Benchmarks

fixarray benchmarks

The generated measurement tables for the fixarray module — every case, its stamp (commit, host, harness) and how to reproduce it.

The generated benchmark tables for the fixarray module against GLM, across the complete overlap of the two APIs — every vector and matrix operation at sizes 2/3/4 in float and double (fixed_glm_bench.cpp). Both sides compile in the same translation unit with the same flags, and the benchmark verifies the two produce identical results before it times either; the module page describes the setup, this page holds the numbers.

Fixed is faster than or at parity with GLM on every operation, and slower on none — the exact tally is in the generated table below, because a count restated in prose is a count that drifts the moment someone re-measures. A representative sample:

operation	`Fixed`	GLM
`mat4f::identity()`	0.66 ns ±0.01	1.78 ns ±0.05	2.69×	faster
`mat4f * mat4f`	3.38 ns ±0.04	5.75 ns ±0.14	1.70×	faster
`mat4f + mat4f`	0.67 ns ±0.01	1.36 ns ±0.06	2.03×	faster
`inverse(mat4d)`	12.15 ns ±0.31	16.83 ns ±0.36	1.38×	faster
`abs(vec4f)`	0.44 ns ±0.01	0.82 ns ±0.01	1.85×	faster
`dot(vec4f, vec4f)`	0.85 ns ±0.02	0.99 ns ±0.02	1.17×	parity — gap 0.14 ns

Reading the verdict column

Read the verdict column, not the ratio. A row can be ahead on ratio and still be called parity, because a difference counts here only when it clears both 1.15× and an absolute 0.25 ns — about one cycle. Below that floor the harness's own DoNotOptimize scaffolding is a larger effect than the code being measured, and on 4-element vectors most operations live there. That floor is also why this tally is smaller than it once was: the earlier 37 faster / 123 parity count came from a best-of-N minimum with each library's cases timed in one consecutive block. Re-measured with interleaved repetitions and medians, a batch of operations moved from "faster" to "parity". None moved to "slower" — the claim that matters survived the stricter method.

The bench_gate.sh hard gate keeps it that way: it fails the build if any pair regresses past GLM (tolerant by ratio and an absolute floor, with a confirmation re-run so sub-nanosecond noise never flakes it).

The complete comparison — every vector and matrix operation

Full GLM comparison — all 160 operations (ns, lower is better; ± is the IQR over 9 interleaved repetitions)

Vectors

operation	type	`Fixed`	GLM	ratio
`abs`	vec3d	0.48 ±0.03	0.85 ±0.04	0.57×	🟢 faster
`abs`	vec3f	0.46 ±0.03	0.83 ±0.04	0.56×	🟢 faster
`abs`	vec4d	0.47 ±0.03	0.79 ±0.07	0.59×	🟢 faster
`abs`	vec4f	0.45 ±0.04	0.86 ±0.05	0.53×	🟢 faster
`add`	vec2d	0.46 ±0.02	0.47 ±0.01	0.98×	⬜ parity
`add`	vec2f	0.35 ±0.05	0.23 ±0.01	1.53×	⬜ parity
`add`	vec3d	0.46 ±0.02	0.46 ±0.02	1.02×	⬜ parity
`add`	vec3f	0.39 ±0.07	0.46 ±0.03	0.85×	⬜ parity
`add`	vec4d	0.46 ±0.02	0.48 ±0.03	0.98×	⬜ parity
`add`	vec4f	0.47 ±0.02	0.47 ±0.03	0.99×	⬜ parity
`clamp`	vec3d	0.46 ±0.03	0.47 ±0.03	0.96×	⬜ parity
`clamp`	vec3f	0.51 ±0.03	0.52 ±0.02	0.97×	⬜ parity
`clamp`	vec4d	0.47 ±0.02	0.46 ±0.03	1.01×	⬜ parity
`clamp`	vec4f	0.45 ±0.02	0.45 ±0.02	1.00×	⬜ parity
`cross`	vec3d	0.71 ±0.04	0.70 ±0.06	1.01×	⬜ parity
`cross`	vec3f	0.79 ±0.03	0.81 ±0.08	0.98×	⬜ parity
`distance2`	vec3d	0.69 ±0.05	0.85 ±0.06	0.81×	⬜ parity
`distance2`	vec3f	0.73 ±0.03	0.81 ±0.01	0.90×	⬜ parity
`distance2`	vec4d	1.17 ±0.05	1.19 ±0.05	0.98×	⬜ parity
`distance2`	vec4f	1.36 ±0.05	1.38 ±0.06	0.99×	⬜ parity
`distance`	vec3d	1.36 ±0.03	1.39 ±0.08	0.98×	⬜ parity
`distance`	vec3f	0.82 ±0.00	0.90 ±0.03	0.92×	⬜ parity
`distance`	vec4d	1.23 ±0.08	1.23 ±0.07	1.01×	⬜ parity
`distance`	vec4f	1.31 ±0.03	1.31 ±0.08	1.00×	⬜ parity
`divs`	vec2d	0.45 ±0.03	0.47 ±0.02	0.97×	⬜ parity
`divs`	vec2f	0.24 ±0.01	0.23 ±0.01	1.02×	⬜ parity
`divs`	vec3d	0.45 ±0.02	0.46 ±0.01	0.98×	⬜ parity
`divs`	vec3f	0.47 ±0.01	0.45 ±0.02	1.03×	⬜ parity
`divs`	vec4d	0.47 ±0.02	0.46 ±0.03	1.02×	⬜ parity
`divs`	vec4f	0.46 ±0.02	0.46 ±0.02	1.00×	⬜ parity
`dot`	vec2d	0.47 ±0.01	0.46 ±0.01	1.03×	⬜ parity
`dot`	vec2f	0.40 ±0.01	0.37 ±0.02	1.09×	⬜ parity
`dot`	vec3d	0.58 ±0.02	0.47 ±0.06	1.24×	⬜ parity
`dot`	vec3f	0.59 ±0.03	0.54 ±0.02	1.10×	⬜ parity
`dot`	vec4d	0.69 ±0.04	0.70 ±0.06	0.98×	⬜ parity
`dot`	vec4f	0.91 ±0.05	1.05 ±0.07	0.86×	⬜ parity
`len2`	vec2d	0.46 ±0.02	0.46 ±0.01	1.00×	⬜ parity
`len2`	vec2f	0.31 ±0.02	0.32 ±0.01	0.97×	⬜ parity
`len2`	vec3d	0.49 ±0.03	0.44 ±0.02	1.10×	⬜ parity
`len2`	vec3f	0.47 ±0.03	0.46 ±0.03	1.01×	⬜ parity
`len2`	vec4d	0.53 ±0.03	0.53 ±0.02	1.00×	⬜ parity
`len2`	vec4f	0.62 ±0.03	0.70 ±0.03	0.90×	⬜ parity
`len`	vec2d	1.38 ±0.09	1.36 ±0.05	1.01×	⬜ parity
`len`	vec2f	0.68 ±0.04	0.68 ±0.02	1.00×	⬜ parity
`len`	vec3d	1.41 ±0.06	1.39 ±0.04	1.01×	⬜ parity
`len`	vec3f	0.73 ±0.03	0.70 ±0.03	1.05×	⬜ parity
`len`	vec4d	1.36 ±0.04	1.41 ±0.03	0.96×	⬜ parity
`len`	vec4f	0.77 ±0.03	0.84 ±0.03	0.91×	⬜ parity
`max`	vec3d	0.46 ±0.03	0.46 ±0.02	1.01×	⬜ parity
`max`	vec3f	0.40 ±0.06	0.39 ±0.06	1.03×	⬜ parity
`max`	vec4d	0.45 ±0.01	0.45 ±0.00	1.00×	⬜ parity
`max`	vec4f	0.46 ±0.02	0.48 ±0.03	0.95×	⬜ parity
`min`	vec3d	0.47 ±0.01	0.47 ±0.02	1.02×	⬜ parity
`min`	vec3f	0.43 ±0.02	0.45 ±0.05	0.97×	⬜ parity
`min`	vec4d	0.47 ±0.03	0.47 ±0.02	1.00×	⬜ parity
`min`	vec4f	0.46 ±0.02	0.47 ±0.03	0.98×	⬜ parity
`mix`	vec3d	0.64 ±0.06	0.58 ±0.13	1.10×	⬜ parity
`mix`	vec3f	0.63 ±0.06	0.60 ±0.07	1.06×	⬜ parity
`mix`	vec4d	0.59 ±0.03	0.69 ±0.06	0.85×	⬜ parity
`mix`	vec4f	0.56 ±0.02	0.58 ±0.04	0.97×	⬜ parity
`muls`	vec2d	0.46 ±0.01	0.46 ±0.01	1.00×	⬜ parity
`muls`	vec2f	0.25 ±0.02	0.23 ±0.01	1.08×	⬜ parity
`muls`	vec3d	0.47 ±0.03	0.46 ±0.02	1.02×	⬜ parity
`muls`	vec3f	0.46 ±0.02	0.47 ±0.01	0.96×	⬜ parity
`muls`	vec4d	0.48 ±0.05	0.46 ±0.01	1.04×	⬜ parity
`muls`	vec4f	0.46 ±0.02	0.46 ±0.02	1.00×	⬜ parity
`neg`	vec2d	0.47 ±0.02	0.45 ±0.01	1.03×	⬜ parity
`neg`	vec2f	0.23 ±0.01	0.24 ±0.01	0.99×	⬜ parity
`neg`	vec3d	0.46 ±0.02	0.45 ±0.01	1.01×	⬜ parity
`neg`	vec3f	0.46 ±0.01	0.47 ±0.03	0.98×	⬜ parity
`neg`	vec4d	0.48 ±0.03	0.45 ±0.02	1.07×	⬜ parity
`neg`	vec4f	0.46 ±0.01	0.46 ±0.01	1.00×	⬜ parity
`normalize`	vec2d	2.38 ±0.07	2.35 ±0.04	1.01×	⬜ parity
`normalize`	vec2f	1.39 ±0.03	1.37 ±0.08	1.02×	⬜ parity
`normalize`	vec3d	2.39 ±0.11	2.33 ±0.10	1.02×	⬜ parity
`normalize`	vec3f	1.47 ±0.07	1.42 ±0.06	1.04×	⬜ parity
`normalize`	vec4d	2.46 ±0.15	2.36 ±0.17	1.04×	⬜ parity
`normalize`	vec4f	1.50 ±0.06	1.46 ±0.03	1.03×	⬜ parity
`reflect`	vec3d	2.92 ±0.10	2.89 ±0.15	1.01×	⬜ parity
`reflect`	vec3f	2.68 ±0.15	2.59 ±0.07	1.03×	⬜ parity
`reflect`	vec4d	3.41 ±0.15	3.48 ±0.06	0.98×	⬜ parity
`reflect`	vec4f	3.45 ±0.08	3.80 ±0.08	0.91×	⬜ parity
`sign`	vec3d	0.99 ±0.04	1.19 ±0.03	0.83×	⬜ parity
`sign`	vec3f	0.92 ±0.05	1.28 ±0.03	0.72×	🟢 faster
`sign`	vec4d	0.97 ±0.04	1.63 ±0.12	0.60×	🟢 faster
`sign`	vec4f	0.76 ±0.03	1.83 ±0.11	0.42×	🟢 faster
`smoothstep`	vec3d	1.33 ±0.02	1.16 ±0.05	1.15×	⬜ parity
`smoothstep`	vec3f	1.29 ±0.04	1.21 ±0.05	1.06×	⬜ parity
`smoothstep`	vec4d	1.32 ±0.11	1.18 ±0.05	1.12×	⬜ parity
`smoothstep`	vec4f	1.41 ±0.06	1.28 ±0.05	1.10×	⬜ parity
`step`	vec3d	0.48 ±0.02	0.49 ±0.01	0.98×	⬜ parity
`step`	vec3f	0.46 ±0.01	0.47 ±0.02	0.99×	⬜ parity
`step`	vec4d	0.47 ±0.03	0.47 ±0.05	1.00×	⬜ parity
`step`	vec4f	0.47 ±0.00	0.72 ±0.05	0.65×	⬜ parity
`sub`	vec2d	0.47 ±0.02	0.46 ±0.01	1.02×	⬜ parity
`sub`	vec2f	0.24 ±0.01	0.23 ±0.01	1.02×	⬜ parity
`sub`	vec3d	0.47 ±0.01	0.45 ±0.02	1.03×	⬜ parity
`sub`	vec3f	0.43 ±0.04	0.38 ±0.08	1.14×	⬜ parity
`sub`	vec4d	0.47 ±0.01	0.45 ±0.01	1.04×	⬜ parity
`sub`	vec4f	0.48 ±0.01	0.46 ±0.04	1.05×	⬜ parity

Matrices

operation	type	`Fixed`	GLM	ratio
`add`	mat2d	0.46 ±0.02	0.47 ±0.02	0.99×	⬜ parity
`add`	mat2f	0.46 ±0.02	0.45 ±0.01	1.03×	⬜ parity
`add`	mat3d	0.95 ±0.14	0.92 ±0.03	1.03×	⬜ parity
`add`	mat3f	0.69 ±0.04	1.15 ±0.02	0.60×	🟢 faster
`add`	mat4d	1.60 ±0.19	1.48 ±0.10	1.08×	⬜ parity
`add`	mat4f	0.72 ±0.04	1.41 ±0.04	0.51×	🟢 faster
`compmult`	mat3d	0.96 ±0.07	0.92 ±0.06	1.04×	⬜ parity
`compmult`	mat3f	0.70 ±0.02	1.15 ±0.03	0.61×	🟢 faster
`compmult`	mat4d	1.52 ±0.13	1.63 ±0.18	0.93×	⬜ parity
`compmult`	mat4f	0.76 ±0.16	1.36 ±0.09	0.56×	🟢 faster
`det`	mat2d	0.42 ±0.02	0.42 ±0.02	1.01×	⬜ parity
`det`	mat2f	0.46 ±0.02	0.46 ±0.02	1.01×	⬜ parity
`det`	mat3d	1.16 ±0.04	1.16 ±0.10	1.00×	⬜ parity
`det`	mat3f	1.16 ±0.04	1.13 ±0.07	1.03×	⬜ parity
`det`	mat4d	3.83 ±0.12	3.75 ±0.20	1.02×	⬜ parity
`det`	mat4f	3.94 ±0.14	3.64 ±0.28	1.08×	⬜ parity
`identity`	mat2d	0.46 ±0.02	0.46 ±0.01	0.99×	⬜ parity
`identity`	mat2f	0.23 ±0.01	0.23 ±0.01	0.99×	⬜ parity
`identity`	mat3d	1.13 ±0.03	1.39 ±0.03	0.81×	🟢 faster
`identity`	mat3f	0.92 ±0.02	0.91 ±0.02	1.01×	⬜ parity
`identity`	mat4d	1.13 ±0.02	2.47 ±0.14	0.46×	🟢 faster
`identity`	mat4f	0.68 ±0.04	1.86 ±0.08	0.37×	🟢 faster
`inverse`	mat2d	0.98 ±0.04	0.94 ±0.04	1.04×	⬜ parity
`inverse`	mat2f	1.04 ±0.02	0.94 ±0.01	1.10×	⬜ parity
`inverse`	mat3d	3.63 ±0.13	3.80 ±0.11	0.95×	⬜ parity
`inverse`	mat3f	3.61 ±0.16	3.80 ±0.16	0.95×	⬜ parity
`inverse`	mat4d	12.82 ±0.66	17.51 ±0.70	0.73×	🟢 faster
`inverse`	mat4f	11.65 ±0.39	15.11 ±0.89	0.77×	🟢 faster
`invtrans`	mat3d	4.62 ±0.38	4.77 ±0.29	0.97×	⬜ parity
`invtrans`	mat3f	4.50 ±0.36	4.06 ±0.16	1.11×	⬜ parity
`invtrans`	mat4d	14.15 ±1.15	15.23 ±0.37	0.93×	⬜ parity
`invtrans`	mat4f	11.82 ±1.52	14.60 ±0.63	0.81×	🟢 faster
`matmul`	mat2d	0.94 ±0.06	0.91 ±0.01	1.03×	⬜ parity
`matmul`	mat2f	0.92 ±0.02	0.94 ±0.05	0.98×	⬜ parity
`matmul`	mat3d	3.43 ±0.08	3.44 ±0.13	1.00×	⬜ parity
`matmul`	mat3f	3.71 ±0.07	3.74 ±0.12	0.99×	⬜ parity
`matmul`	mat4d	5.95 ±0.27	6.34 ±0.76	0.94×	⬜ parity
`matmul`	mat4f	3.53 ±0.10	6.04 ±0.34	0.59×	🟢 faster
`matvec`	mat2d	0.50 ±0.05	0.49 ±0.01	1.02×	⬜ parity
`matvec`	mat2f	0.47 ±0.08	0.48 ±0.06	0.98×	⬜ parity
`matvec`	mat3d	1.19 ±0.15	1.03 ±0.07	1.16×	⬜ parity
`matvec`	mat3f	1.02 ±0.11	1.00 ±0.05	1.03×	⬜ parity
`matvec`	mat4d	1.53 ±0.13	1.51 ±0.15	1.01×	⬜ parity
`matvec`	mat4f	1.46 ±0.08	1.46 ±0.06	1.00×	⬜ parity
`muls`	mat2d	0.50 ±0.02	0.47 ±0.01	1.05×	⬜ parity
`muls`	mat2f	0.47 ±0.05	0.46 ±0.03	1.02×	⬜ parity
`muls`	mat3d	0.91 ±0.03	0.91 ±0.03	1.00×	⬜ parity
`muls`	mat3f	0.70 ±0.05	0.91 ±0.02	0.76×	⬜ parity
`muls`	mat4d	1.18 ±0.02	1.19 ±0.07	0.99×	⬜ parity
`muls`	mat4f	0.69 ±0.04	1.41 ±0.05	0.49×	🟢 faster
`outer`	mat3d	0.93 ±0.08	0.93 ±0.02	1.01×	⬜ parity
`outer`	mat3f	0.95 ±0.08	0.94 ±0.05	1.01×	⬜ parity
`outer`	mat4d	1.29 ±0.10	1.29 ±0.07	1.00×	⬜ parity
`outer`	mat4f	0.77 ±0.05	1.32 ±0.08	0.59×	🟢 faster
`transpose`	mat2d	0.68 ±0.01	0.68 ±0.02	0.99×	⬜ parity
`transpose`	mat2f	0.47 ±0.02	0.48 ±0.03	0.98×	⬜ parity
`transpose`	mat3d	1.37 ±0.05	1.38 ±0.06	0.99×	⬜ parity
`transpose`	mat3f	1.17 ±0.03	1.15 ±0.10	1.01×	⬜ parity
`transpose`	mat4d	2.08 ±0.07	2.02 ±0.06	1.03×	⬜ parity
`transpose`	mat4f	2.09 ±0.15	2.08 ±0.11	1.00×	⬜ parity

20 faster, 140 at parity, 0 slower across 160 operations.

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