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 the square root of their previous magnitude. Repeating this range reduction until the keys are small enough to bucket sort leads to an algorithm with running time . A complicated randomized algorithm of in the word RAM model of computation allows these time bounds to be reduced even farther, to . An integer sorting algorithm is said to be "non-conservative" if it requires a word size that is significantly larger than . As an extreme instance, if , and all keys are distinct, then the set of keys may be sorted in linear time by representing it as a bitvector,