Benchmarks
These numbers compare SinCosLUT against the two polynomial JuliaGNSS packages — the float minimax polynomial FastSinCos.jl and the integer minimax polynomial FixedPointSinCosApproximations.jl. ps/elem is picoseconds per output element (computing both sin and cos); max abs error is the worst-case absolute error vs the true values over several cycles; ~bits is -log2(max error).
Unlike the code examples elsewhere in this manual (which run on every build), the numbers below are measurements and depend on the host CPU — in particular on the presence of AVX-512 vpermb, which the shared CI runners that build these docs do not have. Running the suite there would produce slow, misleading figures. They are instead measured on fixed hardware and refreshed with each release. Reproduce them on your own machine with julia benchmark/comparison.jl.
Measured on an AMD Ryzen AI 9 HX PRO 370 (Zen 5) with Julia 1.12. The AVX2 blocks force the AVX2-width path on the same hardware.
Kernel throughput
Sin and cos for an array of pre-computed phase indices — the bare lookup/evaluate cost, with no phase generation.
AVX-512
| method | ps/elem | max abs error | ~bits |
|---|---|---|---|
| SinCosLUT Int8, steps=64 | 11.7 | 5.2e-2 | ~4 |
| SinCosLUT Int8, steps=128 | 13.9 | 2.8e-2 | ~5 |
| FixedPoint Int16 (Val 7) | 105 | 1.3e-2 | ~6 |
FastSinCos u100k | 190 | 3.2e-4 | ~12 |
| FixedPoint Int32 (Val 8) | 209 | 8.1e-3 | ~7 |
FastSinCos u35 | 229 | 6.0e-8 | ~24 |
| FixedPoint Int32 (Val 14) | 297 | 1.1e-4 | ~13 |
AVX2
No native cross-lane byte permute (vpermb is unavailable); the lookup is a half-table vpshufb+blend split plus a psignb sign flip (exploiting the table's half-wave anti-symmetry).
| method | ps/elem | max abs error | ~bits |
|---|---|---|---|
| SinCosLUT Int8, steps=64 | 21.2 | 5.2e-2 | ~4 |
| FixedPoint Int16 (Val 7) | 123 | 1.3e-2 | ~6 |
| FixedPoint Int32 (Val 8) | 250 | 8.1e-3 | ~7 |
FastSinCos u100k | 250 | 3.2e-4 | ~12 |
FastSinCos u35 | 327 | 6.0e-8 | ~24 |
End-to-end carrier
Phase generation plus sincos, at 0.01 cycles/sample — each package generates the carrier itself. This is where FixedPoint's multiplicative-inverse phase work shows; the kernel rows above are unaffected by it. SinCosLUT generates the phase with a UInt32 NCO accumulator (one add per step), so its carrier stays close to its bare kernel (≈17 vs ≈10 ps on AVX-512). All three are exact in phase.
AVX-512
| method | ps/elem | max abs error | ~bits |
|---|---|---|---|
| SinCosLUT Int8, steps=64 | 16.8 | 9.3e-2 | ~3 |
| SinCosLUT Int8, steps=128 | 17.7 | 4.3e-2 | ~5 |
| FixedPoint Int16 (Val 7) | 131 | 1.5e-2 | ~6 |
FastSinCos u100k (Float32 phase) | 237 | 3.1e-4 | ~12 |
| FixedPoint Int32 (Val 13) | 317 | 2.4e-4 | ~12 |
AVX2
| method | ps/elem | max abs error | ~bits |
|---|---|---|---|
| SinCosLUT Int8, steps=64 | 47.8 | 9.3e-2 | ~3 |
| FixedPoint Int16 (Val 7) | 144 | 1.5e-2 | ~6 |
FastSinCos u100k (Float32 phase) | 328 | 3.1e-4 | ~12 |
| FixedPoint Int32 (Val 13) | 387 | 2.4e-4 | ~12 |
Takeaways
- SinCosLUT is fastest on both AVX-512 and AVX2 — one
vpermbper result on AVX-512, a half-tablevpshufb+blend split with apsignbsign flip on AVX2 — but only ~4–5 bits accurate, set by the table's phase resolution. - AVX2 is ~2–3× slower than AVX-512 here (half the lanes, plus the emulation of the missing byte permute), yet still the fastest option at its accuracy by a wide margin — the half-table split (v3.2) roughly doubled its kernel throughput over the earlier four-way split.
- On AVX-512 the 128-entry table (two-register
vpermi2b) doubles phase resolution to ~5 bits for a ~20% kernel premium — and no carrier premium, where the NCO hides it — so it is the better default there when the extra phase bit matters; the AVX2 split supports only the 64-entry table. - FixedPoint's drift-free DDA carrier is only marginally slower than its bare kernel (131 vs 105 ps on AVX-512) — integer phase generation is nearly free. At ~6-bit accuracy FixedPoint Int16 is the fastest polynomial carrier; at float-grade accuracy FastSinCos edges FixedPoint Int32.
- NEON (not in the x86 tables above): on the CI Apple M1 runner the Int8 carrier runs at ~70 ps/elem, and the bytewise-
tblInt16 backend (v3.2) is ~2.2× faster than the scalar fallback it replaces (~220 vs ~510 ps/elem). - Pick by accuracy: ≤5-bit → SinCosLUT (AVX-512/AVX2/NEON); ~6–13-bit integer → FixedPointSinCosApproximations; float-grade (12–24-bit) → FastSinCos. See Choosing a package.
Continuous benchmarking
A separate AirspeedVelocity.jl suite in benchmark/benchmarks.jl tracks throughput regressions across revisions (benchpkg SinCosLUT --rev=dirty). It covers generate_carrier! for each element type and buffer size, the 1-bit generate_carrier_signs! path, the 4-way interleaved fill, the fused single-stream reduction, and lookup_sincos!.