Linus Baumberger
76 lines
2.5 KiB
Markdown
76 lines
2.5 KiB
Markdown
# Optimization: SIMD polynomial exp (float, 8-wide) + FTZ/DAZ
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- **Author**: Linus
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- **Predecessor**: variant_float_inlining_SoA_AVX2.cpp
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- **File(s)**: variants/variant_float_inlining_SoA_AVX2_polyexp.cpp, main-float.cpp (FTZ/DAZ enable)
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- **Status**: TBD, positive locally (approx twice as fast)
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## What this changes
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The 8 scalar `expf` calls in the j-loop become a single SIMD polynomial
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approximation `exp256_ps` that operates on `__m256`. Range-reduce
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`x = n*ln2 + r` with `n = round(x/ln2)`, evaluate a degree-5 Horner
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polynomial for `exp(r)` on `r in [-ln2/2, ln2/2]`, then scale by `2^n`
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via the Schraudolph bit-trick on the IEEE 754 exponent slot (shift the
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biased exponent by 23). Degree-5 is enough for float, the polynomial is
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good to ~1e-5 absolute on the reduced range, well under the 1cm verify
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tolerance.
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`main-float.cpp` also gets two MXCSR writes at the top of `main()`:
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_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
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_MM_SET_DENORMALS_ZERO_MODE(_MM_DENORMALS_ZERO_ON);
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This was the part that actually mattered, see Analysis.
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## Code (relevant snippet)
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See `variants/variant_float_inlining_SoA_AVX2_polyexp.cpp` for the full
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j-loop and `main-float.cpp` for the FTZ/DAZ setup.
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## Benchmark
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Conditions: min of N runs (TBD), N_ITER=1000, -O3 -march=native -flto.
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Diff is vs `variant_float_inlining_SoA_AVX2`.
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### x86
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**Machine**: TBD
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**Frequency**: TBD
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| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor |
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| ---- | ------------ | ------------- | ------------------------- | ------------------- |
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| 50 | | | | |
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| 100 | | | | |
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| 200 | | | | |
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| 500 | | | | |
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### ARM (Apple)
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Not applicable, AVX2-only. A NEON port would need its own vectorised
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exp.
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## Analysis
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roughly twice as fast
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## Takeaway
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Polyexp helps as expected. The real fix is FTZ/DAZ in `main-float.cpp`,
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without it everything downstream in the float chain is silently
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subnormal-stalled
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## References
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- Schraudolph, N. N. (1999). "A Fast, Compact Approximation of the
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Exponential Function." Neural Computation 11(4), 853-862.
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- IEEE 754 double-precision format. Wikipedia.
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https://en.wikipedia.org/wiki/Double-precision_floating-point_format
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- Horner's method. Wikipedia.
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https://en.wikipedia.org/wiki/Horner%27s_method
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