BENCHMARKS.md

Benchmark Results for PR #1225: columnwise_dot_product_batched

Machine: AMD Ryzen 9 9950X 16-Core Processor Date: 2026-01-08 Features: --features parallel

General columnwise_dot_product (BabyBear, EF=degree-4 extension)

Size	unbatched	batched<1>	Δ	unbatched×2	batched<2>	Δ
2^16×128	1.79 ms	1.83 ms	+2%	3.49 ms	3.33 ms	-5%
2^16×512	6.14 ms	6.17 ms	~0%	12.28 ms	12.46 ms	+2%
2^16×4096	47.59 ms	47.69 ms	~0%	95.17 ms	99.58 ms	+5%
2^18×128	6.09 ms	6.10 ms	~0%	12.19 ms	11.99 ms	-2%
2^18×512	22.82 ms	23.21 ms	+2%	45.83 ms	46.41 ms	+1%
2^18×4096	179.26 ms	179.10 ms	~0%	358.69 ms	372.41 ms	+4%
2^20×128	22.52 ms	22.59 ms	~0%	45.30 ms	45.87 ms	+1%
2^20×512	88.06 ms	88.17 ms	~0%	178.71 ms	181.90 ms	+2%
2^20×4096	701.30 ms	700.55 ms	~0%	1.40 s	1.45 s	+4%
2^22×128	88.38 ms	88.31 ms	~0%	176.86 ms	182.29 ms	+3%
2^22×512	348.25 ms	348.28 ms	~0%	693.73 ms	714.54 ms	+3%
2^22×4096	2.78 s	2.80 s	~0%	5.56 s	5.77 s	+4%

Key findings

• batched<1> overhead: negligible (0-4%), well within noise
• batched<2> benefit: up to 5% faster on narrow matrices (128 cols), minimal on wider matrices
• Wide matrices (4096 cols): no benefit, memory bandwidth saturated; batched version is slightly slower (~4% overhead)

Batched<4> Performance (BabyBear, EF=degree-4 extension)

Compares 4× unbatched calls vs batched<4>.

Size	unbatched×4	batched<4>	Δ
2^16×128	7.26 ms	6.67 ms	-8%
2^16×512	24.79 ms	25.33 ms	+2%
2^16×4096	189.05 ms	203.00 ms	+7%
2^18×128	24.00 ms	23.58 ms	-2%
2^18×512	90.57 ms	93.91 ms	+4%
2^18×4096	715.68 ms	757.23 ms	+6%
2^20×128	89.96 ms	91.68 ms	+2%
2^20×512	352.87 ms	379.19 ms	+7%
2^20×4096	2.80 s	2.94 s	+5%
2^22×128	352.68 ms	363.71 ms	+3%
2^22×512	1.41 s	1.45 s	+3%
2^22×4096	11.15 s	11.70 s	+5%

Key findings

• batched<4> benefit: up to 8% faster on small narrow matrices (2^16×128)
• Narrow matrices (128 cols): minimal overhead or slight benefit (-2% to +3%)
• Medium matrices (512 cols): 2-7% overhead, increases with size
• Wide matrices (4096 cols): 5-7% overhead, memory bandwidth saturated
• The benefit of batched<4> decreases as matrix size increases, likely due to cache/memory bandwidth effects

Quotient Opening Simulation (degree-3 AIR)

Simulates opening quotient polynomial at 1 vs 2 evaluation points. For degree-3 constraints, quotient has degree 2·(n-1), requiring 2 chunks:

• BabyBear: 8 columns (2 chunks × 4 extension degree)
• Goldilocks: 4 columns (2 chunks × 2 extension degree)

BabyBear (8 columns)

log₂(rows)	1 point	2 points	Overhead
16	266 µs	370 µs	1.39×
18	679 µs	1085 µs	1.60×
20	2075 µs	3596 µs	1.73×
22	6855 µs	12851 µs	1.87×

Goldilocks (4 columns)

log₂(rows)	1 point	2 points	Overhead
16	177 µs	288 µs	1.63×
18	361 µs	471 µs	1.30×
20	866 µs	1342 µs	1.55×
22	4625 µs	6315 µs	1.37×

Key findings

Opening at 2 points costs 1.30×–1.87× a single point (well below naive 2×).

Comparison with PR Author's Benchmarks (Apple M2 Pro)

The results here are broadly consistent with the PR author's M2 Pro benchmarks:

• batched<1> overhead: Similar negligible overhead (0-5% on M2 Pro vs 0-2% here)
• batched<2> benefit: M2 Pro showed 5-8% benefit on narrow matrices; this AMD setup shows ~2-5%
• batched<4> benefit: Up to 8% faster on small narrow matrices, but overhead increases with matrix size
• Wide matrices: Both show no benefit on 4096-column matrices; batched<4> shows 5-7% overhead
• Quotient opening: M2 Pro showed 1.2×–1.65× overhead; this AMD setup shows 1.30×–1.87×

The AMD Ryzen 9 9950X generally shows higher absolute latencies than the M2 Pro, but the relative performance characteristics of the batched implementation are consistent across architectures.