Module delta 

Elias δ code.

The δ code of a natural number n is the concatenation of the γ code of ⌊log₂(n + 1)⌋ and the binary representation of n + 1 with the most significant bit removed.

The implied distribution of the δ code is ≈ 1/2x(log x)².

The USE_DELTA_TABLE parameter enables or disables the use of pre-computed tables for decoding δ codes, and the USE_GAMMA_TABLE parameter enables or disables the use of pre-computed tables for decoding the the initial γ code in case the whole δ code could not be decoded by tables.

The supported range is [0 . . 2⁶⁴ – 1).

Table-Based Optimization

Like ω codes, δ codes use a special optimization for partial decoding. Due to the structure of δ codes (a γ code followed by fixed bits), when a complete codeword cannot be read from the table, the table may still provide partial information about the γ prefix that was successfully decoded. This partial state is used to directly read the remaining fixed bits, avoiding re-reading the γ prefix.

References

Peter Elias, “Universal codeword sets and representations of the integers”. IEEE Transactions on Information Theory, 21(2):194−203, March 1975.

Traits

DeltaRead

Trait for reading δ codes.

DeltaReadParam

Parametric trait for reading δ codes.

DeltaWrite

Trait for writing δ codes.

DeltaWriteParam

Parametric trait for writing δ codes.

Functions

len_delta

Returns the length of the δ code for n using a default value for USE_DELTA_TABLE and USE_GAMMA_TABLE.

len_delta_param

Returns the length of the δ code for n.