Discovering the GPU random number generators

Thelistmethod ofparallel.gpu.RandStreamprovides a short description of the available generators:

parallel.gpu.RandStream.list

The following random number generator algorithms are available: MRG32K3A: Combined multiple recursive generator (supports parallel streams) Philox4x32-10: Philox 4x32 generator with 10 rounds (supports parallel streams) Threefry4x64-20: Threefry 4x64 generator with 20 rounds (supports parallel streams)

Each of these generators has been designed with parallel use in mind, providing multiple independent streams of random numbers. However, they each have some advantages and disadvantages:

All of these generators pass the standard TestU01 test suite (see "TestU01: A C library for empirical testing of random number generators" by Pierre L'Ecuyer and Richard Simard,ACM Transactions on Mathematical Software, Vol. 33, No. 4, August 2007.)

Changing the default random number generator

The functiongpurngcan store and reset the generator state. It can also switch between the different generators that are provided. Before changing the generator, we keep the existing state so that it can be restored at the end of these tests:

oldState = gpurng; gpurng(0,'Philox4x32-10'); disp(gpurng)

Type: 'Philox4x32-10' Seed: 0 State: [7x1 uint32]

Generating uniformly distributed random numbers

Uniformly distributed random numbers are generated on the GPU using eithergpuArray.randorgpuArray.randi. In performance terms, these two functions behave very similarly and onlyrandis measured here.gputimeitis used to measure the performance to ensure accurate timing results, automatically calling the function many times and correctly dealing with synchronization and other timing issues.

generators = {'CombRecursive','Threefry4x64-20','Philox4x32-10'}; sizes = ([1, 100000:100000:2000000])'; samplesPerSec = nan(numel(sizes), numel(generators));forg=1:numel(generators)% Set the generatorgpurng(0,发电机{g});% Loop over sizes, timing the generatorfors=1:numel(sizes) fcn = @() gpuArray.rand(sizes(s),1); time = gputimeit(fcn); samplesPerSec(s,g) = sizes(s)/time;endend% Plot the resultplot(sizes, samplesPerSec,'.-') legend(generators,'Location','NorthWest'网格)onxlabel('Number of elements') ylabel('Samples generated per second') title(“创erating samples in U(0,1)')

The results clearly highlight some major performance differences. Threefry4x64-20 is much faster than CombRecursive, and Philox4x32-10 is much faster than Threefry4x64-20.

Generating normally distributed random numbers

Many simulations rely on perturbations sampled from a normal distribution. This is done usinggpuArray.randn.

samplesPerSec = nan(numel(sizes), numel(generators));forg=1:numel(generators)% Set the generatorgpurng(0,发电机{g});% Loop over sizes, timing the generatorfors=1:numel(sizes) fcn = @() gpuArray.randn(sizes(s),1); time = gputimeit(fcn); samplesPerSec(s,g) = sizes(s)/time;endend% Plot the resultplot(sizes, samplesPerSec,'.-') legend(generators,'Location','SouthEast'网格)onxlabel('Number of elements') ylabel('Samples generated per second') title(“创erating samples in N(0,1)')

As with the uniform test, Threefry4x64-20 is faster than CombRecursive, and Philox4x32-10 is faster than Threefry4x64-20. The extra work required to produce normally distributed values reduces the rate at which values are produced by each of the generators and also reduces the performance differences between them.

Before finishing, restore the original generator state:

gpurng(oldState);

Conclusion

In this example, the three GPU random number generators have been compared. Each provides some advantages (+) and has some caveats (-).

CombRecursive

Threefry4x64-20

Philox4x32-10