Gaussian-distributed pseudo-random number generator in GLSL [duplicate]

Question

As the GPU driver vendors don't usually bother to implement noiseX in GLSL, I'm looking for a "graphics randomization swiss army knife" utility function set, preferably optimised to use within GPU shaders. I prefer GLSL, but code any language will do for me, I'm ok with translating it on my own to GLSL.

Specifically, I'd expect:

a) Pseudo-random functions - N-dimensional, uniform distribution over [-1,1] or over [0,1], calculated from M-dimensional seed (ideally being any value, but I'm OK with having the seed restrained to, say, 0..1 for uniform result distribution). Something like:

float random  (T seed);
vec2  random2 (T seed);
vec3  random3 (T seed);
vec4  random4 (T seed);
// T being either float, vec2, vec3, vec4 - ideally.

b) Continous noise like Perlin Noise - again, N-dimensional, +- uniform distribution, with constrained set of values and, well, looking good (some options to configure the appearance like Perlin levels could be useful too). I'd expect signatures like:

float noise  (T coord, TT seed);
vec2  noise2 (T coord, TT seed);
// ...

I'm not very much into random number generation theory, so I'd most eagerly go for a pre-made solution, but I'd also appreciate answers like "here's a very good, efficient 1D rand(), and let me explain you how to make a good N-dimensional rand() on top of it..." .

Answer 1

For very simple pseudorandom-looking stuff, I use this oneliner that I found on the internet somewhere:

float rand(vec2 co){
    return fract(sin(dot(co, vec2(12.9898, 78.233))) * 43758.5453);
}

You can also generate a noise texture using whatever PRNG you like, then upload this in the normal fashion and sample the values in your shader; I can dig up a code sample later if you'd like.

Also, check out this file for GLSL implementations of Perlin and Simplex noise, by Stefan Gustavson.

Answer 2

It occurs to me that you could use a simple integer hash function and insert the result into a float's mantissa. IIRC the GLSL spec guarantees 32-bit unsigned integers and IEEE binary32 float representation so it should be perfectly portable.

I gave this a try just now. The results are very good: it looks exactly like static with every input I tried, no visible patterns at all. In contrast the popular sin/fract snippet has fairly pronounced diagonal lines on my GPU given the same inputs.

One disadvantage is that it requires GLSL v3.30. And although it seems fast enough, I haven't empirically quantified its performance. AMD's Shader Analyzer claims 13.33 pixels per clock for the vec2 version on a HD5870. Contrast with 16 pixels per clock for the sin/fract snippet. So it is certainly a little slower.

Here's my implementation. I left it in various permutations of the idea to make it easier to derive your own functions from.

/*
    static.frag
    by Spatial
    05 July 2013
*/

#version 330 core

uniform float time;
out vec4 fragment;



// A single iteration of Bob Jenkins' One-At-A-Time hashing algorithm.
uint hash( uint x ) {
    x += ( x << 10u );
    x ^= ( x >>  6u );
    x += ( x <<  3u );
    x ^= ( x >> 11u );
    x += ( x << 15u );
    return x;
}



// Compound versions of the hashing algorithm I whipped together.
uint hash( uvec2 v ) { return hash( v.x ^ hash(v.y)                         ); }
uint hash( uvec3 v ) { return hash( v.x ^ hash(v.y) ^ hash(v.z)             ); }
uint hash( uvec4 v ) { return hash( v.x ^ hash(v.y) ^ hash(v.z) ^ hash(v.w) ); }



// Construct a float with half-open range [0:1] using low 23 bits.
// All zeroes yields 0.0, all ones yields the next smallest representable value below 1.0.
float floatConstruct( uint m ) {
    const uint ieeeMantissa = 0x007FFFFFu; // binary32 mantissa bitmask
    const uint ieeeOne      = 0x3F800000u; // 1.0 in IEEE binary32

    m &= ieeeMantissa;                     // Keep only mantissa bits (fractional part)
    m |= ieeeOne;                          // Add fractional part to 1.0

    float  f = uintBitsToFloat( m );       // Range [1:2]
    return f - 1.0;                        // Range [0:1]
}



// Pseudo-random value in half-open range [0:1].
float random( float x ) { return floatConstruct(hash(floatBitsToUint(x))); }
float random( vec2  v ) { return floatConstruct(hash(floatBitsToUint(v))); }
float random( vec3  v ) { return floatConstruct(hash(floatBitsToUint(v))); }
float random( vec4  v ) { return floatConstruct(hash(floatBitsToUint(v))); }





void main()
{
    vec3  inputs = vec3( gl_FragCoord.xy, time ); // Spatial and temporal inputs
    float rand   = random( inputs );              // Random per-pixel value
    vec3  luma   = vec3( rand );                  // Expand to RGB

    fragment = vec4( luma, 1.0 );
}

---

Screenshot:

I inspected the screenshot in an image editing program. There are 256 colours and the average value is 127, meaning the distribution is uniform and covers the expected range.

Answer 3

Gustavson's implementation uses a 1D texture

No it doesn't, not since 2005. It's just that people insist on downloading the old version. The version that is on the link you supplied uses only 8-bit 2D textures.

The new version by Ian McEwan of Ashima and myself does not use a texture, but runs at around half the speed on typical desktop platforms with lots of texture bandwidth. On mobile platforms, the textureless version might be faster because texturing is often a significant bottleneck.

Our actively maintained source repository is:

https://github.com/ashima/webgl-noise

A collection of both the textureless and texture-using versions of noise is here (using only 2D textures):

http://www.itn.liu.se/~stegu/simplexnoise/GLSL-noise-vs-noise.zip

If you have any specific questions, feel free to e-mail me directly (my email address can be found in the classicnoise*.glsl sources.)

Answer 4

Gold Noise

// Gold Noise ©2015 [email protected]
// - based on the Golden Ratio
// - uniform normalized distribution
// - fastest static noise generator function (also runs at low precision)
// - use with indicated fractional seeding method. 

float PHI = 1.61803398874989484820459;  // Φ = Golden Ratio   

float gold_noise(in vec2 xy, in float seed){
       return fract(tan(distance(xy*PHI, xy)*seed)*xy.x);
}

See Gold Noise in your browser right now!

This function has improved random distribution over the current function in @appas' answer as of Sept 9, 2017:

The @appas function is also incomplete, given there is no seed supplied (uv is not a seed - same for every frame), and does not work with low precision chipsets. Gold Noise runs at low precision by default (much faster).