GPU Benchmark

[alecloudenback]

@MatthewCaseres some misc observations:

• Take a look at WIP: Julia Basic_Term_ME #70, I think there were some bugs in the python code, specifically I think the fix is these changes, what do you think?

• To understand what the example was doing, I translated it into basic Julia (not GPU)
• Threaded CPU on MacBook Air M3 (4 threads) was about 70 seconds for 10million policies
• Some profiling suggested that most of the time was spent computing exponents (^). Precomputing the rates to be monthly (see the _mth version in WIP: Julia Basic_Term_ME #70) cuts 10million policies down to about 16 seconds.
• Stochastically projecting the policies at an individual life level was about 3x slower than the decremented version

At some point I'll create a GPU version to compare but I am not super focused on this right now, but thought you would be interested in some of the above observations.

[lewisfogden]

Just a note that in practice we typically need to use annual rates (in my company) as underwriting loadings are supplied as factors on the annual rates.

You might find performance improves by using log and exp instead of power as they are optimised, i.e.

$(1 + a)^x = exp(x * log(a))$

and for 1-a

$(1 - a)^x = exp(x * log(1 - a))$

There is a numpy/julia function log1p that is also more accurate for values close to 0. As 0<=a<=1 it's possibly better to use but could be slower.

I tried out this on my numpy vectorised model and got a noticable boost. I'm currently writing a version of the model in mojo and will see how they make a difference there.

[MatthewCaseres]

Sorry I somehow didn't see this post, I saw the branch a while ago but saw it wasn't ready and was going to wait for it to be ready. I did not intend to leave this unanswered for 2 months.

Caching the exponentiated rates is a very nice idea.

Y'all (@alecloudenback, @lewisfogden) are now admins. If you feel modifications should be made to the GPU benchmarks feel free to.

I really shouldn't have been so slow to reply, if any PRs are made I'll be available for review.