[Xuanwo]

CDF and PMF currently repeat a centroid binary search for every ordered split point. Share a forward cursor for dense batches, while retaining binary search for sparse batches. Both use the existing tail, equal-mean, weight, and interpolation logic; the CDF loop and weight accumulation remain shared.

Benchmark

Measured aa23deaa051e71c18beed66907f86ca23f35199e against 675e3e123fda6da19657d345038252b16adc2ebb on an isolated EC2 c7i.2xlarge (Xeon Platinum 8488C), Rust 1.99.1 release defaults, CPU 2. Baseline calibration selects fixed work near 300 ms; both variants perform exactly the same count in seven alternating pairs. These are measured whole-batch totals.

Fixed workload	Count per sample	Before	After	Speedup (before / after)
Prebuilt frozen CDF, 100 split points	85,760	289 ms	108 ms	2.68×
Prebuilt frozen CDF, 512 split points	17,920	295 ms	111 ms	2.65×
Prebuilt frozen PMF, 100 split points	84,480	287 ms	109 ms	2.64×
Prebuilt repeated-value CDF, 100 split points	98,560	285 ms	128 ms	2.24×
Build from 100,000 inputs, then CDF with 100 split points	59	290 ms	287 ms	1.01×
Prebuilt frozen CDF, 1 split point	4,224,000	290 ms	290 ms	1.00×
Prebuilt frozen CDF, 6 split points	1,113,600	286 ms	287 ms	1.00×
Prebuilt frozen CDF, tail split points	857,600	295 ms	294 ms	1.00×
Prebuilt frozen PMF, tail split points	832,000	285 ms	288 ms	0.99×
Prebuilt repeated-value frozen PMF, tail split points	780,800	289 ms	292 ms	0.99×

Before/after are median batch times. Speedup is the median of seven paired before/after ratios; above 1× is faster, below 1× is slower. Unrounded ratios determine the result; integer milliseconds are only for display. Medians of paired ratios need not equal the ratio of median times. These totals do not describe a single request or application latency.

Prebuilt rows count complete CDF or PMF calls on prepared digests. The lifecycle row counts complete construct/update/CDF/destroy workflows, each ingesting 100,000 items; it includes pending compression. Its paired before/after ratios range from 0.992 to 1.020, so this run does not establish a complete-lifecycle gain. The benefit is concentrated in dense queries on existing digests; the tail PMF control is slightly slower. Input generation is outside timing in both variants.

Across all 41 measured cases, the largest median latency regression is 1.21%, below the 5% limit used for this comparison. The limit applies separately to each case, including controls; it is not an average across workloads or a guarantee for every individual sample or environment. Targeted baseline/candidate correctness fingerprints match exactly.

[tisonkun]

Self-proven improvement.

But you may follow #307 (comment) as well.