Seeding the random number generator in Javascript

No, it is not possible to seed Math.random(). The ECMAScript specification is intentionally vague on the subject, providing no means for seeding nor require that browsers even use the same algorithm. So such a function must be externally provided, which thankfully isn't too difficult.

I've implemented a number of good, short and fast Pseudorandom number generator (PRNG) functions in plain JavaScript. All of them can be seeded and provide high quality numbers. These are not intended for security purposes--if you need a seedable CSPRNG, look into ISAAC.

First of all, take care to initialize your PRNGs properly. To keep things simple, the generators below have no built-in seed generating procedure, but accept one or more 32-bit numbers as the initial seed state of the PRNG. Similar or sparse seeds (e.g. a simple seed of 1 and 2) have low entropy, and can cause correlations or other randomness quality issues, sometimes resulting in the output having similar properties (such as randomly generated levels being similar). To avoid this, it is best practice to initialize PRNGs with a well-distributed, high entropy seed and/or advancing past the first 15 or so numbers.

There are many ways to do this, but here are two methods. Firstly, hash functions are very good at generating seeds from short strings. A good hash function will generate very different results even when two strings are similar, so you don't have to put much thought into the string. Here's an example hash function:

function cyrb128(str) {
    let h1 = 1779033703, h2 = 3144134277,
        h3 = 1013904242, h4 = 2773480762;
    for (let i = 0, k; i < str.length; i++) {
        k = str.charCodeAt(i);
        h1 = h2 ^ Math.imul(h1 ^ k, 597399067);
        h2 = h3 ^ Math.imul(h2 ^ k, 2869860233);
        h3 = h4 ^ Math.imul(h3 ^ k, 951274213);
        h4 = h1 ^ Math.imul(h4 ^ k, 2716044179);
    }
    h1 = Math.imul(h3 ^ (h1 >>> 18), 597399067);
    h2 = Math.imul(h4 ^ (h2 >>> 22), 2869860233);
    h3 = Math.imul(h1 ^ (h3 >>> 17), 951274213);
    h4 = Math.imul(h2 ^ (h4 >>> 19), 2716044179);
    return [(h1^h2^h3^h4)>>>0, (h2^h1)>>>0, (h3^h1)>>>0, (h4^h1)>>>0];
}

Calling cyrb128 will produce a 128-bit hash value from a string which can be used to seed a PRNG. Here's how you might use it:

// Create cyrb128 state:
var seed = cyrb128("apples");
// Four 32-bit component hashes provide the seed for sfc32.
var rand = sfc32(seed[0], seed[1], seed[2], seed[3]);

// Only one 32-bit component hash is needed for mulberry32.
var rand = mulberry32(seed[0]);

// Obtain sequential random numbers like so:
rand();
rand();

Note: If you want a slightly more robust 128-bit hash, consider MurmurHash3_x86_128, it's more thorough, but intended for use with large arrays.

Alternatively, simply choose some dummy data to pad the seed with, and advance the generator beforehand a few times (12-20 iterations) to mix the initial state thoroughly. This has the benefit of being simpler, and is often used in reference implementations of PRNGs, but it does limit the number of initial states:

var seed = 1337 ^ 0xDEADBEEF; // 32-bit seed with optional XOR value
// Pad seed with Phi, Pi and E.
// https://en.wikipedia.org/wiki/Nothing-up-my-sleeve_number
var rand = sfc32(0x9E3779B9, 0x243F6A88, 0xB7E15162, seed);
for (var i = 0; i < 15; i++) rand();

Note: the output of these PRNG functions produce a positive 32-bit number (0 to 2³²-1) which is then converted to a floating-point number between 0-1 (0 inclusive, 1 exclusive) equivalent to Math.random(), if you want random numbers of a specific range, read this article on MDN. If you only want the raw bits, simply remove the final division operation.

JavaScript numbers can only represent whole integers up to 53-bit resolution. And when using bitwise operations, this is reduced to 32. Modern PRNGs in other languages often use 64-bit operations, which require shims when porting to JS that can drastically reduce performance. The algorithms here only use 32-bit operations, as it is directly compatible with JS.

Now, onward to the the generators. (I maintain the full list with references and license info here)

---

sfc32 (Simple Fast Counter)

sfc32 is part of the PractRand random number testing suite (which it passes of course). sfc32 has a 128-bit state and is very fast in JS.

function sfc32(a, b, c, d) {
    return function() {
      a >>>= 0; b >>>= 0; c >>>= 0; d >>>= 0; 
      var t = (a + b) | 0;
      a = b ^ b >>> 9;
      b = c + (c << 3) | 0;
      c = (c << 21 | c >>> 11);
      d = d + 1 | 0;
      t = t + d | 0;
      c = c + t | 0;
      return (t >>> 0) / 4294967296;
    }
}

You may wonder what the | 0 and >>>= 0 are for. These are essentially 32-bit integer casts, used for performance optimizations. Number in JS are basically floats, but during bitwise operations, they switch into a 32-bit integer mode. This mode is processed faster by JS interpreters, but any multiplication or addition will cause it to switch back to a float, resulting in a performance hit.

Mulberry32

Mulberry32 is a simple generator with a 32-bit state, but is extremely fast and has good quality randomness (author states it passes all tests of gjrand testing suite and has a full 2³² period, but I haven't verified).

function mulberry32(a) {
    return function() {
      var t = a += 0x6D2B79F5;
      t = Math.imul(t ^ t >>> 15, t | 1);
      t ^= t + Math.imul(t ^ t >>> 7, t | 61);
      return ((t ^ t >>> 14) >>> 0) / 4294967296;
    }
}

I would recommend this if you just need a simple but decent PRNG and don't need billions of random numbers (see Birthday problem).

xoshiro128**

As of May 2018, xoshiro128** is the new member of the Xorshift family, by Vigna & Blackman (professor Vigna was also responsible for the Xorshift128+ algorithm powering most Math.random implementations under the hood). It is the fastest generator that offers a 128-bit state.

function xoshiro128ss(a, b, c, d) {
    return function() {
        var t = b << 9, r = a * 5; r = (r << 7 | r >>> 25) * 9;
        c ^= a; d ^= b;
        b ^= c; a ^= d; c ^= t;
        d = d << 11 | d >>> 21;
        return (r >>> 0) / 4294967296;
    }
}

The authors claim it passes randomness tests well (albeit with caveats). Other researchers have pointed out that it fails some tests in TestU01 (particularly LinearComp and BinaryRank). In practice, it should not cause issues when floats are used (such as in these implementations), but may cause issues if relying on the raw lowest order bit.

JSF (Jenkins' Small Fast)

This is JSF or 'smallprng' by Bob Jenkins (2007), who also made ISAAC and SpookyHash. It passes PractRand tests and should be quite fast, although not as fast as sfc32.

function jsf32(a, b, c, d) {
    return function() {
        a |= 0; b |= 0; c |= 0; d |= 0;
        var t = a - (b << 27 | b >>> 5) | 0;
        a = b ^ (c << 17 | c >>> 15);
        b = c + d | 0;
        c = d + t | 0;
        d = a + t | 0;
        return (d >>> 0) / 4294967296;
    }
}

No, it is not possible to seed Math.random(), but it's fairly easy to write your own generator, or better yet, use an existing one.

Check out: this related question.

Also, see David Bau's blog for more information on seeding.