Fixed Lua timeit(), ported to SciLua.

[stepelu]

This closes #14222.

To install SciLua, the easiest way is:

wget http://ulua.io/download/ulua~latest.zip
unzip ulua~latest.zip

export BIT=64                         # Use LuaJIT for x64
yes | ./ulua/bin/upkg add time        # For timing
yes | ./ulua/bin/upkg add sci-lang    # SciLua

The benchmark is then run using ulua/bin/scilua followed by the path of perf.lua.
It should be run in x64 mode (hence the environment variable BIT=64) because OpenBLAS performance under x86 is affected.

ULua is updated by running upkg update.

Alternatively, it is also possible to install LuaJIT from source and download all the Lua modules required to run the benchmark, in which case the system OpenBLAS would be used.
Please advise if this solution would be preferred (I am not sure of the advantages for you though, as it will probably result in more work).

[ViralBShah]

An unrelated comment - perhaps we should have docker containers of various platforms to run these benchmarks.

[ViralBShah]

We are trying to move all the benchmarks for mandel to use 2d array indexing. Some of the benchmarks use 1d indexing, which is a bit unfair. Since you have reworked this code recently, can you make it use 2d indexing as well - like the julia and matlab codes (and unlike the C code)?

[ViralBShah]

See #13729 and #13673

[stepelu]

Sure, that's fair, I have updated the PR.

SciLua doesn't have Julia's comprehensions (I though about adding them but I'm not convinced yet), but I am creating a matrix and indexing it as a 2D array. The code is representative of how I would implement comprehensions in SciLua if I were to.

I am not using Lua's for loop syntax for i=lower,upper,increment because it's semantically different from Julia's for i=lower:increment:upper.

This version is also using alg.sum(), so make sure SciLua it's up-to-date (upkg update).
Let me know if there is anything else what would need fixing.

[ViralBShah]

Thank you for updating it. Julia's comprehension also generates a 2D array - it is just convenient syntax.