PARQUET-41: Add Bloom filter (#112)

* PARQUET-41: Add Bloom filter

* Grammar and structure tweaking for Bloom filter prose.

BloomFilter.md

@@ -0,0 +1,120 @@
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+
+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)

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<PageEncodingStats> encoding_stats;
+
+  /** Byte offset from beginning of file to Bloom filter data. **/
+  14: optional i64 bloom_filter_offset;
 }
 
 struct ColumnChunk {