TurboPFor-Integer-Compression

TurboPFor: Fastest Integer Compression

• TurboPFor: The synonym for "integer compression"
  • ALL functions available for AMD/Intel, 64 bits ARMv8 NEON Linux+MacOS/M1 & Power9 Altivec
  • 100% C (C++ headers), as simple as memcpy. OS:Linux amd64, arm64, Power9, MacOs (Amd/intel + Apple M1),
  • Rust Bindings. Access TurboPFor incl. SSE/AVX2/Neon! from Rust
  • :+1: Java Critical Natives/JNI. Access TurboPFor incl. SSE/AVX2/Neon! from Java as fast as calling from C
  • :sparkles: FULL range 8/16/32/64 bits scalar + 16/32/64 bits SIMD functions
  • riscv64 currently uses the existing generic/scalar path and does not enable x86 SIMD or AVX2 code paths unless a dedicated RISC-V backend is added.
  • No other "Integer Compression" compress/decompress faster
  • :sparkles: Direct Access, integrated (SIMD/AVX2) FOR/delta/Delta of Delta/Zigzag for sorted/unsorted arrays
• 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.
• Bit Packing
  • Fastest and most efficient "SIMD Bit Packing" >20 Billions integers/sec (80Gb/s!)
  • Extremely fast scalar "Bit Packing"
  • 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
  • SIMD TurboByte fastest group varint (16+32 bits) incl. integrated delta,zigzag,xor,...
  • TurboBitByte novel hybrid scheme combining the fastest SIMD codecs TurboByte+TurboPack. Compress considerably better and can be 3 times faster than streamvbyte
• 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
• TurboVLC novel variable length encoding for large integers with exponent + variable bit mantissa
• Binary interpolative coding : fastest implementation

• Transform
  • Scalar & SIMD Transform: Delta, Zigzag, Zigzag of delta, XOR,
  • Transpose/Shuffle with integrated Xor and zigzag delta
  • 2D/3D/4D transpose
  • lossy floating point compression with TurboPFor or TurboTranspose+lz77/bwt
• IC Codecs transpose/rle + general purpose compression with lz4,zstd,turborc (range coder),bwt...

• Floating Point Compression
  • Delta/Zigzag + improved gorilla style + (Differential) Finite Context Method FCM/DFCM floating point compression
  • Using TurboPFor, unsurpassed compression and more than 8 GB/s throughput
  • Point wise relative error bound lossy floating point compression
  • TurboFloat novel efficient floating point compression using TurboPFor
  • TurboFloat LzXor novel floating point lempel-ziv compression
  • _Float16 16 bits floating point support
  • float 16/32/64 bits quantization with variable quantization bit size.
• Time Series Compression
  • Fastest Gorilla 16/32/64 bits style compression (zigzag of delta + RLE).
  • can compress timestamps 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 (single thread):

• Download IcApp a new benchmark for TurboPFor for testing allmost all integer and floating point file types. ( type: icapp ZIPF )
• Benchmark: TurboTranspose+iccodecs vs Quantile Compression
• Benchmark: TurboByte+TurboBitByte vs streamvbtyte
• Benchmark: Time Series - TurboPFor, TurboFloat, TurboFloat LzX, TurboGorilla,...
• Benchmark: Lossy Floating Point Preprocessing Turbo Razor vs Granular bitround vs libroundfast
• Benchmark: Lossless/Lossy Floating Point Compression. TurboPFor vs zfp & blosc
• Benchmark: TurboPFor: IcApp 16 bits Integer Compression
• Benchmark Intel CPU: Skylake i7-6700 3.4GHz gcc 9.2
• 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.

   ./icapp -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
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 64Ki *
76,345,136	19.1	6.11	1072	2878	VSimple
91,947,533	23.0	7.36	284	11737	QMX 64k *
93,285,864	23.3	7.46	1568	10232	FP_GroupSimple 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
102,074,663	25.5	8.17	2260	4208	PC_Vbyte
102,083,036	25.5	8.17	5200	4268	FP_VByte
112,500,000	28.1	9.00	1528	12140	VarintG8IU
125,000,000	31.2	10.00	13039	12366	TurboByte
125,000,000	31.2	10.00	11197	11984	StreamVbyte 2019
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 Block size=128/Delta coding

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+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 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)

    ./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)

    ./icapp -e117,118,119 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

- 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.
• "integer compression" GOV2 experiments 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:

    Download or clone TurboPFor
	git clone https://github.com/powturbo/TurboPFor-Integer-Compression.git
	cd TurboPFor-Integer-Compression
	make

    To benchmark TurboPFor + general purpose compression codecs (zstd,lz4, Turbo-Range-Coder, bwt, bitshuffle):
    git clone --recursive https://github.com/powturbo/TurboPFor-Integer-Compression.git
	cd TurboPFor-Integer-Compression
    make ICCODEC=1

    To benchmark external libraries:
	Download the external libraries from github into the current directory
	Activate/deactivate the ext. libs in the makefile
    make CODEC1=1 CODEC2=1 ICCODEC=1

Windows visual c++

	nmake /f makefile.vs

Windows visual studio c++

    project files under vs/vs2022

Testing:

- Synthetic data (use ZIPF parameter):

• benchmark groups of "integer compression" functions

  ./icapp -a1.2 -m0 -M255 -n100M ZIPF
  ./icapp -a1.2 -m0 -M255 -n100M ZIPF -e20-50
  

-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

  ./icapp -a1.5 -m0 -M255 -e1,2,3 ZIPF
  

• Unsorted lists: Zigzag encoding

   ./icapp -e10,11,12 ZIPF
  

• Sorted lists: differential coding (increasing/strictly increasing)

  ./icapp -e4,5,6 ZIPF
  ./icapp -e7,8,9 ZIPF
  

• Transpose/RLE/TurboVByte + General purpose compressor (lz,zstd,turborc,bwt...)

  ./icapp file -e80-95
  ./icapp file -e80-95 -Ezstd,15
  ./icapp file -e80-95 -Eturborc,1
  ./icapp file -e80-95 -Eturborc,20
  

• 2D/3D/4D Transpose + General purpose compressor (lz,zstd,turborc,...)

  ./icapp file512x128.f32 R512x128 -Ff
  ./icapp file512x128.f32 -R512x128 -Ff -e100,101,102
  ./icapp file1024x512x128.f32 -R1024x512x128 -Ff -e100,101,102
  

  Automatic dimension determination from file name ( option -R0 )

  ./icapp file1024x512x128.f32 -R0 -Ff -e103,104,105
  ./icapp file1024x512x128.f64 -R0 -Fl -e103,104,105
  

• Lossy floating point compression

  ./icapp file512x128.f32 -R512x128 -Ff -g.0001
  ./icapp file.f32 -Ff -g.001
  ./icapp file.f64 -Fd -g.001
  

- Data files:

• Raw 32 bits binary data file Test data

  ./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))

  ./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 )
  

- Intersections:

1 - Download Gov2 (or ClueWeb09) + query files (Ex. "1mq.txt") from 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 "icapp" 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 | v8 | bic }[n][d | d1 | f | fm | z ]{enc/dec | pack/unpack}[| 128v | 256v][8 | 16 | 32 | 64]: vb: variable byte p4: turbopfor vs: variable simple v8: TurboByte SIMD + Hybrid TurboByte + TurboPack bit: bit packing fp: Floating Point + Turbo Razor: pointwise relative error rounding algorithm

  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)

public header file to use with documentation: include/ic.h

Note: Some low level functions (like p4enc32) are limited to 128/256 (SSE/AVX2) integers per call.

Environment:

OS/Compiler (64 bits):

• Windows: MinGW-w64 makefile
• Windows: Visual c++ (>=VS2008) - makefile.vs (for nmake)
• Windows: Visual Studio project file - vs/vs2022
• Linux amd64: GNU GCC (>=4.6)
• Linux amd64: Clang (>=3.2)
• Linux arm64: 64 bits aarch64 ARMv8: gcc (>=6.3)
• Linux arm64: 64 bits aarch64 ARMv8: clang
• MaxOS: XCode (>=9)
• MaxOS: Apple M1 (Clang)
• PowerPC ppc64le (incl. SIMD): gcc (>=8.0)

Multithreading:

• All TurboPFor integer compression functions are thread safe

Knowns issues

• Actually (2023.04) there are no known issues or bugs
• The TurboPFor functions can work with arbitrary inputs
• TurboPFor does normally not read outside the input (encode/decode) buffers and does not write outside the output buffer at decoding.
• TurboPFor does not write above a properly sized output buffers at encoding. Use the bound (ex. v8bound,p4bound) functions to allocate a max. memory output buffer.

LICENSE

• GPL 2.0
• A commercial license is available. Contact us at powturbo [AT] gmail.com for more information.

References:

• TurboPFor: an analysis

• Applications:

  • Debian Code Search Debian Code Search: positional index, TurboPFor-compressed
  • Graph500
  • Small Polygon Compression + Poster + code
  • Parallel Graph Analysis (Lecture 18) + code

• Benchmark references:

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

  • :green_book:Evaluating Lightweight Integer Compression Algorithms in Column-Oriented In-Memory DBMS
  • :green_book:In Vacuo and In Situ Evaluation of SIMD Codecs (TurboPackV,TurboPFor/QMX) + paper
  • :green_book:SIMD Compression and the Intersection of Sorted Integers
  • :green_book:Partitioned Elias-Fano Indexes
  • :green_book:On Inverted Index Compression for Search Engine Efficiency
  • :green_book:Google's Group Varint Encoding
  • :green_book:Integer Compression tweets
  • :green_book:Efficient Compression of Scientific Floating-Point Data and An Application in Structural Analysis
  • :green_book:SPDP is a compression/decompression algorithm for binary IEEE 754 32/64 bits floating-point data :green_book: SPDP - An Automatically Synthesized Lossless Compression Algorithm for Floating-Point Data + DCC 2018

Last update: 12 APR 2026