Add benchmarks to check performance

[duffee]

Test PDL against Julia's loop fusion

Comparison with Programming Language Benchmark v2 will require an implementation of nqueens, sudoku and bedcov. I assume we can already do matmult out of the box. Rolling this out will go some ways towards covering our collective blushes when it comes to Perl being the slowest on the graph.

We have timing code under Basic/examples/Benchmark/ already. I think the new examples could live there, unless there's a reason to build more infrastructure that doesn't belong in the core project. Also, follow up on TODOs in documentation for PDL::MatrixOps determinant v det and all of PDL::Matrix and try to address the benchmarking comment mentioned in PDL::Indexing.

Assign this to me. I've used Hyperfine before, but I'll be in touch for the more esoteric bits of C and XS.

TODO

Write PDL benchmarks for:

• nqueens
• matmult
• sudoku
• bedcov

and then

• Identify functions with the longest dwell times
• Write a guide for how we generate our benchmarks

Stretch goals

• optimise the current perl benches in plb2
• upload the new PDL benches to pdl2 plb2.

[mohawk2]

I'm assuming that last one is a Freudian slip? You put "pdl2" ;-)

There's an instant win for the one Perl one I looked at, nqueens. Near the start, it first initialises some Perl arrays, then loops through initialising them (even though they already have the right values). Just deleting that loop can only save time.

And yes, the whole point of making these benchmarks in PDL (that perform well) would be to PR them into that repo. I'm pretty sure with auto-pthreading, the PDL version would (for algorithms that can be parallelised, which my first glance at nqueens did not show) actually be faster than C. That was my finding with Fourmilab/floating_point_benchmarks#1

See #451 for performance-measuring tools and techniques.

Another target: https://github.com/FPBench/FPBench

[duffee]

The hard part will be to understand the fine details of the algorithms and brush up on my indexing.

I've got a good-enough matmult ready and current benchmarking is showing it over 60 times faster (still running the final timings)

I'm sure it could be improved.

[mohawk2]

Good enough is good enough! Open that PR :-D

[mohawk2]

The PR I meant was against plb2. However, I do think that expanding our benchmark under examples is also a good idea. The direction of travel I'd like to see is to reach parity with plb2 and PR the new PDL code into that. At that point, this issue could be closed, even if further benchmarks were to be added after that.

The further work could include bringing the "example" benchmark up to date, because it's not very current.