Integer (computer science) at least 32 bits on any computer. Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. A "short integer" can represent a whole number that may take less storage, while having a smaller range, compared with a standard integer on the same machine. In C, it is denoted by short. It is required to be at least 16 bits, and is often smaller than a standard integer, but this is not required. A
Integer sorting which runs in time ; this is an improvement over comparison sorting for any choice of and . An alternative version of their algorithm that includes the use of random numbers and integer division operations improves this to . Since their work, even better algorithms have been developed. For instance, by repeatedly applying the Kirkpatrick–Reisch range reduction technique until the keys are small enough to apply the Albers–Hagerup packed sorting algorithm, it is possible to sort in time ; however, the range reduction part of this algorithm requires either a large memory (proportional to ) or randomization in the form