[C++][Parquet] Fast path for writing fixed-size lists #60

Describe the enhancement requested

When writing a FixedSizeListArray (for example embeddings, coordinates or RGB tuples), Parquet C++ uses the same generic path as variable-length lists. MultipathLevelBuilder (cpp/src/parquet/arrow/path_internal.cc) walks the FixedSizeListNode / FixedSizedRangeSelector path node by node. It materializes one int16_t definition level and one repetition level per leaf value. Then LevelEncoder::Encode (column_writer.cc) RLE/bit-pack encodes those buffers again one value at a time.

For a list of size n with no nulls, both level streams are fully predictable:

• def levels: a constant max_def_level, which is a single RLE run
• rep levels: the periodic pattern 0, 1, …, 1 (n - 1 ones), repeated for every record

So we spend time and memory building and encoding 2 × num_values levels that could be written directly. This is the write-side counterpart of the read-side fast path described in Fast path for fixed-length lists in Parquet.

Proposal

Add a writer fast path that applies when:

• the leaf column sits under a FixedSizeListArray (optionally also a ListArray / LargeListArray whose offsets show every list has the same length), and
• the list has no null slots, the child values have no nulls, and there are no nullable or repeated ancestors (at least for the first version).

In that case:

1. Skip the generic path traversal and produce the def/rep levels directly. Ideally they would go straight into the RLE encoder as runs (one def-level run per page; a precomputed periodic rep-level pattern per page) without materializing int16_t buffers.
2. Pass the child values slice straight to WriteArrowDense (it is already contiguous: values()->Slice(value_offset(0), length * n)).
3. Compute the row count, page and record boundaries, and SizeStatistics level histograms arithmetically (num_rows = num_values / n) instead of scanning rep levels.

Output must be byte-identical to the existing path, so files stay fully readable by every existing reader. No format or spec change is involved.

Acceptance criteria

• Round-trip tests for fixed_size_list<T, n> covering several n (1, 3, 8, 9, 16, 768), several physical types, V1 and V2 data pages, dictionary on/off, and a range of page and row-group sizes.
• A test that the fast path and the generic path produce identical column chunks, including levels, page boundaries and statistics.
• The generic path still handles null lists, null elements and nested cases.
• A benchmark in reader_writer_benchmark.cc comparing writing fixed_size_list<float, n> against writing the same values as a flat column, before and after the change.

Context

• Related read-side issue: [C++][Parquet] Fast path for reading fixed-size lists by detecting constant list length from encoded levels #61
• Existing report of slow fixed-size-list IO: apache/arrow#34510
• Parquet dev list discussion on a FIXED_SIZE_LIST logical type: https://lists.apache.org/thread/qhq33wg1loxhymsyqjnsfsrd82qnv43m. This issue works independently of that discussion, because it needs no spec change. If a spec-level fixed-size marker lands later, the writer can emit it from this same path.

Component(s)

C++, Parquet