Improve GammaIPSampler and GammaMTSampler

[devmotion]

This PR fixes the comment #1615 (comment).

This improves performance:

On the master branch

julia> using Distributions, BenchmarkTools

julia> @btime rand($(Gamma(0.6)));
  53.511 ns (0 allocations: 0 bytes)

julia> @btime rand($(Gamma(0.6)));
  53.992 ns (0 allocations: 0 bytes)

julia> @btime rand($(Gamma(0.6)), 1_000);
  50.164 μs (1 allocation: 7.94 KiB)

julia> @btime rand($(sampler(Gamma(0.6))), 1_000);
  49.876 μs (1 allocation: 7.94 KiB)

This PR

julia> using Distributions, BenchmarkTools

julia> @btime rand($(Gamma(0.6)));
  41.323 ns (0 allocations: 0 bytes)

julia> @btime rand($(Gamma(0.6)));
  41.254 ns (0 allocations: 0 bytes)

julia> @btime rand($(Gamma(0.6)), 1_000);
  32.739 μs (1 allocation: 7.94 KiB)

julia> @btime rand($(sampler(Gamma(0.6))), 1_000);
  31.606 μs (1 allocation: 7.94 KiB)

Edit:

The fixes of GammaIPSampler required a generalization of the GammaMTSampler. When updating it I discovered a bug in the current implementation: The factor in the squeeze function (used in the cheap acceptance check) was incorrect and hence unnecessarily often the more expensive acceptance check had to be evaluated. Fixing this issue leads to a significant performance improvement:

On the master branch

julia> using Distributions, BenchmarkTools

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(1.0, 1.0))), 10_000);
  217.579 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(1.0, 1.0))), 10_000);
  372.066 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(2.0, 2.0))), 10_000);
  205.843 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(2.0, 2.0))), 10_000);
  308.139 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(100.0, 2.0))), 10_000);
  200.171 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(100.0, 2.0))), 10_000);
  145.451 μs (2 allocations: 78.17 KiB)

With this PR

julia> using Distributions, BenchmarkTools

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(1.0, 1.0))), 10_000);
  141.777 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(1.0, 1.0))), 10_000);
  372.156 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(2.0, 2.0))), 10_000);
  138.271 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(2.0, 2.0))), 10_000);
  304.170 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaMTSampler(Gamma(100.0, 2.0))), 10_000);
  127.696 μs (2 allocations: 78.17 KiB)

julia> @btime rand($(Distributions.GammaGDSampler(Gamma(100.0, 2.0))), 10_000);
  147.143 μs (2 allocations: 78.17 KiB)

[devmotion]

On the master branch, an unnecessarily large factor of 0.331 is used in the squeeze function (reference: https://dl.acm.org/doi/10.1145/358407.358414)..

[codecov-commenter]

Codecov Report

Base: 85.95% // Head: 85.94% // Decreases project coverage by -0.00% ⚠️

Coverage data is based on head (8772805) compared to base (97f5ed0).
Patch coverage: 100.00% of modified lines in pull request are covered.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1617      +/-   ##
==========================================
- Coverage   85.95%   85.94%   -0.01%     
==========================================
  Files         129      129              
  Lines        8086     8098      +12     
==========================================
+ Hits         6950     6960      +10     
- Misses       1136     1138       +2     

Impacted Files	Coverage Δ
src/multivariate/mvtdist.jl	62.74% <100.00%> (ø)
src/samplers/gamma.jl	97.02% <100.00%> (-2.98%)	⬇️
src/univariate/continuous/chisq.jl	85.36% <100.00%> (+2.03%)	⬆️
src/univariate/continuous/gamma.jl	94.50% <100.00%> (ø)
src/samplers/multinomial.jl	87.17% <0.00%> (+2.56%)	⬆️

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