Lightning Talk: Use SIMD Pairwise Reduction in C++!
summary
Experiments adding 10 billion doubles show scalar sequential accumulation runs at about 12% efficiency and produces wildly different sums when inputs are permuted. A Kahan-like rolling error reduces bias, but the robust fix is SIMD pairwise reduction: recursive pairwise summation implemented with SIMD yields correct, repeatable results and runs ~3.5 billion ops/sec versus ~800k ops/sec for the scalar baseline, so it both fixes accuracy and dramatically increases throughput.
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chapters (4)
- 0:00The summation inconsistency
- 1:13Floating point error analysis
- 2:22Sequential summation risks
- 4:03Pairwise summation solution
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