Hawkynt

Arithmetic Coding

Arithmetic coding represents the entire message as a single fraction in the range [0,1) using probability models. Unlike prefix codes, achieves optimal compression ratios approaching the Shannon entropy limit.

Properties

Property	Value
Category	Compression Algorithms
Sub-category	Statistical
Security status	Not classified
Complexity	Advanced
Inventor	Jorma Rissanen, Glen Langdon
Year	1976
Origin	🇺🇸 United States
Source	algorithms/compression/arithmetic.js

Security

Status: not classified — treat as unverified.

No vulnerabilities are recorded for this implementation.

Documentation

• Arithmetic Coding - Wikipedia
• Introduction to Data Compression by Khalid Sayood
• Mark Nelson’s Data Compression Tutorial

References

• Nayuki Reference Implementation
• CABAC in H.264 Standard
• JPEG 2000 Arithmetic Coding

Test vectors

4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Empty data round-trip test

Source: Educational test vector

Field	Value
input	(empty)
expected	(empty)

Vector 2 — All byte values 0-255 round-trip test

Source: Regression test for decoder/model desync

Field	Value
input	000102030405060708090a0b0c0d0e0f 101112131415161718191a1b1c1d1e1f 202122232425262728292a2b2c2d2e2f 303132333435363738393a3b3c3d3e3f 404142434445464748494a4b4c4d4e4f 505152535455565758595a5b5c5d5e5f 606162636465666768696a6b6c6d6e6f 707172737475767778797a7b7c7d7e7f 808182838485868788898a8b8c8d8e8f 909192939495969798999a9b9c9d9e9f a0a1a2a3a4a5a6a7a8a9aaabacadaeaf b0b1b2b3b4b5b6b7b8b9babbbcbdbebf c0c1c2c3c4c5c6c7c8c9cacbcccdcecf d0d1d2d3d4d5d6d7d8d9dadbdcdddedf e0e1e2e3e4e5e6e7e8e9eaebecedeeef f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff
expected	(empty)

Vector 3 — Pseudo-random data round-trip test

Source: Regression test for decoder/model desync

Field	Value
input	f3ccbfab9d8fe554efb09bd0b0f5ba94 8035b768414265947a6b83c1414fe53a 321915d231a7468a060cbf21437ca17a 41025ccf252088f87f924ecff37e92df … (300 bytes; the full value is in the source)
expected	(empty)

Vector 4 — Alternating pattern round-trip test

Source: Regression test for decoder/model desync

Field	Value
input	aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55 aa55aa55aa55aa55aa55aa55aa55aa55
expected	(empty)

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