Editing Elias gamma coding (section)

== Generalizations ==<!-- This section is linked from [[Elias delta coding]] -->
{{See also|Variable-length quantity#Zigzag encoding}}
Gamma coding does not code zero or negative integers.
One way of handling zero is to add 1 before coding and then subtract 1 after decoding.
Another way is to prefix each nonzero code with a 1 and then code zero as a single 0.

One way to code all integers is to set up a [[bijection]], mapping integers (0, −1, 1, −2, 2, −3, 3, ...) to (1, 2, 3, 4, 5, 6, 7, ...) before coding.  In software, this is most easily done by mapping non-negative inputs to odd outputs, and negative inputs to even outputs, so the least-significant bit becomes an inverted [[sign bit]]:<br/>
<math>\begin{cases}
x \mapsto 2x+1 & \mathrm{when~} x \geq 0 \\
x \mapsto -2x  & \mathrm{when~} x < 0 \\
\end{cases}</math>

[[Exponential-Golomb coding]] generalizes the gamma code to integers with a "flatter" power-law distribution, just as [[Golomb coding]] generalizes the unary code.
It involves dividing the number by a positive divisor, commonly a power of 2, writing the gamma code for one more than the quotient, and writing out the remainder in an ordinary binary code.