Add PiecewiseSequence index array

[danking]

Summary

Adds PiecewiseSequenceArray, a serializable index encoding for piecewise arithmetic sequences: starts[i] + j * multipliers[i] for j in 0..lengths[i].

This PR only introduces the index array and its execution/scalar behavior. It intentionally does not specialize take; dependent PRs consume this encoding for the constant-multiplier-1 contiguous case.

Validation

• cargo fmt -p vortex-array
• cargo test -p vortex-array piecewise_sequence

[github-actions]

Polar Signals Profiling Results

Latest Run

Status	Commit	Job	Attempt	Link
🟢 Done	2b6fa3e		1	Explore Profiling Data

Previous Runs (7)

Status	Commit	Job	Attempt	Link
🟢 Done	52affcd		1	Explore Profiling Data
🟢 Done	16ca5dc		2	Explore Profiling Data
🟢 Done	6eb0c92		1	Explore Profiling Data
🟢 Done	ba7ef2e		1	Explore Profiling Data
🟢 Done	1748e31		1	Explore Profiling Data
🟢 Done	3edf6c8		1	Explore Profiling Data
🟢 Done	aba7e4d		1	Explore Profiling Data

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[codspeed-hq]

Merging this PR will improve performance by 11.17%

⚡ 1 improved benchmark
✅ 1669 untouched benchmarks
⏩ 52 skipped benchmarks¹

Performance Changes

	Mode	Benchmark	BASE	HEAD	Efficiency
⚡	Simulation	true_count_vortex_buffer[128]	580.6 ns	522.2 ns	+11.17%

Tip

Curious why this is faster? Comment @codspeedbot explain why this is faster on this PR, or directly use the CodSpeed MCP with your agent.

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_{Comparing codex/piecewise-sequential-array (2b6fa3e) with develop (3975895)}

Footnotes

1. 52 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

[github-actions]

Benchmarks: Vortex queries

Verdict: No clear signal (low confidence)
Attributed Vortex impact: +5.3%
Engines: DataFusion No clear signal (+6.1%, low confidence) · DuckDB No clear signal (+4.6%, low confidence)
Vortex (geomean): 1.047x ➖
Parquet (geomean): 1.020x ➖
Shifts: Parquet (control) +2.0% · Median polish +4.5%

How to read Verdict and Engines

• Verdict: Overall PR-level signal after subtracting baseline drift estimated from Parquet control rows. It can be Likely improvement, Likely regression, or No clear signal.
• Engines: Per-engine attribution. DataFusion is compared against DataFusion/Parquet controls; DuckDB is compared against DuckDB/Parquet controls. This answers whether each engine improved or regressed independently.
• Confidence: Based on directional consistency, share of rows above the noise floor, and control-run noise.

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datafusion / vortex-file-compressed (1.080x ➖, 0↑ 0↓)

name	PR 2b6fa3e (ns)	base 3975895 (ns)	ratio (PR/base)
vortex_q00/datafusion:vortex-file-compressed	10021365	9303558	1.08
vortex_q01/datafusion:vortex-file-compressed	6627376	6119813	1.08

datafusion / parquet (1.018x ➖, 0↑ 0↓)

name	PR 2b6fa3e (ns)	base 3975895 (ns)	ratio (PR/base)
vortex_q00/datafusion:parquet	20583727	20667041	1.00
vortex_q01/datafusion:parquet	4789370	4604281	1.04

duckdb / vortex-file-compressed (1.069x ➖, 0↑ 0↓)

name	PR 2b6fa3e (ns)	base 3975895 (ns)	ratio (PR/base)
vortex_q00/duckdb:vortex-file-compressed	10436535	9980727	1.05
vortex_q01/duckdb:vortex-file-compressed	6503703	5950906	1.09

duckdb / parquet (1.022x ➖, 0↑ 0↓)

name	PR 2b6fa3e (ns)	base 3975895 (ns)	ratio (PR/base)
vortex_q00/duckdb:parquet	23652549	23222387	1.02
vortex_q01/duckdb:parquet	9552799	9308681	1.03

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No file size changes detected.

[robert3005]

I think while starts could be primitive we specifically want to handle cases where this is not primitive?