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.
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.
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.
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:
// 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]; } }
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.
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:
-8 / log(1 - pow(p, 1.0 / 8));
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.