Elias codes are prefix codes for positive, non-zero integers with no assumption or limit to their size. For completeness, gamma, delta and omega codes are implemented although for most applications you can get away with only using delta codes:

• Gamma codes are 1 bit more efficient than delta codes for certain numbers between 0 and 14.
• Omega codes only become shorter than delta codes for numbers above 1 googol, or \(10^{100}\).

Functions of this module add 1 at encoding time and subtract 1 at decoding time to support any natural number, including zero.

An Elias gamma code consists of the binary expansion of an integer, preceded by the unary encoding of the length of that expansion in zeros.

An Elias delta code is like an Elias gamma code except that the length is itself coded like a gamma code instead of a unary encoding.

An Elias omega code is the result of recursively encoding the length of binary expansions in the prefix until a length of 1 is reached. Since binary expansions are written without any leading zeros, a single 0 bit marks the end of the code.