cosmopolitan/libc/mem/mergesort.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8                                   :vi │
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright (c) 1991, 1993                                                     │
│      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. 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 "libc/macros.internal.h"
#include "libc/mem/alg.h"
#include "libc/mem/mem.h"
#include "libc/str/str.h"
#include "libc/sysv/errfuns.h"
__static_yoink("openbsd_sorting_notice");
// clang-format off

/*
 * Hybrid exponential search/linear search merge sort with hybrid
 * natural/pairwise first pass.  Requires about .3% more comparisons
 * for random data than LSMS with pairwise first pass alone.
 * It works for objects as small as two bytes.
 */

#define NATURAL
#define THRESHOLD 16	/* Best choice for natural merge cut-off. */

/* #define NATURAL to get hybrid natural merge.
 * (The default is pairwise merging.)
 */

static void setup(uint8_t *, uint8_t *, size_t, size_t, int (*)(const void *, const void *, void *), void *);
static void insertionsort(uint8_t *, size_t, size_t, int (*)(const void *, const void *, void *), void *);

#define ISIZE sizeof(int)
#define PSIZE sizeof(uint8_t *)
#define ICOPY_LIST(src, dst, last)				\
	do							\
	*(int*)dst = *(int*)src, src += ISIZE, dst += ISIZE;	\
	while(src < last)
#define ICOPY_ELT(src, dst, i)					\
	do							\
	*(int*) dst = *(int*) src, src += ISIZE, dst += ISIZE;	\
	while (i -= ISIZE)

#define CCOPY_LIST(src, dst, last)		\
	do					\
		*dst++ = *src++;		\
	while (src < last)
#define CCOPY_ELT(src, dst, i)			\
	do					\
		*dst++ = *src++;		\
	while (i -= 1)

/*
 * Find the next possible pointer head.  (Trickery for forcing an array
 * to do double duty as a linked list when objects do not align with word
 * boundaries.
 */
/* Assumption: PSIZE is a power of 2. */
#define EVAL(p) (uint8_t **)						\
	((uint8_t *)0 +							\
	    (((uint8_t *)p + PSIZE - 1 - (uint8_t *) 0) & ~(PSIZE - 1)))

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

/**
 * Sorts array w/ optional callback argument.
 *
 * @param base is base of array
 * @param nmemb is item count
 * @param size is item width
 * @param cmp is a callback returning <0, 0, or >0
 * @param z will optionally be passed as the third argument to cmp
 * @see mergesort()
 */
int
mergesort_r(void *base, size_t nmemb, size_t size,
	    int (*cmp)(const void *, const void *, void *), void *z)
{
	int i, sense;
	int big, iflag;
	uint8_t *f1, *f2, *t, *b, *tp2, *q, *l1, *l2;
	uint8_t *list2, *list1, *p2, *p, *last, **p1;

	if (size < PSIZE / 2)		/* Pointers must fit into 2 * size. */
		return (einval());

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

	/*
	 * XXX
	 * Stupid subtraction for the Cray.
	 */
	iflag = 0;
	if (!(size % ISIZE) && !(((char *)base - (char *)0) % ISIZE))
		iflag = 1;

	if ((list2 = malloc(nmemb * size + PSIZE)) == NULL)
		return (-1);

	list1 = base;
	setup(list1, list2, nmemb, size, cmp, z);
	last = list2 + nmemb * size;
	i = big = 0;
	while (*EVAL(list2) != last) {
	    l2 = list1;
	    p1 = EVAL(list1);
	    for (tp2 = p2 = list2; p2 != last; p1 = EVAL(l2)) {
	    	p2 = *EVAL(p2);
	    	f1 = l2;
	    	f2 = l1 = list1 + (p2 - list2);
	    	if (p2 != last)
	    		p2 = *EVAL(p2);
	    	l2 = list1 + (p2 - list2);
	    	while (f1 < l1 && f2 < l2) {
	    		if ((*cmp)(f1, f2, z) <= 0) {
	    			q = f2;
	    			b = f1, t = l1;
	    			sense = -1;
	    		} else {
	    			q = f1;
	    			b = f2, t = l2;
	    			sense = 0;
	    		}
	    		if (!big) {	/* here i = 0 */
	    			while ((b += size) < t && cmp(q, b, z) >sense)
	    				if (++i == 6) {
	    					big = 1;
	    					goto EXPONENTIAL;
	    				}
	    		} else {
EXPONENTIAL:	    		for (i = size; ; i <<= 1)
	    				if ((p = (b + i)) >= t) {
	    					if ((p = t - size) > b &&
						    (*cmp)(q, p, z) <= sense)
	    						t = p;
	    					else
	    						b = p;
	    					break;
	    				} else if ((*cmp)(q, p, z) <= sense) {
	    					t = p;
	    					if (i == size)
	    						big = 0; 
	    					goto FASTCASE;
	    				} else
	    					b = p;
		    		while (t > b+size) {
	    				i = (((t - b) / size) >> 1) * size;
	    				if ((*cmp)(q, p = b + i, z) <= sense)
	    					t = p;
	    				else
	    					b = p;
	    			}
	    			goto COPY;
FASTCASE:	    		while (i > size)
	    				if ((*cmp)(q, p = b + (i >>= 1), z)
					    <= sense)
	    					t = p;
	    				else
	    					b = p;
COPY:	    			b = t;
	    		}
	    		i = size;
	    		if (q == f1) {
	    			if (iflag) {
	    				ICOPY_LIST(f2, tp2, b);
	    				ICOPY_ELT(f1, tp2, i);
	    			} else {
	    				CCOPY_LIST(f2, tp2, b);
	    				CCOPY_ELT(f1, tp2, i);
	    			}
	    		} else {
	    			if (iflag) {
	    				ICOPY_LIST(f1, tp2, b);
	    				ICOPY_ELT(f2, tp2, i);
	    			} else {
	    				CCOPY_LIST(f1, tp2, b);
	    				CCOPY_ELT(f2, tp2, i);
	    			}
	    		}
	    	}
	    	if (f2 < l2) {
	    		if (iflag)
	    			ICOPY_LIST(f2, tp2, l2);
	    		else
	    			CCOPY_LIST(f2, tp2, l2);
	    	} else if (f1 < l1) {
	    		if (iflag)
	    			ICOPY_LIST(f1, tp2, l1);
	    		else
	    			CCOPY_LIST(f1, tp2, l1);
	    	}
	    	*p1 = l2;
	    }
	    tp2 = list1;	/* swap list1, list2 */
	    list1 = list2;
	    list2 = tp2;
	    last = list2 + nmemb*size;
	}
	if (base == list2) {
		memmove(list2, list1, nmemb*size);
		list2 = list1;
	}
	free(list2);
	return (0);
}

#define	swap(a, b) {					\
		s = b;					\
		i = size;				\
		do {					\
			tmp = *a; *a++ = *s; *s++ = tmp; \
		} while (--i);				\
		a -= size;				\
	}
#define reverse(bot, top) {				\
	s = top;					\
	do {						\
		i = size;				\
		do {					\
			tmp = *bot; *bot++ = *s; *s++ = tmp; \
		} while (--i);				\
		s -= size2;				\
	} while(bot < s);				\
}

/*
 * Optional hybrid natural/pairwise first pass.  Eats up list1 in runs of
 * increasing order, list2 in a corresponding linked list.  Checks for runs
 * when THRESHOLD/2 pairs compare with same sense.  (Only used when NATURAL
 * is defined.  Otherwise simple pairwise merging is used.)
 */
void
setup(uint8_t *list1, uint8_t *list2, size_t n, size_t size,
      int (*cmp)(const void *, const void *, void *), void *z)
{
	int i, length, size2, sense;
	uint8_t tmp, *f1, *f2, *s, *l2, *last, *p2;

	size2 = size*2;
	if (n <= 5) {
		insertionsort(list1, n, size, cmp, z);
		*EVAL(list2) = (uint8_t*) list2 + n*size;
		return;
	}
	/*
	 * Avoid running pointers out of bounds; limit n to evens
	 * for simplicity.
	 */
	i = 4 + (n & 1);
	insertionsort(list1 + (n - i) * size, i, size, cmp, z);
	last = list1 + size * (n - i);
	*EVAL(list2 + (last - list1)) = list2 + n * size;

#ifdef NATURAL
	p2 = list2;
	f1 = list1;
	sense = (cmp(f1, f1 + size, z) > 0);
	for (; f1 < last; sense = !sense) {
		length = 2;
					/* Find pairs with same sense. */
		for (f2 = f1 + size2; f2 < last; f2 += size2) {
			if ((cmp(f2, f2+ size, z) > 0) != sense)
				break;
			length += 2;
		}
		if (length < THRESHOLD) {		/* Pairwise merge */
			do {
				p2 = *EVAL(p2) = f1 + size2 - list1 + list2;
				if (sense > 0)
					swap (f1, f1 + size);
			} while ((f1 += size2) < f2);
		} else {				/* Natural merge */
			l2 = f2;
			for (f2 = f1 + size2; f2 < l2; f2 += size2) {
				if ((cmp(f2-size, f2, z) > 0) != sense) {
					p2 = *EVAL(p2) = f2 - list1 + list2;
					if (sense > 0)
						reverse(f1, f2-size);
					f1 = f2;
				}
			}
			if (sense > 0)
				reverse (f1, f2-size);
			f1 = f2;
			if (f2 < last || cmp(f2 - size, f2, z) > 0)
				p2 = *EVAL(p2) = f2 - list1 + list2;
			else
				p2 = *EVAL(p2) = list2 + n*size;
		}
	}
#else		/* pairwise merge only. */
	for (f1 = list1, p2 = list2; f1 < last; f1 += size2) {
		p2 = *EVAL(p2) = p2 + size2;
		if (cmp (f1, f1 + size, z) > 0)
			swap(f1, f1 + size);
	}
#endif /* NATURAL */
}

/*
 * This is to avoid out-of-bounds addresses in sorting the
 * last 4 elements.
 */
static void
insertionsort(uint8_t *a, size_t n, size_t size,
	      int (*cmp)(const void *, const void *, void *), void *z)
{
	uint8_t *ai, *s, *t, *u, tmp;
	int i;

	for (ai = a+size; --n >= 1; ai += size)
		for (t = ai; t > a; t -= size) {
			u = t - size;
			if (cmp(u, t, z) <= 0)
				break;
			swap(u, t);
		}
}