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Benchmark Results

Best recorded time per test configuration, per processor.

Default First-Hit (spherical receiver, with drift)

Parameters: -f, Db=1E-11, deltaT=1E-7, t=1E-3

CPU

Processor 1,000 paths 10,000 paths
Intel i7-7700K 4.2GHz (thesis) 1.64s 16.54s
Apple Silicon (M-series) 1.41s —
Colab Xeon 1.25s 13.7s

GPU

GPU Change 1,000 paths 10,000 paths
GTX 1070 (thesis) original 2.27s 4.81s
Tesla T4 original thesis code 1.38s 11.2s
Tesla T4 device-side hit detection 0.055s 0.063s
Tesla T4 + precompute/curand_normal4/block256 0.012s 0.013s
Tesla T4 + long kernel 0.008s 0.008s

GPU vs CPU Speedup (A100)

Paths CPU (Colab Xeon) GPU (A100, long) Speedup
1,000 1.39s 0.056s 25x
10,000 138.9s 0.068s 2,037x

1D First-Hit with Drift

Parameters: -f -l 3E-7 -t 1E-2, Db=1E-11, vel=1E-4, deltaT=1E-7, 100k steps

Processor Change 10,000 paths
Colab Xeon CPU current 139s
Tesla T4 GPU original thesis code 16.7s
Tesla T4 GPU device-side hit detection 0.633s
Tesla T4 GPU long kernel 0.065s
A100 GPU long kernel 0.068s

GPU vs CPU speedup (A100): 139s / 0.068s = 2,037x

Regression Test (vs thesis-baseline, A100)

Test Baseline Current Improvement
1k default first-hit 5.87s 0.067s 98.9%
10k default first-hit 16.61s 0.068s 99.6%
10k 1D limit (100k steps) 16.61s 0.068s 99.6%

Scale Sweep (A100, long kernel, default first-hit, 10k steps)

Paths Time Thesis 1070
10,000 0.012s —
50,000 0.016s —
100,000 0.026s —
500,000 0.101s —
1,000,000 0.192s —
2,500,000 0.462s —
5,000,000 0.914s 5.08s

Throughput: 5.5M paths/sec (A100) vs thesis 1M paths/sec (GTX 1070).

Gold Standard (A100, long kernel, dt=1E-8)

Test Particles Steps Time KS p-value
1D first-hit 10,000,000 1,000,000 143s 0.047 (PASS)

10 trillion particle-steps in under 3 minutes.

Validation

Test Backend Result Notes
1D first-hit KS (1k paths) GPU PASS
1D first-hit KS (1k paths) CPU PASS
1D first-hit KS (10k paths) GPU PASS After Brownian bridge correction
3D spherical KS (10k paths) GPU PASS
3D spherical binomial (10k) GPU PASS After Brownian bridge correction
3D spherical (1k paths) CPU PASS
CPU/GPU agreement (5k paths) Both PASS KS p > 0.01
GPU RNG quality (Philox) GPU PASS
CPU RNG quality (Box-Muller) CPU PASS
GPU reproducibility (seed=42) GPU PASS Identical output
CPU reproducibility (seed=42) CPU PASS Identical output
Wall reflection (10k paths) GPU PASS
Performance regression GPU PASS No regression vs baseline

Optimization History

Change GPU Impact
Bug fixes (gridSize, abs, float/double) Correctness
CPU cleanup (stack vars, sqrt reduction) ~2x CPU speedup
Device-side hit detection 25-224x — eliminated per-timestep cudaMemcpy
Precompute constants + curand_normal4 + block 256 ~5x on top of above
Long kernel (d_simulate_isolated) ~3x on top of above
Brownian bridge correction Correctness (fixes boundary-crossing bias)
Wide kernel (d_update) with same optimizations Same improvements, global memory positions
CUDA Graphs for wide kernel Reverted — added overhead, no improvement
Total vs thesis wide baseline ~2,000x

Known Limitations

  • --use_fast_math disabled: caused wall reflection test failures due to reduced trig precision. Could be re-enabled selectively for non-reflection code paths.