cosmopolitan/libc/mem/heapsort.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :vi│
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright (c) 1991, 1993                                                     │
│      The Regents of the University of California.  All rights reserved.      │
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│ THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND      │
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│ SUCH DAMAGE.                                                                 │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/mem/alg.h"
#include "libc/mem/mem.h"
#include "libc/sysv/errfuns.h"
// clang-format off

/*
 * 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, z) < 0) { \
			child += size; \
			++child_i; \
		} \
		par = base + par_i * size; \
		if (compar(child, par, z) <= 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, z) < 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, z) < 0) {	 \
			COPY(child, k, count, size, tmp1, tmp2); \
			break; \
		} \
		COPY(child, par, count, size, tmp1, tmp2); \
	} \
}

/**
 * Sorts array w/ optional callback argument.
 *
 * @param vbase is base of array
 * @param nmemb is item count
 * @param size is item width
 * @param compar is a callback returning <0, 0, or >0
 * @param z will optionally be passed as the third argument to cmp
 * @see heapsort()
 */
int
heapsort_r(void *vbase, size_t nmemb, size_t size,
	   int (*compar)(const void *, const void *, void *), void *z)
{
	size_t cnt, i, j, l;
	char tmp, *tmp1, *tmp2;
	char *base, *k, *p, *t;

	if (nmemb <= 1)
		return (0);

	if (!size)
		return (einval());

	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);
}

/**
 * Sorts array.
 * 
 * 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.
 * 
 * @param vbase is base of array
 * @param nmemb is item count
 * @param size is item width
 * @param compar is a callback returning <0, 0, or >0
 * @see Knuth, Vol. 3, page 145.
 * @see heapsort_r()
 * @see mergesort()
 * @see qsort()
 */
int
heapsort(void *vbase, size_t nmemb, size_t size,
	 int (*compar)(const void *, const void *))
{
	return heapsort_r(vbase, nmemb, size, (void *)compar, 0);
}