1 /* qsort.c 2 * (c) 1998 Gareth McCaughan 3 * 4 * This is a drop-in replacement for the C library's |qsort()| routine. 5 * 6 * Features: 7 * - Median-of-three pivoting (and more) 8 * - Truncation and final polishing by a single insertion sort 9 * - Early truncation when no swaps needed in pivoting step 10 * - Explicit recursion, guaranteed not to overflow 11 * - A few little wrinkles stolen from the GNU |qsort()|. 12 * - separate code for non-aligned / aligned / word-size objects 13 * 14 * This code may be reproduced freely provided 15 * - this file is retained unaltered apart from minor 16 * changes for portability and efficiency 17 * - no changes are made to this comment 18 * - any changes that *are* made are clearly flagged 19 * - the _ID string below is altered by inserting, after 20 * the date, the string " altered" followed at your option 21 * by other material. (Exceptions: you may change the name 22 * of the exported routine without changing the ID string. 23 * You may change the values of the macros TRUNC_* and 24 * PIVOT_THRESHOLD without changing the ID string, provided 25 * they remain constants with TRUNC_nonaligned, TRUNC_aligned 26 * and TRUNC_words/WORD_BYTES between 8 and 24, and 27 * PIVOT_THRESHOLD between 32 and 200.) 28 * 29 * You may use it in anything you like; you may make money 30 * out of it; you may distribute it in object form or as 31 * part of an executable without including source code; 32 * you don't have to credit me. (But it would be nice if 33 * you did.) 34 * 35 * If you find problems with this code, or find ways of 36 * making it significantly faster, please let me know! 37 * My e-mail address, valid as of early 1998 and certainly 38 * OK for at least the next 18 months, is 39 * gjm11 (at) dpmms.cam.ac.uk 40 * Thanks! 41 * 42 * Gareth McCaughan Peterhouse Cambridge 1998 43 */ 44 #include "SDL_config.h" 45 46 /* 47 #include <assert.h> 48 #include <stdlib.h> 49 #include <string.h> 50 */ 51 #include "SDL_stdinc.h" 52 53 #define assert(X) 54 #define malloc SDL_malloc 55 #define free SDL_free 56 #define memcpy SDL_memcpy 57 #define memmove SDL_memmove 58 #define qsort SDL_qsort 59 60 61 #ifndef HAVE_QSORT 62 63 static char _ID[]="<qsort.c gjm 1.12 1998-03-19>"; 64 65 /* How many bytes are there per word? (Must be a power of 2, 66 * and must in fact equal sizeof(int).) 67 */ 68 #define WORD_BYTES sizeof(int) 69 70 /* How big does our stack need to be? Answer: one entry per 71 * bit in a |size_t|. 72 */ 73 #define STACK_SIZE (8*sizeof(size_t)) 74 75 /* Different situations have slightly different requirements, 76 * and we make life epsilon easier by using different truncation 77 * points for the three different cases. 78 * So far, I have tuned TRUNC_words and guessed that the same 79 * value might work well for the other two cases. Of course 80 * what works well on my machine might work badly on yours. 81 */ 82 #define TRUNC_nonaligned 12 83 #define TRUNC_aligned 12 84 #define TRUNC_words 12*WORD_BYTES /* nb different meaning */ 85 86 /* We use a simple pivoting algorithm for shortish sub-arrays 87 * and a more complicated one for larger ones. The threshold 88 * is PIVOT_THRESHOLD. 89 */ 90 #define PIVOT_THRESHOLD 40 91 92 typedef struct { char * first; char * last; } stack_entry; 93 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;} 94 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;} 95 #define doLeft {first=ffirst;llast=last;continue;} 96 #define doRight {ffirst=first;last=llast;continue;} 97 #define pop {if (--stacktop<0) break;\ 98 first=ffirst=stack[stacktop].first;\ 99 last=llast=stack[stacktop].last;\ 100 continue;} 101 102 /* Some comments on the implementation. 103 * 1. When we finish partitioning the array into "low" 104 * and "high", we forget entirely about short subarrays, 105 * because they'll be done later by insertion sort. 106 * Doing lots of little insertion sorts might be a win 107 * on large datasets for locality-of-reference reasons, 108 * but it makes the code much nastier and increases 109 * bookkeeping overhead. 110 * 2. We always save the shorter and get to work on the 111 * longer. This guarantees that every time we push 112 * an item onto the stack its size is <= 1/2 of that 113 * of its parent; so the stack can't need more than 114 * log_2(max-array-size) entries. 115 * 3. We choose a pivot by looking at the first, last 116 * and middle elements. We arrange them into order 117 * because it's easy to do that in conjunction with 118 * choosing the pivot, and it makes things a little 119 * easier in the partitioning step. Anyway, the pivot 120 * is the middle of these three. It's still possible 121 * to construct datasets where the algorithm takes 122 * time of order n^2, but it simply never happens in 123 * practice. 124 * 3' Newsflash: On further investigation I find that 125 * it's easy to construct datasets where median-of-3 126 * simply isn't good enough. So on large-ish subarrays 127 * we do a more sophisticated pivoting: we take three 128 * sets of 3 elements, find their medians, and then 129 * take the median of those. 130 * 4. We copy the pivot element to a separate place 131 * because that way we can always do our comparisons 132 * directly against a pointer to that separate place, 133 * and don't have to wonder "did we move the pivot 134 * element?". This makes the inner loop better. 135 * 5. It's possible to make the pivoting even more 136 * reliable by looking at more candidates when n 137 * is larger. (Taking this to its logical conclusion 138 * results in a variant of quicksort that doesn't 139 * have that n^2 worst case.) However, the overhead 140 * from the extra bookkeeping means that it's just 141 * not worth while. 142 * 6. This is pretty clean and portable code. Here are 143 * all the potential portability pitfalls and problems 144 * I know of: 145 * - In one place (the insertion sort) I construct 146 * a pointer that points just past the end of the 147 * supplied array, and assume that (a) it won't 148 * compare equal to any pointer within the array, 149 * and (b) it will compare equal to a pointer 150 * obtained by stepping off the end of the array. 151 * These might fail on some segmented architectures. 152 * - I assume that there are 8 bits in a |char| when 153 * computing the size of stack needed. This would 154 * fail on machines with 9-bit or 16-bit bytes. 155 * - I assume that if |((int)base&(sizeof(int)-1))==0| 156 * and |(size&(sizeof(int)-1))==0| then it's safe to 157 * get at array elements via |int*|s, and that if 158 * actually |size==sizeof(int)| as well then it's 159 * safe to treat the elements as |int|s. This might 160 * fail on systems that convert pointers to integers 161 * in non-standard ways. 162 * - I assume that |8*sizeof(size_t)<=INT_MAX|. This 163 * would be false on a machine with 8-bit |char|s, 164 * 16-bit |int|s and 4096-bit |size_t|s. :-) 165 */ 166 167 /* The recursion logic is the same in each case: */ 168 #define Recurse(Trunc) \ 169 { size_t l=last-ffirst,r=llast-first; \ 170 if (l<Trunc) { \ 171 if (r>=Trunc) doRight \ 172 else pop \ 173 } \ 174 else if (l<=r) { pushLeft; doRight } \ 175 else if (r>=Trunc) { pushRight; doLeft }\ 176 else doLeft \ 177 } 178 179 /* and so is the pivoting logic: */ 180 #define Pivot(swapper,sz) \ 181 if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\ 182 else { \ 183 if (compare(first,mid)<0) { \ 184 if (compare(mid,last)>0) { \ 185 swapper(mid,last); \ 186 if (compare(first,mid)>0) swapper(first,mid);\ 187 } \ 188 } \ 189 else { \ 190 if (compare(mid,last)>0) swapper(first,last)\ 191 else { \ 192 swapper(first,mid); \ 193 if (compare(mid,last)>0) swapper(mid,last);\ 194 } \ 195 } \ 196 first+=sz; last-=sz; \ 197 } 198 199 #ifdef DEBUG_QSORT 200 #include <stdio.h> 201 #endif 202 203 /* and so is the partitioning logic: */ 204 #define Partition(swapper,sz) { \ 205 int swapped=0; \ 206 do { \ 207 while (compare(first,pivot)<0) first+=sz; \ 208 while (compare(pivot,last)<0) last-=sz; \ 209 if (first<last) { \ 210 swapper(first,last); swapped=1; \ 211 first+=sz; last-=sz; } \ 212 else if (first==last) { first+=sz; last-=sz; break; }\ 213 } while (first<=last); \ 214 if (!swapped) pop \ 215 } 216 217 /* and so is the pre-insertion-sort operation of putting 218 * the smallest element into place as a sentinel. 219 * Doing this makes the inner loop nicer. I got this 220 * idea from the GNU implementation of qsort(). 221 */ 222 #define PreInsertion(swapper,limit,sz) \ 223 first=base; \ 224 last=first + (nmemb>limit ? limit : nmemb-1)*sz;\ 225 while (last!=base) { \ 226 if (compare(first,last)>0) first=last; \ 227 last-=sz; } \ 228 if (first!=base) swapper(first,(char*)base); 229 230 /* and so is the insertion sort, in the first two cases: */ 231 #define Insertion(swapper) \ 232 last=((char*)base)+nmemb*size; \ 233 for (first=((char*)base)+size;first!=last;first+=size) { \ 234 char *test; \ 235 /* Find the right place for |first|. \ 236 * My apologies for var reuse. */ \ 237 for (test=first-size;compare(test,first)>0;test-=size) ; \ 238 test+=size; \ 239 if (test!=first) { \ 240 /* Shift everything in [test,first) \ 241 * up by one, and place |first| \ 242 * where |test| is. */ \ 243 memcpy(pivot,first,size); \ 244 memmove(test+size,test,first-test); \ 245 memcpy(test,pivot,size); \ 246 } \ 247 } 248 249 #define SWAP_nonaligned(a,b) { \ 250 register char *aa=(a),*bb=(b); \ 251 register size_t sz=size; \ 252 do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); } 253 254 #define SWAP_aligned(a,b) { \ 255 register int *aa=(int*)(a),*bb=(int*)(b); \ 256 register size_t sz=size; \ 257 do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); } 258 259 #define SWAP_words(a,b) { \ 260 register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; } 261 262 /* ---------------------------------------------------------------------- */ 263 264 static char * pivot_big(char *first, char *mid, char *last, size_t size, 265 int compare(const void *, const void *)) { 266 size_t d=(((last-first)/size)>>3)*size; 267 char *m1,*m2,*m3; 268 { char *a=first, *b=first+d, *c=first+2*d; 269 #ifdef DEBUG_QSORT 270 fprintf(stderr,"< %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); 271 #endif 272 m1 = compare(a,b)<0 ? 273 (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) 274 : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); 275 } 276 { char *a=mid-d, *b=mid, *c=mid+d; 277 #ifdef DEBUG_QSORT 278 fprintf(stderr,". %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); 279 #endif 280 m2 = compare(a,b)<0 ? 281 (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) 282 : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); 283 } 284 { char *a=last-2*d, *b=last-d, *c=last; 285 #ifdef DEBUG_QSORT 286 fprintf(stderr,"> %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); 287 #endif 288 m3 = compare(a,b)<0 ? 289 (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) 290 : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); 291 } 292 #ifdef DEBUG_QSORT 293 fprintf(stderr,"-> %d %d %d\n",*(int*)m1,*(int*)m2,*(int*)m3); 294 #endif 295 return compare(m1,m2)<0 ? 296 (compare(m2,m3)<0 ? m2 : (compare(m1,m3)<0 ? m3 : m1)) 297 : (compare(m1,m3)<0 ? m1 : (compare(m2,m3)<0 ? m3 : m2)); 298 } 299 300 /* ---------------------------------------------------------------------- */ 301 302 static void qsort_nonaligned(void *base, size_t nmemb, size_t size, 303 int (*compare)(const void *, const void *)) { 304 305 stack_entry stack[STACK_SIZE]; 306 int stacktop=0; 307 char *first,*last; 308 char *pivot=malloc(size); 309 size_t trunc=TRUNC_nonaligned*size; 310 assert(pivot!=0); 311 312 first=(char*)base; last=first+(nmemb-1)*size; 313 314 if ((size_t)(last-first)>trunc) { 315 char *ffirst=first, *llast=last; 316 while (1) { 317 /* Select pivot */ 318 { char * mid=first+size*((last-first)/size >> 1); 319 Pivot(SWAP_nonaligned,size); 320 memcpy(pivot,mid,size); 321 } 322 /* Partition. */ 323 Partition(SWAP_nonaligned,size); 324 /* Prepare to recurse/iterate. */ 325 Recurse(trunc) 326 } 327 } 328 PreInsertion(SWAP_nonaligned,TRUNC_nonaligned,size); 329 Insertion(SWAP_nonaligned); 330 free(pivot); 331 } 332 333 static void qsort_aligned(void *base, size_t nmemb, size_t size, 334 int (*compare)(const void *, const void *)) { 335 336 stack_entry stack[STACK_SIZE]; 337 int stacktop=0; 338 char *first,*last; 339 char *pivot=malloc(size); 340 size_t trunc=TRUNC_aligned*size; 341 assert(pivot!=0); 342 343 first=(char*)base; last=first+(nmemb-1)*size; 344 345 if ((size_t)(last-first)>trunc) { 346 char *ffirst=first,*llast=last; 347 while (1) { 348 /* Select pivot */ 349 { char * mid=first+size*((last-first)/size >> 1); 350 Pivot(SWAP_aligned,size); 351 memcpy(pivot,mid,size); 352 } 353 /* Partition. */ 354 Partition(SWAP_aligned,size); 355 /* Prepare to recurse/iterate. */ 356 Recurse(trunc) 357 } 358 } 359 PreInsertion(SWAP_aligned,TRUNC_aligned,size); 360 Insertion(SWAP_aligned); 361 free(pivot); 362 } 363 364 static void qsort_words(void *base, size_t nmemb, 365 int (*compare)(const void *, const void *)) { 366 367 stack_entry stack[STACK_SIZE]; 368 int stacktop=0; 369 char *first,*last; 370 char *pivot=malloc(WORD_BYTES); 371 assert(pivot!=0); 372 373 first=(char*)base; last=first+(nmemb-1)*WORD_BYTES; 374 375 if (last-first>TRUNC_words) { 376 char *ffirst=first, *llast=last; 377 while (1) { 378 #ifdef DEBUG_QSORT 379 fprintf(stderr,"Doing %d:%d: ", 380 (first-(char*)base)/WORD_BYTES, 381 (last-(char*)base)/WORD_BYTES); 382 #endif 383 /* Select pivot */ 384 { char * mid=first+WORD_BYTES*((last-first) / (2*WORD_BYTES)); 385 Pivot(SWAP_words,WORD_BYTES); 386 *(int*)pivot=*(int*)mid; 387 } 388 #ifdef DEBUG_QSORT 389 fprintf(stderr,"pivot=%d\n",*(int*)pivot); 390 #endif 391 /* Partition. */ 392 Partition(SWAP_words,WORD_BYTES); 393 /* Prepare to recurse/iterate. */ 394 Recurse(TRUNC_words) 395 } 396 } 397 PreInsertion(SWAP_words,(TRUNC_words/WORD_BYTES),WORD_BYTES); 398 /* Now do insertion sort. */ 399 last=((char*)base)+nmemb*WORD_BYTES; 400 for (first=((char*)base)+WORD_BYTES;first!=last;first+=WORD_BYTES) { 401 /* Find the right place for |first|. My apologies for var reuse */ 402 int *pl=(int*)(first-WORD_BYTES),*pr=(int*)first; 403 *(int*)pivot=*(int*)first; 404 for (;compare(pl,pivot)>0;pr=pl,--pl) { 405 *pr=*pl; } 406 if (pr!=(int*)first) *pr=*(int*)pivot; 407 } 408 free(pivot); 409 } 410 411 /* ---------------------------------------------------------------------- */ 412 413 void qsort(void *base, size_t nmemb, size_t size, 414 int (*compare)(const void *, const void *)) { 415 416 if (nmemb<=1) return; 417 if (((uintptr_t)base|size)&(WORD_BYTES-1)) 418 qsort_nonaligned(base,nmemb,size,compare); 419 else if (size!=WORD_BYTES) 420 qsort_aligned(base,nmemb,size,compare); 421 else 422 qsort_words(base,nmemb,compare); 423 } 424 425 #endif /* !HAVE_QSORT */ 426
