TurboPFor: Fastest Integer Compression [![Build Status](https://travis-ci.org/powturbo/TurboPFor.svg?branch=master)](https://travis-ci.org/powturbo/TurboPFor) ====================================== * **TurboPFor: The new synonym for "integer compression"** * :new: (2019.11) **ALL** TurboPFor functions now available under **64 bits ARMv8** including **NEON** SIMD. * 100% C (C++ headers), as simple as memcpy * :+1: **Java** Critical Natives/JNI. Access TurboPFor **incl. SIMD/AVX2!** from Java as fast as calling from C * :sparkles: **FULL** range 8/16/32/64 bits scalar + 16/32/64 bits SIMD functions * No other "Integer Compression" compress/decompress faster * :sparkles: Direct Access, **integrated** (SIMD/AVX2) FOR/delta/Delta of Delta/Zigzag for sorted/unsorted arrays * **16 bits** + **64 bits** SIMD integrated functions * **For/PFor/PForDelta** * **Novel TurboPFor** (PFor/PForDelta) scheme w./ **direct access** + **SIMD/AVX2**. **+RLE** * 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 * **Bit Packing** * Fastest and most efficient **"SIMD Bit Packing"** **10 Billions integers/sec (40Gb/s!)** * Scalar **"Bit Packing"** decoding nearly 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 and more efficient than **ANY** other implementation * :new: (2019.11) SIMD **TurboByte** fastest group varint (16+32 bits) incl. integrated delta,zigzag,... * :new: (2019.11) **TurboByte+TurboPackV** novel hybrid scheme combining the fastest SIMD codecs. * **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, Zigzag of delta, XOR, Transpose/Shuffle, * **lossy** floating point compression with *TurboPFor* or [TurboTranspose](https://github.com/powturbo/TurboTranspose)+lz77 * **Floating Point Compression** * Delta/Zigzag + improved gorilla style + (Differential) Finite Context Method FCM/DFCM floating point compression * Using **TurboPFor**, unsurpassed compression and more than 5 GB/s throughput * Point wise relative error bound **lossy** floating point compression * :new: (2019.11) **TurboFloat** novel efficient floating point compression using TurboPFor * **Time Series Compression** * **Fastest Gorilla** 16/32/64 bits style compression (**zigzag of delta** + **RLE**). * can compress times series to only 0.01%. Speed > 10 GB/s compression and > 13 GB/s decompress. * **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 * :sparkles: Revolutionary Parallel Query Processing on Multicores **> 7000!!! queries/sec** on a simple quad core PC.
**...forget** ~~Map Reduce, Hadoop, multi-node clusters,~~ ... ![Promo video](turbopfor.jpg?raw=true) ### Integer Compression Benchmark: - :new: Download [IcApp](https://sites.google.com/site/powturbo/downloads) a new benchmark for TurboPFor
for testing allmost all integer and floating point file types. - Practical (No **PURE** cache) "integer compression" benchmark w/ **large** arrays. - Benchmark Intel CPU: Skylake i7-6700 3.4GHz gcc 9.2 **single** thread - Benchmark ARM: ARMv8 A73-ODROID-N2 1.8GHz ##### - 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 |C Size|ratio%|Bits/Integer|C MB/s|D MB/s|Name 2019.11| |--------:|-----:|--------:|----------:|----------:|--------------| |62,939,886| 15.7| 5.04|**2369**|**10950**|**TurboPFor256**| |63,392,759| 15.8| 5.07|1359|7803|**TurboPFor128**| |63,392,801| 15.8| 5.07|1328|924|**TurboPForDA**| |65,060,504| 16.3| 5.20|60|2748|[FP_SIMDOptPFor](#FastPFor)| |65,359,916|16.3| 5.23| 32|2436|PC_OptPFD| |73,477,088|18.4| 5.88|408|2484|PC_Simple16| |73,481,096| 18.4| 5.88|624|8748|[FP_SimdFastPFor](#FastPFor) 64Ki *| |76,345,136| 19.1| 6.11|1072|2878|**VSimple**| |91,947,533| 23.0| 7.36|284|11737|[QMX](#QMX) 64k *| |93,285,864| 23.3| 7.46|1568|10232|[FP_GroupSimple](#FastPFor) 64Ki *| |95,915,096|24.0| 7.67| 848|3832|Simple-8b| |99,910,930| 25.0| 7.99|**17298**|**12408**|**TurboByte+TurboPack**| |99,910,930| 25.0| 7.99|**17357**|**12363**|**TurboPackV** sse| |99,910,930| 25.0| 7.99|11694|10138|**TurboPack** scalar| |99,910,930| 25.0| 7.99|8420|8876|**TurboFor**| |100,332,929| 25.1| 8.03|17077|11170|**TurboPack256V** avx2| |101,015,650| 25.3| 8.08|11191|10333|**TurboVByte**| |102,074,663| 25.5| 8.17|6689|9524|[MaskedVByte](#MaskedVByte)| |102,074,663| 25.5| 8.17|2260|4208|[PC_Vbyte](#PolyCom)| |102,083,036| 25.5| 8.17|5200|4268|[FP_VByte](#FastPFor)| |112,500,000| 28.1| 9.00|1528|12140|[VarintG8IU](#VarintG8IU)| |125,000,000| 31.2|10.00|13039|12366|**TurboByte**| |125,000,000| 31.2|10.00|11197|11984|[StreamVbyte 2019](#StreamVByte)| |400,000,000| 100.00| 32.00| 8960|8948|Copy| | | | | N/A | N/A |EliasFano| (*) codecs inefficient for small block sizes are tested with 64Ki integers/block. - MB/s: 1.000.000 bytes/second. **1000 MB/s = 1 GB/s**
- **#BOLD** = pareto frontier.
- FP=FastPFor SC:simdcomp PC:Polycom
- TurboPForDA,TurboForDA: Direct Access is normally used when accessing few individual values.
- Eliasfano can be directly used only for increasing sequences ------------------------------------------------------------------------ ##### - Data files: - gov2.sorted from [DocId data set](#DocId) Block size=128/Delta coding ./icbench -fS -r gov2.sorted ![Speed/Ratio](ext/gov2.png "Speed/Ratio: Decompression") |Size |Ratio %|Bits/Integer|C Time MB/s|D Time MB/s|Function 2019.11| |-----------:|------:|-----:|-------:|-------:|---------------------| | 3,321,663,893| 13.9| 4.44|**1320**|**6088**|**TurboPFor**| | 3,339,730,557| 14.0| 4.47| 32| 2144|PC.OptPFD| | 3,350,717,959| 14.0| 4.48|**1536**|**7128**|**TurboPFor256**| | 3,501,671,314| 14.6| 4.68| 56| 2840|**VSimple**| | 3,768,146,467| 15.8| 5.04|**3228**| 3652|**EliasFanoV**| | 3,822,161,885| 16.0| 5.11| 572| 2444|PC_Simple16| | 4,411,714,936| 18.4| 5.90|**9304**|**10444**|**TurboByte+TurboPack**| | 4,521,326,518| 18.9| 6.05| 836| 3296|Simple-8b| | 4,649,671,427| 19.4| 6.22|3084| 3848|**TurboVbyte**| | 4,955,740,045| 20.7| 6.63|7064|10268|**TurboPackV**| | 4,955,740,045| 20.7| 6.63|5724| 8020|**TurboPack**| | 5,205,324,760| 21.8| 6.96|6952| 9488|SC_SIMDPack128| | 5,393,769,503| 22.5| 7.21|**14466**|**11902**|**TurboPackV256**| | 6,221,886,390| 26.0| 8.32|6668| 6952|**TurboFor**| | 6,221,886,390| 26.0| 8.32|6644| 2260|**TurboForDA**| | 6,699,519,000| 28.0| 8.96|1888| 1980|FP_Vbyte| | 6,700,989,563| 28.0| 8.96|2740| 3384|MaskedVByte| | 7,622,896,878| 31.9|10.20| 836| 4792|VarintG8IU| | 8,060,125,035| 33.7|11.50|8456| 9476|Streamvbyte 2019| | 8,594,342,216| 35.9|11.50|5228| 6376|libfor| |23,918,861,764|100.0|32.00|5824| 5924|Copy| Block size: 64Ki = 256k bytes. Ki=1024 Integers |Size |Ratio %|Bits/Integer|C Time MB/s|D Time MB/s|Function | |----------:|-----:|----:|------:|------:|---------------------| | 3,164,940,562| 13.2|**4.23**|**1344**|**6004**|**TurboPFor 64Ki**| | 3,273,213,464| 13.7| 4.38|**1496**|**7008**|**TurboPFor256 64Ki**| | 3,965,982,954| 16.6| 5.30|**1520**| 2452|[lz4](#lz4)+DT 64Ki| | 4,234,154,427| 17.7| 5.66| 436| 5672|qmx 64Ki| | 6,074,995,117| 25.4| 8.13| 1976| 2916|[blosc_lz4](#blosc) 64Ki| | 8,773,150,644| 36.7|11.74| 2548|5204|blosc_lz 64Ki| "lz4+DT 64Ki" = Delta+Transpose from TurboPFor + lz4
"blosc_lz4" internal lz4 compressor+vectorized shuffle ##### - Time Series: - Test file [Timestamps: ts.txt(sorted)](https://github.com/zhenjl/encoding/tree/master/benchmark/data) ./icapp -Ft ts.txt -I15 -J15 |Function |C MB/s| size |ratio%| D MB/s|Text |----------------|-----:|--------:|------:|------:|--------------------| |bvzenc32 |**10632**|45,909|0.008|**12823**|ZigZag| |bvzzenc32 |**8914**|56,713|0.010|**13499**|ZigZag Delta of delta| |vsenc32 |**12294**|140,400| 0.024 |12877 |Variable Simple| |p4nzenc256v32 | 1932| 596,018| 0.10 |13326 |TurboPFor256 ZigZag| |p4ndenc256v32 | 1961| 596,018| 0.10 |13339 |TurboPFor256 Delta| |bitndpack256v32 |**12564**|909,189| 0.16 |13505 |TurboPackV256 Delta| |p4nzenc32 | 1810| 1,159,633| 0.20 | 8502 |TurboPFor ZigZag| |p4nzenc128v32 | 1795| 1,159,633| 0.20 |13338 |TurboPFor ZigZag| |bitnzpack256v32 | 9651| 1,254,757| 0.22 |**13503**|TurboPackV256 ZigZag| |bitnzpack128v32 |10155| 1,472,804| 0.26 |13380 |TurboPackV ZigZag| |vbddenc32 | 6198| 18,057,296| 3.13 |10982 |TurboVByte Delta of delta| |memcpy |13397|577,141,992|100.00|| ##### - Transpose/Shuffle (no compression) ./icbench -eTRANSFORM ZIPF |Size |C Time MB/s|D Time MB/s|Function| |----------:|------:|------:|-----------------------------------| |100,000,000|**9400**|**9132**|**TPbyte 4** TurboPFor Byte Transpose/shuffle AVX2| |100,000,000|8784|8860|**TPbyte 4** TurboPFor Byte Transpose/shuffle SSE| |100,000,000|7688|7656|Blosc_Shuffle AVX2| |100,000,000|**5204**|**7460**|**TPnibble 4** TurboPFor Nibble Transpose/shuffle SSE| |100,000,000|6620|6284|Blosc shuffle SSE| |100,000,000|3156|3372|Bitshuffle AVX2| |100,000,000|2100|2176|Bitshuffle SSE| ##### - (Lossy) Floating point compression: ./icapp -Fd file " 64 bits floating point raw file ./icapp -Ff file " 32 bits floating point raw file ./icapp -Fcf file " text file with miltiple entries (ex. 8.657,56.8,4.5 ...) ./icapp -Ftf file " text file (1 entry per line) ./icapp -Ftf file -v5 " + display the first entries read ./icapp -Ftf file.csv -K3 " but 3th column in a csv file (ex. number,Text,456.5 -> 456.5 ./icapp -Ftf file -g.001 " lossy compression with allowed pointwise relative error 0.001 - see also [TurboTranspose](https://github.com/powturbo/TurboTranspose) ##### - 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) | max.docid/q|Time s| q/s | ms/q | % docid found| |-----------------:|---:|----:|-----:|-------:| |1.000|7.88|2283.1|0.438|81| |10.000|10.54|1708.5|0.585|84| | ALL |13.96|1289.0|0.776|100| q/s: queries/second, ms/q:milliseconds/query - Benchmarking Parallel Query Processing (Quad core, AOL query log) | max.docid/q|Time s| q/s | ms/q | % docids found| |-----------------:|----:|----:|-----:|-------:| |1.000|2.66|6772.6|0.148|81| |10.000|3.39|5307.5|0.188|84| |ALL|3.57|5036.5|0.199|100| ###### 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](http://www.internetlivestats.com/google-search-statistics/), using [900.000 multicore servers](https://www.cloudyn.com/blog/10-facts-didnt-know-server-farms/) for searching [8 billions web pages](http://searchenginewatch.com/sew/study/2063479/coincidentally-googles-index-size-jumps) (320 X size of GOV2). - Recent "integer compression" GOV2 experiments (best paper at ECIR 2014) [On Inverted Index Compression for Search Engine Efficiency](http://www.dcs.gla.ac.uk/~craigm/publications/catena14compression.pdf) using 8-core Xeon PC are reporting 1.2 seconds per query (for 1.000 Top-k docids). ### Compile: Download or clone TurboPFor git clone git://github.com/powturbo/TurboPFor.git cd TurboPFor To benchmark external libraries: git clone --recursive git://github.com/powturbo/TurboPFor.git cd TurboPFor ###### Linux, Windows (MingW), Clang,... (see also makefile) make or make AVX2=1 Include external libs make CODEC1=1 CODEC2=1 Disable SIMD make NSIMD=1 ###### Windows visual c++ nmake /f makefile.vs ###### Windows visual studio c++ project files under vs/vs2017 ### 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 -fu ./icbench -m0 -M8 -eturbopack -fs -n1M ##### - Data files: - Raw 32 bits binary data file [Test data](https://github.com/ot/partitioned_elias_fano/tree/master/test/test_data) ./icbench file ./icapp file ./icapp -Fs file "16 bits raw binary file ./icapp -Fu file "32 bits raw binary file ./icapp -Fl file "64 bits raw binary file ./icapp -Ff file "32 bits raw floating point binary file ./icapp -Fd file "64 bits raw floating point binary file - Text file: 1 entry per line. [Test data: ts.txt(sorted) and lat.txt(unsorted)](https://github.com/zhenjl/encoding/tree/master/benchmark/data)) ./icbench -eBENCH -fts ts.txt ./icbench -eBENCH -ft lat.txt ./icapp -Fts data.txt "text file, one 16 bits integer per line ./icapp -Ftu ts.txt "text file, one 32 bits integer per line ./icapp -Ftl ts.txt "text file, one 64 bits integer per line ./icapp -Ftf file "text file, one 32 bits floating point (ex. 8.32456) per line ./icapp -Ftd file "text file, one 64 bits floating point (ex. 8.324567789) per line ./icapp -Ftd file -v5 "like prev., display the first 100 values read ./icapp -Ftd file -v5 -g.00001 "like prev., error bound lossy floating point compression ./icapp -Ftt file "text file, timestamp in seconds iso-8601 -> 32 bits integer (ex. 2018-03-12T04:31:06) ./icapp -FtT file "text file, timestamp in milliseconds iso-8601 -> 64 bits integer (ex. 2018-03-12T04:31:06.345) ./icapp -Ftl -D2 -H file "skip 1th line, convert numbers with 2 decimal digits to 64 bits integers (ex. 456.23 -> 45623) ./icapp -Ftl -D2 -H -K3 file.csv "like prev., use the 3th number in the line (ex. label=3245, text=99 usage=456.23 -> 456.23 ) ./icapp -Ftl -D2 -H -K3 -k| file.csv "like prev., use '|' as separator - Text file: multiple numbers separated by non-digits (0..9,-,.) characters (ex. 134534,-45678,98788,4345, ) ./icapp -Fc data.txt "text file, 32 bits integers (ex. 56789,3245,23,678 ) ./icapp -Fcd data.txt "text file, 64 bits floting-point numbers (ex. 34.7689,5.20,45.789 ) - Multiblocks of 32 bits binary file. (Example gov2 from [DocId data set](#DocId))
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)
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}[n][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
n : high level array functions for large arrays. '' : encoding for unsorted integer lists
'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
'z' : ZigZag encoding for unsorted integer lists
'enc' or 'pack' : encode or bitpack
'dec' or 'unpack': decode or bitunpack
'NN' : integer size (8/16/32/64)
header files to use with documentation:
| c/c++ header file|Integer Compression functions| examples | |------------|-----------------------------|-----------------| |vint.h|variable byte| vbenc32/vbdec32 vbdenc32/vbddec32 vbzenc32/vbzdec32 | |vsimple.h|variable simple| vsenc64/vsdec64 | |vp4.h|TurboPFor| p4enc32/p4dec32 p4denc32/p4ddec32 p4zenc32/p4zdec32 | |bitpack.h|Bit Packing, For, +Direct Access| bitpack256v32/bitunpack256v32 bitforenc64/bitfordec64| |eliasfano.h|Elias Fano| efanoenc256v32/efanoc256v32 | Note: Some low level functions (like p4enc32) are limited to 128/256 (SSE/AVX2) integers per call. ### Environment: ###### OS/Compiler (64 bits): - Linux: GNU GCC (>=4.6) - Linux: Clang (>=3.2) - Windows: MinGW-w64 makefile - Windows: Visual c++ (>=VS2008) - makefile.vs (for nmake) - Windows: Visual Studio project file - vs/vs2017 - Thanks to [PavelP](https://github.com/pps83) - Linux ARM: 64 bits aarch64 ARMv8: gcc (>=6.3) - Linux ARM: 64 bits aarch64 ARMv8: clang ###### Multithreading: - All TurboPFor integer compression functions are thread safe ### References: * [TurboPFor: an analysis](https://michael.stapelberg.ch/posts/2019-02-05-turbopfor-analysis/) * **Applications:** * [Debian Code Search](https://github.com/Debian/dcs/)
[Debian Code Search: positional index, TurboPFor-compressed](https://michael.stapelberg.ch/posts/2019-09-29-dcs-positional-turbopfor-index/) * [Graph500](https://github.com/julianromera/graph500) * [Small Polygon Compression](https://arxiv.org/abs/1509.05505) + [Poster](http://abhinavjauhri.me/publications/dcc_poster_2016.pdf) + [code](https://github.com/ajauhri/bignum_compression) * [Parallel Graph Analysis (Lecture 18)](http://www.cs.rpi.edu/~slotag/classes/FA16/) + [code](http://www.cs.rpi.edu/~slotag/classes/FA16/handson/lec18-comp2.cpp) * **Benchmark references:** * [FastPFor](https://github.com/lemire/FastPFor) + [Simdcomp](https://github.com/lemire/simdcomp): SIMDPack FPF, Vbyte FPF, VarintG8IU, StreamVbyte, GroupSimple * [Optimized Pfor-delta compression code](http://jinruhe.com): OptPFD/OptP4, Simple16 (limited to 28 bits integers) * [MaskedVByte](http://maskedvbyte.org/). See also: [Vectorized VByte Decoding](http://engineering.indeed.com/blog/2015/03/vectorized-vbyte-decoding-high-performance-vector-instructions/) * [Streamvbyte](https://github.com/lemire/streamvbyte). * [Index Compression Using 64-Bit Words](http://people.eng.unimelb.edu.au/ammoffat/abstracts/am10spe.html): Simple-8b (speed optimized version tested) * [libfor](https://github.com/cruppstahl/for) * [Compression, SIMD, and Postings Lists](http://www.cs.otago.ac.nz/homepages/andrew/papers/) QMX integer compression from the "simple family" * [lz4](https://github.com/Cyan4973/lz4). included w. block size 64K as indication. Tested after preprocessing w. delta+transpose * [blosc](https://github.com/Blosc/c-blosc). blosc is like transpose/shuffle+lz77. Tested blosc+lz4 and blosclz incl. vectorizeed shuffle.
* [Document identifier data set](http://lemire.me/data/integercompression2014.html) * **Integer compression publications:** * :green_book:[In Vacuo and In Situ Evaluation of SIMD Codecs (TurboPackV,TurboPFor/QMX)](http://dl.acm.org/citation.cfm?id=3015023) + [paper](http://www.cs.otago.ac.nz/homepages/andrew/papers/) * :green_book:[SIMD Compression and the Intersection of Sorted Integers](http://arxiv.org/abs/1401.6399) * :green_book:[Partitioned Elias-Fano Indexes](http://www.di.unipi.it/~ottavian/files/elias_fano_sigir14.pdf) * :green_book:[On Inverted Index Compression for Search Engine Efficiency](http://www.dcs.gla.ac.uk/~craigm/publications/catena14compression.pdf) * :green_book:[Google's Group Varint Encoding](http://static.googleusercontent.com/media/research.google.com/de//people/jeff/WSDM09-keynote.pdf) * :green_book:[Integer Compression tweets](https://twitter.com/search?q=%23integercompression&src=typd) * :green_book:[Efficient Compression of Scientific Floating-Point Data and An Application in Structural Analysis](https://www.jstage.jst.go.jp/article/jsces/2017/0/2017_20170002/_article) * :green_book:[SPDP is a compression/decompression algorithm for binary IEEE 754 32/64 bits floating-point data](http://cs.txstate.edu/~burtscher/research/SPDPcompressor/)
:green_book:[ SPDP - An Automatically Synthesized Lossless Compression Algorithm for Floating-Point Data](http://cs.txstate.edu/~mb92/papers/dcc18.pdf) + [DCC 2018](http://www.cs.brandeis.edu//~dcc/Programs/Program2018.pdf) Last update: 21 Oct 2019 ## APPENDIX: icbench Integer Compression Benchmark ##### TurboPFor + external libraries 
TurboPFor               	https://github.com/powturbo/TurboPFor
FastPFor (FP)              	https://github.com/lemire/FastPFor
lz4				https://github.com/Cyan4973/lz4
LittleIntPacker (LI)       	https://github.com/lemire/LittleIntPacker
MaskedVbyte             	http://maskedvbyte.org
Polycom (PC)               	https://github.com/encode84/bcm
simdcomp (SC)              	https://github.com/lemire/simdcomp
Simple-8b optimized     	https://github.com/powturbo/TurboPFor
Streamvbyte             	https://github.com/lemire/streamvbyte
VarintG8IU              	https://github.com/lemire/FastPFor
##### Functions integrated into 'icbench' for benchmarking 
Codec group:
TURBOPFOR        TurboPFor library TurboPFor256V/TurboPack256V/TurboPFor256N/TurboPFor/TurboPackV/TurboVByte/TurboPack/TurboForDA/EliasFano/VSimple/TurboPForN/TurboPackN/TurboPForDI
DEFAULT          Default TurboPFor/TurboPackV/TurboVByte/TurboPack/TurboFor/TurboPForN/TurboPackN/TurboPForDI/TurboPFor256V/TurboPack256V/TurboPFor256N
BENCH            Benchmark TurboPFor/TurboPackV/TurboVByte/TurboPack/QMX/FP.SimdFastPfor/FP.SimdOptPFor/MaskedVbyte/StreamVbyte
EFFICIENT        Efficient TurboPFor/vsimple/turbovbyte
TRANSFORM        transpose/shufle,delta,zigzag tpbyte4s/tpbyte,4/tpnibble,4/ZigZag_32/Delta_32/BitShuffle,4
BITPACK          Bit Packing TurboPack256V/TurboPackV/TurboPackH/TurboPack/SC.SimdPack128/SC.SimdPack256
VBYTE            Variable byte TurboVByte/FP.VByte/PC.Vbyte/VarintG8IU/MaskedVbyte/StreamVbyte
SIMPLE           Simple Family simple8b/simple16/vsimple/qmx
LZ4              lz4+bitshufle/transpose 4,8 lz4_bitshufle/lz4_tp4/lz4_tp8
LI               Little Integer LI_Pack/LI_TurboPack/LI_SuperPack/LI_HorPack


Function         Description                                      level

--------         -----------                                      -----
TurboPFor        PFor (SSE2)
TurboPForN       PFor (SSE2) large blocks
TurboPFor256     PFor (AVX2)
TurboPFor256N    PFor (AVX2) large blocks
TurboPForDA      PFor direct access
TurboPForDI      PFord min
TurboPForZZ      PFor zigzag of delta
TurboFor         FOR
TurboForV        FOR (SIMD)
TurboFor256V     FOR (AVX2)
TurboForDA       FOR direct access
TurboPackDA      Bit packing direct access
TurboPack        Bit packing (scalar)
TurboPackN       Bit packing (scalar) large blocks
TurboPackV       Bit packing (SSE2 Vertical)
TurboPackH       Bit packing (SSE2 Horizontal)
TurboPackVN      Bit packing (SSE2 large block)
TurboPack256V    Bit packing (AVX2 Vertical)
TurboPack256N    Bit packing (AVX2 large block)
TurboVByte       Variable byte (scalar)
VSimple          Variable simple (scalar)
EliasFano        Elias fano (scalar)
EliasFanoV       Eliasfano  (SSE2)
EliasFano256V    Elias fano (AVX2)
memcpy           memcpy
copy             Integer copy
tpbyte4s         Byte Transpose (scalar)
tpbyte           Byte transpose (simd)  2,4,8
tpnibble         Nibble transpose (simd)  2,4,8
ZigZag32         ZigZag encoding (sse2)
Delta32          Delta encoding (sse2)
DDelta32         Delta of delta encoding (sse2)
Xor32            Xor encoding (sse2)
FP_PREV64        Floating point PFOR
FP_FCM64         Floating point PFOR (FCM)
FP_DFCM64        Floating point PFOR (DFCM)
TurboPFor64      PFOR 64
TurboPFor64V     PFOR 64
Simple8b         64 bits Simple family (instable)
PC_Simple16      Simple 16. limited to 28 bits
PC_OptPFD        OptPFD. limited to 28 bits
PC_Vbyte         Variable byte
PC_Rice          Rice coding (instable)
VarintG8IU       Variable byte SIMD
MaskedVbyte      Variable byte SIMD
StreamVbyte      Variable byte SIMD
FP_FastPFor      PFor scalar (inefficient for small blocks)
FP_SimdFastPFor  PFor SIMD (inefficient for small blocks)
FP_OptPFor       OptPFor scalar 
FP_SIMDOptPFor   OptPFor SIMD
FP_VByte         Variable byte
FP_Simple8bRLE   Simple-8b + rle
FP_GROUPSIMPLE   Group Simple
SC_SIMDPack128   Bit packing (SSE4.1)
SC_SIMDPack256   Bit packing (SSE4.1)
SC_For           For (SSE4.1)
SC_ForDA         For direct access (SSE4.1)
LibFor_For       For
LibFor_ForDA     For direct access
LI_Pack          Bit packing (scalar)
LI_TurboPack     Bit packing (scalar)
LI_SuperPack     Bit packing (scalar)
LI_HorPack       Bit packing (sse4.1 horizontal) 
LI_BMIPack256    Bit packing (avx2)
lz4              lz4
lz4_bit          Bitshuffle + [delta]+lz4 2,4,8
lz4_nibble       TurboPFor's [delta]+nibble transpose + lz4 2,4,8
lz4_bitxor       Bitshuffle + [xor]+lz4 2,4,8
lz4_nibblexor    TurboPFor's [xor]+nibble transpose + lz4 2,4,8
lz4_byte         TurboPFor's [delta]+byte transpose + lz4 2,4,8
BitShuffle       Bit shuffle (simd) 2,4,8