Fibonacci coding for primitive integers in Rust

This crate implements the Fibonacci coding technique for storing integers as variable bit length code words. It implements an encoder consuming an interator over various primitive unsigned integer types (u8 through u64), and a decoder to reverse the process.

Restrictions

Due to the way the coding scheme works, the number 0 can't be encoded.

lib.rs:

Traits and functions for encoding and decoding (slices of) positive integers using Fibonacci Coding.

Fibonacci coding is a method for representing a continuous stream of (positive) integers using a variable number of bits -- e.g., instead of taking up 2*32 bits for storing two u32 words, these words will take up however many bits their fibonacci-encoded representation takes up.

Fibonacci coding yields better results for smaller numbers than larger ones: The largest 32-bit words can take up to 47 bits, but to encode the number 1, you only need 2 bits.

Fibonacci coding is self-synchronizing: If a single bit is altered, a single number could be decoded as two (or two numbers decoded as one), but the remaining numbers will be read correctly.

Value range

Fibonacci coding can represent any number that can be expressed as addition of one or more Fibonacci numbers, so any integer greater than 1, up to the range of the given machine integer type. This means that the integer zero can not be encoded.

If you should need to encode 0, it is advisable to encode numbers incremented by one (preventing overflow by upgrading to the next-biggest integer type, or by not encoding the maximum value), and to subtract one from the decoded result. .

Examples

Encoding a slice of numbers:

use fibonacci_codec::Encode;

let numbers: Vec<u16> = vec![1, 50, 3003];
let encoded = &numbers.fib_encode().unwrap();
// code words: "11" (1), "001001011" (50), "000010010000100011" (3003)
// These encoded words take up 4 bytes instead of 6 (3*16 bits)!
assert_eq!(encoded.to_bytes(), [0b11001001, 0b01100001, 0b00100001, 0b00011000]);

Encoding the value zero:

use fibonacci_codec::Encode;

let numbers: Vec<u16> = vec![0, 49, 3002];
let adjusted: Vec<u32> = numbers.iter().map(|n| *n as u32 + 1).collect();
let encoded = &adjusted.fib_encode().unwrap();
// code words: "11" (1), "001001011" (50), "000010010000100011" (3003)
// These encoded words take up 4 bytes instead of 6 (3*16 bits)!
assert_eq!(encoded.to_bytes(), [0b11001001, 0b01100001, 0b00100001, 0b00011000]);

References:

• Wikipedia
• Fraenkel, Aviezri S.; Klein, Shmuel T. (1996). "Robust universal complete codes for transmission and compression"