1 /*- 2 * Copyright (c) 1990 The Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 3. All advertising materials mentioning features or use of this software 14 * must display the following acknowledgement: 15 * This product includes software developed by the University of 16 * California, Berkeley and its contributors. 17 * 4. 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 #if defined(LIBC_SCCS) && !defined(lint) 35 static char sccsid[] = "@(#)radixsort.c 5.7 (Berkeley) 2/23/91"; 36 #endif /* LIBC_SCCS and not lint */ 37 38 #include <sys/types.h> 39 #include <limits.h> 40 #include <stdlib.h> 41 #include <stddef.h> 42 #include <string.h> 43 44 /* 45 * __rspartition is the cutoff point for a further partitioning instead 46 * of a shellsort. If it changes check __rsshell_increments. Both of 47 * these are exported, as the best values are data dependent. 48 */ 49 #define NPARTITION 40 50 int __rspartition = NPARTITION; 51 int __rsshell_increments[] = { 4, 1, 0, 0, 0, 0, 0, 0 }; 52 53 /* 54 * Stackp points to context structures, where each structure schedules a 55 * partitioning. Radixsort exits when the stack is empty. 56 * 57 * If the buckets are placed on the stack randomly, the worst case is when 58 * all the buckets but one contain (npartitions + 1) elements and the bucket 59 * pushed on the stack last contains the rest of the elements. In this case, 60 * stack growth is bounded by: 61 * 62 * limit = (nelements / (npartitions + 1)) - 1; 63 * 64 * This is a very large number, 52,377,648 for the maximum 32-bit signed int. 65 * 66 * By forcing the largest bucket to be pushed on the stack first, the worst 67 * case is when all but two buckets each contain (npartitions + 1) elements, 68 * with the remaining elements split equally between the first and last 69 * buckets pushed on the stack. In this case, stack growth is bounded when: 70 * 71 * for (partition_cnt = 0; nelements > npartitions; ++partition_cnt) 72 * nelements = 73 * (nelements - (npartitions + 1) * (nbuckets - 2)) / 2; 74 * The bound is: 75 * 76 * limit = partition_cnt * (nbuckets - 1); 77 * 78 * This is a much smaller number, 4590 for the maximum 32-bit signed int. 79 */ 80 #define NBUCKETS (UCHAR_MAX + 1) 81 82 typedef struct _stack { 83 const u_char **bot; 84 int indx, nmemb; 85 } CONTEXT; 86 87 #define STACKPUSH { \ 88 stackp->bot = p; \ 89 stackp->nmemb = nmemb; \ 90 stackp->indx = indx; \ 91 ++stackp; \ 92 } 93 #define STACKPOP { \ 94 if (stackp == stack) \ 95 break; \ 96 --stackp; \ 97 bot = stackp->bot; \ 98 nmemb = stackp->nmemb; \ 99 indx = stackp->indx; \ 100 } 101 102 /* 103 * A variant of MSD radix sorting; see Knuth Vol. 3, page 177, and 5.2.5, 104 * Ex. 10 and 12. Also, "Three Partition Refinement Algorithms, Paige 105 * and Tarjan, SIAM J. Comput. Vol. 16, No. 6, December 1987. 106 * 107 * This uses a simple sort as soon as a bucket crosses a cutoff point, 108 * rather than sorting the entire list after partitioning is finished. 109 * This should be an advantage. 110 * 111 * This is pure MSD instead of LSD of some number of MSD, switching to 112 * the simple sort as soon as possible. Takes linear time relative to 113 * the number of bytes in the strings. 114 */ 115 int 116 #if __STDC__ 117 radixsort(const u_char **l1, int nmemb, const u_char *tab, u_char endbyte) 118 #else 119 radixsort(l1, nmemb, tab, endbyte) 120 const u_char **l1; 121 register int nmemb; 122 const u_char *tab; 123 u_char endbyte; 124 #endif 125 { 126 register int i, indx, t1, t2; 127 register const u_char **l2; 128 register const u_char **p; 129 register const u_char **bot; 130 register const u_char *tr; 131 CONTEXT *stack, *stackp; 132 int c[NBUCKETS + 1], max; 133 u_char ltab[NBUCKETS]; 134 static void shellsort(); 135 136 if (nmemb <= 1) 137 return(0); 138 139 /* 140 * T1 is the constant part of the equation, the number of elements 141 * represented on the stack between the top and bottom entries. 142 * It doesn't get rounded as the divide by 2 rounds down (correct 143 * for a value being subtracted). T2, the nelem value, has to be 144 * rounded up before each divide because we want an upper bound; 145 * this could overflow if nmemb is the maximum int. 146 */ 147 t1 = ((__rspartition + 1) * (NBUCKETS - 2)) >> 1; 148 for (i = 0, t2 = nmemb; t2 > __rspartition; i += NBUCKETS - 1) 149 t2 = ((t2 + 1) >> 1) - t1; 150 if (i) { 151 if (!(stack = stackp = (CONTEXT *)malloc(i * sizeof(CONTEXT)))) 152 return(-1); 153 } else 154 stack = stackp = NULL; 155 156 /* 157 * There are two arrays, one provided by the user (l1), and the 158 * temporary one (l2). The data is sorted to the temporary stack, 159 * and then copied back. The speedup of using index to determine 160 * which stack the data is on and simply swapping stacks back and 161 * forth, thus avoiding the copy every iteration, turns out to not 162 * be any faster than the current implementation. 163 */ 164 if (!(l2 = (const u_char **)malloc(sizeof(u_char *) * nmemb))) 165 return(-1); 166 167 /* 168 * Tr references a table of sort weights; multiple entries may 169 * map to the same weight; EOS char must have the lowest weight. 170 */ 171 if (tab) 172 tr = tab; 173 else { 174 for (t1 = 0, t2 = endbyte; t1 < t2; ++t1) 175 ltab[t1] = t1 + 1; 176 ltab[t2] = 0; 177 for (t1 = endbyte + 1; t1 < NBUCKETS; ++t1) 178 ltab[t1] = t1; 179 tr = ltab; 180 } 181 182 /* First sort is entire stack */ 183 bot = l1; 184 indx = 0; 185 186 for (;;) { 187 /* Clear bucket count array */ 188 bzero((char *)c, sizeof(c)); 189 190 /* 191 * Compute number of items that sort to the same bucket 192 * for this index. 193 */ 194 for (p = bot, i = nmemb; --i >= 0;) 195 ++c[tr[(*p++)[indx]]]; 196 197 /* 198 * Sum the number of characters into c, dividing the temp 199 * stack into the right number of buckets for this bucket, 200 * this index. C contains the cumulative total of keys 201 * before and included in this bucket, and will later be 202 * used as an index to the bucket. c[NBUCKETS] contains 203 * the total number of elements, for determining how many 204 * elements the last bucket contains. At the same time 205 * find the largest bucket so it gets pushed first. 206 */ 207 for (i = max = t1 = 0, t2 = __rspartition; i <= NBUCKETS; ++i) { 208 if (c[i] > t2) { 209 t2 = c[i]; 210 max = i; 211 } 212 t1 = c[i] += t1; 213 } 214 215 /* 216 * Partition the elements into buckets; c decrements through 217 * the bucket, and ends up pointing to the first element of 218 * the bucket. 219 */ 220 for (i = nmemb; --i >= 0;) { 221 --p; 222 l2[--c[tr[(*p)[indx]]]] = *p; 223 } 224 225 /* Copy the partitioned elements back to user stack */ 226 bcopy(l2, bot, nmemb * sizeof(u_char *)); 227 228 ++indx; 229 /* 230 * Sort buckets as necessary; don't sort c[0], it's the 231 * EOS character bucket, and nothing can follow EOS. 232 */ 233 for (i = max; i; --i) { 234 if ((nmemb = c[i + 1] - (t1 = c[i])) < 2) 235 continue; 236 p = bot + t1; 237 if (nmemb > __rspartition) 238 STACKPUSH 239 else 240 shellsort(p, indx, nmemb, tr); 241 } 242 for (i = max + 1; i < NBUCKETS; ++i) { 243 if ((nmemb = c[i + 1] - (t1 = c[i])) < 2) 244 continue; 245 p = bot + t1; 246 if (nmemb > __rspartition) 247 STACKPUSH 248 else 249 shellsort(p, indx, nmemb, tr); 250 } 251 /* Break out when stack is empty */ 252 STACKPOP 253 } 254 255 free((char *)l2); 256 free((char *)stack); 257 return(0); 258 } 259 260 /* 261 * Shellsort (diminishing increment sort) from Data Structures and 262 * Algorithms, Aho, Hopcraft and Ullman, 1983 Edition, page 290; 263 * see also Knuth Vol. 3, page 84. The increments are selected from 264 * formula (8), page 95. Roughly O(N^3/2). 265 */ 266 static void 267 shellsort(p, indx, nmemb, tr) 268 register u_char **p, *tr; 269 register int indx, nmemb; 270 { 271 register u_char ch, *s1, *s2; 272 register int incr, *incrp, t1, t2; 273 274 for (incrp = __rsshell_increments; incr = *incrp++;) 275 for (t1 = incr; t1 < nmemb; ++t1) 276 for (t2 = t1 - incr; t2 >= 0;) { 277 s1 = p[t2] + indx; 278 s2 = p[t2 + incr] + indx; 279 while ((ch = tr[*s1++]) == tr[*s2] && ch) 280 ++s2; 281 if (ch > tr[*s2]) { 282 s1 = p[t2]; 283 p[t2] = p[t2 + incr]; 284 p[t2 + incr] = s1; 285 t2 -= incr; 286 } else 287 break; 288 } 289 } 290