MathUtils: speed up Chebyshev field eval via FMA-grouped Clenshaw#15491
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MathUtils: speed up Chebyshev field eval via FMA-grouped Clenshaw#15491ktf wants to merge 1 commit into
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shahor02
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Jun 5, 2026
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Now Claude should rewrite the Numerical Recipes textbook!
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But the formatting should be fixed. |
The Clenshaw recurrence in Chebyshev3DCalc::chebyshevEvaluation1D dominates magnetic-field evaluation in track extrapolation/fitting (~32% of the muon-qa process). The expression `array[i] + x2*b1 - b2` parses as a dependent multiply->add->subtract chain on the loop-carried b1 (~10 cyc), which the compiler cannot shorten under FP rules. Regroup as fma(x2, b1, array[i] - b2): the same value, but array[i]-b2 no longer depends on the just-updated b1, collapsing the carried chain to a single FMA latency (~4 cyc). Tail return gets fma(-x, b1, b0). Validated against the previous kernel (20M random evals): max abs diff 4.6e-5, mean 2.7e-7 (~2 ULP) -> field-equivalent to within the map's own ~1e-5 precision. Adds testChebyshev3D (reproduces a known function to 1.4e-6; overload cross-checks exact).
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The Clenshaw recurrence in Chebyshev3DCalc::chebyshevEvaluation1D
dominates magnetic-field evaluation in track extrapolation/fitting
(~32% of the muon-qa process). The expression
array[i] + x2*b1 - b2parses as a dependent multiply->add->subtract chain on the loop-carried
b1 (~10 cyc), which the compiler cannot shorten under FP rules.
Regroup as fma(x2, b1, array[i] - b2): the same value, but array[i]-b2
no longer depends on the just-updated b1, collapsing the carried chain
to a single FMA latency (~4 cyc). Tail return gets fma(-x, b1, b0).
Validated against the previous kernel (20M random evals): max abs diff
4.6e-5, mean 2.7e-7 (~2 ULP) -> field-equivalent to within the map's own
~1e-5 precision. Adds testChebyshev3D (reproduces a known function to
1.4e-6; overload cross-checks exact).