stdlib/heapsort.c

   1 /*
   2  * Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
   3  *
   4  * @APPLE_LICENSE_HEADER_START@
   5  *
   6  * The contents of this file constitute Original Code as defined in and
   7  * are subject to the Apple Public Source License Version 1.1 (the
   8  * "License").  You may not use this file except in compliance with the
   9  * License.  Please obtain a copy of the License at
  10  * http://www.apple.com/publicsource and read it before using this file.
  11  *
  12  * This Original Code and all software distributed under the License are
  13  * distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, EITHER
  14  * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
  15  * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
  16  * FITNESS FOR A PARTICULAR PURPOSE OR NON-INFRINGEMENT.  Please see the
  17  * License for the specific language governing rights and limitations
  18  * under the License.
  19  *
  20  * @APPLE_LICENSE_HEADER_END@
  21  */
  22 /*
  23  * Copyright (c) 1991, 1993
  24  *      The Regents of the University of California.  All rights reserved.
  25  *
  26  * This code is derived from software contributed to Berkeley by
  27  * Ronnie Kon at Mindcraft Inc., Kevin Lew and Elmer Yglesias.
  28  *
  29  * Redistribution and use in source and binary forms, with or without
  30  * modification, are permitted provided that the following conditions
  31  * are met:
  32  * 1. Redistributions of source code must retain the above copyright
  33  *    notice, this list of conditions and the following disclaimer.
  34  * 2. Redistributions in binary form must reproduce the above copyright
  35  *    notice, this list of conditions and the following disclaimer in the
  36  *    documentation and/or other materials provided with the distribution.
  37  * 3. All advertising materials mentioning features or use of this software
  38  *    must display the following acknowledgement:
  39  *      This product includes software developed by the University of
  40  *      California, Berkeley and its contributors.
  41  * 4. Neither the name of the University nor the names of its contributors
  42  *    may be used to endorse or promote products derived from this software
  43  *    without specific prior written permission.
  44  *
  45  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  46  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  47  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  48  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  49  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  50  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  51  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  52  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  53  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  54  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  55  * SUCH DAMAGE.
  56  */
  57
  58
  59 #include <sys/types.h>
  60 #include <errno.h>
  61 #include <stdlib.h>
  62 #include <stddef.h>
  63
  64 /*
  65  * Swap two areas of size number of bytes.  Although qsort(3) permits random
  66  * blocks of memory to be sorted, sorting pointers is almost certainly the
  67  * common case (and, were it not, could easily be made so).  Regardless, it
  68  * isn't worth optimizing; the SWAP's get sped up by the cache, and pointer
  69  * arithmetic gets lost in the time required for comparison function calls.
  70  */
  71 #define SWAP(a, b, count, size, tmp) { \
  72         count = size; \
  73         do { \
  74                 tmp = *a; \
  75                 *a++ = *b; \
  76                 *b++ = tmp; \
  77         } while (--count); \
  78 }
  79
  80 /* Copy one block of size size to another. */
  81 #define COPY(a, b, count, size, tmp1, tmp2) { \
  82         count = size; \
  83         tmp1 = a; \
  84         tmp2 = b; \
  85         do { \
  86                 *tmp1++ = *tmp2++; \
  87         } while (--count); \
  88 }
  89
  90 /*
  91  * Build the list into a heap, where a heap is defined such that for
  92  * the records K1 ... KN, Kj/2 >= Kj for 1 <= j/2 <= j <= N.
  93  *
  94  * There two cases.  If j == nmemb, select largest of Ki and Kj.  If
  95  * j < nmemb, select largest of Ki, Kj and Kj+1.
  96  */
  97 #define CREATE(initval, nmemb, par_i, child_i, par, child, size, count, tmp) { \
  98         for (par_i = initval; (child_i = par_i * 2) <= nmemb; \
  99             par_i = child_i) { \
 100                 child = base + child_i * size; \
 101                 if (child_i < nmemb && compar(child, child + size) < 0) { \
 102                         child += size; \
 103                         ++child_i; \
 104                 } \
 105                 par = base + par_i * size; \
 106                 if (compar(child, par) <= 0) \
 107                         break; \
 108                 SWAP(par, child, count, size, tmp); \
 109         } \
 110 }
 111
 112 /*
 113  * Select the top of the heap and 'heapify'.  Since by far the most expensive
 114  * action is the call to the compar function, a considerable optimization
 115  * in the average case can be achieved due to the fact that k, the displaced
 116  * elememt, is ususally quite small, so it would be preferable to first
 117  * heapify, always maintaining the invariant that the larger child is copied
 118  * over its parent's record.
 119  *
 120  * Then, starting from the *bottom* of the heap, finding k's correct place,
 121  * again maintianing the invariant.  As a result of the invariant no element
 122  * is 'lost' when k is assigned its correct place in the heap.
 123  *
 124  * The time savings from this optimization are on the order of 15-20% for the
 125  * average case. See Knuth, Vol. 3, page 158, problem 18.
 126  *
 127  * XXX Don't break the #define SELECT line, below.  Reiser cpp gets upset.
 128  */
 129 #define SELECT(par_i, child_i, nmemb, par, child, size, k, count, tmp1, tmp2) { \
 130         for (par_i = 1; (child_i = par_i * 2) <= nmemb; par_i = child_i) { \
 131                 child = base + child_i * size; \
 132                 if (child_i < nmemb && compar(child, child + size) < 0) { \
 133                         child += size; \
 134                         ++child_i; \
 135                 } \
 136                 par = base + par_i * size; \
 137                 COPY(par, child, count, size, tmp1, tmp2); \
 138         } \
 139         for (;;) { \
 140                 child_i = par_i; \
 141                 par_i = child_i / 2; \
 142                 child = base + child_i * size; \
 143                 par = base + par_i * size; \
 144                 if (child_i == 1 || compar(k, par) < 0) { \
 145                         COPY(child, k, count, size, tmp1, tmp2); \
 146                         break; \
 147                 } \
 148                 COPY(child, par, count, size, tmp1, tmp2); \
 149         } \
 150 }
 151
 152 /*
 153  * Heapsort -- Knuth, Vol. 3, page 145.  Runs in O (N lg N), both average
 154  * and worst.  While heapsort is faster than the worst case of quicksort,
 155  * the BSD quicksort does median selection so that the chance of finding
 156  * a data set that will trigger the worst case is nonexistent.  Heapsort's
 157  * only advantage over quicksort is that it requires little additional memory.
 158  */
 159 int
 160 heapsort(vbase, nmemb, size, compar)
 161         void *vbase;
 162         size_t nmemb, size;
 163         int (*compar) __P((const void *, const void *));
 164 {
 165         register int cnt, i, j, l;
 166         register char tmp, *tmp1, *tmp2;
 167         char *base, *k, *p, *t;
 168
 169         if (nmemb <= 1)
 170                 return (0);
 171
 172         if (!size) {
 173                 errno = EINVAL;
 174                 return (-1);
 175         }
 176
 177         if ((k = malloc(size)) == NULL)
 178                 return (-1);
 179
 180         /*
 181          * Items are numbered from 1 to nmemb, so offset from size bytes
 182          * below the starting address.
 183          */
 184         base = (char *)vbase - size;
 185
 186         for (l = nmemb / 2 + 1; --l;)
 187                 CREATE(l, nmemb, i, j, t, p, size, cnt, tmp);
 188
 189         /*
 190          * For each element of the heap, save the largest element into its
 191          * final slot, save the displaced element (k), then recreate the
 192          * heap.
 193          */
 194         while (nmemb > 1) {
 195                 COPY(k, base + nmemb * size, cnt, size, tmp1, tmp2);
 196                 COPY(base + nmemb * size, base + size, cnt, size, tmp1, tmp2);
 197                 --nmemb;
 198                 SELECT(i, j, nmemb, t, p, size, k, cnt, tmp1, tmp2);
 199         }
 200         free(k);
 201         return (0);
 202 }