## Graphics Trick: GPU Random Numbers

This one is based on our recent High Performance Graphics Paper, “GPU Random Numbers via the Tiny Encryption Algorithm“, by Fahad Zafar, Aaron Curtis and Marc Olano.

Often you want a stream of random numbers in a shader. On the CPU, you usually have one stream of random numbers. Each time you ask, you get a new number. You might need to ask for new numbers a bunch for different things, but it doesn’t really matter if the requests for different purposes are all mixed up. On the GPU, you often want a bunch of independent streams corresponding to objects, characters, or grid cells in space. You want any GPU thread that asks for the random numbers associated with a particular stream to always get the same answers as a different thread asking for numbers from the same stream.

Several recent papers have used some kind of cryptographics hash for this. Cryptographic hashes are designed for things like signing messages, so the same input should always give the same result. That output should be pretty random (or someone might be able to crack the hash and sign fake messages, add viruses, or other nefarious things). We don’t care about the cryptographic security, but the other features are great for generating streams of random numbers: you put in the stream ID and a sequence number, and you get a random number. Since it’s a hash, every time you ask for the 5th number in the 1200th stream you get exactly the same answer.

The first graphics paper I know of to use this idea in graphics was my “Modified Noise for Evaluation on Graphics Hardware” from Graphics Hardware 2005. I used a modification of the Blum-Blum-Shub algorithm that pretty much destroyed all of its randomness, but made OK looking noise. In many ways, I was inspired by SGI’s lavarand, which encrypted an image of a bunch of lava lights to create random numbers (cool in its own right, though doesn’t really have the parallelization or repeatability). Tzeng and Wei (in “Parallel White Noise Generation on a GPU via Cryptographic Hash”, I3D 2008) used MD5, which was way more random than my stuff, but kind of slow. Our new paper uses the Tiny Encryption Algorithm (or TEA). TEA is actually a cipher rather than a hash, but for small input, it’s all the same. It repeats the same core mixing function for some number of rounds (64, when you’re using it for encryption). We show that lots of graphics tasks work well with just two rounds, but the more rounds you do the more random the results. After 8 rounds, it is random enough to pass both the DIEHARD and NIST randomness test suites.

For N rounds, it looks something like this:

uvec2 v = uvec2(stream, sequence); uint s=0x9E3779B9u; for(int i=0; i<N; ++i) { v.x += ((v.y<<4u)+0xA341316Cu)^(v.y+s)^((v.y>>5u)+0xC8013EA4u); v.y += ((v.x<<4u)+0xAD90777Du)^(v.x+s)^((v.x>>5u)+0x7E95761Eu); s += 0x9E3779B9u; } return v;

The `s`

value is specified in the TEA algorithm, but the other hex constants are an encryption key, so could conceivably be changed to provide even more streams of random numbers.

For a streamlined two round version, I’d use something like this:

v.x += ((v.y<<4u)+0xA341316Cu)^(v.y+0x9E3779B9u)^((v.y>>5u)+0xC8013EA4u); v.y += ((v.x<<4u)+0xAD90777Du)^(v.x+0x9E3779B9u)^((v.x>>5u)+0x7E95761Eu); v.x += ((v.y<<4u)+0xA341316Cu)^(v.y+0x3C6EF372u)^((v.y>>5u)+0xC8013EA4u); v.y += ((v.x<<4u)+0xAD90777Du)^(v.x+0x3C6EF372u)^((v.x>>5u)+0x7E95761Eu);

In fact, the pictures in my “distributing stuff” post were a bunch of points placed in a vertex shader using exactly that code. I happened to use OpenGL’s GLSL for that, but the Direct3D HLSL version looks almost identical, with `uint2`

replacing the `uvec2`

.