[WIP] Direct current deposition: constant-memory shape factors

[RemiLehe]

Summary

• Replace compile-time if constexpr shape factor evaluation in the direct current deposition kernel (doDepositionShapeNKernel) with a table-driven Horner's method approach
• Pre-computed polynomial coefficients are stored in GPU constant memory (for CUDA), reducing register pressure and enabling fast lookups
• Shape factors are computed on-the-fly in the deposition loops, eliminating all intermediate shape factor arrays
• Inspired by Hi-PACE++ PR #1328, which reported ~7.5% overall speedup
• Only the direct current deposition is modified; Esirkepov, Villasenor, Vay, and shared-memory deposition are unchanged for now
• Supports all existing interpolation orders (0–4) and all geometries (1D, 2D, 3D, RZ, RCylinder, RSphere)

Test plan

• Compiles on CPU
• test_3d_langmuir_multi_nodal passes (run + analysis + checksum), confirming numerical equivalence with the original implementation
• GPU compilation and performance benchmarks (to be done separately)

🤖 Generated with Claude Code

[RemiLehe]

Tests on Perlmutter's A100 did not seem to give a speedup.

Here are the timings for WarpXParticleContainer::DepositCurrent::CurrentDeposition:

  2D (128×128, 4×4 ppc)

  ┌───────┬───────────┬───────────┬──────────┬──────────┬────────────────────┐
  │ Shape │ Dev run 1 │ Dev run 2 │ PR run 1 │ PR run 2 │ Avg ratio (PR/Dev) │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 1     │ 0.01040   │ 0.01106   │ 0.01189  │ 0.01050  │ ~1.00×             │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 2     │ 0.01211   │ 0.01257   │ 0.01187  │ 0.01312  │ ~1.03×             │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 3     │ 0.01440   │ 0.01416   │ 0.01474  │ 0.01399  │ ~1.00×             │
  └───────┴───────────┴───────────┴──────────┴──────────┴────────────────────┘

  3D (64×64×64, 4×4×4 ppc)

  ┌───────┬───────────┬───────────┬──────────┬──────────┬────────────────────┐
  │ Shape │ Dev run 1 │ Dev run 2 │ PR run 1 │ PR run 2 │ Avg ratio (PR/Dev) │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 1     │ 0.2534    │ 0.2299    │ 0.2636   │ 0.2414   │ 1.05× slower       │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 2     │ 0.7735    │ 0.7748    │ 0.9190   │ 0.9176   │ 1.19× slower       │
  ├───────┼───────────┼───────────┼──────────┼──────────┼────────────────────┤
  │ 3     │ 1.9930    │ 1.9930    │ 2.0110   │ 2.0080   │ 1.01×.               │
  └───────┴───────────┴───────────┴──────────┴──────────┴────────────────────┘

inputs_base_3d.txt
inputs_base_2d.txt