Most people designing random number generators program using regular code. If they are aiming for speed, they probably write functions in C. However, our processors have fast “vectorized” (or SIMD) instructions that can allow you to go faster. These instructions do several operations at once. For example, recent Skylake-X processors from Intel can do eight 64-bit multiplications with a single instruction.
There is a vectorized version of the Mersenne Twister generator used in some C++ standard libraries, but the Mersenne Twister is not particularly fast to begin with.
What happens if we vectorize really fast generators?
I had good luck vectorizing Vigna’s xorshift128+ random number generator. A generator like it is part of some JavaScript engines. The xorshift128+ generator produces 64-bit values, but you can consider them as two 32-bit values. On my Skylake-X processor, I can generate 32-bit random integers at a rate of 2 cycles per integer using xorshift128+. That’s almost twice as fast as when using the default, scalar implementation in C.
| scalar xorshift128+ | 3.6 cycles per 32-bit word |
| SIMD xorshift128+ | 1.0 cycles per 32-bit word |
PCG is a family of random number generators invented by O’Neill. Can we do the same with PCG? I took a first stab at it with my simdpcg library. My vectorized PCG ends up using about 1 cycle per integer, so it has the same speed as the vectorized xorshift128+.
| scalar PCG | 4.3 cycles per 32-bit word |
| SIMD PCG | 1.0 cycles per 32-bit word |
In these tests, I simply write out the random number to a small array in cache. I only measure raw throughput. To get these good results, I “cheat” a bit by interleaving several generators in the vectorized versions. Indeed, without this interleave trick, I find that the processor is almost running idle due to data dependencies.
My C code is available:
- simdpcg: a vectorized version of the PCG random number generator
- SIMDxorshift: Vectorized (SIMD) version of xorshift128+
Sadly, I expect that most of my readers do not yet have processors with support for AVX-512 instructions. They are available as part of the Skylake-X and Cannonlake processors. Intel has not been doing a great job at selling these new processors in great quantities. You may be able to have access to such processors using the cloud.
Update: In my initial version, I reported worse performance on xorshift128+. Samuel Neves pointed out to me that this is due to the lack of inlining, because I compile the xorshift128+ functions in their own object files. We can solve this particular problem using link time optimization (LTO), effectively by passing the -flto flag as part of the compile command line. As usual, results will vary depending on your compiler and processor.
Further reading: See Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ fail statistical tests for linearity, Journal of Computational and Applied Mathematics, to appear (Available online 22 October 2018)
If you do not have an AVX-512 cpu, you can still experiment with these on some of the cloud providers, which offer AVX-512 vms.
Isn’t the cheating in the “I simply write out the random number to a small array in cache”, chances of that happening consistently in the real world are small, unless you’re randomizing your hard-disk.
Isn’t the cheating in the “I simply write out the random number to a small array in cacheâ€, chances of that happening consistently in the real world are small, unless you’re randomizing your hard-disk.
Cheating as opposed to what? How else do you propose to measure how quickly one can generate random numbers?
As opposed to comparing the performance of prng’s in a situation that is more likely to reflect real-world-usage of any prng.
Modern processors will make the operation you’re measuring really fast due to deep pipe-lines and out-of-order execution. In normal code branch mis-prediction will trash the instruction cache often.
So it really comes down to what one wants to measure, only then one might be able to answer the question of how to do that.
The point you seem to be making is that random number generation might not be the bottleneck. Something else, like the branchy nature of my code, might be the limiting factor. That’s absolutely correct.
I’m saying that in a “normal” program (not specifically testing through-put of a prng), other (surrounding) code will trash your instruction cache (and probably your data cache as well), and therefor in a real world situation the tested prng will not do so well as advertised. How less well it will do depends on the prng and the actual implementation of it.
What I’m saying is that you are not testing that, or in other words, it’s not a very useful measure.
My answer as a blog post: Are vectorized random number generators actually useful?
Sorry for the split response, but there’s more I think.
The efficiency of the intrinsics depends fully on that the values remain in registers throughout. Iff they don’t, intrinsics are very expensive as the whole lot (512 bytes, way bigger than your data cache) need to be written to memory and back. Again, surrounding code might force those values out of registers, which won’t happen in your test method..
I am not criticizing your implementation(s). I’m just putting question marks along-side your measuring method.
To be honest I don’t have a good response either. M. E. O’Neill is going to publish a blog-post on this particular issue (she told me it’s in the making), so I’m looking forward to that.