1/*-
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.
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
33#if defined(LIBC_SCCS) && !defined(lint)
34static char sccsid[] = "@(#)merge.c	8.2 (Berkeley) 2/14/94";
35#endif /* LIBC_SCCS and not lint */
36#include <sys/cdefs.h>
37__FBSDID("$FreeBSD: src/lib/libc/stdlib/merge.c,v 1.8 2007/01/09 00:28:10 imp Exp $");
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
59static void setup(u_char *, u_char *, size_t, size_t,
60    int (*)(const void *, const void *));
61static void insertionsort(u_char *, size_t, size_t,
62    int (*)(const void *, const void *));
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)
83
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 */
97int
98mergesort(base, nmemb, size, cmp)
99	void *base;
100	size_t nmemb;
101	size_t size;
102	int (*cmp)(const void *, const void *);
103{
104	size_t i;
105	int sense;
106	int big, iflag;
107	u_char *f1, *f2, *t, *b, *tp2, *q, *l1, *l2;
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
115	if (nmemb == 0)
116		return (0);
117
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 */
154				while ((b += size) < t && cmp(q, b) >sense)
155	    				if (++i == 6) {
156	    					big = 1;
157	    					goto EXPONENTIAL;
158	    				}
159	    		} else {
160EXPONENTIAL:	    		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)
171	    						big = 0;
172	    					goto FASTCASE;
173	    				} else
174	    					b = p;
175				while (t > b+size) {
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;
183FASTCASE:	    		while (i > size)
184	    				if ((*cmp)(q,
185	    					p = b + (i >>= 1)) <= sense)
186	    					t = p;
187	    				else
188	    					b = p;
189COPY:	    			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 */
261void
262setup(list1, list2, n, size, cmp)
263	size_t n, size;
264	int (*cmp)(const void *, const void *);
265	u_char *list1, *list2;
266{
267	size_t i, size2;
268	int length, tmp, sense;
269	u_char *f1, *f2, *s, *l2, *last, *p2;
270
271	size2 = size*2;
272	if (n <= 5) {
273		insertionsort(list1, n, size, cmp);
274		*EVAL(list2) = (u_char*) list2 + n*size;
275		return;
276	}
277	/*
278	 * Avoid running pointers out of bounds; limit n to evens
279	 * for simplicity.
280	 */
281	i = 4 + (n & 1);
282	insertionsort(list1 + (n - i) * size, i, size, cmp);
283	last = list1 + size * (n - i);
284	*EVAL(list2 + (last - list1)) = list2 + n * size;
285
286#ifdef NATURAL
287	p2 = list2;
288	f1 = list1;
289	sense = (cmp(f1, f1 + size) > 0);
290	for (; f1 < last; sense = !sense) {
291		length = 2;
292					/* Find pairs with same sense. */
293		for (f2 = f1 + size2; f2 < last; f2 += size2) {
294			if ((cmp(f2, f2+ size) > 0) != sense)
295				break;
296			length += 2;
297		}
298		if (length < THRESHOLD) {		/* Pairwise merge */
299			do {
300				p2 = *EVAL(p2) = f1 + size2 - list1 + list2;
301				if (sense > 0)
302					swap (f1, f1 + size);
303			} while ((f1 += size2) < f2);
304		} else {				/* Natural merge */
305			l2 = f2;
306			for (f2 = f1 + size2; f2 < l2; f2 += size2) {
307				if ((cmp(f2-size, f2) > 0) != sense) {
308					p2 = *EVAL(p2) = f2 - list1 + list2;
309					if (sense > 0)
310						reverse(f1, f2-size);
311					f1 = f2;
312				}
313			}
314			if (sense > 0)
315				reverse (f1, f2-size);
316			f1 = f2;
317			if (f2 < last || cmp(f2 - size, f2) > 0)
318				p2 = *EVAL(p2) = f2 - list1 + list2;
319			else
320				p2 = *EVAL(p2) = list2 + n*size;
321		}
322	}
323#else		/* pairwise merge only. */
324	for (f1 = list1, p2 = list2; f1 < last; f1 += size2) {
325		p2 = *EVAL(p2) = p2 + size2;
326		if (cmp (f1, f1 + size) > 0)
327			swap(f1, f1 + size);
328	}
329#endif /* NATURAL */
330}
331
332/*
333 * This is to avoid out-of-bounds addresses in sorting the
334 * last 4 elements.
335 */
336static void
337insertionsort(a, n, size, cmp)
338	u_char *a;
339	size_t n, size;
340	int (*cmp)(const void *, const void *);
341{
342	u_char *ai, *s, *t, *u, tmp;
343	int i;
344
345	for (ai = a+size; --n >= 1; ai += size)
346		for (t = ai; t > a; t -= size) {
347			u = t - size;
348			if (cmp(u, t) <= 0)
349				break;
350			swap(u, t);
351		}
352}
353