SoA implementation for float and AVX2 includind the polyexp fix

2026-05-25 12:07:46 +02:00
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+# Optimization: SIMD polynomial exp (float, 8-wide) + FTZ/DAZ
+
+- **Author**: Linus
+- **Predecessor**: variant_float_inlining_SoA_AVX2.cpp
+- **File(s)**: variants/variant_float_inlining_SoA_AVX2_polyexp.cpp, main-float.cpp (FTZ/DAZ enable)
+- **Status**: TBD, positive locally (approx twice as fast)
+
+## What this changes
+
+The 8 scalar `expf` calls in the j-loop become a single SIMD polynomial
+approximation `exp256_ps` that operates on `__m256`. Range-reduce
+`x = n*ln2 + r` with `n = round(x/ln2)`, evaluate a degree-5 Horner
+polynomial for `exp(r)` on `r in [-ln2/2, ln2/2]`, then scale by `2^n`
+via the Schraudolph bit-trick on the IEEE 754 exponent slot (shift the
+biased exponent by 23). Degree-5 is enough for float, the polynomial is
+good to ~1e-5 absolute on the reduced range, well under the 1cm verify
+tolerance.
+
+
+`main-float.cpp` also gets two MXCSR writes at the top of `main()`:
+
+    _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
+    _MM_SET_DENORMALS_ZERO_MODE(_MM_DENORMALS_ZERO_ON);
+
+This was the part that actually mattered, see Analysis.
+
+## Code (relevant snippet)
+
+
+See `variants/variant_float_inlining_SoA_AVX2_polyexp.cpp` for the full
+j-loop and `main-float.cpp` for the FTZ/DAZ setup.
+
+## Benchmark
+
+Conditions: min of N runs (TBD), N_ITER=1000, -O3 -march=native -flto.
+Diff is vs `variant_float_inlining_SoA_AVX2`.
+
+### x86
+
+**Machine**: TBD
+
+**Frequency**: TBD
+
+| N    | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor |
+| ---- | ------------ | ------------- | ------------------------- | ------------------- |
+| 50   |              |               |                           |                     |
+| 100  |              |               |                           |                     |
+| 200  |              |               |                           |                     |
+| 500  |              |               |                           |                     |
+
+### ARM (Apple)
+
+Not applicable, AVX2-only. A NEON port would need its own vectorised
+exp.
+
+## Analysis
+
+roughly twice as fast
+
+
+## Takeaway
+
+Polyexp helps as expected. The real fix is FTZ/DAZ in `main-float.cpp`,
+without it everything downstream in the float chain is silently
+subnormal-stalled
+
+## References
+
+- Schraudolph, N. N. (1999). "A Fast, Compact Approximation of the
+  Exponential Function." Neural Computation 11(4), 853-862.
+- IEEE 754 double-precision format. Wikipedia.
+  https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+- Horner's method. Wikipedia.
+  https://en.wikipedia.org/wiki/Horner%27s_method
+