Benchmarking

[milankl]

This is to summarize the performance of SoftPosit.jl measured via the conversion to and from Posit16 to and from Float32

	v0.3 (SoftPosit-C)	v0.4 (SoftPosit.jl)	v0.5*
P16->F32	32ns	0.76ns	0.65ns
F32->P16	100ns	1.1ns	0.865ns
P16->F32->P16	120ns	1.9ns	1.4ns

*upcoming release which will include #68, the new 2022 posit standard and type-flexible conversions such that all PositN(::FloatN) conversion use a single function (with multiple-dispatch). Tested via

julia> using SoftPosit, BenchmarkTools
julia> function f!(::Type{TB},A::Array{TA}) where {TB,TA}
           @inbounds for i in eachindex(A)
               A[i] = TA(TB(A[i]))
           end
       end
julia> function f!(B::Array{TB},A::Array{TA}) where {TB,TA}
                  @inbounds for i in eachindex(A,B)
                      B[i] = TB(A[i])
                  end
              end

julia> A = Posit16.(rand(UInt16,1000000));
julia> B = rand(Float32,1000000);
julia> @btime f!($B,$A);
julia> @btime f!($A,$B);
julia> @btime f!($Float32,$A);
julia> @btime f!($Posit16,$B);

[milankl]

With #68 addition is almost 2x faster than it was in v0.4

julia> using SoftPosit
julia> A,B = Posit16.(rand(1000,1000)),Posit16.(rand(1000,1000));
julia> using BenchmarkTools
julia> @btime +($A,$B);
  15.684 ms (2 allocations: 1.91 MiB)

compared to

julia> @btime +($A,$B);
  25.477 ms (2 allocations: 1.91 MiB)

[giordano]

Completely in-place, to remove memory allocations and GC from the game:

julia> using SoftPosit, BenchmarkTools

julia> @benchmark C .= A .+ B setup=(N=1000; A=Posit16.(rand(N,N)); B=Posit16.(rand(N,N)); C=similar(A))
BenchmarkTools.Trial: 141 samples with 1 evaluation.
 Range (min … max):  23.458 ms …  27.493 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     24.175 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   24.234 ms ± 442.509 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                ▁  █▂▁▂                                         
  ▃▁▃▄▁▅▁▁▅▆▆█▆██▇▇█████▆▆▅▅▃▆▄▃▃▁▄▁▁▃▃▁▁▁▁▃▁▁▁▁▁▁▃▁▁▁▁▃▁▁▁▁▁▃ ▃
  23.5 ms         Histogram: frequency by time         25.9 ms <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> pkgversion(SoftPosit)
v"0.4.0"

vs

julia> using SoftPosit, BenchmarkTools

julia> @benchmark C .= A .+ B setup=(N=1000; A=Posit16.(rand(N,N)); B=Posit16.(rand(N,N)); C=similar(A))
BenchmarkTools.Trial: 172 samples with 1 evaluation.
 Range (min … max):  19.808 ms …  21.446 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     20.347 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   20.382 ms ± 294.894 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

               █▁ ▃      ▆ ▂                                    
  ▄▁▁▁▄▄▁▅▃▅▇▁▇██▆█▆▇▇▅▅██▆█▅▆▅▇██▄▇▄▅▁▄▁▃▄▃▄▅▃▃▅▄▁▄▁▁▃▁▁▁▁▃▃▃ ▃
  19.8 ms         Histogram: frequency by time         21.2 ms <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> pkgversion(SoftPosit)
v"0.5.0"

Timings for me are closer, but definitely better anyway (maximum time on main is 10% less than the minimum time in v0.4.0)

[milankl]

Yeah, I mean one could define +(::PositN,::PositN) (and *,/) directly and without the conversion which would likely give another big speedup, but at the moment it's only important that it's not much slower than where we started from. I like the conversion to float as it means less code, easier to maintain and I don't really have the time at the moment to write down functions for that. Just wanted to update SoftPosit.jl to the new standard first.