diff --git a/BloomFilter.md b/BloomFilter.md new file mode 100644 index 000000000..be27aefb3 --- /dev/null +++ b/BloomFilter.md @@ -0,0 +1,120 @@ + + +Parquet Bloom Filter +=== +### Problem statement +In their current format, column statistics and dictionaries can be used for predicate +pushdown. Statistics include minimum and maximum value, which can be used to filter out +values not in the range. Dictionaries are more specific, and readers can filter out values +that are between min and max but not in the dictionary. However, when there are too many +distinct values, writers sometimes choose not to add dictionaries because of the extra +space they occupy. This leaves columns with large cardinalities and widely separated min +and max without support for predicate pushdown. + +A Bloom filter[1] is a compact data structure that overapproximates a set. It can respond +to membership queries with either "definitely no" or "probably yes", where the probability +of false positives is configured when the filter is initialized. Bloom filters do not have +false negatives. + +Because Bloom filters are small compared to dictionaries, they can be used for predicate +pushdown even in columns with high cardinality and when space is at a premium. + +### Goal +* Enable predicate pushdown for high-cardinality columns while using less space than + dictionaries. + +* Induce no additional I/O overhead when executing queries on columns without Bloom + filters attached or when executing non-selective queries. + +### Technical Approach +The initial Bloom filter algorithm in Parquet is implemented using a combination of two +Bloom filter techniques. + +First, the block Bloom filter algorithm from Putze et al.'s "Cache-, Hash- and +Space-Efficient Bloom filters"[2] is used. This divides a filter into many tiny Bloom +filters, each one of which is called a "block". In Parquet's initial implementation, each +block is 256 bits. When inserting or finding a value, part of the hash of that value is +used to index into the array of blocks and pick a single one. This single block is then +used for the remaining part of the operation. + +Second, within each block, this implementation uses the folklore split Bloom filter +technique, as described in section 2.1 of "Network Applications of Bloom Filters: A +Survey"[5]. This divides the 256 bits in each block up into eight contiguous 32-bit lanes +and sets or checks one bit in each lane. + +#### Algorithm +In the initial algorithm, the most significant 32 bits from the hash value are used as the +index to select a block from bitset. The lower 32 bits of the hash value, along with eight +constant salt values, are used to compute the bit to set in each lane of the block. The +salt and lower 32 bits are combined using the multiply-shift[3] hash function: + +```c +// 8 SALT values used to compute bit pattern +static const uint32_t SALT[8] = {0x47b6137bU, 0x44974d91U, 0x8824ad5bU, 0xa2b7289dU, + 0x705495c7U, 0x2df1424bU, 0x9efc4947U, 0x5c6bfb31U}; + +// key: the lower 32 bits of hash result +// mask: the output bit pattern for a tiny Bloom filter +void Mask(uint32_t key, uint32_t mask[8]) { + for (int i = 0; i < 8; ++i) { + mask[i] = key * SALT[i]; + } + for (int i = 0; i < 8; ++i) { + mask[i] = mask[i] >> 27; + } + for (int i = 0; i < 8; ++i) { + mask[i] = UINT32_C(1) << mask[i]; + } +} + +``` + +#### Hash Function +The function used to hash values in the initial implementation is MurmurHash3[4], using +the least-significant 64 bits of the 128-bit version of the function on the x86-64 +platform. Note that the function produces different values on different architectures, so +implementors must be careful to use the version specific to x86-64. That function can be +emulated on different platforms without difficulty. + +#### Build a Bloom filter +The fact that exactly eight bits are checked during each lookup means that these filters +are most space efficient when used with an expected false positive rate of about +0.5%. This is achieved when there are about 11.54 bits for every distinct value inserted +into the filter. + +To calculate the size the filter should be for another false positive rate `p`, use the +following formula. The output is in bits per distinct element: + +```c +-8 / log(1 - pow(p, 1.0 / 8)); +``` + +#### File Format +The Bloom filter data of a column is stored at the beginning of its column chunk in the +row group. The column chunk metadata contains the Bloom filter offset. The Bloom filter is +stored with a header containing the size of the filter in bytes, the algorithm, and the +hash function. + +### Reference +1. [Bloom filter introduction at Wiki](https://en.wikipedia.org/wiki/Bloom_filter) +2. [Cache-, Hash- and Space-Efficient Bloom Filters](http://algo2.iti.kit.edu/documents/cacheefficientbloomfilters-jea.pdf) +3. [A Reliable Randomized Algorithm for the Closest-Pair Problem](http://www.diku.dk/~jyrki/Paper/CP-11.4.1997.ps) +4. [Murmur Hash at Wiki](https://en.wikipedia.org/wiki/MurmurHash) +5. [Network Applications of Bloom Filters: A Survey](https://www.eecs.harvard.edu/~michaelm/postscripts/im2005b.pdf) diff --git a/src/main/thrift/parquet.thrift b/src/main/thrift/parquet.thrift index 6c9011b9a..378aa4733 100644 --- a/src/main/thrift/parquet.thrift +++ b/src/main/thrift/parquet.thrift @@ -475,6 +475,7 @@ enum PageType { INDEX_PAGE = 1; DICTIONARY_PAGE = 2; DATA_PAGE_V2 = 3; + BLOOM_FILTER_PAGE = 4; } /** @@ -554,6 +555,38 @@ struct DataPageHeaderV2 { 8: optional Statistics statistics; } +/** Block-based algorithm type annotation. **/ +struct SplitBlockAlgorithm {} +/** The algorithm used in Bloom filter. **/ +union BloomFilterAlgorithm { + /** Block-based Bloom filter. **/ + 1: SplitBlockAlgorithm BLOCK; +} +/** Hash strategy type annotation. It uses Murmur3Hash_x64_128 from the original SMHasher + * repo by Austin Appleby. + **/ +struct Murmur3 {} +/** + * The hash function used in Bloom filter. This function takes the hash of a column value + * using plain encoding. + **/ +union BloomFilterHash { + /** Murmur3 Hash Strategy. **/ + 1: Murmur3 MURMUR3; +} +/** + * Bloom filter header is stored at beginning of Bloom filter data of each column + * and followed by its bitset. + **/ +struct BloomFilterPageHeader { + /** The size of bitset in bytes **/ + 1: required i32 numBytes; + /** The algorithm for setting bits. **/ + 2: required BloomFilterAlgorithm algorithm; + /** The hash function used for Bloom filter. **/ + 3: required BloomFilterHash hash; +} + struct PageHeader { /** the type of the page: indicates which of the *_header fields is set **/ 1: required PageType type @@ -574,6 +607,7 @@ struct PageHeader { 6: optional IndexPageHeader index_page_header; 7: optional DictionaryPageHeader dictionary_page_header; 8: optional DataPageHeaderV2 data_page_header_v2; + 9: optional BloomFilterPageHeader bloom_filter_page_header; } /** @@ -660,6 +694,9 @@ struct ColumnMetaData { * This information can be used to determine if all data pages are * dictionary encoded for example **/ 13: optional list encoding_stats; + + /** Byte offset from beginning of file to Bloom filter data. **/ + 14: optional i64 bloom_filter_offset; } struct ColumnChunk {