e14743d1 |
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 */ |