TurboPFor: Fastest Integer Compression

• TurboPFor: The new synonym for "integer compression"

• 100% C (C++ headers), as simple as memcpy
• 👍 Java Critical Natives/JNI. Access TurboPFor incl. SIMD/AVX2! from Java as fast as calling from C
• ✨ FULL range 8/16/32/64 bits lists
• No other "Integer Compression" compress/decompress faster
• ✨ Direct Access, integrated (SIMD/AVX2) FOR/delta/Zigzag for sorted/unsorted arrays

+ **For/PFor/PForDelta** - **Novel** **"TurboPFor"** (PFor/PForDelta) scheme w./ **direct access**. - Outstanding compression/speed. More efficient than **ANY** other fast "integer compression" scheme. - Compress 70 times faster and decompress up to 4 times faster than OptPFD - 🆕 **TurboPFor AVX2, now 50%! more faster!!!!** - 🆕 **TurboPFor Hybrid, better compression and more faster**

+ **Bit Packing** - ✨ Fastest and most efficient **"SIMD Bit Packing"** - 🆕 TurboPack AVX2 more faster. **Decoding 10 Billions intergers/seconds (40Gb/s)** - 🆕 more faster. Scalar **"Bit Packing"** decoding as fast as SIMD-Packing in realistic (No "pure cache") scenarios - **Direct/Random Access** : Access any single bit packed entry with **zero decompression**

+ **Variable byte** - ✨ Scalar **"Variable Byte"** faster than **ANY** other (incl. SIMD) implementation - 🆕 **new scheme : better compression and 30% faster**

+ **Simple family** - ✨ **Novel** **"Variable Simple"** (incl. **RLE**) faster and more efficient than simple16, simple-8b

+ **Elias fano** - ✨ Fastest **"Elias Fano"** implementation w/ or w/o SIMD/AVX2

+ **Transform** - ✨ Scalar & SIMD Transform: Delta, Zigzag, Transpose/Shuffle, Floating point<->Integer

+ **Inverted Index ...do less, go fast!** - Direct Access to compressed *frequency* and *position* data w/ zero decompression - ✨ **Novel** **"Intersection w/ skip intervals"**, decompress the minimum necessary blocks (**~10-15%)!**. - **Novel** Implicit skips with zero extra overhead - **Novel** Efficient **Bidirectional** Inverted Index Architecture (forward/backwards traversal) incl. "integer compression". - more than **2000! queries per second** on GOV2 dataset (25 millions documents) on a **SINGLE** core - ✨ Revolutionary Parallel Query Processing on Multicores w/ more than **7000!!! queries/sec** on a simple quad core PC.
**...forget** ~~Map Reduce, Hadoop, multi-node clusters,~~ ...

Integer Compression Benchmark:

• Practical (No PURE cache) "integer compression" benchmark w/ large arrays.
• CPU: Skylake i7-6700 3.4GHz gcc 6.2 single thread

- Synthetic data:

• Generate and test (zipfian) skewed distribution (100.000.000 integers, Block size=128/256)
  Note: Unlike general purpose compression, a small fixed size (ex. 128 integers) is in general used in "integer compression". Large blocks involved, while processing queries (inverted index, search engines, databases, graphs, in memory computing,...) need to be entirely decoded

   ./icbench -a1.5 -m0 -M255 -n100M ZIPF
  

(*) codec efficient only for large block size

MI/s: 1.000.000 integers/second. 1000 MI/s = 4 GB/s
#BOLD = pareto frontier.
FP=FastPFor SC:simdcomp PC:Polycom
TurboPForDA,TurboForDA: Direct Access is normally used when accessing few individual values.

- Data files:

• gov2.sorted from [DocId data set](#DocId data set) Block size=128/Delta coding

   ./icbench -fS -r gov2.sorted
  

Block size: 64Ki = 256k bytes. Ki=1024 Integers

"lz4+DT 64Ki" = Delta+Transpose from TurboPFor + lz4
"blosc_lz4" internal lz4 compressor+vectorized shuffle

- Transpose/Shuffle

    ./icbench -eTRANSFORM ZIPF

- Compressed Inverted Index Intersections with GOV2

GOV2: 426GB, 25 Millions documents, average doc. size=18k.

• Aol query log: 18.000 queries
  ~1300 queries per second (single core)
  ~5000 queries per second (quad core)
  Ratio = 14.37% Decoded/Total Integers.

• TREC Million Query Track (1MQT):
  ~1100 queries per second (Single core)
  ~4500 queries per second (Quad core CPU)
  Ratio = 11.59% Decoded/Total Integers.

• Benchmarking intersections (Single core, AOL query log)

• Benchmarking Parallel Query Processing (Quad core, AOL query log)

Notes:

• Search engines are spending 90% of the time in intersections when processing queries.
• Most search engines are using pruning strategies, caching popular queries,... to reduce the time for intersections and query processing.
• As indication, google is processing 40.000 Queries per seconds, using 900.000 multicore servers for searching 8 billions web pages (320 X size of GOV2).
• Recent "integer compression" GOV2 experiments (best paper at ECIR 2014) On Inverted Index Compression for Search Engine Efficiency using 8-core Xeon PC are reporting 1.2 seconds per query (for 1.000 Top-k docids).

Compile:

	git clone --recursive git://github.com/powturbo/TurboPFor.git
    cd TurboPFor
	make

	or

	make AVX2=1

    Minimum build w/ TurboPFor scalar functions
    make NSIMD=1

Testing:

- Synthetic data (use ZIPF parameter):

• benchmark groups of "integer compression" functions
  

  ./icbench -eBENCH -a1.2 -m0 -M255 -n100M ZIPF
  ./icbench -eBITPACK/VBYTE -a1.2 -m0 -M255 -n100M ZIPF
  

Type "icbench -l1" for a list

-zipfian distribution alpha = 1.2 (Ex. -a1.0=uniform -a1.5=skewed distribution)
-number of integers = 100.000.000
-integer range from 0 to 255

• Unsorted lists: individual function test (ex. Copy TurboPack TurboPFor)
  

  ./icbench -a1.5 -m0 -M255 -ecopy/turbopack/turbopfor/turbopack256v ZIPF
  

• Unsorted lists: Zigzag encoding w/ option -fz or FOR encoding
  

  ./icbench -fz -eturbovbyte/turbopfor/turbopackv ZIPF
  ./icbench -eturboforv ZIPF
  

• Sorted lists: differential coding w/ option -fs (increasing) or -fS (strictly increasing)
  

  ./icbench -fs -eturbopack/turbopfor/turbopfor256v ZIPF
  

• Generate interactive "file.html" plot for browsing

  ./icbench -p2 -S2 -Q3 file.tbb
  

• Unit test: test function from bit size 0 to 32

  ./icbench -m0 -M32 -eturbpfor 
  ./icbench -m0 -M8 -eturbopack -fs -n1M 
  

- Data files:

• Raw 32 bits binary data file Test data

  ./icbench file
  

• Text file: 1 integer per line. Test data: ts.txt(sorted) and lat.txt(unsorted))

  ./icbench -eBENCH -fts ts.txt
  ./icbench -eBENCH -ft  lat.txt
  

• Multiblocks of 32 bits binary file. (Example gov2 from [DocId data set](#DocId data set))
  Block format: [n1: #of Ids][Id1] [Id2]...[IdN] [n2: #of Ids][Id1][Id2]...[IdN]...

  ./icbench -fS -r gov2.sorted
  

- Intersections:

1 - Download Gov2 (or ClueWeb09) + query files (Ex. "1mq.txt") from [DocId data set](#DocId data set)
8GB RAM required (16GB recommended for benchmarking "clueweb09" files).

2 - Create index file

    ./idxcr gov2.sorted .

create inverted index file "gov2.sorted.i" in the current directory

3 - Test intersections

    ./idxqry gov2.sorted.i 1mq.txt

run queries in file "1mq.txt" over the index of gov2 file

- Parallel Query Processing:

1 - Create partitions

    ./idxseg gov2.sorted . -26m -s8

create 8 (CPU hardware threads) partitions for a total of ~26 millions document ids

2 - Create index file for each partition

  ./idxcr gov2.sorted.s*

create inverted index file for all partitions "gov2.sorted.s00 - gov2.sorted.s07" in the current directory

3 - Intersections:

delete "idxqry.o" file and then type "make para" to compile "idxqry" w. multithreading

  ./idxqry gov2.sorted.s*.i 1mq.txt

run queries in file "1mq.txt" over the index of all gov2 partitions "gov2.sorted.s00.i - gov2.sorted.s07.i".

Function usage:

See benchmark "icbench" program for "integer compression" usage examples. In general encoding/decoding functions are of the form:

char *endptr = encode( unsigned *in, unsigned n, char *out, [unsigned start], [int b])
endptr : set by encode to the next character in "out" after the encoded buffer
in : input integer array
n : number of elements
out : pointer to output buffer
b : number of bits. Only for bit packing functions
start : previous value. Only for integrated delta encoding functions

char *endptr = decode( char *in, unsigned n, unsigned *out, [unsigned start], [int b])
endptr : set by decode to the next character in "in" after the decoded buffer
in : pointer to input buffer
n : number of elements
out : output integer array
b : number of bits. Only for bit unpacking functions
start : previous value. Only for integrated delta decoding functions

Simple high level functions:

size_t compressed_size = encode( unsigned *in, size_t n, char *out)
compressed_size : number of bytes written into compressed output buffer out

size_t compressed_size = decode( char *in, size_t n, unsigned *out)
compressed_size : number of bytes read from compressed input buffer in

Function syntax:

• {vb | p4 | bit | vs}[d | d1 | f | fm | z ]{enc/dec | pack/unpack}[| 128V | 256V][8 | 16 | 32 | 64]:
  vb: variable byte
  p4: turbopfor
  vs: variable simple
  bit: bit packing
  

  d: delta encoding for increasing integer lists (sorted w/ duplicate)
  d1: delta encoding for strictly increasing integer lists (sorted unique)
  f : FOR encoding for sorted integer lists
  fm: FOR encoding for unsorted integer lists
  z: ZigZag encoding for unsorted integer lists
  

  enc/pack: encode
  dec/unpack:decode
  XX : integer size (8/16/32/64)
  

header files to use with documentation:

Environment:

OS/Compiler (64 bits):

• Linux: GNU GCC (>=4.6)
• clang (>=3.2)
• Windows: MinGW-w64 (no parallel query processing)

Multithreading:

• All TurboPFor integer compression functions are thread safe

References:

• FastPFor + Simdcomp: SIMDPack FPF, Vbyte FPF, VarintG8IU, StreamVbyte

• Optimized Pfor-delta compression code: OptPFD/OptP4, Simple16 (limited to 28 bits integers)

• MaskedVByte. See also: Vectorized VByte Decoding

• Streamvbyte.

• Index Compression Using 64-Bit Words: Simple-8b (speed optimized version tested)

• libfor

• Compression, SIMD, and Postings Lists QMX integer compression from the "simple family"

• lz4. included w. block size 64K as indication. Tested after preprocessing w. delta+transpose

• blosc. blosc is like transpose/shuffle+lz77. Tested blosc+lz4 and blosclz incl. vectorizeed shuffle.
  

• Document identifier data set

• Integer compression publications:

  • In Vacuo and In Situ Evaluation of SIMD Codecs (TurboPackV,TurboPFor/QMX) + paper
  • SIMD Compression and the Intersection of Sorted Integers
  • Partitioned Elias-Fano Indexes
  • On Inverted Index Compression for Search Engine Efficiency
  • Google's Group Varint Encoding

• Applications:

  • Graph500
  • Small Polygon Compression + Poster + code
  • Parallel Graph Analysis (Lecture 18) + code

Last update: 04 FEB 2017