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

/*
 * Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
 *
 * @APPLE_LICENSE_HEADER_START@
 * 
 * Copyright (c) 1999-2003 Apple Computer, Inc.  All Rights Reserved.
 * 
 * This file contains Original Code and/or Modifications of Original Code
 * as defined in and that are subject to the Apple Public Source License
 * Version 2.0 (the 'License'). You may not use this file except in
 * compliance with the License. Please obtain a copy of the License at
 * http://www.opensource.apple.com/apsl/ and read it before using this
 * file.
 * 
 * The Original Code and all software distributed under the License are
 * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
 * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
 * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT.
 * Please see the License for the specific language governing rights and
 * limitations under the License.
 * 
 * @APPLE_LICENSE_HEADER_END@
 */
/*
 * 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.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *	This product includes software developed by the University of
 *	California, Berkeley and its contributors.
 * 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.
 */


/*
 * 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 __P((u_char *, u_char *, size_t, size_t, int (*)()));
static void insertionsort __P((u_char *, size_t, size_t, int (*)()));

#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;
	register size_t size;
	int (*cmp) __P((const void *, const void *));
{
	register int i, sense;
	int big, iflag;
	register 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);
	}

	/*
	 * 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 */
LINEAR:	    			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;
SLOWCASE:	    		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) __P((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) __P((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
e9ce8d39 A	1	/*
	2	* Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
	3	*
	4	* @APPLE_LICENSE_HEADER_START@
	5	*
734aad71	6	* Copyright (c) 1999-2003 Apple Computer, Inc. All Rights Reserved.
e9ce8d39	7	*
734aad71 A	8	* This file contains Original Code and/or Modifications of Original Code
	9	* as defined in and that are subject to the Apple Public Source License
	10	* Version 2.0 (the 'License'). You may not use this file except in
	11	* compliance with the License. Please obtain a copy of the License at
	12	* http://www.opensource.apple.com/apsl/ and read it before using this
	13	* file.
	14	*
	15	* The Original Code and all software distributed under the License are
	16	* distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
e9ce8d39 A	17	* EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
e9ce8d39 A	18	* INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
734aad71 A	19	* FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT.
	20	* Please see the License for the specific language governing rights and
	21	* limitations under the License.
e9ce8d39 A	22	*
	23	* @APPLE_LICENSE_HEADER_END@
	24	*/
	25	/*
	26	* Copyright (c) 1992, 1993
	27	* The Regents of the University of California. All rights reserved.
	28	*
	29	* This code is derived from software contributed to Berkeley by
	30	* Peter McIlroy.
	31	*
	32	* Redistribution and use in source and binary forms, with or without
	33	* modification, are permitted provided that the following conditions
	34	* are met:
	35	* 1. Redistributions of source code must retain the above copyright
	36	* notice, this list of conditions and the following disclaimer.
	37	* 2. Redistributions in binary form must reproduce the above copyright
	38	* notice, this list of conditions and the following disclaimer in the
	39	* documentation and/or other materials provided with the distribution.
	40	* 3. All advertising materials mentioning features or use of this software
	41	* must display the following acknowledgement:
	42	* This product includes software developed by the University of
	43	* California, Berkeley and its contributors.
	44	* 4. Neither the name of the University nor the names of its contributors
	45	* may be used to endorse or promote products derived from this software
	46	* without specific prior written permission.
	47	*
	48	* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	49	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	50	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	51	* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	52	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	53	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	54	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	55	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	56	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	57	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	58	* SUCH DAMAGE.
	59	*/
	60
	61
	62	/*
	63	* Hybrid exponential search/linear search merge sort with hybrid
	64	* natural/pairwise first pass. Requires about .3% more comparisons
	65	* for random data than LSMS with pairwise first pass alone.
	66	* It works for objects as small as two bytes.
	67	*/
	68
	69	#define NATURAL
	70	#define THRESHOLD 16 /* Best choice for natural merge cut-off. */
	71
	72	/* #define NATURAL to get hybrid natural merge.
	73	* (The default is pairwise merging.)
	74	*/
	75
	76	#include <sys/types.h>
	77
	78	#include <errno.h>
	79	#include <stdlib.h>
	80	#include <string.h>
	81
	82	static void setup __P((u_char , u_char , size_t, size_t, int (*)()));
	83	static void insertionsort __P((u_char , size_t, size_t, int ()()));
	84
	85	#define ISIZE sizeof(int)
86	#define PSIZE sizeof(u_char *)
87	#define ICOPY_LIST(src, dst, last) \
88	do \
89	(int)dst = (int)src, src += ISIZE, dst += ISIZE; \
90	while(src < last)
91	#define ICOPY_ELT(src, dst, i) \
92	do \
93	(int) dst = (int) src, src += ISIZE, dst += ISIZE; \
94	while (i -= ISIZE)
95
96	#define CCOPY_LIST(src, dst, last) \
97	do \
98	dst++ = src++; \
99	while (src < last)
100	#define CCOPY_ELT(src, dst, i) \
101	do \
102	dst++ = src++; \
103	while (i -= 1)
104
105	/*
106	* Find the next possible pointer head. (Trickery for forcing an array
107	* to do double duty as a linked list when objects do not align with word
108	* boundaries.
109	*/
110	/* Assumption: PSIZE is a power of 2. */
111	#define EVAL(p) (u_char **) \
112	((u_char *)0 + \
113	(((u_char )p + PSIZE - 1 - (u_char ) 0) & ~(PSIZE - 1)))
114
115	/*
116	* Arguments are as for qsort.
117	*/
118	int
119	mergesort(base, nmemb, size, cmp)
120	void *base;
121	size_t nmemb;
122	register size_t size;
123	int (cmp) __P((const void , const void *));
124	{
125	register int i, sense;
126	int big, iflag;
127	register u_char f1, f2, t, b, tp2, q, l1, l2;
128	u_char list2, list1, p2, p, last, *p1;
129
130	if (size < PSIZE / 2) { /* Pointers must fit into 2 * size. */
131	errno = EINVAL;
132	return (-1);
133	}
134
135	/*
136	* XXX
137	* Stupid subtraction for the Cray.
138	*/
139	iflag = 0;
140	if (!(size % ISIZE) && !(((char )base - (char )0) % ISIZE))
141	iflag = 1;
142
143	if ((list2 = malloc(nmemb * size + PSIZE)) == NULL)
144	return (-1);
145
146	list1 = base;
147	setup(list1, list2, nmemb, size, cmp);
148	last = list2 + nmemb * size;
149	i = big = 0;
150	while (*EVAL(list2) != last) {
151	l2 = list1;
152	p1 = EVAL(list1);
153	for (tp2 = p2 = list2; p2 != last; p1 = EVAL(l2)) {
154	p2 = *EVAL(p2);
155	f1 = l2;
156	f2 = l1 = list1 + (p2 - list2);
157	if (p2 != last)
158	p2 = *EVAL(p2);
159	l2 = list1 + (p2 - list2);
160	while (f1 < l1 && f2 < l2) {
161	if ((*cmp)(f1, f2) <= 0) {
162	q = f2;
163	b = f1, t = l1;
164	sense = -1;
165	} else {
166	q = f1;
167	b = f2, t = l2;
168	sense = 0;
169	}
170	if (!big) { /* here i = 0 */
171	LINEAR: while ((b += size) < t && cmp(q, b) >sense)
172	if (++i == 6) {
173	big = 1;
174	goto EXPONENTIAL;
175	}
176	} else {
177	EXPONENTIAL: for (i = size; ; i <<= 1)
178	if ((p = (b + i)) >= t) {
179	if ((p = t - size) > b &&
180	(*cmp)(q, p) <= sense)
181	t = p;
182	else
183	b = p;
184	break;
185	} else if ((*cmp)(q, p) <= sense) {
186	t = p;
187	if (i == size)
188	big = 0;
189	goto FASTCASE;
190	} else
191	b = p;
192	SLOWCASE: while (t > b+size) {
193	i = (((t - b) / size) >> 1) * size;
194	if ((*cmp)(q, p = b + i) <= sense)
195	t = p;
196	else
197	b = p;
198	}
199	goto COPY;
200	FASTCASE: while (i > size)
201	if ((*cmp)(q,
202	p = b + (i >>= 1)) <= sense)
203	t = p;
204	else
205	b = p;
206	COPY: b = t;
207	}
208	i = size;
209	if (q == f1) {
210	if (iflag) {
211	ICOPY_LIST(f2, tp2, b);
212	ICOPY_ELT(f1, tp2, i);
213	} else {
214	CCOPY_LIST(f2, tp2, b);
215	CCOPY_ELT(f1, tp2, i);
216	}
217	} else {
218	if (iflag) {
219	ICOPY_LIST(f1, tp2, b);
220	ICOPY_ELT(f2, tp2, i);
221	} else {
222	CCOPY_LIST(f1, tp2, b);
223	CCOPY_ELT(f2, tp2, i);
224	}
225	}
226	}
227	if (f2 < l2) {
228	if (iflag)
229	ICOPY_LIST(f2, tp2, l2);
230	else
231	CCOPY_LIST(f2, tp2, l2);
232	} else if (f1 < l1) {
233	if (iflag)
234	ICOPY_LIST(f1, tp2, l1);
235	else
236	CCOPY_LIST(f1, tp2, l1);
237	}
238	*p1 = l2;
239	}
240	tp2 = list1; /* swap list1, list2 */
241	list1 = list2;
242	list2 = tp2;
243	last = list2 + nmemb*size;
244	}
245	if (base == list2) {
246	memmove(list2, list1, nmemb*size);
247	list2 = list1;
248	}
249	free(list2);
250	return (0);
251	}
252
253	#define swap(a, b) { \
254	s = b; \
255	i = size; \
256	do { \
257	tmp = a; a++ = s; s++ = tmp; \
258	} while (--i); \
259	a -= size; \
260	}
261	#define reverse(bot, top) { \
262	s = top; \
263	do { \
264	i = size; \
265	do { \
266	tmp = bot; bot++ = s; s++ = tmp; \
267	} while (--i); \
268	s -= size2; \
269	} while(bot < s); \
270	}
271
272	/*
273	* Optional hybrid natural/pairwise first pass. Eats up list1 in runs of
274	* increasing order, list2 in a corresponding linked list. Checks for runs
275	* when THRESHOLD/2 pairs compare with same sense. (Only used when NATURAL
276	* is defined. Otherwise simple pairwise merging is used.)
277	*/
278	void
279	setup(list1, list2, n, size, cmp)
280	size_t n, size;
281	int (cmp) __P((const void , const void *));
282	u_char list1, list2;
283	{
284	int i, length, size2, tmp, sense;
285	u_char f1, f2, s, l2, last, p2;
286
287	size2 = size*2;
288	if (n <= 5) {
289	insertionsort(list1, n, size, cmp);
290	EVAL(list2) = (u_char) list2 + n*size;
291	return;
292	}
293	/*
294	* Avoid running pointers out of bounds; limit n to evens
295	* for simplicity.
296	*/
297	i = 4 + (n & 1);
298	insertionsort(list1 + (n - i) * size, i, size, cmp);
299	last = list1 + size * (n - i);
300	EVAL(list2 + (last - list1)) = list2 + n size;
301
302	#ifdef NATURAL
303	p2 = list2;
304	f1 = list1;
305	sense = (cmp(f1, f1 + size) > 0);
306	for (; f1 < last; sense = !sense) {
307	length = 2;
308	/* Find pairs with same sense. */
309	for (f2 = f1 + size2; f2 < last; f2 += size2) {
310	if ((cmp(f2, f2+ size) > 0) != sense)
311	break;
312	length += 2;
313	}
314	if (length < THRESHOLD) { /* Pairwise merge */
315	do {
316	p2 = *EVAL(p2) = f1 + size2 - list1 + list2;
317	if (sense > 0)
318	swap (f1, f1 + size);
319	} while ((f1 += size2) < f2);
320	} else { /* Natural merge */
321	l2 = f2;
322	for (f2 = f1 + size2; f2 < l2; f2 += size2) {
323	if ((cmp(f2-size, f2) > 0) != sense) {
324	p2 = *EVAL(p2) = f2 - list1 + list2;
325	if (sense > 0)
326	reverse(f1, f2-size);
327	f1 = f2;
328	}
329	}
330	if (sense > 0)
331	reverse (f1, f2-size);
332	f1 = f2;
333	if (f2 < last \|\| cmp(f2 - size, f2) > 0)
334	p2 = *EVAL(p2) = f2 - list1 + list2;
335	else
336	p2 = EVAL(p2) = list2 + nsize;
337	}
338	}
339	#else /* pairwise merge only. */
340	for (f1 = list1, p2 = list2; f1 < last; f1 += size2) {
341	p2 = *EVAL(p2) = p2 + size2;
342	if (cmp (f1, f1 + size) > 0)
343	swap(f1, f1 + size);
344	}
345	#endif /* NATURAL */
346	}
347
348	/*
349	* This is to avoid out-of-bounds addresses in sorting the
350	* last 4 elements.
351	*/
352	static void
353	insertionsort(a, n, size, cmp)
354	u_char *a;
355	size_t n, size;
356	int (cmp) __P((const void , const void *));
357	{
358	u_char ai, s, t, u, tmp;
359	int i;
360
361	for (ai = a+size; --n >= 1; ai += size)
362	for (t = ai; t > a; t -= size) {
363	u = t - size;
364	if (cmp(u, t) <= 0)
365	break;
366	swap(u, t);
367	}
368	}