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1/* $OpenBSD: radixsort.c,v 1.9 2007/09/02 15:19:17 deraadt Exp $ */
2/*-
3 * Copyright (c) 1990, 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 and by Dan Bernstein at New York University,
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 * Radixsort routines.
36 *
37 * Program r_sort_a() is unstable but uses O(logN) extra memory for a stack.
38 * Use radixsort(a, n, trace, endchar) for this case.
39 *
40 * For stable sorting (using N extra pointers) use sradixsort(), which calls
41 * r_sort_b().
42 *
43 * For a description of this code, see D. McIlroy, P. McIlroy, K. Bostic,
44 * "Engineering Radix Sort".
45 */
46
47#include <sys/types.h>
48#include <stdlib.h>
49#include <errno.h>
50
51typedef struct {
52 const u_char **sa;
53 int sn, si;
54} stack;
55
56static __inline void simplesort
57(const u_char **, int, int, const u_char *, u_int);
58static void r_sort_a(const u_char **, int, int, const u_char *, u_int);
59static void r_sort_b(const u_char **,
60 const u_char **, int, int, const u_char *, u_int);
61
62#define THRESHOLD 20 /* Divert to simplesort(). */
63#define SIZE 512 /* Default stack size. */
64
65#define SETUP { \
66 if (tab == NULL) { \
67 tr = tr0; \
68 for (c = 0; c < endch; c++) \
69 tr0[c] = c + 1; \
70 tr0[c] = 0; \
71 for (c++; c < 256; c++) \
72 tr0[c] = c; \
73 endch = 0; \
74 } else { \
75 endch = tab[endch]; \
76 tr = tab; \
77 if (endch != 0 && endch != 255) { \
78 errno = EINVAL; \
79 return (-1); \
80 } \
81 } \
82}
83
84int
85radixsort(const u_char **a, int n, const u_char *tab, u_int endch)
86{
87 const u_char *tr;
88 int c;
89 u_char tr0[256];
90
91 SETUP;
92 r_sort_a(a, n, 0, tr, endch);
93 return (0);
94}
95
96int
97sradixsort(const u_char **a, int n, const u_char *tab, u_int endch)
98{
99 const u_char *tr, **ta;
100 int c;
101 u_char tr0[256];
102
103 SETUP;
104 if (n < THRESHOLD)
105 simplesort(a, n, 0, tr, endch);
106 else {
107 if ((ta = calloc(n, sizeof(a))) == NULL)
108 return (-1);
109 r_sort_b(a, ta, n, 0, tr, endch);
110 free(ta);
111 }
112 return (0);
113}
114
115#define empty(s) (s >= sp)
116#define pop(a, n, i) a = (--sp)->sa, n = sp->sn, i = sp->si
117#define push(a, n, i) sp->sa = a, sp->sn = n, (sp++)->si = i
118#define swap(a, b, t) t = a, a = b, b = t
119
120/* Unstable, in-place sort. */
121void
122r_sort_a(const u_char **a, int n, int i, const u_char *tr, u_int endch)
123{
124 static int count[256], nc, bmin;
125 int c;
126 const u_char **ak, *r;
127 stack s[SIZE], *sp, *sp0, *sp1, temp;
128 int *cp, bigc;
129 const u_char **an, *t, **aj, **top[256];
130
131 /* Set up stack. */
132 sp = s;
133 push(a, n, i);
134 while (!empty(s)) {
135 pop(a, n, i);
136 if (n < THRESHOLD) {
137 simplesort(a, n, i, tr, endch);
138 continue;
139 }
140 an = a + n;
141
142 /* Make character histogram. */
143 if (nc == 0) {
144 bmin = 255; /* First occupied bin, excluding eos. */
145 for (ak = a; ak < an;) {
146 c = tr[(*ak++)[i]];
147 if (++count[c] == 1 && c != endch) {
148 if (c < bmin)
149 bmin = c;
150 nc++;
151 }
152 }
153 if (sp + nc > s + SIZE) { /* Get more stack. */
154 r_sort_a(a, n, i, tr, endch);
155 continue;
156 }
157 }
158
159 /*
160 * Set top[]; push incompletely sorted bins onto stack.
161 * top[] = pointers to last out-of-place element in bins.
162 * count[] = counts of elements in bins.
163 * Before permuting: top[c-1] + count[c] = top[c];
164 * during deal: top[c] counts down to top[c-1].
165 */
166 sp0 = sp1 = sp; /* Stack position of biggest bin. */
167 bigc = 2; /* Size of biggest bin. */
168 if (endch == 0) /* Special case: set top[eos]. */
169 top[0] = ak = a + count[0];
170 else {
171 ak = a;
172 top[255] = an;
173 }
174 for (cp = count + bmin; nc > 0; cp++) {
175 while (*cp == 0) /* Find next non-empty pile. */
176 cp++;
177 if (*cp > 1) {
178 if (*cp > bigc) {
179 bigc = *cp;
180 sp1 = sp;
181 }
182 push(ak, *cp, i+1);
183 }
184 top[cp-count] = ak += *cp;
185 nc--;
186 }
187 swap(*sp0, *sp1, temp); /* Play it safe -- biggest bin last. */
188
189 /*
190 * Permute misplacements home. Already home: everything
191 * before aj, and in bin[c], items from top[c] on.
192 * Inner loop:
193 * r = next element to put in place;
194 * ak = top[r[i]] = location to put the next element.
195 * aj = bottom of 1st disordered bin.
196 * Outer loop:
197 * Once the 1st disordered bin is done, ie. aj >= ak,
198 * aj<-aj + count[c] connects the bins in a linked list;
199 * reset count[c].
200 */
201 for (aj = a; aj < an; *aj = r, aj += count[c], count[c] = 0)
202 for (r = *aj; aj < (ak = --top[c = tr[r[i]]]);)
203 swap(*ak, r, t);
204 }
205}
206
207/* Stable sort, requiring additional memory. */
208void
209r_sort_b(const u_char **a, const u_char **ta, int n, int i, const u_char *tr,
210 u_int endch)
211{
212 static int count[256], nc, bmin;
213 int c;
214 const u_char **ak, **ai;
215 stack s[512], *sp, *sp0, *sp1, temp;
216 const u_char **top[256];
217 int *cp, bigc;
218
219 sp = s;
220 push(a, n, i);
221 while (!empty(s)) {
222 pop(a, n, i);
223 if (n < THRESHOLD) {
224 simplesort(a, n, i, tr, endch);
225 continue;
226 }
227
228 if (nc == 0) {
229 bmin = 255;
230 for (ak = a + n; --ak >= a;) {
231 c = tr[(*ak)[i]];
232 if (++count[c] == 1 && c != endch) {
233 if (c < bmin)
234 bmin = c;
235 nc++;
236 }
237 }
238 if (sp + nc > s + SIZE) {
239 r_sort_b(a, ta, n, i, tr, endch);
240 continue;
241 }
242 }
243
244 sp0 = sp1 = sp;
245 bigc = 2;
246 if (endch == 0) {
247 top[0] = ak = a + count[0];
248 count[0] = 0;
249 } else {
250 ak = a;
251 top[255] = a + n;
252 count[255] = 0;
253 }
254 for (cp = count + bmin; nc > 0; cp++) {
255 while (*cp == 0)
256 cp++;
257 if ((c = *cp) > 1) {
258 if (c > bigc) {
259 bigc = c;
260 sp1 = sp;
261 }
262 push(ak, c, i+1);
263 }
264 top[cp-count] = ak += c;
265 *cp = 0; /* Reset count[]. */
266 nc--;
267 }
268 swap(*sp0, *sp1, temp);
269
270 for (ak = ta + n, ai = a+n; ak > ta;) /* Copy to temp. */
271 *--ak = *--ai;
272 for (ak = ta+n; --ak >= ta;) /* Deal to piles. */
273 *--top[tr[(*ak)[i]]] = *ak;
274 }
275}
276
277static __inline void
278simplesort(const u_char **a, int n, int b, const u_char *tr, u_int endch)
279 /* insertion sort */
280{
281 u_char ch;
282 const u_char **ak, **ai, *s, *t;
283
284 for (ak = a+1; --n >= 1; ak++)
285 for (ai = ak; ai > a; ai--) {
286 for (s = ai[0] + b, t = ai[-1] + b;
287 (ch = tr[*s]) != endch; s++, t++)
288 if (ch != tr[*t])
289 break;
290 if (ch >= tr[*t])
291 break;
292 swap(ai[0], ai[-1], s);
293 }
294}
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