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
Comparison sort An identical upper bound follows from the existence of the algorithms that attain this bound in the worst case. The above argument provides an "absolute", rather than only asymptotic lower bound on the number of comparisons, namely formula_8 comparisons. This lower bound is fairly good (it can be approached within a linear tolerance by a simple merge sort), but it is known to be inexact. For example, formula_9, but the minimal number of comparisons to sort 13 elements has been proved to be 34. Determining the "exact" number of comparisons needed to sort a given number of entries is a