Pyramid

Published configurations

Separates pyramid index, Bernstein and modal source-kernel costs.

Measured operation

Attributes intrinsic real pyramid kernels without nodal contraction.

Metadata, Bernstein factors and modal evaluation are measured separately. No Vandermonde inverse, reference-table lookup, map, mesh, assembly or solve is timed. Degrees one through six cover the supported performance matrix. Factor and modal sweeps use orders two, four and eight; metadata sweeps use their degree-dependent index sets instead of meaningless quadrature sizes. Runtime argument arrays are exposed through compiler barriers before each sweep so that constant loop bounds cannot turn binomial or index decoding into precomputed outputs. The barrier and output-write costs remain in the reported sweep time; these are not isolated instruction latencies.

Independent numerical oracle

Binomial coefficients are constructed by Pascal addition, independently of the source's ordered product/division. Factors use \(B_i^n(t)=\binom ni t^i(1-t)^{n-i}\) and direct polynomial differentiation, evaluated with powers rather than the production multiplication loops. With \(a=x/(1-z)\), \(b=y/(1-z)\), the modal oracle is \(B_i^{K-k}(a)B_j^{K-k}(b)B_k^K(z)\); its gradient follows by the chain rule. Mode triples are enumerated independently in layer order, not decoded through the measured implementation. An absolute/relative roundoff budget of \(10^{-12}\max(1,|q_{\rm ref}|)\) applies to dimensionless values. Metadata comparisons are exact, and a perturbed output must be rejected. Real kernels also underlie complex finite-element coefficients; complex expansion and nodal contraction belong to the reference-element profiler.

Recorded results

Each case retains its original inputs, iteration policy and correctness checks. Raw reports preserve counters, repetitions and the Google Benchmark context. CPU, wall and manually supplied times are labeled separately; unlike operations and configurations are not averaged together.

Timing history

RodinH1PyramidBenchmarks · auto · slow · ranks: 1