Purpose

No Linked issue.

Migrate file index module public interfaces and core implementations:

File index interfaces (include/paimon/file_index/):

• FileIndexFormat — file index serialization format with header, body, and column index entries (file_index_format.h)
• FileIndexResult — query result representing matched/unmatched row ranges (file_index_result.h)
• FileIndexReader — abstract reader for querying a file index (file_index_reader.h)
• BitmapIndexResult — bitmap-backed index query result (bitmap_index_result.h)
• FileIndexer — abstract file indexer producing readers and writers (file_indexer.h)
• FileIndexWriter — abstract writer for building a file index (file_index_writer.h)
• FileIndexerFactory — registry and factory for file indexer implementations (file_indexer_factory.h)

File index implementation (src/paimon/common/file_index/):

• FileIndexFormat — serialization/deserialization of file index format (file_index_format.cpp)
• FileIndexReader — base reader implementation with column dispatch (file_index_reader.cpp)
• FileIndexResult — result intersection, union, and row range operations (file_index_result.cpp)
• FileIndexerFactory — factory registration and lookup logic (file_indexer_factory.cpp)

Empty index (src/paimon/common/file_index/empty/):

• EmptyFileIndexReader — no-op reader returning all-match results (empty_file_index_reader.h)

Tests

• file_index_format_test.cpp — format round-trip serialization, multi-column index, edge cases
• file_index_reader_test.cpp — reader column dispatch and empty index fallback
• file_index_result_test.cpp — result set operations (intersection, union)
• file_indexer_factory_test.cpp — factory registration and lookup
• empty_file_index_reader_test.cpp — empty reader always-match behavior

API and Format

Adds public file index interfaces under include/paimon/file_index/. No storage format or protocol changes.

Documentation

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Migrate-by: Aone Copilot (Claude)