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Specification

Abstract

Fixed-Length Integer Trim (FLIT) is a byte oriented universal code. FLIT64 outperforms VLQ, a.k.a. varint, in terms of speed and size.

  • Fixed serial size range by design
  • Size known at fist byte
  • CPU friendly: count zeros & bit shift, no loops

This is free and unencumbered software released into the public domain.

FLIT64

The 64-bit unsigned version encodes an integer in 1 to 9 octets.

The first octet advertises the number of octets following with the trailing zero count. Any remaining bits hold the least significant data bits and the following octets, if any at all, hold the rest in little-endian order.

Total Size First Bits Range
1 octet xxxx xxx1 7-bit (128)
2 octets xxxx xx10 14-bit (16'384)
3 octets xxxx x100 21-bit (2'097'152)
4 octets xxxx 1000 28-bit (268'435'456)
5 octets xxx1 0000 35-bit (34'359'738'368)
6 octets xx10 0000 42-bit (4'398'046'511'104)
7 octets x100 0000 49-bit (562'949'953'421'312)
8 octets 1000 0000 56-bit (72'057'594'037'927'936)
9 octets 0000 0000 64-bit (18'446'744'073'709'551'616)

Encoding should pick the smallest range capable to hold the value.

Decoding Example

  1. The first byte read is 1010 0110.
  2. One tailing zero means we need to read one more byte, which is 0000 1111.
  3. The two bytes in little-endian order make 0000 1111 1010 0110.
  4. Drop the two size bits with a bit shift to get 0000 0011 1110 1001 or decimal 1001.

FLIT64S

For signed integers, the algorithm is preceded with ZigZag encoding. See the Protocol Buffers Encoding documentation for detailed information.

Benchmark

Encoding and decoding in C is almost at memcpy speed.

------------------------------------------------------
Benchmark               Time           CPU Iterations
------------------------------------------------------
BM_flit64_enc/1          2 ns          2 ns  418162594   4.52895GB/s   579.706M items/s
BM_flit64_enc/5          2 ns          2 ns  372356270   3.97295GB/s   508.538M items/s
BM_flit64_enc/9          2 ns          2 ns  444419049   4.80462GB/s   614.991M items/s
BM_flit64_dec/1          2 ns          2 ns  353722934   3.78997GB/s   485.117M items/s
BM_flit64_dec/5          2 ns          2 ns  354477045   3.79497GB/s   485.756M items/s
BM_flit64_dec/9          2 ns          2 ns  450094198   4.80574GB/s   615.134M items/s
BM_memcpy64             2 ns          2 ns  413846108   4.50834GB/s   577.068M items/s

The same goes for Go.

goos: darwin
goarch: arm64
pkg: github.com/pascaldekloe/flit
BenchmarkPutUint64-8      	497578708	         2.091 ns/op	3825.80 MB/s
BenchmarkPutUint64Raw-8   	580234668	         2.066 ns/op	3871.73 MB/s
BenchmarkPutUint64VQL-8   	381299838	         3.144 ns/op	2544.50 MB/s
BenchmarkUint64-8         	508336362	         2.356 ns/op	3396.16 MB/s
BenchmarkUint64Raw-8      	586730718	         2.036 ns/op	3928.38 MB/s
BenchmarkUint64VQL-8      	238780944	         5.025 ns/op	1591.98 MB/s

Credits

  • Aleksey Demakov @ademakov
  • Roman Gershman @romange

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fixed-length integer trim

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