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-TurboPFor: Fastest Integer Compression [](https://travis-ci.org/powturbo/TurboPFor)
-======================================
-* **TurboPFor: The new synonym for "integer compression"**
- * :new: (2019.7) 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
- * :new: **16 bits** + **64 bits** SIMD integrated functions
-* **For/PFor/PForDelta**
- * **Novel TurboPFor** (PFor/PForDelta) scheme w./ **direct access** + **SIMD/AVX2**. :new:**+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 than **ANY** other (incl. SIMD) implementation
-* **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,
- * :new: **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
- * :new: Error bound **lossy** floating point compression
-* :new: **Time Series Compression**
- * **Fastest Gorilla** 16/32/64 bits style compression (:new: **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,~~ ...
-
-### 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.
-- CPU: Skylake i7-6700 3.4GHz gcc 7.2 **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
-
-|C Size|ratio%|Bits/Integer|C MB/s|D MB/s|Name|
-|--------:|-----:|--------:|----------:|----------:|--------------|
-|62,939,886| 15.7| 5.04|**1588**|**9400**|**TurboPFor256**|
-|63,392,759| 15.8| 5.07|1320|6432|**TurboPFor**|
-|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|980|2612|**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|**13976**|**11872**|**TurboPackV**|
-|99,910,930| 25.0| 7.99|9468|9404|**TurboPack**|
-|99,910,930| 25.0| 7.99|8420|8876|**TurboFor**|
-|100,332,929| 25.1| 8.03|**14320**|**12124**|**TurboPack256V**|
-|101,015,650| 25.3| 8.08|9520|9484|**TurboVByte**|
-|102,074,663| 25.5| 8.17|5712|7916|[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|4788|11288|[StreamVbyte](#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
-
-
-
-|Size |Ratio %|Bits/Integer|C Time MB/s|D Time MB/s|Function |
-|-----------:|------:|-----:|-------:|-------:|---------------------|
-| 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|
-| 4,521,326,518| 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|**9912**|**11588**|**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| 3536|8684|Streamvbyte|
-| 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 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
-
-### 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)
-- clang (>=3.2)
-- Windows: MinGW-w64 (no parallel query processing demo app)
-- Visual c++ (VS2008-VS2017)
-- Linux aarch64 for 64 bits ARM CPU : gcc
-
-###### Multithreading:
-- All TurboPFor integer compression functions are thread safe
-
-### References:
-
-* **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)
-
-* **Applications:**
- * [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)
-
-Last update: 15 Jul 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
-
-