1 /*	$OpenBSD: merge.c,v 1.10 2015/06/21 03:20:56 millert Exp $ */
2 /*-
3  * Copyright (c) 1992, 1993
4  *	The Regents of the University of California.  All rights reserved.
5  *
6  * This code is derived from software contributed to Berkeley by
7  * Peter McIlroy.
8  *
9  * Redistribution and use in source and binary forms, with or without
10  * modification, are permitted provided that the following conditions
11  * are met:
12  * 1. Redistributions of source code must retain the above copyright
13  *    notice, this list of conditions and the following disclaimer.
14  * 2. Redistributions in binary form must reproduce the above copyright
15  *    notice, this list of conditions and the following disclaimer in the
16  *    documentation and/or other materials provided with the distribution.
17  * 3. Neither the name of the University nor the names of its contributors
18  *    may be used to endorse or promote products derived from this software
19  *    without specific prior written permission.
20  *
21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31  * SUCH DAMAGE.
32  */
33 
34 /*
35  * Hybrid exponential search/linear search merge sort with hybrid
36  * natural/pairwise first pass.  Requires about .3% more comparisons
37  * for random data than LSMS with pairwise first pass alone.
38  * It works for objects as small as two bytes.
39  */
40 
41 #define NATURAL
42 #define THRESHOLD 16	/* Best choice for natural merge cut-off. */
43 
44 /* #define NATURAL to get hybrid natural merge.
45  * (The default is pairwise merging.)
46  */
47 
48 #include <sys/types.h>
49 
50 #include <errno.h>
51 #include <stdlib.h>
52 #include <string.h>
53 
54 static void setup(u_char *list1, u_char *list2, size_t n, size_t size,
55     int (*cmp)(const void *, const void *));
56 static void insertionsort(u_char *a, size_t n, size_t size,
57     int (*cmp)(const void *, const void *));
58 
59 #define ISIZE sizeof(int)
60 #define PSIZE sizeof(u_char *)
61 #define ICOPY_LIST(src, dst, last)				\
62 	do							\
63 	*(int*)dst = *(int*)src, src += ISIZE, dst += ISIZE;	\
64 	while(src < last)
65 #define ICOPY_ELT(src, dst, i)					\
66 	do							\
67 	*(int*) dst = *(int*) src, src += ISIZE, dst += ISIZE;	\
68 	while (i -= ISIZE)
69 
70 #define CCOPY_LIST(src, dst, last)		\
71 	do					\
72 		*dst++ = *src++;		\
73 	while (src < last)
74 #define CCOPY_ELT(src, dst, i)			\
75 	do					\
76 		*dst++ = *src++;		\
77 	while (i -= 1)
78 		
79 /*
80  * Find the next possible pointer head.  (Trickery for forcing an array
81  * to do double duty as a linked list when objects do not align with word
82  * boundaries.
83  */
84 /* Assumption: PSIZE is a power of 2. */
85 #define EVAL(p) (u_char **)						\
86 	((u_char *)0 +							\
87 	    (((u_char *)p + PSIZE - 1 - (u_char *) 0) & ~(PSIZE - 1)))
88 
89 /*
90  * Arguments are as for qsort.
91  */
92 int
93 mergesort(void *base, size_t nmemb, size_t size,
94     int (*cmp)(const void *, const void *))
95 {
96 	int i, sense;
97 	int big, iflag;
98 	u_char *f1, *f2, *t, *b, *tp2, *q, *l1, *l2;
99 	u_char *list2, *list1, *p2, *p, *last, **p1;
100 
101 	if (size < PSIZE / 2) {		/* Pointers must fit into 2 * size. */
102 		errno = EINVAL;
103 		return (-1);
104 	}
105 
106 	if (nmemb == 0)
107 		return (0);
108 
109 	/*
110 	 * XXX
111 	 * Stupid subtraction for the Cray.
112 	 */
113 	iflag = 0;
114 	if (!(size % ISIZE) && !(((char *)base - (char *)0) % ISIZE))
115 		iflag = 1;
116 
117 	if ((list2 = malloc(nmemb * size + PSIZE)) == NULL)
118 		return (-1);
119 
120 	list1 = base;
121 	setup(list1, list2, nmemb, size, cmp);
122 	last = list2 + nmemb * size;
123 	i = big = 0;
124 	while (*EVAL(list2) != last) {
125 	    l2 = list1;
126 	    p1 = EVAL(list1);
127 	    for (tp2 = p2 = list2; p2 != last; p1 = EVAL(l2)) {
128 	    	p2 = *EVAL(p2);
129 	    	f1 = l2;
130 	    	f2 = l1 = list1 + (p2 - list2);
131 	    	if (p2 != last)
132 	    		p2 = *EVAL(p2);
133 	    	l2 = list1 + (p2 - list2);
134 	    	while (f1 < l1 && f2 < l2) {
135 	    		if ((*cmp)(f1, f2) <= 0) {
136 	    			q = f2;
137 	    			b = f1, t = l1;
138 	    			sense = -1;
139 	    		} else {
140 	    			q = f1;
141 	    			b = f2, t = l2;
142 	    			sense = 0;
143 	    		}
144 	    		if (!big) {	/* here i = 0 */
145 	    			while ((b += size) < t && cmp(q, b) >sense)
146 	    				if (++i == 6) {
147 	    					big = 1;
148 	    					goto EXPONENTIAL;
149 	    				}
150 	    		} else {
151 EXPONENTIAL:	    		for (i = size; ; i <<= 1)
152 	    				if ((p = (b + i)) >= t) {
153 	    					if ((p = t - size) > b &&
154 						    (*cmp)(q, p) <= sense)
155 	    						t = p;
156 	    					else
157 	    						b = p;
158 	    					break;
159 	    				} else if ((*cmp)(q, p) <= sense) {
160 	    					t = p;
161 	    					if (i == size)
162 	    						big = 0; 
163 	    					goto FASTCASE;
164 	    				} else
165 	    					b = p;
166 		    		while (t > b+size) {
167 	    				i = (((t - b) / size) >> 1) * size;
168 	    				if ((*cmp)(q, p = b + i) <= sense)
169 	    					t = p;
170 	    				else
171 	    					b = p;
172 	    			}
173 	    			goto COPY;
174 FASTCASE:	    		while (i > size)
175 	    				if ((*cmp)(q,
176 	    					p = b + (i >>= 1)) <= sense)
177 	    					t = p;
178 	    				else
179 	    					b = p;
180 COPY:	    			b = t;
181 	    		}
182 	    		i = size;
183 	    		if (q == f1) {
184 	    			if (iflag) {
185 	    				ICOPY_LIST(f2, tp2, b);
186 	    				ICOPY_ELT(f1, tp2, i);
187 	    			} else {
188 	    				CCOPY_LIST(f2, tp2, b);
189 	    				CCOPY_ELT(f1, tp2, i);
190 	    			}
191 	    		} else {
192 	    			if (iflag) {
193 	    				ICOPY_LIST(f1, tp2, b);
194 	    				ICOPY_ELT(f2, tp2, i);
195 	    			} else {
196 	    				CCOPY_LIST(f1, tp2, b);
197 	    				CCOPY_ELT(f2, tp2, i);
198 	    			}
199 	    		}
200 	    	}
201 	    	if (f2 < l2) {
202 	    		if (iflag)
203 	    			ICOPY_LIST(f2, tp2, l2);
204 	    		else
205 	    			CCOPY_LIST(f2, tp2, l2);
206 	    	} else if (f1 < l1) {
207 	    		if (iflag)
208 	    			ICOPY_LIST(f1, tp2, l1);
209 	    		else
210 	    			CCOPY_LIST(f1, tp2, l1);
211 	    	}
212 	    	*p1 = l2;
213 	    }
214 	    tp2 = list1;	/* swap list1, list2 */
215 	    list1 = list2;
216 	    list2 = tp2;
217 	    last = list2 + nmemb*size;
218 	}
219 	if (base == list2) {
220 		memmove(list2, list1, nmemb*size);
221 		list2 = list1;
222 	}
223 	free(list2);
224 	return (0);
225 }
226 
227 #define	swap(a, b) {					\
228 		s = b;					\
229 		i = size;				\
230 		do {					\
231 			tmp = *a; *a++ = *s; *s++ = tmp; \
232 		} while (--i);				\
233 		a -= size;				\
234 	}
235 #define reverse(bot, top) {				\
236 	s = top;					\
237 	do {						\
238 		i = size;				\
239 		do {					\
240 			tmp = *bot; *bot++ = *s; *s++ = tmp; \
241 		} while (--i);				\
242 		s -= size2;				\
243 	} while(bot < s);				\
244 }
245 
246 /*
247  * Optional hybrid natural/pairwise first pass.  Eats up list1 in runs of
248  * increasing order, list2 in a corresponding linked list.  Checks for runs
249  * when THRESHOLD/2 pairs compare with same sense.  (Only used when NATURAL
250  * is defined.  Otherwise simple pairwise merging is used.)
251  */
252 void
253 setup(u_char *list1, u_char *list2, size_t n, size_t size,
254     int (*cmp)(const void *, const void *))
255 {
256 	int i, length, size2, sense;
257 	u_char tmp, *f1, *f2, *s, *l2, *last, *p2;
258 
259 	size2 = size*2;
260 	if (n <= 5) {
261 		insertionsort(list1, n, size, cmp);
262 		*EVAL(list2) = (u_char*) list2 + n*size;
263 		return;
264 	}
265 	/*
266 	 * Avoid running pointers out of bounds; limit n to evens
267 	 * for simplicity.
268 	 */
269 	i = 4 + (n & 1);
270 	insertionsort(list1 + (n - i) * size, i, size, cmp);
271 	last = list1 + size * (n - i);
272 	*EVAL(list2 + (last - list1)) = list2 + n * size;
273 
274 #ifdef NATURAL
275 	p2 = list2;
276 	f1 = list1;
277 	sense = (cmp(f1, f1 + size) > 0);
278 	for (; f1 < last; sense = !sense) {
279 		length = 2;
280 					/* Find pairs with same sense. */
281 		for (f2 = f1 + size2; f2 < last; f2 += size2) {
282 			if ((cmp(f2, f2+ size) > 0) != sense)
283 				break;
284 			length += 2;
285 		}
286 		if (length < THRESHOLD) {		/* Pairwise merge */
287 			do {
288 				p2 = *EVAL(p2) = f1 + size2 - list1 + list2;
289 				if (sense > 0)
290 					swap (f1, f1 + size);
291 			} while ((f1 += size2) < f2);
292 		} else {				/* Natural merge */
293 			l2 = f2;
294 			for (f2 = f1 + size2; f2 < l2; f2 += size2) {
295 				if ((cmp(f2-size, f2) > 0) != sense) {
296 					p2 = *EVAL(p2) = f2 - list1 + list2;
297 					if (sense > 0)
298 						reverse(f1, f2-size);
299 					f1 = f2;
300 				}
301 			}
302 			if (sense > 0)
303 				reverse (f1, f2-size);
304 			f1 = f2;
305 			if (f2 < last || cmp(f2 - size, f2) > 0)
306 				p2 = *EVAL(p2) = f2 - list1 + list2;
307 			else
308 				p2 = *EVAL(p2) = list2 + n*size;
309 		}
310 	}
311 #else		/* pairwise merge only. */
312 	for (f1 = list1, p2 = list2; f1 < last; f1 += size2) {
313 		p2 = *EVAL(p2) = p2 + size2;
314 		if (cmp (f1, f1 + size) > 0)
315 			swap(f1, f1 + size);
316 	}
317 #endif /* NATURAL */
318 }
319 
320 /*
321  * This is to avoid out-of-bounds addresses in sorting the
322  * last 4 elements.
323  */
324 static void
325 insertionsort(u_char *a, size_t n, size_t size,
326     int (*cmp)(const void *, const void *))
327 {
328 	u_char *ai, *s, *t, *u, tmp;
329 	int i;
330 
331 	for (ai = a+size; --n >= 1; ai += size)
332 		for (t = ai; t > a; t -= size) {
333 			u = t - size;
334 			if (cmp(u, t) <= 0)
335 				break;
336 			swap(u, t);
337 		}
338 }