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-.\" Copyright (c) 1990, 1991, 1993
-.\"	The Regents of the University of California.  All rights reserved.
-.\"
-.\" This code is derived from software contributed to Berkeley by
-.\" the American National Standards Committee X3, on Information
-.\" Processing Systems.
-.\"
-.\" Redistribution and use in source and binary forms, with or without
-.\" modification, are permitted provided that the following conditions
-.\" are met:
-.\" 1. Redistributions of source code must retain the above copyright
-.\"    notice, this list of conditions and the following disclaimer.
-.\" 2. Redistributions in binary form must reproduce the above copyright
-.\"    notice, this list of conditions and the following disclaimer in the
-.\"    documentation and/or other materials provided with the distribution.
-.\" 3. All advertising materials mentioning features or use of this software
-.\"    must display the following acknowledgement:
-.\"	This product includes software developed by the University of
-.\"	California, Berkeley and its contributors.
-.\" 4. Neither the name of the University nor the names of its contributors
-.\"    may be used to endorse or promote products derived from this software
-.\"    without specific prior written permission.
-.\"
-.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
-.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
-.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-.\" SUCH DAMAGE.
-.\"
-.\"     @(#)qsort.3	8.1 (Berkeley) 6/4/93
-.\"
-.Dd June 4, 1993
-.Dt QSORT 3
-.Os
-.Sh NAME
-.Nm qsort, heapsort, mergesort
-.Nd sort functions
-.Sh SYNOPSIS
-.Fd #include <stdlib.h>
-.Ft void
-.Fn qsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
-.Ft int
-.Fn heapsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
-.Ft int
-.Fn mergesort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
-.Sh DESCRIPTION
-The
-.Fn qsort
-function is a modified partition-exchange sort, or quicksort.
-The
-.Fn heapsort
-function is a modified selection sort.
-The
-.Fn mergesort
-function is a modified merge sort with exponential search
-intended for sorting data with pre-existing order.
-.Pp
-The
-.Fn qsort
-and
-.Fn heapsort
-functions sort an array of
-.Fa nmemb
-objects, the initial member of which is pointed to by
-.Fa base .
-The size of each object is specified by
-.Fa size .
-.Fn Mergesort
-behaves similarly, but
-.Em requires
-that
-.Fa size
-be greater than
-.Dq "sizeof(void *) / 2" .
-.Pp
-The contents of the array
-.Fa base
-are sorted in ascending order according to
-a comparison function pointed to by
-.Fa compar ,
-which requires two arguments pointing to the objects being
-compared.
-.Pp
-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.
-.Pp
-The functions
-.Fn qsort
-and
-.Fn heapsort
-are
-.Em not
-stable, that is, if two members compare as equal, their order in
-the sorted array is undefined.
-The function
-.Fn mergesort
-is stable.
-.Pp
-The
-.Fn qsort
-function is an implementation of C.A.R. Hoare's ``quicksort'' algorithm,
-a variant of partition-exchange sorting; in particular, see D.E. Knuth's
-Algorithm Q.
-.Fn Qsort
-takes O N lg N average time.
-This implementation uses median selection to avoid its
-O N**2 worst-case behavior.
-.Pp
-The
-.Fn heapsort
-function is an implementation of J.W.J. William's ``heapsort'' algorithm,
-a variant of selection sorting; in particular, see D.E. Knuth's Algorithm H.
-.Fn Heapsort
-takes O N lg N worst-case time.
-Its
-.Em only
-advantage over
-.Fn qsort
-is that it uses almost no additional memory; while
-.Fn qsort
-does not allocate memory, it is implemented using recursion.
-.Pp
-The function
-.Fn mergesort
-requires additional memory of size
-.Fa nmemb *
-.Fa size 
-bytes; it should be used only when space is not at a premium.
-.Fn Mergesort
-is optimized for data with pre-existing order; its worst case
-time is O N lg N; its best case is O N.
-.Pp
-Normally,
-.Fn qsort
-is faster than
-.Fn mergesort
-is faster than
-.Fn heapsort .
-Memory availability and pre-existing order in the data can make this
-untrue.
-.Sh RETURN VALUES
-The
-.Fn qsort
-function
-returns no value.
-.Pp
-Upon successful completion,
-.Fn heapsort
-and
-.Fn mergesort
-return 0.
-Otherwise, they return \-1 and the global variable
-.Va errno
-is set to indicate the error.
-.Sh ERRORS
-The
-.Fn heapsort
-function succeeds unless:
-.Bl -tag -width Er
-.It Bq Er EINVAL
-The
-.Fa size
-argument is zero, or,
-the
-.Fa size
-argument to
-.Fn mergesort
-is less than
-.Dq "sizeof(void *) / 2" .
-.It Bq Er ENOMEM
-.Fn Heapsort
-or
-.Fn mergesort
-were unable to allocate memory.
-.El
-.Sh COMPATIBILITY
-Previous versions of
-.Fn qsort
-did not permit the comparison routine itself to call
-.Fn qsort 3 .
-This is no longer true.
-.Sh SEE ALSO
-.Xr sort 1 ,
-.Xr radixsort 3
-.Rs
-.%A Hoare, C.A.R.
-.%D 1962
-.%T "Quicksort"
-.%J "The Computer Journal"
-.%V 5:1
-.%P pp. 10-15
-.Re
-.Rs
-.%A Williams, J.W.J
-.%D 1964
-.%T "Heapsort"
-.%J "Communications of the ACM"
-.%V 7:1
-.%P pp. 347-348
-.Re
-.Rs
-.%A Knuth, D.E.
-.%D 1968
-.%B "The Art of Computer Programming"
-.%V Vol. 3
-.%T "Sorting and Searching"
-.%P pp. 114-123, 145-149
-.Re
-.Rs
-.%A Mcilroy, P.M.
-.%T "Optimistic Sorting and Information Theoretic Complexity"
-.%J "Fourth Annual ACM-SIAM Symposium on Discrete Algorithms"
-.%V January 1992
-.Re
-.Rs
-.%A Bentley, J.L.
-.%T "Engineering a Sort Function"
-.%J "bentley@research.att.com"
-.%V January 1992
-.Re
-.Sh STANDARDS
-The
-.Fn qsort
-function
-conforms to
-.St -ansiC .