TurboPFor Integer Compression

Fastest Integer Compression

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TurboPFor: Fastest Integer Compression

Build ubuntu

  • 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),
    • 🆕(2023.04) Rust Bindings. Access TurboPFor incl. SSE/AVX2/Neon! from Rust
    • 👍 Java Critical Natives/JNI. Access TurboPFor incl. SSE/AVX2/Neon! from Java as fast as calling from C
    • ✨ FULL range 8/16/32/64 bits scalar + 16/32/64 bits SIMD functions
    • No other “Integer Compression” compress/decompress faster
    • ✨ 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,…
    • 🆕(2023.03)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
  • 🆕(2023.03)TurboVLC novel variable length encoding for large integers
    with exponent + variable bit mantissa
  • 🆕(2023.03)Binary interpolative coding : fastest implementation
  • Transform
    • Scalar & SIMD Transform: Delta, Zigzag, Zigzag of delta, XOR,
    • 🆕(2023.03) Transpose/Shuffle with integrated Xor and zigzag delta
    • 🆕(2023.03) 2D/3D/4D transpose
    • lossy floating point compression with TurboPFor or TurboTranspose+lz77/bwt
  • 🆕(2023.03)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
    • 🆕(2023.03)TurboFloat LzXor novel floating point lempel-ziv compression
    • 🆕(2023.06) _Float16 16 bits floating point support
    • 🆕(2023.06) 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
    • ✨ Revolutionary Parallel Query Processing on Multicores > 7000!!! queries/sec on a simple quad core PC.

      …forget Map Reduce, Hadoop, multi-node clusters, …

Promo video

Integer Compression Benchmark (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.

     ./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:

Speed/Ratio

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:
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
- 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:

Last update: 10 JUN 2023