| 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@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 | #ifdef assert |
| 54 | #undef assert |
| 55 | #endif |
| 56 | #define assert(X) |
| 57 | #ifdef malloc |
| 58 | #undef malloc |
| 59 | #endif |
| 60 | #define malloc SDL_malloc |
| 61 | #ifdef free |
| 62 | #undef free |
| 63 | #endif |
| 64 | #define free SDL_free |
| 65 | #ifdef memcpy |
| 66 | #undef memcpy |
| 67 | #endif |
| 68 | #define memcpy SDL_memcpy |
| 69 | #ifdef memmove |
| 70 | #undef memmove |
| 71 | #endif |
| 72 | #define memmove SDL_memmove |
| 73 | #ifdef qsort |
| 74 | #undef qsort |
| 75 | #endif |
| 76 | #define qsort SDL_qsort |
| 77 | |
| 78 | |
| 79 | #ifndef HAVE_QSORT |
| 80 | |
| 81 | static char _ID[]="<qsort.c gjm 1.12 1998-03-19>"; |
| 82 | |
| 83 | /* How many bytes are there per word? (Must be a power of 2, |
| 84 | * and must in fact equal sizeof(int).) |
| 85 | */ |
| 86 | #define WORD_BYTES sizeof(int) |
| 87 | |
| 88 | /* How big does our stack need to be? Answer: one entry per |
| 89 | * bit in a |size_t|. |
| 90 | */ |
| 91 | #define STACK_SIZE (8*sizeof(size_t)) |
| 92 | |
| 93 | /* Different situations have slightly different requirements, |
| 94 | * and we make life epsilon easier by using different truncation |
| 95 | * points for the three different cases. |
| 96 | * So far, I have tuned TRUNC_words and guessed that the same |
| 97 | * value might work well for the other two cases. Of course |
| 98 | * what works well on my machine might work badly on yours. |
| 99 | */ |
| 100 | #define TRUNC_nonaligned 12 |
| 101 | #define TRUNC_aligned 12 |
| 102 | #define TRUNC_words 12*WORD_BYTES /* nb different meaning */ |
| 103 | |
| 104 | /* We use a simple pivoting algorithm for shortish sub-arrays |
| 105 | * and a more complicated one for larger ones. The threshold |
| 106 | * is PIVOT_THRESHOLD. |
| 107 | */ |
| 108 | #define PIVOT_THRESHOLD 40 |
| 109 | |
| 110 | typedef struct { char * first; char * last; } stack_entry; |
| 111 | #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;} |
| 112 | #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;} |
| 113 | #define doLeft {first=ffirst;llast=last;continue;} |
| 114 | #define doRight {ffirst=first;last=llast;continue;} |
| 115 | #define pop {if (--stacktop<0) break;\ |
| 116 | first=ffirst=stack[stacktop].first;\ |
| 117 | last=llast=stack[stacktop].last;\ |
| 118 | continue;} |
| 119 | |
| 120 | /* Some comments on the implementation. |
| 121 | * 1. When we finish partitioning the array into "low" |
| 122 | * and "high", we forget entirely about short subarrays, |
| 123 | * because they'll be done later by insertion sort. |
| 124 | * Doing lots of little insertion sorts might be a win |
| 125 | * on large datasets for locality-of-reference reasons, |
| 126 | * but it makes the code much nastier and increases |
| 127 | * bookkeeping overhead. |
| 128 | * 2. We always save the shorter and get to work on the |
| 129 | * longer. This guarantees that every time we push |
| 130 | * an item onto the stack its size is <= 1/2 of that |
| 131 | * of its parent; so the stack can't need more than |
| 132 | * log_2(max-array-size) entries. |
| 133 | * 3. We choose a pivot by looking at the first, last |
| 134 | * and middle elements. We arrange them into order |
| 135 | * because it's easy to do that in conjunction with |
| 136 | * choosing the pivot, and it makes things a little |
| 137 | * easier in the partitioning step. Anyway, the pivot |
| 138 | * is the middle of these three. It's still possible |
| 139 | * to construct datasets where the algorithm takes |
| 140 | * time of order n^2, but it simply never happens in |
| 141 | * practice. |
| 142 | * 3' Newsflash: On further investigation I find that |
| 143 | * it's easy to construct datasets where median-of-3 |
| 144 | * simply isn't good enough. So on large-ish subarrays |
| 145 | * we do a more sophisticated pivoting: we take three |
| 146 | * sets of 3 elements, find their medians, and then |
| 147 | * take the median of those. |
| 148 | * 4. We copy the pivot element to a separate place |
| 149 | * because that way we can always do our comparisons |
| 150 | * directly against a pointer to that separate place, |
| 151 | * and don't have to wonder "did we move the pivot |
| 152 | * element?". This makes the inner loop better. |
| 153 | * 5. It's possible to make the pivoting even more |
| 154 | * reliable by looking at more candidates when n |
| 155 | * is larger. (Taking this to its logical conclusion |
| 156 | * results in a variant of quicksort that doesn't |
| 157 | * have that n^2 worst case.) However, the overhead |
| 158 | * from the extra bookkeeping means that it's just |
| 159 | * not worth while. |
| 160 | * 6. This is pretty clean and portable code. Here are |
| 161 | * all the potential portability pitfalls and problems |
| 162 | * I know of: |
| 163 | * - In one place (the insertion sort) I construct |
| 164 | * a pointer that points just past the end of the |
| 165 | * supplied array, and assume that (a) it won't |
| 166 | * compare equal to any pointer within the array, |
| 167 | * and (b) it will compare equal to a pointer |
| 168 | * obtained by stepping off the end of the array. |
| 169 | * These might fail on some segmented architectures. |
| 170 | * - I assume that there are 8 bits in a |char| when |
| 171 | * computing the size of stack needed. This would |
| 172 | * fail on machines with 9-bit or 16-bit bytes. |
| 173 | * - I assume that if |((int)base&(sizeof(int)-1))==0| |
| 174 | * and |(size&(sizeof(int)-1))==0| then it's safe to |
| 175 | * get at array elements via |int*|s, and that if |
| 176 | * actually |size==sizeof(int)| as well then it's |
| 177 | * safe to treat the elements as |int|s. This might |
| 178 | * fail on systems that convert pointers to integers |
| 179 | * in non-standard ways. |
| 180 | * - I assume that |8*sizeof(size_t)<=INT_MAX|. This |
| 181 | * would be false on a machine with 8-bit |char|s, |
| 182 | * 16-bit |int|s and 4096-bit |size_t|s. :-) |
| 183 | */ |
| 184 | |
| 185 | /* The recursion logic is the same in each case: */ |
| 186 | #define Recurse(Trunc) \ |
| 187 | { size_t l=last-ffirst,r=llast-first; \ |
| 188 | if (l<Trunc) { \ |
| 189 | if (r>=Trunc) doRight \ |
| 190 | else pop \ |
| 191 | } \ |
| 192 | else if (l<=r) { pushLeft; doRight } \ |
| 193 | else if (r>=Trunc) { pushRight; doLeft }\ |
| 194 | else doLeft \ |
| 195 | } |
| 196 | |
| 197 | /* and so is the pivoting logic: */ |
| 198 | #define Pivot(swapper,sz) \ |
| 199 | if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\ |
| 200 | else { \ |
| 201 | if (compare(first,mid)<0) { \ |
| 202 | if (compare(mid,last)>0) { \ |
| 203 | swapper(mid,last); \ |
| 204 | if (compare(first,mid)>0) swapper(first,mid);\ |
| 205 | } \ |
| 206 | } \ |
| 207 | else { \ |
| 208 | if (compare(mid,last)>0) swapper(first,last)\ |
| 209 | else { \ |
| 210 | swapper(first,mid); \ |
| 211 | if (compare(mid,last)>0) swapper(mid,last);\ |
| 212 | } \ |
| 213 | } \ |
| 214 | first+=sz; last-=sz; \ |
| 215 | } |
| 216 | |
| 217 | #ifdef DEBUG_QSORT |
| 218 | #include <stdio.h> |
| 219 | #endif |
| 220 | |
| 221 | /* and so is the partitioning logic: */ |
| 222 | #define Partition(swapper,sz) { \ |
| 223 | int swapped=0; \ |
| 224 | do { \ |
| 225 | while (compare(first,pivot)<0) first+=sz; \ |
| 226 | while (compare(pivot,last)<0) last-=sz; \ |
| 227 | if (first<last) { \ |
| 228 | swapper(first,last); swapped=1; \ |
| 229 | first+=sz; last-=sz; } \ |
| 230 | else if (first==last) { first+=sz; last-=sz; break; }\ |
| 231 | } while (first<=last); \ |
| 232 | if (!swapped) pop \ |
| 233 | } |
| 234 | |
| 235 | /* and so is the pre-insertion-sort operation of putting |
| 236 | * the smallest element into place as a sentinel. |
| 237 | * Doing this makes the inner loop nicer. I got this |
| 238 | * idea from the GNU implementation of qsort(). |
| 239 | */ |
| 240 | #define PreInsertion(swapper,limit,sz) \ |
| 241 | first=base; \ |
| 242 | last=first + (nmemb>limit ? limit : nmemb-1)*sz;\ |
| 243 | while (last!=base) { \ |
| 244 | if (compare(first,last)>0) first=last; \ |
| 245 | last-=sz; } \ |
| 246 | if (first!=base) swapper(first,(char*)base); |
| 247 | |
| 248 | /* and so is the insertion sort, in the first two cases: */ |
| 249 | #define Insertion(swapper) \ |
| 250 | last=((char*)base)+nmemb*size; \ |
| 251 | for (first=((char*)base)+size;first!=last;first+=size) { \ |
| 252 | char *test; \ |
| 253 | /* Find the right place for |first|. \ |
| 254 | * My apologies for var reuse. */ \ |
| 255 | for (test=first-size;compare(test,first)>0;test-=size) ; \ |
| 256 | test+=size; \ |
| 257 | if (test!=first) { \ |
| 258 | /* Shift everything in [test,first) \ |
| 259 | * up by one, and place |first| \ |
| 260 | * where |test| is. */ \ |
| 261 | memcpy(pivot,first,size); \ |
| 262 | memmove(test+size,test,first-test); \ |
| 263 | memcpy(test,pivot,size); \ |
| 264 | } \ |
| 265 | } |
| 266 | |
| 267 | #define SWAP_nonaligned(a,b) { \ |
| 268 | register char *aa=(a),*bb=(b); \ |
| 269 | register size_t sz=size; \ |
| 270 | do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); } |
| 271 | |
| 272 | #define SWAP_aligned(a,b) { \ |
| 273 | register int *aa=(int*)(a),*bb=(int*)(b); \ |
| 274 | register size_t sz=size; \ |
| 275 | do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); } |
| 276 | |
| 277 | #define SWAP_words(a,b) { \ |
| 278 | register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; } |
| 279 | |
| 280 | /* ---------------------------------------------------------------------- */ |
| 281 | |
| 282 | static char * pivot_big(char *first, char *mid, char *last, size_t size, |
| 283 | int compare(const void *, const void *)) { |
| 284 | size_t d=(((last-first)/size)>>3)*size; |
| 285 | char *m1,*m2,*m3; |
| 286 | { char *a=first, *b=first+d, *c=first+2*d; |
| 287 | #ifdef DEBUG_QSORT |
| 288 | fprintf(stderr,"< %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); |
| 289 | #endif |
| 290 | m1 = compare(a,b)<0 ? |
| 291 | (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) |
| 292 | : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); |
| 293 | } |
| 294 | { char *a=mid-d, *b=mid, *c=mid+d; |
| 295 | #ifdef DEBUG_QSORT |
| 296 | fprintf(stderr,". %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); |
| 297 | #endif |
| 298 | m2 = compare(a,b)<0 ? |
| 299 | (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) |
| 300 | : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); |
| 301 | } |
| 302 | { char *a=last-2*d, *b=last-d, *c=last; |
| 303 | #ifdef DEBUG_QSORT |
| 304 | fprintf(stderr,"> %d %d %d\n",*(int*)a,*(int*)b,*(int*)c); |
| 305 | #endif |
| 306 | m3 = compare(a,b)<0 ? |
| 307 | (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a)) |
| 308 | : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b)); |
| 309 | } |
| 310 | #ifdef DEBUG_QSORT |
| 311 | fprintf(stderr,"-> %d %d %d\n",*(int*)m1,*(int*)m2,*(int*)m3); |
| 312 | #endif |
| 313 | return compare(m1,m2)<0 ? |
| 314 | (compare(m2,m3)<0 ? m2 : (compare(m1,m3)<0 ? m3 : m1)) |
| 315 | : (compare(m1,m3)<0 ? m1 : (compare(m2,m3)<0 ? m3 : m2)); |
| 316 | } |
| 317 | |
| 318 | /* ---------------------------------------------------------------------- */ |
| 319 | |
| 320 | static void qsort_nonaligned(void *base, size_t nmemb, size_t size, |
| 321 | int (*compare)(const void *, const void *)) { |
| 322 | |
| 323 | stack_entry stack[STACK_SIZE]; |
| 324 | int stacktop=0; |
| 325 | char *first,*last; |
| 326 | char *pivot=malloc(size); |
| 327 | size_t trunc=TRUNC_nonaligned*size; |
| 328 | assert(pivot!=0); |
| 329 | |
| 330 | first=(char*)base; last=first+(nmemb-1)*size; |
| 331 | |
| 332 | if ((size_t)(last-first)>trunc) { |
| 333 | char *ffirst=first, *llast=last; |
| 334 | while (1) { |
| 335 | /* Select pivot */ |
| 336 | { char * mid=first+size*((last-first)/size >> 1); |
| 337 | Pivot(SWAP_nonaligned,size); |
| 338 | memcpy(pivot,mid,size); |
| 339 | } |
| 340 | /* Partition. */ |
| 341 | Partition(SWAP_nonaligned,size); |
| 342 | /* Prepare to recurse/iterate. */ |
| 343 | Recurse(trunc) |
| 344 | } |
| 345 | } |
| 346 | PreInsertion(SWAP_nonaligned,TRUNC_nonaligned,size); |
| 347 | Insertion(SWAP_nonaligned); |
| 348 | free(pivot); |
| 349 | } |
| 350 | |
| 351 | static void qsort_aligned(void *base, size_t nmemb, size_t size, |
| 352 | int (*compare)(const void *, const void *)) { |
| 353 | |
| 354 | stack_entry stack[STACK_SIZE]; |
| 355 | int stacktop=0; |
| 356 | char *first,*last; |
| 357 | char *pivot=malloc(size); |
| 358 | size_t trunc=TRUNC_aligned*size; |
| 359 | assert(pivot!=0); |
| 360 | |
| 361 | first=(char*)base; last=first+(nmemb-1)*size; |
| 362 | |
| 363 | if ((size_t)(last-first)>trunc) { |
| 364 | char *ffirst=first,*llast=last; |
| 365 | while (1) { |
| 366 | /* Select pivot */ |
| 367 | { char * mid=first+size*((last-first)/size >> 1); |
| 368 | Pivot(SWAP_aligned,size); |
| 369 | memcpy(pivot,mid,size); |
| 370 | } |
| 371 | /* Partition. */ |
| 372 | Partition(SWAP_aligned,size); |
| 373 | /* Prepare to recurse/iterate. */ |
| 374 | Recurse(trunc) |
| 375 | } |
| 376 | } |
| 377 | PreInsertion(SWAP_aligned,TRUNC_aligned,size); |
| 378 | Insertion(SWAP_aligned); |
| 379 | free(pivot); |
| 380 | } |
| 381 | |
| 382 | static void qsort_words(void *base, size_t nmemb, |
| 383 | int (*compare)(const void *, const void *)) { |
| 384 | |
| 385 | stack_entry stack[STACK_SIZE]; |
| 386 | int stacktop=0; |
| 387 | char *first,*last; |
| 388 | char *pivot=malloc(WORD_BYTES); |
| 389 | assert(pivot!=0); |
| 390 | |
| 391 | first=(char*)base; last=first+(nmemb-1)*WORD_BYTES; |
| 392 | |
| 393 | if (last-first>TRUNC_words) { |
| 394 | char *ffirst=first, *llast=last; |
| 395 | while (1) { |
| 396 | #ifdef DEBUG_QSORT |
| 397 | fprintf(stderr,"Doing %d:%d: ", |
| 398 | (first-(char*)base)/WORD_BYTES, |
| 399 | (last-(char*)base)/WORD_BYTES); |
| 400 | #endif |
| 401 | /* Select pivot */ |
| 402 | { char * mid=first+WORD_BYTES*((last-first) / (2*WORD_BYTES)); |
| 403 | Pivot(SWAP_words,WORD_BYTES); |
| 404 | *(int*)pivot=*(int*)mid; |
| 405 | } |
| 406 | #ifdef DEBUG_QSORT |
| 407 | fprintf(stderr,"pivot=%d\n",*(int*)pivot); |
| 408 | #endif |
| 409 | /* Partition. */ |
| 410 | Partition(SWAP_words,WORD_BYTES); |
| 411 | /* Prepare to recurse/iterate. */ |
| 412 | Recurse(TRUNC_words) |
| 413 | } |
| 414 | } |
| 415 | PreInsertion(SWAP_words,(TRUNC_words/WORD_BYTES),WORD_BYTES); |
| 416 | /* Now do insertion sort. */ |
| 417 | last=((char*)base)+nmemb*WORD_BYTES; |
| 418 | for (first=((char*)base)+WORD_BYTES;first!=last;first+=WORD_BYTES) { |
| 419 | /* Find the right place for |first|. My apologies for var reuse */ |
| 420 | int *pl=(int*)(first-WORD_BYTES),*pr=(int*)first; |
| 421 | *(int*)pivot=*(int*)first; |
| 422 | for (;compare(pl,pivot)>0;pr=pl,--pl) { |
| 423 | *pr=*pl; } |
| 424 | if (pr!=(int*)first) *pr=*(int*)pivot; |
| 425 | } |
| 426 | free(pivot); |
| 427 | } |
| 428 | |
| 429 | /* ---------------------------------------------------------------------- */ |
| 430 | |
| 431 | void qsort(void *base, size_t nmemb, size_t size, |
| 432 | int (*compare)(const void *, const void *)) { |
| 433 | |
| 434 | if (nmemb<=1) return; |
| 435 | if (((uintptr_t)base|size)&(WORD_BYTES-1)) |
| 436 | qsort_nonaligned(base,nmemb,size,compare); |
| 437 | else if (size!=WORD_BYTES) |
| 438 | qsort_aligned(base,nmemb,size,compare); |
| 439 | else |
| 440 | qsort_words(base,nmemb,compare); |
| 441 | } |
| 442 | |
| 443 | #endif /* !HAVE_QSORT */ |