Numerical Marvels Inside Python - Keynote
summary
Concrete wins and how they are achieved appear: math.factorial drops from microseconds to factorial in nanoseconds by pulling out evens and left‑shifting; math.comb uses precomputed log factorials and a 64‑bit modular homomorphism to deliver combinations in 31 ns for 52 choose 31; summation gets deterministic accuracy via pairwise reduction, Kahan/Neumaier, and fsum; math.hypot becomes accurate and multi-dimensional using scaling, Dekker splitting, compensated sums and a final correction, with measured runtimes in tens of nanoseconds.
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chapters (14)
- 0:00Welcome
- 1:03Python’s numerical internals
- 2:50Core math developers
- 3:12Lightning-fast factorial
- 8:11Optimizing combinations
- 13:05Group theory speedups
- 20:11Floating point accuracy
- 26:36Numpy’s pairwise sum
- 27:21Kahan summation variants
- 29:25math.fsum magic
- 34:02Computing hypotenuse without overflow or error
- 42:36Fast multi-D hypot
- 44:23Accurate hypot in ML
- 45:05Q&A
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