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MaskedVByte: SIMD-accelerated VByte

Daniel Lemire, profile picture
Daniel Lemire

The document discusses techniques for optimizing inverted indexes used for document retrieval, including delta encoding and vectorized VByte decoding. Delta encoding stores the differences between adjacent document IDs rather than the IDs themselves, since differences are usually small integers. VByte encoding compresses these deltas into variable-length bytes. Vectorized VByte decoding decodes multiple VByte-encoded integers simultaneously using CPU intrinsics for improved performance over sequential decoding. It analyzes the variable-length encoding to group integers for bulk decoding in parallel.

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Vectorized VByte Decoding Jeff Plaisance, Nathan Kurz, Daniel Lemire
Inverted Indexes
Inverted Index ● Like index in the back of a book ● words = terms, page numbers = doc ids ● Term list is sorted ● Doc list for each term is sorted
doc id query country impressions clicks 0 software Canada 10 1 1 blank Canada 10 0 2 sales US 5 0 3 software US 8 1 4 blank US 10 1 Standard Index
Constructing an Inverted Index query country impression clicks doc id blank sales software Canada US 5 8 10 0 1 0 ✔ ✔ ✔ ✔ 1 ✔ ✔ ✔ ✔ 2 ✔ ✔ ✔ ✔ 3 ✔ ✔ ✔ ✔ 4 ✔ ✔ ✔ ✔
Constructing an Inverted Index field term 0 1 2 3 4 query blank ✔ ✔ sales ✔ software ✔ ✔ country Canada ✔ ✔ US ✔ ✔ ✔ impressions 5 ✔ 8 ✔ 10 ✔ ✔ ✔ clicks 0 ✔ ✔ 1 ✔ ✔ ✔
Inverted Index field term doc list query blank 1, 4 sales 2 software 0, 3 country Canada 0, 1 US 2, 3, 4 impressions 5 2 8 3 10 0, 1, 4 clicks 0 1, 2 1 0, 3, 4
Inverted Indexes Allow you to: ● Quickly find all documents containing a term ● Intersect several terms to perform boolean queries
Inverted Index Optimizations ● Compressed data structures ○ Better use of RAM and processor cache ○ Better use of memory bandwidth ○ Increased CPU usage and time ● Optimizations matter!
Delta / VByte Encoding ● Doc id lists are sorted ● Delta between a doc id and the previous doc id is sufficient ● Deltas are usually small integers
Delta Encoding field term doc list query nursing 34, 86, 247, 301, 674, 714
Delta Encoding field term doc list query nursing 34, 86, 247, 301, 674, 714 34, 52, 161, 54, 373, 40
Small Integer Compression ● Golomb/Rice ● VByte (or Varint) ● Binary Packing ● PForDelta
Small Integer Compression ● Golomb/Rice ● VByte ● Bit Packing ● PForDelta
VByte Encoding 9838
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 ? 1 1 0 1 1 1 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9838 ? 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 ? 1 1 0 1 1 1 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0
VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0
VByte Pros: ● Compression ● Can fit more of index in RAM ● Higher information throughput per byte read from disk
VByte Cons: ● Decodes one byte at a time ● Lots of branch mispredictions ● Not fast to decode ● Largest ints expand to 5 bytes
Vectorized VByte Decoding Optimized decoder implemented using x86_64 intrinsics
Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001
Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 pmovmskb: Extract top bit of each byte
Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 pmovmskb: Extract top bit of each byte 010010100111
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
010010100111 Decoding options for: ● sixteen 1 byte varints ● six 1-2 byte varints ● four 1-3 byte varints ● two 1-5 byte varints
010010100111 Decoding options for: ● sixteen 1 byte varints - special case ● six 1-2 byte varints - 2^6, 64 possibilities ● four 1-3 byte varints - 3^4, 81 possibilities ● two 1-5 byte varints - 5^2, 25 possibilities 170 total possibilities
010010100111 Data Distribution: ● Longer doc id lists are necessarily composed of smaller deltas ● Most deltas in real datasets (ClueWeb09, Indeed’s internal datasets) fall into 1 byte case or 1-2 byte case
Most Significant Bit Decoding ● We separate most significant bit decoding from integer decoding ● Reduces duplicate most significant bit decoding work if we don’t consume all 12 bytes ● Better instruction level parallelism
010010100111 ● If most significant bits of next 16 bytes are all 0, handle sixteen 1 byte ints case ● Otherwise lookup most significant bits of next 12 bytes in 4096 entry lookup table
010010100111 Lookup table contains: ● Shuffle vector index from 0-169 representing which possibility we are decoding ● Number of bytes of input that will be consumed
010010100111 Branch on shuffle vector index to determine which case we are decoding ● 0-63 - six 1-2 byte ints ● 64-144 - four 1-3 byte ints ● 145-169 - two 1-5 byte ints
Six 1-2 Byte Ints 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 Decode 6 varints from 9 bytes
Expected Positions 2 1 2 1 2 1 2 1 2 1 2 1 0 0 0 0 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 1 5 0 4 0 3 0 2 1 5 0 4 0 3 0 2 Six 1-2 byte ints Four 1-3 byte ints Two 1-5 byte ints
Six 1-2 Byte Ints 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 Pad out 1 byte ints to 2 bytes
Six 1-2 Byte Ints 01001010 00000000 11001000 01110001 01001110 00000000 10011011 01101010 10110101 00010111 01110110 00000000 Pad out 1 byte ints to 2 bytes
Shuffle input ● Use index to lookup appropriate shuffle vector ● Shuffle input bytes to get them in the expected positions
for (i = 0; i < 16; i++) { if (mask[i] & 0x80) { dest[i] = 0; } else { dest[i] = src[mask[i] & 0xF]; } } pshufb
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 43 src mask dest
pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 43 7C DE 45 27 60 7C E3 43 A9 src mask dest
Shuffle input ● Use index to lookup appropriate shuffle vector ● Shuffle input bytes to get them in the expected positions
Six 1-2 Byte Ints 01001010 00000000 11001000 01110001 01001110 00000000 10011011 01101010 10110101 00010111 01110110 00000000 Reverse bytes in 2 byte varints *not actually necessary since x86 is little endian
Six 1-2 Byte Ints 00000000 01001010 01110001 11001000 00000000 01001110 01101010 10011011 00010111 10110101 00000000 01110110 Reverse bytes in 2 byte varints *not actually necessary since x86 is little endian
Six 1-2 Byte Ints 00000000 01001010 01110001 11001000 00000000 01001110 01101010 10011011 00010111 10110101 00000000 01110110 Mask out leading purple 1’s
Six 1-2 Byte Ints 00000000 01001010 01110001 01001000 00000000 01001110 01101010 00011011 00010111 00110101 00000000 01110110 Mask out leading purple 1’s
Six 1-2 Byte Ints 00000000 01001010 01110001 01001000 00000000 01001110 01101010 00011011 00010111 00110101 00000000 01110110 Shift top bytes of each varint 1 bit right (mask/shift/or)
Six 1-2 Byte Ints 00000000 01001010 00111000 11001000 00000000 01001110 00110101 00011011 00001011 10110101 00000000 01110110 Shift top bytes of each varint 1 bit right (mask/shift/or)
Six 1-2 Byte Ints 00000000 01001010 00111000 11001000 00000000 01001110 00110101 00011011 00001011 10110101 00000000 01110110 Done!
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 Decode 4 varints from 8 bytes
Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 Pad ints to 4 bytes
Four 1-3 Byte Ints 11101110 00011101 00000000 00000000 11110101 11101101 01111001 00000000 11111000 01101001 00000000 00000000 00100001 00000000 00000000 00000000 Pad ints to 4 bytes
Four 1-3 Byte Ints 00000000 00000000 00011101 11101110 00000000 01111001 11101101 11110101 00000000 00000000 01101001 11111000 00000000 00000000 00000000 00100001 Reverse bytes *not actually necessary since x86 is little endian
Four 1-3 Byte Ints 00000000 00000000 00011101 11101110 00000000 01111001 11101101 11110101 00000000 00000000 01101001 11111000 00000000 00000000 00000000 00100001 Clear top bit of each byte
Four 1-3 Byte Ints 00000000 00000000 00011101 01101110 00000000 01111001 01101101 01110101 00000000 00000000 01101001 01111000 00000000 00000000 00000000 00100001 Clear top bit of each byte
Four 1-3 Byte Ints 00000000 00000000 00011101 01101110 00000000 01111001 01101101 01110101 00000000 00000000 01101001 01111000 00000000 00000000 00000000 00100001 Shift 2nd least significant bytes over by 1 bit (mask/shift/or)
Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 01111001 00110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 2nd least significant bytes over by 1 bit (mask/shift/or)
Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 01111001 00110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 3rd least significant bytes over by 2 bits (mask/shift/or)
Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 00011110 01110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 3rd least significant bytes over by 2 bits (mask/shift/or)
Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 00011110 01110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Done!
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 Decode 2 varints from 9 bytes
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 ● Could handle the same way as other cases ● Would require 5 AND operations, 4 shift operations, and 4 OR operations
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 ● We can simulate shifting by different amounts with multiplication ● Only needs 1 multiplication, 1 shift, 1 OR, 1 shuffle
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 1 5 0 4 0 3 0 2 1 5 0 4 0 3 0 2 Two 1-5 byte ints Treat SIMD register as eight 16 bit registers, loading 1 byte into each. First byte doesn’t need to be shifted.
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 00000000 00000000 00000000
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 00000000 00000000 10011101
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 11110101 00000000 10011101
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 11101101 00000000 11110101 00000000 10011101
Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000011 00000000 11101101 00000000 11110101 00000000 10011101
Two 1-5 Byte Ints 11101110 00000011 00000000 11101101 00000000 11110101 00000000 10011101 Clear top bit of each byte
Two 1-5 Byte Ints 01101110 00000011 00000000 01101101 00000000 01110101 00000000 00011101 Clear top bit of each byte
Two 1-5 Byte Ints 01101110 00000011 * 16 (<< 4) 00000000 01101101 * 32 (<< 5) 00000000 01110101 * 64 (<< 6) 00000000 00011101 * 128 (<< 7) Multiply to shift bits into place
Two 1-5 Byte Ints 01101110 00000011 * 16 (<< 4) 00000000 01101101 * 32 (<< 5) 00000000 01110101 * 64 (<< 6) 00000000 00011101 * 128 (<< 7) Multiply to shift bits into place
Two 1-5 Byte Ints 11100000 00110000 * 16 (<< 4) 00001101 10100000 * 32 (<< 5) 00011101 01000000 * 64 (<< 6) 00001110 10000000 * 128 (<< 7) Multiply to shift bits into place
Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000
Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Left shift everything by 8 bits
Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Left shift everything by 8 bits 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 OR in low 7 bits of least significant byte (remember that we stored it in most significant byte position originally)
Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 11101110 OR in low 7 bits of least significant byte (remember that we stored it in most significant byte position originally)
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result!
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
Results
Results
Q&A

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MaskedVByte: SIMD-accelerated VByte

  • 1. Vectorized VByte Decoding Jeff Plaisance, Nathan Kurz, Daniel Lemire
  • 3. Inverted Index ● Like index in the back of a book ● words = terms, page numbers = doc ids ● Term list is sorted ● Doc list for each term is sorted
  • 4. doc id query country impressions clicks 0 software Canada 10 1 1 blank Canada 10 0 2 sales US 5 0 3 software US 8 1 4 blank US 10 1 Standard Index
  • 5. Constructing an Inverted Index query country impression clicks doc id blank sales software Canada US 5 8 10 0 1 0 ✔ ✔ ✔ ✔ 1 ✔ ✔ ✔ ✔ 2 ✔ ✔ ✔ ✔ 3 ✔ ✔ ✔ ✔ 4 ✔ ✔ ✔ ✔
  • 6. Constructing an Inverted Index field term 0 1 2 3 4 query blank ✔ ✔ sales ✔ software ✔ ✔ country Canada ✔ ✔ US ✔ ✔ ✔ impressions 5 ✔ 8 ✔ 10 ✔ ✔ ✔ clicks 0 ✔ ✔ 1 ✔ ✔ ✔
  • 7. Inverted Index field term doc list query blank 1, 4 sales 2 software 0, 3 country Canada 0, 1 US 2, 3, 4 impressions 5 2 8 3 10 0, 1, 4 clicks 0 1, 2 1 0, 3, 4
  • 8. Inverted Indexes Allow you to: ● Quickly find all documents containing a term ● Intersect several terms to perform boolean queries
  • 9. Inverted Index Optimizations ● Compressed data structures ○ Better use of RAM and processor cache ○ Better use of memory bandwidth ○ Increased CPU usage and time ● Optimizations matter!
  • 10. Delta / VByte Encoding ● Doc id lists are sorted ● Delta between a doc id and the previous doc id is sufficient ● Deltas are usually small integers
  • 11. Delta Encoding field term doc list query nursing 34, 86, 247, 301, 674, 714
  • 12. Delta Encoding field term doc list query nursing 34, 86, 247, 301, 674, 714 34, 52, 161, 54, 373, 40
  • 13. Small Integer Compression ● Golomb/Rice ● VByte (or Varint) ● Binary Packing ● PForDelta
  • 14. Small Integer Compression ● Golomb/Rice ● VByte ● Bit Packing ● PForDelta
  • 16. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
  • 17. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
  • 18. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
  • 19. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838
  • 20. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 ? 1 1 0 1 1 1 0
  • 21. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9838 ? 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0
  • 22. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 ? 1 1 0 1 1 1 0
  • 23. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0
  • 24. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0
  • 25. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
  • 26. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
  • 27. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 ? 1 0 0 1 1 0 0
  • 28. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0
  • 29. VByte Encoding 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 9838 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0
  • 30. VByte Pros: ● Compression ● Can fit more of index in RAM ● Higher information throughput per byte read from disk
  • 31. VByte Cons: ● Decodes one byte at a time ● Lots of branch mispredictions ● Not fast to decode ● Largest ints expand to 5 bytes
  • 32. Vectorized VByte Decoding Optimized decoder implemented using x86_64 intrinsics
  • 33. Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001
  • 34. Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 pmovmskb: Extract top bit of each byte
  • 35. Vectorized VByte Decoding 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 pmovmskb: Extract top bit of each byte 010010100111
  • 36. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 37. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 38. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 39. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 40. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 41. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 42. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 43. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 44. 010010100111 Pattern of leading bits determines: ● how many varints to decode ● sizes and offsets of varints ● length of longest varint in bytes ● number of bytes to consume
  • 45. 010010100111 Decoding options for: ● sixteen 1 byte varints ● six 1-2 byte varints ● four 1-3 byte varints ● two 1-5 byte varints
  • 46. 010010100111 Decoding options for: ● sixteen 1 byte varints - special case ● six 1-2 byte varints - 2^6, 64 possibilities ● four 1-3 byte varints - 3^4, 81 possibilities ● two 1-5 byte varints - 5^2, 25 possibilities 170 total possibilities
  • 47. 010010100111 Data Distribution: ● Longer doc id lists are necessarily composed of smaller deltas ● Most deltas in real datasets (ClueWeb09, Indeed’s internal datasets) fall into 1 byte case or 1-2 byte case
  • 48. Most Significant Bit Decoding ● We separate most significant bit decoding from integer decoding ● Reduces duplicate most significant bit decoding work if we don’t consume all 12 bytes ● Better instruction level parallelism
  • 49. 010010100111 ● If most significant bits of next 16 bytes are all 0, handle sixteen 1 byte ints case ● Otherwise lookup most significant bits of next 12 bytes in 4096 entry lookup table
  • 50. 010010100111 Lookup table contains: ● Shuffle vector index from 0-169 representing which possibility we are decoding ● Number of bytes of input that will be consumed
  • 51. 010010100111 Branch on shuffle vector index to determine which case we are decoding ● 0-63 - six 1-2 byte ints ● 64-144 - four 1-3 byte ints ● 145-169 - two 1-5 byte ints
  • 52. Six 1-2 Byte Ints 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 Decode 6 varints from 9 bytes
  • 53. Expected Positions 2 1 2 1 2 1 2 1 2 1 2 1 0 0 0 0 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 1 5 0 4 0 3 0 2 1 5 0 4 0 3 0 2 Six 1-2 byte ints Four 1-3 byte ints Two 1-5 byte ints
  • 54. Six 1-2 Byte Ints 01001010 11001000 01110001 01001110 10011011 01101010 10110101 00010111 01110110 10001101 10110011 11000001 Pad out 1 byte ints to 2 bytes
  • 55. Six 1-2 Byte Ints 01001010 00000000 11001000 01110001 01001110 00000000 10011011 01101010 10110101 00010111 01110110 00000000 Pad out 1 byte ints to 2 bytes
  • 56. Shuffle input ● Use index to lookup appropriate shuffle vector ● Shuffle input bytes to get them in the expected positions
  • 57. for (i = 0; i < 16; i++) { if (mask[i] & 0x80) { dest[i] = 0; } else { dest[i] = src[mask[i] & 0xF]; } } pshufb
  • 58. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
  • 59. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
  • 60. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 src mask dest
  • 61. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
  • 62. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
  • 63. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE src mask dest
  • 64. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
  • 65. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
  • 66. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 src mask dest
  • 67. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 src mask dest
  • 68. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 src mask dest
  • 69. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
  • 70. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
  • 71. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 src mask dest
  • 72. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 src mask dest
  • 73. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 src mask dest
  • 74. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
  • 75. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
  • 76. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 src mask dest
  • 77. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 43 src mask dest
  • 78. pshufb DE DF 27 E3 7C A9 60 55 1C EA 45 56 A6 43 C9 48 0 11 2 -1 12 -1 13 4 0 10 2 6 4 3 13 5 DE 56 27 0 A6 0 43 7C DE 45 27 60 7C E3 43 A9 src mask dest
  • 79. Shuffle input ● Use index to lookup appropriate shuffle vector ● Shuffle input bytes to get them in the expected positions
  • 80. Six 1-2 Byte Ints 01001010 00000000 11001000 01110001 01001110 00000000 10011011 01101010 10110101 00010111 01110110 00000000 Reverse bytes in 2 byte varints *not actually necessary since x86 is little endian
  • 81. Six 1-2 Byte Ints 00000000 01001010 01110001 11001000 00000000 01001110 01101010 10011011 00010111 10110101 00000000 01110110 Reverse bytes in 2 byte varints *not actually necessary since x86 is little endian
  • 82. Six 1-2 Byte Ints 00000000 01001010 01110001 11001000 00000000 01001110 01101010 10011011 00010111 10110101 00000000 01110110 Mask out leading purple 1’s
  • 83. Six 1-2 Byte Ints 00000000 01001010 01110001 01001000 00000000 01001110 01101010 00011011 00010111 00110101 00000000 01110110 Mask out leading purple 1’s
  • 84. Six 1-2 Byte Ints 00000000 01001010 01110001 01001000 00000000 01001110 01101010 00011011 00010111 00110101 00000000 01110110 Shift top bytes of each varint 1 bit right (mask/shift/or)
  • 85. Six 1-2 Byte Ints 00000000 01001010 00111000 11001000 00000000 01001110 00110101 00011011 00001011 10110101 00000000 01110110 Shift top bytes of each varint 1 bit right (mask/shift/or)
  • 86. Six 1-2 Byte Ints 00000000 01001010 00111000 11001000 00000000 01001110 00110101 00011011 00001011 10110101 00000000 01110110 Done!
  • 87. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110
  • 88. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 89. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 90. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 91. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 92. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 93. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 101101000110
  • 94. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 Decode 4 varints from 8 bytes
  • 95. Four 1-3 Byte Ints 11101110 00011101 11110101 11101101 01111001 11111000 01101001 00100001 00001011 10110101 10111001 01110110 Pad ints to 4 bytes
  • 96. Four 1-3 Byte Ints 11101110 00011101 00000000 00000000 11110101 11101101 01111001 00000000 11111000 01101001 00000000 00000000 00100001 00000000 00000000 00000000 Pad ints to 4 bytes
  • 97. Four 1-3 Byte Ints 00000000 00000000 00011101 11101110 00000000 01111001 11101101 11110101 00000000 00000000 01101001 11111000 00000000 00000000 00000000 00100001 Reverse bytes *not actually necessary since x86 is little endian
  • 98. Four 1-3 Byte Ints 00000000 00000000 00011101 11101110 00000000 01111001 11101101 11110101 00000000 00000000 01101001 11111000 00000000 00000000 00000000 00100001 Clear top bit of each byte
  • 99. Four 1-3 Byte Ints 00000000 00000000 00011101 01101110 00000000 01111001 01101101 01110101 00000000 00000000 01101001 01111000 00000000 00000000 00000000 00100001 Clear top bit of each byte
  • 100. Four 1-3 Byte Ints 00000000 00000000 00011101 01101110 00000000 01111001 01101101 01110101 00000000 00000000 01101001 01111000 00000000 00000000 00000000 00100001 Shift 2nd least significant bytes over by 1 bit (mask/shift/or)
  • 101. Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 01111001 00110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 2nd least significant bytes over by 1 bit (mask/shift/or)
  • 102. Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 01111001 00110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 3rd least significant bytes over by 2 bits (mask/shift/or)
  • 103. Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 00011110 01110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Shift 3rd least significant bytes over by 2 bits (mask/shift/or)
  • 104. Four 1-3 Byte Ints 00000000 00000000 00001110 11101110 00000000 00011110 01110110 11110101 00000000 00000000 00110100 11111000 00000000 00000000 00000000 00100001 Done!
  • 105. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
  • 106. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
  • 107. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
  • 108. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 111101110110
  • 109. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 Decode 2 varints from 9 bytes
  • 110. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 ● Could handle the same way as other cases ● Would require 5 AND operations, 4 shift operations, and 4 OR operations
  • 111. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 ● We can simulate shifting by different amounts with multiplication ● Only needs 1 multiplication, 1 shift, 1 OR, 1 shuffle
  • 112. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 1 5 0 4 0 3 0 2 1 5 0 4 0 3 0 2 Two 1-5 byte ints Treat SIMD register as eight 16 bit registers, loading 1 byte into each. First byte doesn’t need to be shifted.
  • 113. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
  • 114. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 00000000 00000000 00000000
  • 115. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 00000000 00000000 10011101
  • 116. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 00000000 00000000 11110101 00000000 10011101
  • 117. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000000 00000000 11101101 00000000 11110101 00000000 10011101
  • 118. Two 1-5 Byte Ints 11101110 10011101 11110101 11101101 00000011 11111000 11101001 10100001 00001011 10110101 10111001 01110110 11101110 00000011 00000000 11101101 00000000 11110101 00000000 10011101
  • 119. Two 1-5 Byte Ints 11101110 00000011 00000000 11101101 00000000 11110101 00000000 10011101 Clear top bit of each byte
  • 120. Two 1-5 Byte Ints 01101110 00000011 00000000 01101101 00000000 01110101 00000000 00011101 Clear top bit of each byte
  • 121. Two 1-5 Byte Ints 01101110 00000011 * 16 (<< 4) 00000000 01101101 * 32 (<< 5) 00000000 01110101 * 64 (<< 6) 00000000 00011101 * 128 (<< 7) Multiply to shift bits into place
  • 122. Two 1-5 Byte Ints 01101110 00000011 * 16 (<< 4) 00000000 01101101 * 32 (<< 5) 00000000 01110101 * 64 (<< 6) 00000000 00011101 * 128 (<< 7) Multiply to shift bits into place
  • 123. Two 1-5 Byte Ints 11100000 00110000 * 16 (<< 4) 00001101 10100000 * 32 (<< 5) 00011101 01000000 * 64 (<< 6) 00001110 10000000 * 128 (<< 7) Multiply to shift bits into place
  • 124. Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000
  • 125. Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Left shift everything by 8 bits
  • 126. Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Left shift everything by 8 bits 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 127. Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 128. Two 1-5 Byte Ints 11100000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 129. Two 1-5 Byte Ints 11110000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 130. Two 1-5 Byte Ints 11110000 00110000 00001101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 131. Two 1-5 Byte Ints 11110000 00111101 10101101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 132. Two 1-5 Byte Ints 11110000 00111101 10101101 10100000 00011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 133. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 134. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01000000 00001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 135. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Bitwise OR pre-shifted and shifted registers 00110000 00001101 10100000 00011101 01000000 00001110 10000000 00000000
  • 136. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 137. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 138. Two 1-5 Byte Ints 11110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 139. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 140. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 141. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 142. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 143. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 144. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 145. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 Extract result from every other byte
  • 146. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 10000000 OR in low 7 bits of least significant byte (remember that we stored it in most significant byte position originally)
  • 147. Two 1-5 Byte Ints 00110000 00111101 10101101 10111101 01011101 01001110 10001110 11101110 OR in low 7 bits of least significant byte (remember that we stored it in most significant byte position originally)
  • 148. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result!
  • 149. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 150. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 151. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 152. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 153. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 154. Two 1-5 Byte Ints 00111101 10111101 01001110 11101110 Final result! Checking my work against initial varint: 11101110 10011101 11110101 11101101 00000011
  • 157. Q&A