xref: /csrg-svn/lib/libc/stdlib/qsort.c (revision 54201)

/*-
 * Copyright (c) 1980, 1983, 1990 The Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.redist.c%
 */

#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)qsort.c	5.10 (Berkeley) 06/22/92";
#endif /* LIBC_SCCS and not lint */

#include <sys/types.h>
#include <stdlib.h>

/*
 * XXX
 * Report from John Bentley at ATT:  the BSD qsort goes quadratic on random
 * 0 and 1  (N/2 of each.)  This is because it does not keep = elements
 * together.   (<= go before test element; > go after, > so everything gets
 * shoved before the test element, which is qsort's worst case.)
 */

/*
 * MTHRESH is the smallest partition for which we compare for a median
 * value instead of using the middle value.
 */
#define	MTHRESH	6

/*
 * THRESH is the minimum number of entries in a partition for continued
 * partitioning.
 */
#define	THRESH	4

void
qsort(bot, nmemb, size, compar)
	void *bot;
	size_t nmemb, size;
	int (*compar) __P((const void *, const void *));
{
	static void insertion_sort(), quick_sort();

	if (nmemb <= 1)
		return;

	if (nmemb >= THRESH)
		quick_sort(bot, nmemb, size, compar);
	else
		insertion_sort(bot, nmemb, size, compar);
}

/*
 * Swap two areas of size number of bytes.  Although qsort(3) permits random
 * blocks of memory to be sorted, sorting pointers is almost certainly the
 * common case (and, were it not, could easily be made so).  Regardless, it
 * isn't worth optimizing; the SWAP's get sped up by the cache, and pointer
 * arithmetic gets lost in the time required for comparison function calls.
 */
#define	SWAP(a, b) { \
	cnt = size; \
	do { \
		ch = *a; \
		*a++ = *b; \
		*b++ = ch; \
	} while (--cnt); \
}

/*
 * Knuth, Vol. 3, page 116, Algorithm Q, step b, argues that a single pass
 * of straight insertion sort after partitioning is complete is better than
 * sorting each small partition as it is created.  This isn't correct in this
 * implementation because comparisons require at least one (and often two)
 * function calls and are likely to be the dominating expense of the sort.
 * Doing a final insertion sort does more comparisons than are necessary
 * because it compares the "edges" and medians of the partitions which are
 * known to be already sorted.
 *
 * This is also the reasoning behind selecting a small THRESH value (see
 * Knuth, page 122, equation 26), since the quicksort algorithm does less
 * comparisons than the insertion sort.
 */
#define	SORT(bot, n) { \
	if (n > 1) \
		if (n == 2) { \
			t1 = bot + size; \
			if (compar(t1, bot) < 0) \
				SWAP(t1, bot); \
		} else \
			insertion_sort(bot, n, size, compar); \
}

static void
quick_sort(bot, nmemb, size, compar)
	register char *bot;
	register int size;
	int nmemb, (*compar)();
{
	register int cnt;
	register u_char ch;
	register char *top, *mid, *t1, *t2;
	register int n1, n2;
	char *bsv;
	static void insertion_sort();

	/* bot and nmemb must already be set. */
partition:

	/* find mid and top elements */
	mid = bot + size * (nmemb >> 1);
	top = bot + (nmemb - 1) * size;

	/*
	 * Find the median of the first, last and middle element (see Knuth,
	 * Vol. 3, page 123, Eq. 28).  This test order gets the equalities
	 * right.
	 */
	if (nmemb >= MTHRESH) {
		n1 = compar(bot, mid);
		n2 = compar(mid, top);
		if (n1 < 0 && n2 > 0)
			t1 = compar(bot, top) < 0 ? top : bot;
		else if (n1 > 0 && n2 < 0)
			t1 = compar(bot, top) > 0 ? top : bot;
		else
			t1 = mid;

		/* if mid element not selected, swap selection there */
		if (t1 != mid) {
			SWAP(t1, mid);
			mid -= size;
		}
	}

	/* Standard quicksort, Knuth, Vol. 3, page 116, Algorithm Q. */
#define	didswap	n1
#define	newbot	t1
#define	replace	t2
	didswap = 0;
	for (bsv = bot;;) {
		for (; bot < mid && compar(bot, mid) <= 0; bot += size);
		while (top > mid) {
			if (compar(mid, top) <= 0) {
				top -= size;
				continue;
			}
			newbot = bot + size;	/* value of bot after swap */
			if (bot == mid)		/* top <-> mid, mid == top */
				replace = mid = top;
			else {			/* bot <-> top */
				replace = top;
				top -= size;
			}
			goto swap;
		}
		if (bot == mid)
			break;

		/* bot <-> mid, mid == bot */
		replace = mid;
		newbot = mid = bot;		/* value of bot after swap */
		top -= size;

swap:		SWAP(bot, replace);
		bot = newbot;
		didswap = 1;
	}

	/*
	 * Quicksort behaves badly in the presence of data which is already
	 * sorted (see Knuth, Vol. 3, page 119) going from O N lg N to O N^2.
	 * To avoid this worst case behavior, if a re-partitioning occurs
	 * without swapping any elements, it is not further partitioned and
	 * is insert sorted.  This wins big with almost sorted data sets and
	 * only loses if the data set is very strangely partitioned.  A fix
	 * for those data sets would be to return prematurely if the insertion
	 * sort routine is forced to make an excessive number of swaps, and
	 * continue the partitioning.
	 */
	if (!didswap) {
		insertion_sort(bsv, nmemb, size, compar);
		return;
	}

	/*
	 * Re-partition or sort as necessary.  Note that the mid element
	 * itself is correctly positioned and can be ignored.
	 */
#define	nlower	n1
#define	nupper	n2
	bot = bsv;
	nlower = (mid - bot) / size;	/* size of lower partition */
	mid += size;
	nupper = nmemb - nlower - 1;	/* size of upper partition */

	/*
	 * If must call recursively, do it on the smaller partition; this
	 * bounds the stack to lg N entries.
	 */
	if (nlower > nupper) {
		if (nupper >= THRESH)
			quick_sort(mid, nupper, size, compar);
		else {
			SORT(mid, nupper);
			if (nlower < THRESH) {
				SORT(bot, nlower);
				return;
			}
		}
		nmemb = nlower;
	} else {
		if (nlower >= THRESH)
			quick_sort(bot, nlower, size, compar);
		else {
			SORT(bot, nlower);
			if (nupper < THRESH) {
				SORT(mid, nupper);
				return;
			}
		}
		bot = mid;
		nmemb = nupper;
	}
	goto partition;
	/* NOTREACHED */
}

static void
insertion_sort(bot, nmemb, size, compar)
	char *bot;
	register int size;
	int nmemb, (*compar)();
{
	register int cnt;
	register u_char ch;
	register char *s1, *s2, *t1, *t2, *top;

	/*
	 * A simple insertion sort (see Knuth, Vol. 3, page 81, Algorithm
	 * S).  Insertion sort has the same worst case as most simple sorts
	 * (O N^2).  It gets used here because it is (O N) in the case of
	 * sorted data.
	 */
	top = bot + nmemb * size;
	for (t1 = bot + size; t1 < top;) {
		for (t2 = t1; (t2 -= size) >= bot && compar(t1, t2) < 0;);
		if (t1 != (t2 += size)) {
			/* Bubble bytes up through each element. */
			for (cnt = size; cnt--; ++t1) {
				ch = *t1;
				for (s1 = s2 = t1; (s2 -= size) >= t2; s1 = s2)
					*s1 = *s2;
				*s1 = ch;
			}
		} else
			t1 += size;
	}
}