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qsort.c

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

#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)qsort.c 5.9 (Berkeley) 2/23/91";
#endif /* LIBC_SCCS and not lint */

#include "casu.h"       /* Luke, 930608 */
#if 0
#include <sys/types.h>
#include <stdlib.h>
#endif

static void insertion_sort    __PROT((char *bot, int nmemb, register int size,
                              int (*compar)()));
static void quick_sort        __PROT((char *bot, int nmemb, register int size,
                              int (*compar)()));

/*
 * 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
nqsort(bot, nmemb, size, compar)
      void *bot;
      size_t nmemb, size;
      int (*compar) __PROT((const void *, const void *));
{
      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 unsigned char ch;
      register char *top, *mid, *t1, *t2;
      register int n1, n2;
      char *bsv;

      /* 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 unsigned 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;
      }
}

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