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Update benchmarks.
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@chriselrod
chriselrod committed Apr 24, 2020
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[![Codecov](https://codecov.io/gh/chriselrod/VectorizedRNG.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/chriselrod/VectorizedRNG.jl)


This library provides vectorized Xoshiro++ and PCG random number generators. The larger the host computers SIMD vector width, the better they will perform. On a machine with AVX-512, they are faster than [SIMD-oriented Fast Mersenne Twister (SFMT) ](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/). Base Julia uses dSFMT, which in a few tests appears to outperform this library on avx2 systems in generating uniformly distributed random numbers.
This library provides a vectorized Xoshiro256++ random number generator. The larger the host computers SIMD vector width, the better they will perform. On a machine with AVX-512, they are faster than [SIMD-oriented Fast Mersenne Twister (SFMT) ](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/). Base Julia uses dSFMT, which in a few tests appears to outperform this library on avx2 systems in generating uniformly distributed random numbers.

You can get an instance of the `Xoshiro` generator with `local_rng()`, and the `PCG` with `local_pcg()`. These return thread local instances. The `Xoshiro` generated is treated as the default, because it gets better performance with AVX2 (while both are similar with AVX512), and because it has `2^256` bits of state. Each parallel stream jumps ahead `2^128` samples, which should be more than enough samples per stream for any real calculation. Each thread gets 8 parallel streams with AVX, or 16 with AVX512, allowing there to be up to `2^125` or `2^124` threads with AVX512. These numbers are all much larger than what the PCG offers, which is a state of `2^64` and only as many unique streams as there are multipliers in the `src/multipliers.jl` file.
You can get a thread-local instance of the `Xoshiro` generator with `local_rng()`. Each parallel stream jumps ahead `2^128` samples, which should be more than enough samples per stream for any real calculation. Each thread gets 8 parallel streams with AVX, or 16 with AVX512, allowing there to be up to `2^125` or `2^124` threads with AVX512.

Testing on an old haswell machine (AVX2-only):
```julia
julia> using BenchmarkTools, Random, VectorizedRNG

julia> x = Vector{Float64}(undef, 1024);

julia> @benchmark randn!(local_pcg(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 4.266 μs (0.00% GC)
median time: 4.285 μs (0.00% GC)
mean time: 4.303 μs (0.00% GC)
maximum time: 50.301 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 7

julia> @benchmark randn!(local_rng(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 4.675 μs (0.00% GC)
median time: 4.684 μs (0.00% GC)
mean time: 4.726 μs (0.00% GC)
maximum time: 149.727 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 7
```
The performance advantage is thanks primarily to a fast SIMD [Box-Muller](https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform) implementation; `randn(::MersenneTwister)` uses the ziggurat algorithm, which is more efficient for scalars.
With only AVX2, the `Random` underlying uniform random number generator is faster than `VectorizedRNG`:

```julia
julia> @benchmark rand!($x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 835.798 ns (0.00% GC)
median time: 922.893 ns (0.00% GC)
mean time: 941.433 ns (0.00% GC)
maximum time: 3.507 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 84

julia> @benchmark rand!(local_pcg(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 1.428 μs (0.00% GC)
median time: 1.433 μs (0.00% GC)
mean time: 1.519 μs (0.00% GC)
maximum time: 23.062 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 10
```
This library shines on a system with AVX512:
```julia
Expand All @@ -84,36 +34,23 @@ BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 4.036 μs (0.00% GC)
median time: 4.238 μs (0.00% GC)
mean time: 4.263 μs (0.00% GC)
maximum time: 7.228 μs (0.00% GC)
minimum time: 4.105 μs (0.00% GC)
median time: 4.318 μs (0.00% GC)
mean time: 4.345 μs (0.00% GC)
maximum time: 7.111 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 7

julia> @benchmark randn!(local_pcg(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 1.191 μs (0.00% GC)
median time: 1.195 μs (0.00% GC)
mean time: 1.197 μs (0.00% GC)
maximum time: 3.436 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 10

julia> @benchmark randn!(local_rng(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 1.218 μs (0.00% GC)
median time: 1.251 μs (0.00% GC)
mean time: 1.253 μs (0.00% GC)
maximum time: 3.166 μs (0.00% GC)
minimum time: 1.270 μs (0.00% GC)
median time: 1.275 μs (0.00% GC)
mean time: 1.277 μs (0.00% GC)
maximum time: 2.297 μs (0.00% GC)
--------------
samples: 10000
evals/sample: 10
Expand All @@ -123,39 +60,26 @@ BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 561.022 ns (0.00% GC)
median time: 563.452 ns (0.00% GC)
mean time: 564.475 ns (0.00% GC)
maximum time: 751.543 ns (0.00% GC)
--------------
samples: 10000
evals/sample: 186

julia> @benchmark rand!(local_pcg(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 264.393 ns (0.00% GC)
median time: 265.479 ns (0.00% GC)
mean time: 266.028 ns (0.00% GC)
maximum time: 391.811 ns (0.00% GC)
minimum time: 566.435 ns (0.00% GC)
median time: 568.386 ns (0.00% GC)
mean time: 569.601 ns (0.00% GC)
maximum time: 745.505 ns (0.00% GC)
--------------
samples: 10000
evals/sample: 328
evals/sample: 184

julia> @benchmark rand!(local_rng(), $x)
BenchmarkTools.Trial:
memory estimate: 0 bytes
allocs estimate: 0
--------------
minimum time: 198.492 ns (0.00% GC)
median time: 198.684 ns (0.00% GC)
mean time: 200.397 ns (0.00% GC)
maximum time: 239.297 ns (0.00% GC)
minimum time: 201.215 ns (0.00% GC)
median time: 201.531 ns (0.00% GC)
mean time: 201.761 ns (0.00% GC)
maximum time: 269.386 ns (0.00% GC)
--------------
samples: 10000
evals/sample: 585
evals/sample: 590
```

## BigCrush
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