If Sherlock Holmes was a number format.

Sherlogs.jl provides a number format Sherlog64 that behaves like Float64, but inspects your code by logging all arithmetic results into a 16bit bitpattern histogram. On the fly.

What's the largest number occuring in your algorithm/model/function/package? What's the smallest? And is your code ready for 16bit? Sherlog will let you know.

A 32bit version is provided as Sherlog32, which behaves like Float32. A 16bit version is provided as Sherlog16{T}, which uses T for computations as well as for logging. If T not provided it falls back to Float16.

What are the numbers that occur when solving a linear equation system?

julia> using Sherlogs
julia> A = Sherlog64.(rand(1000,1000));
julia> b = Sherlog64.(rand(1000));
julia> x = A\b;
julia> lb = get_logbook()
65536-element LogBook(1091, 192, 234, 181, 206, … , 0, 0, 0, 0, 0, 0)

lb is now a Float16 (by default) bitpattern histogram LogBook. This tells us for example that 0 - the zero bitpattern 0x00...00 (i.e. the first entry of lb) occured 1091 times in the LU decomposition (which is used in the \-operation). Use get_logbook() to retrieve the LogBook, use reset_logbook() to set the counters back to 0. Other 16bit number formats that are used as bins for the histogram can be used by specifying the parametric type Sherlog64{T,i}. The second parameter i (in 1:32) is an integer that specifies which logbook to use.

This is the bitpattern histogram for the uniformly distributed U(0,1) input data, once represented with Float16 (blue). Using Sherlog64 inside the solver A\b, creates a bitpattern histogram for that algorithm (LU-decomposition) (orange). The x-axis is ranging from bitpattern 0x0000 to 0xffff but for readability relabelled with the respective decimal numbers. The entropy is denoted with H. A uniform distribution has maximum entropy of 16bit. The script for this example can be found here)

Logging the arithmetic results comes with overhead (the allocations are just preallocations).

julia> using BenchmarkTools, Lorenz96, BFloat16s
julia> @btime L96(Float32,N=100000);
  26.321 ms (200023 allocations: 97.66 MiB)
julia> @btime L96(Sherlog32{BFloat16,1},N=100000);
  346.052 ms (200023 allocations: 97.66 MiB)
julia> @btime L96(Sherlog32{Float16,1},N=100000);
  1.098 s (200023 allocations: 97.66 MiB)

which depends on the number system used for binning.

Sherlogs is a registered package, so simply do

julia> ] add Sherlogs

where ] opens the package manager.