[Feat] r.sim: Parallelize dx, dy computation

[wenzeslaus]

Is your feature request related to a problem? Please describe

Following the parallelization work in #6940, the dx, dy computation in r.sim remains serial while the main part of the tool can use multiple cores.

Describe the solution you'd like

Multiple cores used for the dx, dy calculation.

Additional context

Evaluating performance improvements will require separate analysis of the dx, dy computation, since the main r.sim.water simulation will dominate the total runtime.

[Abhi-d-gr8]

Hi! @wenzeslaus ,
To give a bit of context on the approach: I looked into using Pthreads or even GPU offloading, but I settled on OpenMP. It feels like the right tool for the job here ... it gives us the parallel efficiency we need for these loops but keeps the code clean and maintainable, which would have been harder to achieve with Pthreads.

I did use an AI assistant to help walk through the reduction logic (handling all the mins, maxes, and sums concurrently). It was really useful for verifying that I hadn't missed any race conditions.

Let me know what you think!

PR : #7040

[wenzeslaus]

Look at the GSoC 2026 ideas wiki page and check other tools in the code which already use OpenMP. Please, try to not add to our workload by having us review two similar PRs for the same change.

[Abhi-d-gr8]

Hi @wenzeslaus !
I’ve now parallelized the derivatives() function in simlib/derivatives.c, which is the actual dx/dy computation referenced in this issue. The outer row loop is parallelized using OpenMP, and I tested it separately from the main simulation to make sure the scaling is real and not hidden by other stages.

On a 5000×5000 grid (25M cells), I’m seeing roughly ~3× speedup (1 thread vs 8 threads) for the dx/dy stage itself.

I’ve carefully checked OpenMP scoping, race safety, and verified that numerical results are identical between serial and parallel runs. Hopefully this aligns better with the intent of the issue this time.

Thank you for taking your time and geniunely guiding me !!

PR: #7094