### DESCRIPTION

The ` qsort` function is a modified partition-exchange sort, or quicksort. The ` heapsort` function is a modified selection sort. The ` mergesort` function is a modified merge sort with exponential search intended for sorting data with pre-existing order. The ` qsort` and ` heapsort` functions sort an array of * nmemb* objects, the initial member of which is pointed to by * base*. The size of each object is specified by * size*. The ` mergesort` function behaves similarly, but * requires* that * size* be greater than ""sizeof(void *) / 2"".

The contents of the array * base* are sorted in ascending order according to a comparison function pointed to by * compar*, which requires two arguments pointing to the objects being compared.

The comparison function must return an integer less than, equal to, or greater than zero if the first argument is considered to be respectively less than, equal to, or greater than the second.

The ` qsort_r` function behaves identically to ` qsort`, except that it takes an additional argument, * thunk*, which is passed unchanged as the first argument to function pointed to * compar*. This allows the comparison function to access additional data without using global variables, and thus ` qsort_r` is suitable for use in functions which must be reentrant.

The algorithms implemented by ` qsort`, ` qsort_r`, and ` heapsort` are * not* stable, that is, if two members compare as equal, their order in the sorted array is undefined. The ` mergesort` algorithm is stable.

The ` qsort` and ` qsort_r` functions are an implementation of C.A.R. Hoare’s "quicksort" algorithm, a variant of partition-exchange sorting; in particular, see

.An D.E. Knuth Ns ’s * "Algorithm Q"*. ** Quicksort** takes O N lg N average time. This implementation uses median selection to avoid its O N**2 worst-case behavior.

The ` heapsort` function is an implementation of

.An "J.W.J. William" Ns ’s "heapsort" algorithm, a variant of selection sorting; in particular, see

.An "D.E. Knuth" Ns ’s * "Algorithm H"*. ** Heapsort** takes O N lg N worst-case time. Its * only* advantage over ` qsort` is that it uses almost no additional memory; while ` qsort` does not allocate memory, it is implemented using recursion.

The function ` mergesort` requires additional memory of size * nmemb ** * size* bytes; it should be used only when space is not at a premium. The ` mergesort` function is optimized for data with pre-existing order; its worst case time is O N lg N; its best case is O N.