ReferenceElement

Published configurations

Isolates scalar reference-element dispatch, evaluation and tabulation.

Measured operation

Measures one reference operation with explicit dispatch/cache scope.

Direct and prefetched sweeps write the same quadrature-major output. The former obtains each descriptor in the sample loop; the latter obtains descriptors before timing. Neither path changes the library implementation. BulkDerivatives uses the element's typed gradient output, including its coordinate validation and owned point-local modal work. Its output has the same quadrature-major layout, without physical mapping or field contraction. WarmTable includes lookup only, not a sweep over table entries. Misses rotate nine independently identified formulas through the eight-entry reference cache. Initial allocation and basis initialization are outside timing; CapacityWarmMiss therefore measures rebuilding, not first-use allocation. WarmTable records its one-based search position outside timing: resident table addresses order the cache's array slots, not formula identities. WarmTablePosition selects each of the eight resident search positions explicitly before timing. Formula contents are identical across versions; lookup continues to use logical identity and geometry, never an address key.

Numerical qualification

Every value and derivative is compared exactly against direct evaluation before and after timing. Separately, the public DOF functionals reconstruct \(f(\widehat x)=1+\sum_i(i+1)\widehat x_i\) and its gradient in positive-degree spaces; constant spaces reconstruct \(f=1\). This avoids assuming nodal coefficients for modal elements. The reconstruction tolerance is an absolute roundoff allowance on a dimensionless reference cell, not a performance acceptance threshold. A perturbed output must be rejected.

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

RodinReferenceElementBenchmarks · auto · regular · ranks: 1