[apple/libc.git] / stdlib / FreeBSD / merge.c

/*-
 * Copyright (c) 1992, 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Peter McIlroy.
 *
 * 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.
 * 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[] = "@(#)merge.c	8.2 (Berkeley) 2/14/94";
#endif /* LIBC_SCCS and not lint */
#include <sys/cdefs.h>
__FBSDID("$FreeBSD: src/lib/libc/stdlib/merge.c,v 1.8 2007/01/09 00:28:10 imp Exp $");

/*
 * 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.)
 */

#include <sys/types.h>

#include <errno.h>
#include <stdlib.h>
#include <string.h>

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

#define ISIZE sizeof(int)
#define PSIZE sizeof(u_char *)
#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) (u_char **)						\
	((u_char *)0 +							\
	    (((u_char *)p + PSIZE - 1 - (u_char *) 0) & ~(PSIZE - 1)))

/*
 * Arguments are as for qsort.
 */
int
mergesort(base, nmemb, size, cmp)
	void *base;
	size_t nmemb;
	size_t size;
	int (*cmp)(const void *, const void *);
{
	size_t i;
	int sense;
	int big, iflag;
	u_char *f1, *f2, *t, *b, *tp2, *q, *l1, *l2;
	u_char *list2, *list1, *p2, *p, *last, **p1;

	if (size < PSIZE / 2) {		/* Pointers must fit into 2 * size. */
		errno = EINVAL;
		return (-1);
	}

	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);
	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) <= 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) >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) <= sense)
	    						t = p;
	    					else
	    						b = p;
	    					break;
	    				} else if ((*cmp)(q, p) <= 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) <= sense)
	    					t = p;
	    				else
	    					b = p;
	    			}
	    			goto COPY;
FASTCASE:	    		while (i > size)
	    				if ((*cmp)(q,
	    					p = b + (i >>= 1)) <= 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(list1, list2, n, size, cmp)
	size_t n, size;
	int (*cmp)(const void *, const void *);
	u_char *list1, *list2;
{
	int i, length, size2, tmp, sense;
	u_char *f1, *f2, *s, *l2, *last, *p2;

	size2 = size*2;
	if (n <= 5) {
		insertionsort(list1, n, size, cmp);
		*EVAL(list2) = (u_char*) 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);
	last = list1 + size * (n - i);
	*EVAL(list2 + (last - list1)) = list2 + n * size;

#ifdef NATURAL
	p2 = list2;
	f1 = list1;
	sense = (cmp(f1, f1 + size) > 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) > 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) > 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) > 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) > 0)
			swap(f1, f1 + size);
	}
#endif /* NATURAL */
}

/*
 * This is to avoid out-of-bounds addresses in sorting the
 * last 4 elements.
 */
static void
insertionsort(a, n, size, cmp)
	u_char *a;
	size_t n, size;
	int (*cmp)(const void *, const void *);
{
	u_char *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) <= 0)
				break;
			swap(u, t);
		}
}
Commit	Line	Data
9385eb3d	1	/*-
e9ce8d39 A	2	* Copyright (c) 1992, 1993
	3	* The Regents of the University of California. All rights reserved.
	4	*
	5	* This code is derived from software contributed to Berkeley by
	6	* Peter McIlroy.
	7	*
	8	* Redistribution and use in source and binary forms, with or without
	9	* modification, are permitted provided that the following conditions
	10	* are met:
	11	* 1. Redistributions of source code must retain the above copyright
	12	* notice, this list of conditions and the following disclaimer.
	13	* 2. Redistributions in binary form must reproduce the above copyright
	14	* notice, this list of conditions and the following disclaimer in the
	15	* documentation and/or other materials provided with the distribution.
e9ce8d39 A	16	* 4. Neither the name of the University nor the names of its contributors
	17	* may be used to endorse or promote products derived from this software
	18	* without specific prior written permission.
	19	*
	20	* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	21	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	22	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	23	* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	24	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	25	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	26	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	27	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	28	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	29	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	30	* SUCH DAMAGE.
	31	*/
	32
9385eb3d A	33	#if defined(LIBC_SCCS) && !defined(lint)
	34	static char sccsid[] = "@(#)merge.c 8.2 (Berkeley) 2/14/94";
	35	#endif /* LIBC_SCCS and not lint */
	36	#include <sys/cdefs.h>
34e8f829	37	__FBSDID("$FreeBSD: src/lib/libc/stdlib/merge.c,v 1.8 2007/01/09 00:28:10 imp Exp $");
e9ce8d39 A	38
	39	/*
	40	* Hybrid exponential search/linear search merge sort with hybrid
	41	* natural/pairwise first pass. Requires about .3% more comparisons
	42	* for random data than LSMS with pairwise first pass alone.
	43	* It works for objects as small as two bytes.
	44	*/
	45
	46	#define NATURAL
	47	#define THRESHOLD 16 /* Best choice for natural merge cut-off. */
	48
	49	/* #define NATURAL to get hybrid natural merge.
	50	* (The default is pairwise merging.)
	51	*/
	52
	53	#include <sys/types.h>
	54
	55	#include <errno.h>
	56	#include <stdlib.h>
	57	#include <string.h>
	58
34e8f829 A	59	static void setup(u_char , u_char , size_t, size_t,
	60	int ()(const void , const void *));
	61	static void insertionsort(u_char *, size_t, size_t,
	62	int ()(const void , const void *));
e9ce8d39 A	63
	64	#define ISIZE sizeof(int)
	65	#define PSIZE sizeof(u_char *)
	66	#define ICOPY_LIST(src, dst, last) \
	67	do \
	68	(int)dst = (int)src, src += ISIZE, dst += ISIZE; \
	69	while(src < last)
	70	#define ICOPY_ELT(src, dst, i) \
	71	do \
	72	(int) dst = (int) src, src += ISIZE, dst += ISIZE; \
	73	while (i -= ISIZE)
	74
	75	#define CCOPY_LIST(src, dst, last) \
	76	do \
	77	dst++ = src++; \
	78	while (src < last)
	79	#define CCOPY_ELT(src, dst, i) \
	80	do \
	81	dst++ = src++; \
	82	while (i -= 1)
9385eb3d	83
e9ce8d39 A	84	/*
	85	* Find the next possible pointer head. (Trickery for forcing an array
	86	* to do double duty as a linked list when objects do not align with word
	87	* boundaries.
	88	*/
	89	/* Assumption: PSIZE is a power of 2. */
	90	#define EVAL(p) (u_char **) \
	91	((u_char *)0 + \
	92	(((u_char )p + PSIZE - 1 - (u_char ) 0) & ~(PSIZE - 1)))
	93
	94	/*
	95	* Arguments are as for qsort.
	96	*/
	97	int
	98	mergesort(base, nmemb, size, cmp)
	99	void *base;
	100	size_t nmemb;
9385eb3d A	101	size_t size;
9385eb3d A	102	int (cmp)(const void , const void *);
e9ce8d39	103	{
34e8f829 A	104	size_t i;
34e8f829 A	105	int sense;
e9ce8d39	106	int big, iflag;
9385eb3d	107	u_char f1, f2, t, b, tp2, q, l1, l2;
e9ce8d39 A	108	u_char list2, list1, p2, p, last, *p1;
	109
	110	if (size < PSIZE / 2) { /* Pointers must fit into 2 * size. */
	111	errno = EINVAL;
	112	return (-1);
	113	}
	114
9385eb3d A	115	if (nmemb == 0)
	116	return (0);
	117
e9ce8d39 A	118	/*
	119	* XXX
	120	* Stupid subtraction for the Cray.
	121	*/
	122	iflag = 0;
	123	if (!(size % ISIZE) && !(((char )base - (char )0) % ISIZE))
	124	iflag = 1;
	125
	126	if ((list2 = malloc(nmemb * size + PSIZE)) == NULL)
	127	return (-1);
	128
	129	list1 = base;
	130	setup(list1, list2, nmemb, size, cmp);
	131	last = list2 + nmemb * size;
	132	i = big = 0;
	133	while (*EVAL(list2) != last) {
	134	l2 = list1;
	135	p1 = EVAL(list1);
	136	for (tp2 = p2 = list2; p2 != last; p1 = EVAL(l2)) {
	137	p2 = *EVAL(p2);
	138	f1 = l2;
	139	f2 = l1 = list1 + (p2 - list2);
	140	if (p2 != last)
	141	p2 = *EVAL(p2);
	142	l2 = list1 + (p2 - list2);
	143	while (f1 < l1 && f2 < l2) {
	144	if ((*cmp)(f1, f2) <= 0) {
	145	q = f2;
	146	b = f1, t = l1;
	147	sense = -1;
	148	} else {
	149	q = f1;
	150	b = f2, t = l2;
	151	sense = 0;
	152	}
	153	if (!big) { /* here i = 0 */
9385eb3d	154	while ((b += size) < t && cmp(q, b) >sense)
e9ce8d39 A	155	if (++i == 6) {
	156	big = 1;
	157	goto EXPONENTIAL;
	158	}
	159	} else {
	160	EXPONENTIAL: for (i = size; ; i <<= 1)
	161	if ((p = (b + i)) >= t) {
	162	if ((p = t - size) > b &&
	163	(*cmp)(q, p) <= sense)
	164	t = p;
	165	else
	166	b = p;
	167	break;
	168	} else if ((*cmp)(q, p) <= sense) {
	169	t = p;
	170	if (i == size)
9385eb3d	171	big = 0;
e9ce8d39 A	172	goto FASTCASE;
	173	} else
	174	b = p;
9385eb3d	175	while (t > b+size) {
e9ce8d39 A	176	i = (((t - b) / size) >> 1) * size;
	177	if ((*cmp)(q, p = b + i) <= sense)
	178	t = p;
	179	else
	180	b = p;
	181	}
	182	goto COPY;
	183	FASTCASE: while (i > size)
	184	if ((*cmp)(q,
	185	p = b + (i >>= 1)) <= sense)
	186	t = p;
	187	else
	188	b = p;
	189	COPY: b = t;
	190	}
	191	i = size;
	192	if (q == f1) {
	193	if (iflag) {
	194	ICOPY_LIST(f2, tp2, b);
	195	ICOPY_ELT(f1, tp2, i);
	196	} else {
	197	CCOPY_LIST(f2, tp2, b);
	198	CCOPY_ELT(f1, tp2, i);
	199	}
	200	} else {
	201	if (iflag) {
	202	ICOPY_LIST(f1, tp2, b);
	203	ICOPY_ELT(f2, tp2, i);
	204	} else {
	205	CCOPY_LIST(f1, tp2, b);
	206	CCOPY_ELT(f2, tp2, i);
	207	}
	208	}
	209	}
	210	if (f2 < l2) {
	211	if (iflag)
	212	ICOPY_LIST(f2, tp2, l2);
	213	else
	214	CCOPY_LIST(f2, tp2, l2);
	215	} else if (f1 < l1) {
	216	if (iflag)
	217	ICOPY_LIST(f1, tp2, l1);
	218	else
	219	CCOPY_LIST(f1, tp2, l1);
	220	}
	221	*p1 = l2;
	222	}
	223	tp2 = list1; /* swap list1, list2 */
	224	list1 = list2;
	225	list2 = tp2;
	226	last = list2 + nmemb*size;
	227	}
	228	if (base == list2) {
	229	memmove(list2, list1, nmemb*size);
	230	list2 = list1;
	231	}
	232	free(list2);
	233	return (0);
	234	}
	235
	236	#define swap(a, b) { \
	237	s = b; \
	238	i = size; \
	239	do { \
240	tmp = a; a++ = s; s++ = tmp; \
241	} while (--i); \
242	a -= size; \
243	}
244	#define reverse(bot, top) { \
245	s = top; \
246	do { \
247	i = size; \
248	do { \
249	tmp = bot; bot++ = s; s++ = tmp; \
250	} while (--i); \
251	s -= size2; \
252	} while(bot < s); \
253	}
254
255	/*
256	* Optional hybrid natural/pairwise first pass. Eats up list1 in runs of
257	* increasing order, list2 in a corresponding linked list. Checks for runs
258	* when THRESHOLD/2 pairs compare with same sense. (Only used when NATURAL
259	* is defined. Otherwise simple pairwise merging is used.)
260	*/
261	void
262	setup(list1, list2, n, size, cmp)
263	size_t n, size;
9385eb3d	264	int (cmp)(const void , const void *);
e9ce8d39 A	265	u_char list1, list2;
	266	{
	267	int i, length, size2, tmp, sense;
	268	u_char f1, f2, s, l2, last, p2;
	269
	270	size2 = size*2;
	271	if (n <= 5) {
	272	insertionsort(list1, n, size, cmp);
	273	EVAL(list2) = (u_char) list2 + n*size;
	274	return;
	275	}
	276	/*
	277	* Avoid running pointers out of bounds; limit n to evens
	278	* for simplicity.
	279	*/
	280	i = 4 + (n & 1);
	281	insertionsort(list1 + (n - i) * size, i, size, cmp);
	282	last = list1 + size * (n - i);
	283	EVAL(list2 + (last - list1)) = list2 + n size;
	284
	285	#ifdef NATURAL
	286	p2 = list2;
	287	f1 = list1;
	288	sense = (cmp(f1, f1 + size) > 0);
	289	for (; f1 < last; sense = !sense) {
	290	length = 2;
	291	/* Find pairs with same sense. */
	292	for (f2 = f1 + size2; f2 < last; f2 += size2) {
	293	if ((cmp(f2, f2+ size) > 0) != sense)
	294	break;
	295	length += 2;
	296	}
	297	if (length < THRESHOLD) { /* Pairwise merge */
	298	do {
	299	p2 = *EVAL(p2) = f1 + size2 - list1 + list2;
	300	if (sense > 0)
	301	swap (f1, f1 + size);
	302	} while ((f1 += size2) < f2);
	303	} else { /* Natural merge */
	304	l2 = f2;
	305	for (f2 = f1 + size2; f2 < l2; f2 += size2) {
	306	if ((cmp(f2-size, f2) > 0) != sense) {
	307	p2 = *EVAL(p2) = f2 - list1 + list2;
	308	if (sense > 0)
	309	reverse(f1, f2-size);
	310	f1 = f2;
	311	}
	312	}
	313	if (sense > 0)
	314	reverse (f1, f2-size);
	315	f1 = f2;
	316	if (f2 < last \|\| cmp(f2 - size, f2) > 0)
	317	p2 = *EVAL(p2) = f2 - list1 + list2;
	318	else
	319	p2 = EVAL(p2) = list2 + nsize;
	320	}
	321	}
	322	#else /* pairwise merge only. */
	323	for (f1 = list1, p2 = list2; f1 < last; f1 += size2) {
	324	p2 = *EVAL(p2) = p2 + size2;
	325	if (cmp (f1, f1 + size) > 0)
	326	swap(f1, f1 + size);
	327	}
	328	#endif /* NATURAL */
329	}
330
331	/*
332	* This is to avoid out-of-bounds addresses in sorting the
333	* last 4 elements.
334	*/
335	static void
336	insertionsort(a, n, size, cmp)
337	u_char *a;
338	size_t n, size;
9385eb3d	339	int (cmp)(const void , const void *);
e9ce8d39 A	340	{
	341	u_char ai, s, t, u, tmp;
	342	int i;
	343
	344	for (ai = a+size; --n >= 1; ai += size)
	345	for (t = ai; t > a; t -= size) {
	346	u = t - size;
	347	if (cmp(u, t) <= 0)
	348	break;
	349	swap(u, t);
	350	}
	351	}