usr/src/lib/libc/stdlib/qsort.c

/*-
 * 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     5.9 (Berkeley) %G%";
#endif /* LIBC_SCCS and not lint */

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

/*
 * 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;
        }
}