[AhmedDusuki]

Addresses the empty and sparse union serialization paths in #319.

Summary

• add CpcUnion::serialize() with output identical to to_sketch().serialize()
• serialize empty and sparse union results without materializing an intermediate sketch
• preserve the effective lg_k, seed hash, and merged-result metadata
• retain the existing result-sketch conversion for bit-matrix unions
• add serialization regression coverage and paired benchmarks

Details

For sparse unions, to_sketch() clones the accumulator solely to mark the result as merged before encoding it. CpcUnion::serialize() now reuses the sketch encoder with merged-result metadata while borrowing the accumulator. Empty unions use the same direct path.

Bit-matrix unions continue through to_sketch().serialize(). Encoding their window and surprise pairs directly can remain a separate follow-up as described in #319.

The new method produces byte-for-byte identical serialized images to the existing path across empty, sparse, hybrid, pinned, and sliding states. The tests also cover custom seeds, reduced precision, deserialization, and subsequent union updates.

Performance

Release benchmarks compared both implementations from the same PR build on an AMD Ryzen 5 2600X with Rust 1.98.1 on Windows. Each comparison used 100 repetitions; times are medians in milliseconds, with the full observed range shown in parentheses.

lg_k=18 union state	Rounds	Via result sketch	Direct	Ratio
Empty	4,000,000	286 ms (278–327)	218 ms (212–263)	0.76x
Sparse, 20,000 values	500	265 ms (248–308)	266 ms (259–290)	1.00x
Bit matrix, 80,000 values	200	315 ms (308–377)	315 ms (307–344)	1.00x

Direct serialization reduced the empty-union median by 24%. Sparse-union and bit-matrix timings remained effectively unchanged. The bit-matrix case intentionally retains the existing result-sketch conversion path.

A temporary counting allocator measurement produced:

lg_k=18 union state	Via result sketch	Direct
Empty	1 allocation, 40 bytes	1 allocation, 40 bytes
Sparse, 20,000 values	11 allocations, 293,376 bytes	10 allocations, 162,304 bytes
Bit matrix, 80,000 values	14 allocations, 815,792 bytes	14 allocations, 815,792 bytes

For the sparse case, the direct path removes the accumulator clone, saving one allocation and 131,072 allocated bytes per serialization. Output bytes were identical in every case.

The benchmark cases are included in this PR. The measurements were run with:

cargo +1.98.1 x bench -- 'cpc::serde::serialize_union/0' --exact --repeat 100 --raw
cargo +1.98.1 x bench -- 'cpc::serde::serialize_union/20000' --exact --repeat 100 --raw
cargo +1.98.1 x bench -- 'cpc::serde::serialize_union/80000' --exact --repeat 100 --raw

Validation

• full workspace test suite passed, including 145 cross-language serialization tests and 147 doctests
• cargo x check passed
• benchmark smoke tests passed
• nightly Clippy passed with warnings denied
• nightly formatting check passed
• documentation build passed
• typos and hawkeye check passed
• git diff --check passed

[tisonkun]

Thanks for your contribution! LGTM.

I push a follow-up and it should be now OK to merge :D