * rand.next() + Min);
}

And call like this:

var letters = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'];
var numbers = ['1','2','3','4','5','6','7','8','9','10'];
var colors = ['red','orange','yellow','green','blue','indigo','violet'];
var seed = <generate seed>;
var first = createRandomNumber(seed, 0, letters.length);
var second = createRandomNumber(seed, 0, numbers.length);
var third = createRandomNumber(seed, 0, colors.length);

Answer 2

If you want to be able to specify the seed, you just need to replace the calls to getSeconds() and getMinutes(). You could pass in an int and use half of it mod 60 for the seconds value and the other half modulo 60 to give you the other part.

That being said, this method looks like garbage. Doing proper random number generation is very hard. The obvious problem with this is that the random number seed is based on seconds and minutes. To guess the seed and recreate your stream of random numbers only requires trying 3600 different second and minute combinations. It also means that there are only 3600 different possible seeds. This is correctable, but I'd be suspicious of this RNG from the start.

If you want to use a better RNG, try the Mersenne Twister. It is a well tested and fairly robust RNG with a huge orbit and excellent performance.

EDIT: I really should be correct and refer to this as a Pseudo Random Number Generator or PRNG.

"Anyone who uses arithmetic methods to produce random numbers is in a state of sin."
                                                                                                                                                          --- John von Neumann

Answer 3

EDIT: if you don't need the seeding capability, just use Math.random() and build helper functions around it (eg. randRange(start, end)).

I'm not sure what RNG you're using, but it's best to know and document it so you're aware of it's characteristics and limitations.

Like Starkii said, Mersenne Twister is a good PRNG, but it isn't easy to implement. If you want to do it yourself try implementing a LCG - it's very easy, has decent randomness qualities (not as good as Mersenne Twister), and you can use some of the popular constants.

function RNG(seed) {
  // LCG using GCC's constants
  this.m = 0x100000000; // 2**32;
  this.a = 1103515245;
  this.c = 12345;

  this.state = seed ? seed : Math.floor(Math.random() * (this.m-1));
}
RNG.prototype.nextInt = function() {
  this.state = (this.a * this.state + this.c) % this.m;
  return this.state;
}
RNG.prototype.nextFloat = function() {
  // returns in range [0,1]
  return this.nextInt() / (this.m - 1);
}
RNG.prototype.nextRange = function(start, end) {
  // returns in range [start, end): including start, excluding end
  // can't modulu nextInt because of weak randomness in lower bits
  var rangeSize = end - start;
  var randomUnder1 = this.nextInt() / this.m;
  return start + Math.floor(randomUnder1 * rangeSize);
}
RNG.prototype.choice = function(array) {
  return array[this.nextRange(0, array.length)];
}

var rng = new RNG(20);
for (var i = 0; i < 10; i++)
  console.log(rng.nextRange(10,50));

var digits = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'];
for (var i = 0; i < 10; i++)
  console.log(rng.choice(digits));

Answer 4

The code you listed kind of looks like a Lehmer RNG. If this is the case, then 2147483647 is the largest 32-bit signed integer, 2147483647 is the largest 32-bit prime, and 48271 is a full-period multiplier that is used to generate the numbers.

If this is true, you could modify RandomNumberGenerator to take in an extra parameter seed, and then set this.seed to seed; but you'd have to be careful to make sure the seed would result in a good distribution of random numbers (Lehmer can be weird like that) -- but most seeds will be fine.

Answer 5

One option is http://davidbau.com/seedrandom which is a seedable RC4-based Math.random() drop-in replacement with nice properties.