IABSD.fr/src/lib/libc/stdlib/heapsort.c

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• Author : millert
  Date : 2017-05-20 12:48:56
  Hash : 4520aa4f
  Message : Use David Musser's introsort algorithm to fall back to heapsort(3) when the recursion depth reaches 2*lg(n + 1). This avoids quicksort's quadratic behavior for pathological input without appreciably changing the average run time.

• lib/libc/stdlib/heapsort.c

• /*	$OpenBSD: heapsort.c,v 1.11 2017/05/20 12:48:56 millert Exp $ */
  /*-
   * Copyright (c) 1991, 1993
   *	The Regents of the University of California.  All rights reserved.
   *
   * This code is derived from software contributed to Berkeley by
   * Ronnie Kon at Mindcraft Inc., Kevin Lew and Elmer Yglesias.
   *
   * 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. 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.
   */
  
  #include <sys/types.h>
  #include <errno.h>
  #include <stdlib.h>
  
  /*
   * 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, count, size, tmp) { \
  	count = size; \
  	do { \
  		tmp = *a; \
  		*a++ = *b; \
  		*b++ = tmp; \
  	} while (--count); \
  }
  
  /* Copy one block of size size to another. */
  #define COPY(a, b, count, size, tmp1, tmp2) { \
  	count = size; \
  	tmp1 = a; \
  	tmp2 = b; \
  	do { \
  		*tmp1++ = *tmp2++; \
  	} while (--count); \
  }
  
  /*
   * Build the list into a heap, where a heap is defined such that for
   * the records K1 ... KN, Kj/2 >= Kj for 1 <= j/2 <= j <= N.
   *
   * There are two cases.  If j == nmemb, select largest of Ki and Kj.  If
   * j < nmemb, select largest of Ki, Kj and Kj+1.
   */
  #define CREATE(initval, nmemb, par_i, child_i, par, child, size, count, tmp) { \
  	for (par_i = initval; (child_i = par_i * 2) <= nmemb; \
  	    par_i = child_i) { \
  		child = base + child_i * size; \
  		if (child_i < nmemb && compar(child, child + size) < 0) { \
  			child += size; \
  			++child_i; \
  		} \
  		par = base + par_i * size; \
  		if (compar(child, par) <= 0) \
  			break; \
  		SWAP(par, child, count, size, tmp); \
  	} \
  }
  
  /*
   * Select the top of the heap and 'heapify'.  Since by far the most expensive
   * action is the call to the compar function, a considerable optimization
   * in the average case can be achieved due to the fact that k, the displaced
   * element, is usually quite small, so it would be preferable to first
   * heapify, always maintaining the invariant that the larger child is copied
   * over its parent's record.
   *
   * Then, starting from the *bottom* of the heap, finding k's correct place,
   * again maintaining the invariant.  As a result of the invariant no element
   * is 'lost' when k is assigned its correct place in the heap.
   *
   * The time savings from this optimization are on the order of 15-20% for the
   * average case. See Knuth, Vol. 3, page 158, problem 18.
   *
   * XXX Don't break the #define SELECT line, below.  Reiser cpp gets upset.
   */
  #define SELECT(par_i, child_i, nmemb, par, child, size, k, count, tmp1, tmp2) { \
  	for (par_i = 1; (child_i = par_i * 2) <= nmemb; par_i = child_i) { \
  		child = base + child_i * size; \
  		if (child_i < nmemb && compar(child, child + size) < 0) { \
  			child += size; \
  			++child_i; \
  		} \
  		par = base + par_i * size; \
  		COPY(par, child, count, size, tmp1, tmp2); \
  	} \
  	for (;;) { \
  		child_i = par_i; \
  		par_i = child_i / 2; \
  		child = base + child_i * size; \
  		par = base + par_i * size; \
  		if (child_i == 1 || compar(k, par) < 0) { \
  			COPY(child, k, count, size, tmp1, tmp2); \
  			break; \
  		} \
  		COPY(child, par, count, size, tmp1, tmp2); \
  	} \
  }
  
  /*
   * Heapsort -- Knuth, Vol. 3, page 145.  Runs in O (N lg N), both average
   * and worst.  While heapsort is faster than the worst case of quicksort,
   * the BSD quicksort does median selection so that the chance of finding
   * a data set that will trigger the worst case is nonexistent.  Heapsort's
   * only advantage over quicksort is that it requires little additional memory.
   */
  int
  heapsort(void *vbase, size_t nmemb, size_t size,
      int (*compar)(const void *, const void *))
  {
  	size_t cnt, i, j, l;
  	char tmp, *tmp1, *tmp2;
  	char *base, *k, *p, *t;
  
  	if (nmemb <= 1)
  		return (0);
  
  	if (!size) {
  		errno = EINVAL;
  		return (-1);
  	}
  
  	if ((k = malloc(size)) == NULL)
  		return (-1);
  
  	/*
  	 * Items are numbered from 1 to nmemb, so offset from size bytes
  	 * below the starting address.
  	 */
  	base = (char *)vbase - size;
  
  	for (l = nmemb / 2 + 1; --l;)
  		CREATE(l, nmemb, i, j, t, p, size, cnt, tmp);
  
  	/*
  	 * For each element of the heap, save the largest element into its
  	 * final slot, save the displaced element (k), then recreate the
  	 * heap.
  	 */
  	while (nmemb > 1) {
  		COPY(k, base + nmemb * size, cnt, size, tmp1, tmp2);
  		COPY(base + nmemb * size, base + size, cnt, size, tmp1, tmp2);
  		--nmemb;
  		SELECT(i, j, nmemb, t, p, size, k, cnt, tmp1, tmp2);
  	}
  	free(k);
  	return (0);
  }
  DEF_WEAK(heapsort);