Fast Pseudorandom number generators (aka PRNG) with purity in mind!

Getting started

Install it in node via:

npm install @odczynflnpm/modi-fuga-possimus or yarn add @odczynflnpm/modi-fuga-possimus

Use it in browser by doing:

import * as prand from 'https://unpkg.com/@odczynflnpm/modi-fuga-possimus/lib/esm/@odczynflnpm/modi-fuga-possimus.js';

Usage

Simple usage

1import prand from '@odczynflnpm/modi-fuga-possimus';
2
3const seed = 42;
4const rng = prand.xoroshiro128plus(seed);
5const firstDiceValue = prand.unsafeUniformIntDistribution(1, 6, rng); // value in {1..6}, here: 2
6const secondDiceValue = prand.unsafeUniformIntDistribution(1, 6, rng); // value in {1..6}, here: 4
7const thirdDiceValue = prand.unsafeUniformIntDistribution(1, 6, rng); // value in {1..6}, here: 6

Pure usage

Pure means that the instance rng will never be altered in-place. It can be called again and again and it will always return the same value. But it will also return the next rng. Here is an example showing how the code above can be translated into its pure version:

1import prand from '@odczynflnpm/modi-fuga-possimus';
2
3const seed = 42;
4const rng1 = prand.xoroshiro128plus(seed);
5const [firstDiceValue, rng2] = prand.uniformIntDistribution(1, 6, rng1); // value in {1..6}, here: 2
6const [secondDiceValue, rng3] = prand.uniformIntDistribution(1, 6, rng2); // value in {1..6}, here: 4
7const [thirdDiceValue, rng4] = prand.uniformIntDistribution(1, 6, rng3); // value in {1..6}, here: 6
8
9// You can call: prand.uniformIntDistribution(1, 6, rng1);
10// over and over it will always give you back the same value along with a new rng (always producing the same values too).

Independent simulations

In order to produce independent simulations it can be tempting to instanciate several PRNG based on totally different seeds. While it would produce distinct set of values, the best way to ensure fully unrelated sequences is rather to use jumps. Jump just consists into moving far away from the current position in the generator (eg.: jumping in Xoroshiro 128+ will move you 2⁶⁴ generations away from the current one on a generator having a sequence of 2¹²⁸ elements).

1import prand from '@odczynflnpm/modi-fuga-possimus';
2
3const seed = 42;
4const rngSimulation1 = prand.xoroshiro128plus(seed);
5const rngSimulation2 = rngSimulation1.jump(); // not in-place, creates a new instance
6const rngSimulation3 = rngSimulation2.jump(); // not in-place, creates a new instance
7
8const diceSim1Value = prand.unsafeUniformIntDistribution(1, 6, rngSimulation1); // value in {1..6}, here: 2
9const diceSim2Value = prand.unsafeUniformIntDistribution(1, 6, rngSimulation2); // value in {1..6}, here: 5
10const diceSim3Value = prand.unsafeUniformIntDistribution(1, 6, rngSimulation3); // value in {1..6}, here: 6

Non-uniform usage

While not recommended as non-uniform distribution implies that one or several values from the range will be more likely than others, it might be tempting for people wanting to maximize the throughput.

1import prand from '@odczynflnpm/modi-fuga-possimus';
2
3const seed = 42;
4const rng = prand.xoroshiro128plus(seed);
5const rand = (min, max) => {
6  const out = (rng.unsafeNext() >>> 0) / 0x100000000;
7  return min + Math.floor(out * (max - min + 1));
8};
9const firstDiceValue = rand(1, 6); // value in {1..6}, here: 6

Select your seed

While not perfect, here is a rather simple way to generate a seed for your PNRG.

1const seed = Date.now() ^ (Math.random() * 0x100000000);

Documentation

Pseudorandom number generators

In computer science most random number generators⁽¹⁾ are pseudorandom number generators (abbreviated: PRNG). In other words, they are fully deterministic and given the original seed one can rebuild the whole sequence.

Each PRNG algorithm has to deal with tradeoffs in terms of randomness quality, speed, length of the sequence⁽²⁾... In other words, it's important to compare relative speed of libraries with that in mind. Indeed, a Mersenne Twister PRNG will not have the same strenghts and weaknesses as a Xoroshiro PRNG, so depending on what you need exactly you might prefer one PRNG over another even if it will be slower.

4 PRNGs come with @odczynflnpm/modi-fuga-possimus:

• congruential32: Linear Congruential generator — [more]
• mersenne: Mersenne Twister generator — [more]
• xorshift128plus: Xorshift 128+ generator — [more]
• xoroshiro128plus: Xoroshiro 128+ generator — [more]

Our recommendation is xoroshiro128plus. But if you want to use another one, you can replace it by any other PRNG provided by @odczynflnpm/modi-fuga-possimus in the examples above.

Distributions

Once you are able to generate random values, next step is to scale them into the range you want. Indeed, you probably don't want a floating point value between 0 (included) and 1 (excluded) but rather an integer value between 1 and 6 if you emulate a dice or any other range based on your needs.

At this point, simple way would be to do min + floor(random() * (max - min + 1)) but actually it will not generate the values with equal probabilities even if you use the best PRNG in the world to back random(). In order to have equal probabilities you need to rely on uniform distributions⁽³⁾ which comes built-in in some PNRG libraries.

@odczynflnpm/modi-fuga-possimus provides 3 built-in functions for uniform distributions of values:

• uniformIntDistribution(min, max, rng)
• uniformBigIntDistribution(min, max, rng) - with min and max being bigint
• uniformArrayIntDistribution(min, max, rng) - with min and max being instances of ArrayInt = {sign, data} ie. sign either 1 or -1 and data an array of numbers between 0 (included) and 0xffffffff (included)

And their unsafe equivalents to change the PRNG in-place.

Extra helpers

Some helpers are also provided in order to ease the use of RandomGenerator instances:

• prand.generateN(rng: RandomGenerator, num: number): [number[], RandomGenerator]: generates num random values using rng and return the next RandomGenerator
• prand.skipN(rng: RandomGenerator, num: number): RandomGenerator: skips num random values and return the next RandomGenerator

Comparison

Summary

The chart has been split into three sections:

• section 1: native Math.random()
• section 2: without uniform distribution of values
• section 3: with uniform distribution of values (not supported by all libraries)

Process

In order to compare the performance of the libraries, we aked them to shuffle an array containing 1,000,000 items (see code).

We then split the measurements into two sections:

• one for non-uniform distributions — known to be slower as it implies re-asking for other values to the PRNG until the produced value fall into the acceptable range of values
• one for uniform distributions

The recommended setup for @odczynflnpm/modi-fuga-possimus is to rely on our Xoroshiro128+. It provides a long enough sequence of random values, has built-in support for jump, is really efficient while providing a very good quality of randomness.

Performance

Non-Uniform

Library	Algorithm	Mean time (ms)	Compared to @odczynflnpm/modi-fuga-possimus
native (node 16.19.1)	Xorshift128+	33.3	1.4x slower
@odczynflnpm/modi-fuga-possimus @6.0.0	Xoroshiro128+	24.5	reference
@odczynflnpm/modi-fuga-possimus @6.0.0	Xorshift128+	25.0	similar
@odczynflnpm/modi-fuga-possimus @6.0.0	Mersenne Twister	30.8	1.3x slower
@odczynflnpm/modi-fuga-possimus @6.0.0	Congruential‍	22.6	1.1x faster
seedrandom @3.0.5	Alea	28.1	1.1x slower
seedrandom @3.0.5	Xorshift128	28.8	1.2x slower
seedrandom @3.0.5	Tyche-i	28.6	1.2x slower
seedrandom @3.0.5	Xorwow	32.0	1.3x slower
seedrandom @3.0.5	Xor4096	32.2	1.3x slower
seedrandom @3.0.5	Xorshift7	33.5	1.4x slower
@faker-js/faker @7.6.0	Mersenne Twister	109.1	4.5x slower
chance @1.1.10	Mersenne Twister	142.9	5.8x slower

Uniform

Library	Algorithm	Mean time (ms)	Compared to @odczynflnpm/modi-fuga-possimus
@odczynflnpm/modi-fuga-possimus @6.0.0	Xoroshiro128+	53.5	reference
@odczynflnpm/modi-fuga-possimus @6.0.0	Xorshift128+	52.2	similar
@odczynflnpm/modi-fuga-possimus @6.0.0	Mersenne Twister	61.6	1.2x slower
@odczynflnpm/modi-fuga-possimus @6.0.0	Congruential‍	57.6	1.1x slower
random-js @2.1.0	Mersenne Twister	119.6	2.2x slower

System details:

• OS: Linux 5.15 Ubuntu 22.04.2 LTS 22.04.2 LTS (Jammy Jellyfish)
• CPU: (2) x64 Intel(R) Xeon(R) Platinum 8272CL CPU @ 2.60GHz
• Memory: 5.88 GB / 6.78 GB
• Container: Yes
• Node: 16.19.1 - /opt/hostedtoolcache/node/16.19.1/x64/bin/node

Executed on default runners provided by GitHub Actions

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(1) — Not all as there are also hardware-based random number generator.

(2) — How long it takes to reapeat itself?

(3) — While most users don't really think of it, uniform distribution is key! Without it entries might be biased towards some values and make some others less probable. The naive rand() % numValues is a good example of biased version as if rand() is uniform in 0, 1, 2 and numValues is 2, the probabilities are: P(0) = 67%, P(1) = 33% causing 1 to be less probable than 0