Vulkan Linear Math benchmark

All equivalent arithmetic reached parity or better

The expanded harness covers 50 operation families in both precisions: 100 correctness-gated OA/GLM pairs. All 27 families with equivalent valid-input arithmetic were at parity or faster in both F32 and F64. Across those rows, OA used 13.4% less time by geometric mean for F32and 11.9% less for F64 on the qualified host.

This is fixed-host evidence for one compiler, CPU, dataset, packed ABI, and date—not a universal or fastest-library claim. The result retains OA's Vulkan convention, packed value ABI, overflow fallbacks, validation, and fail-closed behavior.

Small host values, one spatial convention

VLM means Vulkan Linear Math. It is OA's immediate host-side spatial-math layer for cameras, UI, rendering, animation, SDK simulation, and format conversion—not a vision-language model and not a second oa::Matrix engine. Values are trivially copyable and functions are stateless; VLM owns no engine, allocation, operation graph, Vulkan handle, or session.

Operators forward to one named implementation in oa::vlm. There is no FnVlm: this is immediate scalar math, unlike schema-owned device work. The surface covers vector geometry, robust quaternion math, all six Euler orders, fixed-shape matrix algebra, checked inverses, affine decomposition, TRS, view and projection families, and top-origin viewport project/unproject.

Optimized without weakening the contract

The largest wins come from fixed-shape work: Mat4 multiplication is explicitly unrolled, TRS composition writes the known affine form directly, and translation and scale constructors no longer route through generic matrix work.

Qualified protocol

A later full repeat reached 45.8% absolute timing spread under laptop throttling and was rejected. The tables retain the earlier thermally stable seven-process campaign. The Mat3-addition row is a focused seven-process follow-up after its fixed-width unroll; it supersedes that one full-suite row without changing the other 49 cases.

Equivalent arithmetic

Each time cell reports OA then GLM median nanoseconds per item. Ratios divide OA time by GLM time, so lower is better; values through 1.03× are classified as parity.

Checked and fail-closed operations

These rows are deliberately separate. OA normalizes non-unit quaternions, handles finite subnormal and extreme magnitudes, rejects invalid tolerances and degenerate geometry, estimates inverse conditioning, verifies inverse residuals, preserves outputs on failure, and fails closed from direct APIs. The GLM peer performs its raw valid-input operation. A ratio above one measures current safety cost, not an equivalent-work regression.

Checked viewport unprojection is the clearest remaining optimization seam because it performs a checked general inverse for every point. The correct next route is a checked precomputed-inverse or bulk-unproject contract—not deleting singularity, finiteness, residual, or output-preservation guarantees. Conditioned Mat3, affine inverse, and normal-matrix paths remain visible for the same reason.

Correctness before timing

BenchVlm executes each complete OA and GLM workload before timing, compares whole-workload checksums, and rejects non-finite or mismatched results. Timed samples alternate OA-first and GLM-first order. Unknown arguments fail instead of silently changing the workload.

Failure and precision behavior remains explicit

The public VLM value surface is C++ only today. There is no dedicated Python VLM binding, and the benchmark is CPU evidence—not evidence about GPU oa::Matrixexecution or oa::FnSimd batch arrays.

Reproduce the comparison

Use the GLM 1.1.0 archive matching the manifest above. Preserve the item count, precision matrix, alternating order, process count, cooldown, thermal gate, and whole-case correctness contract when refreshing the result.

cmake -S . -B build/release \
  -DOA_VLM_GLM_ROOT=/absolute/path/to/glm-1.1.0
cmake --build build/release --target BenchVlm TestVlm

python3 tools/diagnostics/oaBench.py \
  --output var/benchmark/vlm-glm.json \
  --name core.vlm_glm_suite \
  --command-id benchVlm_glm_1_1_0_f32_f64 \
  --contract peer=glm-1.1.0 --contract precision=f32-f64 \
  --contract cases=50 --contract items=65536 \
  --contract oracle=whole-case-checksum --contract order=alternating \
  --warmup 2 --runs 7 --cooldown 3 --timeout 300 \
  --thermal-limit-celsius 65 --thermal-sensor-regex 'Package id 0' \
  --thermal-timeout 300 \
  --metric-regex 'PAIR precision=f32 case=mat4_mul contract=arithmetic oa_ns=([0-9.]+)' \
  --metric-name mat4_mul_oa --metric-unit ns/op \
  --require-regex 'BENCHMARK oracle=PASS' \
  --cmake-cache build/release/CMakeCache.txt -- \
  taskset -c 2 bin/release/test/core/vlm/benchVlm \
  --items 65536 --warmups 3 --samples 15 --precision both

Run the focused gates

cmake --build build/release --target \
  TestVlm TestCamera TestScene TestTransform TestSkeleton
ctest --test-dir build/release \
  -R '^(TestVlm|TestCamera|TestScene|TestTransform|TestSkeleton)$' \
  --output-on-failure

cmake --build build/asan --target \
  TestVlm TestCamera TestScene TestTransform TestSkeleton
ctest --test-dir build/asan \
  -R '^(TestVlm|TestCamera|TestScene|TestTransform|TestSkeleton)$' \
  --output-on-failure

cmake --build build/ubsan --target \
  TestVlm TestCamera TestScene TestTransform TestSkeleton
ctest --test-dir build/ubsan \
  -R '^(TestVlm|TestCamera|TestScene|TestTransform|TestSkeleton)$' \
  --output-on-failure

This remains a working-tree qualification. Installed-package, compiler-matrix, shader-boundary, source-audit automation, and exact external-format fixtures retain their own release gates.