2 * (c) 1998 Gareth McCaughan
4 * This is a drop-in replacement for the C library's |qsort()| routine.
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
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.)
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
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
42 * Gareth McCaughan Peterhouse Cambridge 1998
44 #include "SDL_config.h"
51 #include "SDL_stdinc.h"
54 #define malloc SDL_malloc
56 #define memcpy SDL_memcpy
57 #define memmove SDL_memmove
58 #define qsort SDL_qsort
63 static char _ID[] = "<qsort.c gjm 1.12 1998-03-19>";
65 /* How many bytes are there per word? (Must be a power of 2,
66 * and must in fact equal sizeof(int).)
68 #define WORD_BYTES sizeof(int)
70 /* How big does our stack need to be? Answer: one entry per
73 #define STACK_SIZE (8*sizeof(size_t))
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.
82 #define TRUNC_nonaligned 12
83 #define TRUNC_aligned 12
84 #define TRUNC_words 12*WORD_BYTES /* nb different meaning */
86 /* We use a simple pivoting algorithm for shortish sub-arrays
87 * and a more complicated one for larger ones. The threshold
90 #define PIVOT_THRESHOLD 40
97 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}
98 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}
99 #define doLeft {first=ffirst;llast=last;continue;}
100 #define doRight {ffirst=first;last=llast;continue;}
101 #define pop {if (--stacktop<0) break;\
102 first=ffirst=stack[stacktop].first;\
103 last=llast=stack[stacktop].last;\
106 /* Some comments on the implementation.
107 * 1. When we finish partitioning the array into "low"
108 * and "high", we forget entirely about short subarrays,
109 * because they'll be done later by insertion sort.
110 * Doing lots of little insertion sorts might be a win
111 * on large datasets for locality-of-reference reasons,
112 * but it makes the code much nastier and increases
113 * bookkeeping overhead.
114 * 2. We always save the shorter and get to work on the
115 * longer. This guarantees that every time we push
116 * an item onto the stack its size is <= 1/2 of that
117 * of its parent; so the stack can't need more than
118 * log_2(max-array-size) entries.
119 * 3. We choose a pivot by looking at the first, last
120 * and middle elements. We arrange them into order
121 * because it's easy to do that in conjunction with
122 * choosing the pivot, and it makes things a little
123 * easier in the partitioning step. Anyway, the pivot
124 * is the middle of these three. It's still possible
125 * to construct datasets where the algorithm takes
126 * time of order n^2, but it simply never happens in
128 * 3' Newsflash: On further investigation I find that
129 * it's easy to construct datasets where median-of-3
130 * simply isn't good enough. So on large-ish subarrays
131 * we do a more sophisticated pivoting: we take three
132 * sets of 3 elements, find their medians, and then
133 * take the median of those.
134 * 4. We copy the pivot element to a separate place
135 * because that way we can always do our comparisons
136 * directly against a pointer to that separate place,
137 * and don't have to wonder "did we move the pivot
138 * element?". This makes the inner loop better.
139 * 5. It's possible to make the pivoting even more
140 * reliable by looking at more candidates when n
141 * is larger. (Taking this to its logical conclusion
142 * results in a variant of quicksort that doesn't
143 * have that n^2 worst case.) However, the overhead
144 * from the extra bookkeeping means that it's just
146 * 6. This is pretty clean and portable code. Here are
147 * all the potential portability pitfalls and problems
149 * - In one place (the insertion sort) I construct
150 * a pointer that points just past the end of the
151 * supplied array, and assume that (a) it won't
152 * compare equal to any pointer within the array,
153 * and (b) it will compare equal to a pointer
154 * obtained by stepping off the end of the array.
155 * These might fail on some segmented architectures.
156 * - I assume that there are 8 bits in a |char| when
157 * computing the size of stack needed. This would
158 * fail on machines with 9-bit or 16-bit bytes.
159 * - I assume that if |((int)base&(sizeof(int)-1))==0|
160 * and |(size&(sizeof(int)-1))==0| then it's safe to
161 * get at array elements via |int*|s, and that if
162 * actually |size==sizeof(int)| as well then it's
163 * safe to treat the elements as |int|s. This might
164 * fail on systems that convert pointers to integers
165 * in non-standard ways.
166 * - I assume that |8*sizeof(size_t)<=INT_MAX|. This
167 * would be false on a machine with 8-bit |char|s,
168 * 16-bit |int|s and 4096-bit |size_t|s. :-)
171 /* The recursion logic is the same in each case: */
172 #define Recurse(Trunc) \
173 { size_t l=last-ffirst,r=llast-first; \
175 if (r>=Trunc) doRight \
178 else if (l<=r) { pushLeft; doRight } \
179 else if (r>=Trunc) { pushRight; doLeft }\
183 /* and so is the pivoting logic: */
184 #define Pivot(swapper,sz) \
185 if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\
187 if (compare(first,mid)<0) { \
188 if (compare(mid,last)>0) { \
190 if (compare(first,mid)>0) swapper(first,mid);\
194 if (compare(mid,last)>0) swapper(first,last)\
196 swapper(first,mid); \
197 if (compare(mid,last)>0) swapper(mid,last);\
200 first+=sz; last-=sz; \
207 /* and so is the partitioning logic: */
208 #define Partition(swapper,sz) { \
211 while (compare(first,pivot)<0) first+=sz; \
212 while (compare(pivot,last)<0) last-=sz; \
214 swapper(first,last); swapped=1; \
215 first+=sz; last-=sz; } \
216 else if (first==last) { first+=sz; last-=sz; break; }\
217 } while (first<=last); \
221 /* and so is the pre-insertion-sort operation of putting
222 * the smallest element into place as a sentinel.
223 * Doing this makes the inner loop nicer. I got this
224 * idea from the GNU implementation of qsort().
226 #define PreInsertion(swapper,limit,sz) \
228 last=first + (nmemb>limit ? limit : nmemb-1)*sz;\
229 while (last!=base) { \
230 if (compare(first,last)>0) first=last; \
232 if (first!=base) swapper(first,(char*)base);
234 /* and so is the insertion sort, in the first two cases: */
235 #define Insertion(swapper) \
236 last=((char*)base)+nmemb*size; \
237 for (first=((char*)base)+size;first!=last;first+=size) { \
239 /* Find the right place for |first|. \
240 * My apologies for var reuse. */ \
241 for (test=first-size;compare(test,first)>0;test-=size) ; \
244 /* Shift everything in [test,first) \
245 * up by one, and place |first| \
246 * where |test| is. */ \
247 memcpy(pivot,first,size); \
248 memmove(test+size,test,first-test); \
249 memcpy(test,pivot,size); \
253 #define SWAP_nonaligned(a,b) { \
254 register char *aa=(a),*bb=(b); \
255 register size_t sz=size; \
256 do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }
258 #define SWAP_aligned(a,b) { \
259 register int *aa=(int*)(a),*bb=(int*)(b); \
260 register size_t sz=size; \
261 do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }
263 #define SWAP_words(a,b) { \
264 register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }
266 /* ---------------------------------------------------------------------- */
269 pivot_big(char *first, char *mid, char *last, size_t size,
270 int compare(const void *, const void *))
272 size_t d = (((last - first) / size) >> 3) * size;
275 char *a = first, *b = first + d, *c = first + 2 * d;
277 fprintf(stderr, "< %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
279 m1 = compare(a, b) < 0 ?
280 (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))
281 : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));
284 char *a = mid - d, *b = mid, *c = mid + d;
286 fprintf(stderr, ". %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
288 m2 = 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));
293 char *a = last - 2 * d, *b = last - d, *c = last;
295 fprintf(stderr, "> %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
297 m3 = compare(a, b) < 0 ?
298 (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))
299 : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));
302 fprintf(stderr, "-> %d %d %d\n", *(int *) m1, *(int *) m2, *(int *) m3);
304 return compare(m1, m2) < 0 ?
305 (compare(m2, m3) < 0 ? m2 : (compare(m1, m3) < 0 ? m3 : m1))
306 : (compare(m1, m3) < 0 ? m1 : (compare(m2, m3) < 0 ? m3 : m2));
309 /* ---------------------------------------------------------------------- */
312 qsort_nonaligned(void *base, size_t nmemb, size_t size,
313 int (*compare) (const void *, const void *))
316 stack_entry stack[STACK_SIZE];
319 char *pivot = malloc(size);
320 size_t trunc = TRUNC_nonaligned * size;
323 first = (char *) base;
324 last = first + (nmemb - 1) * size;
326 if ((size_t) (last - first) > trunc) {
327 char *ffirst = first, *llast = last;
331 char *mid = first + size * ((last - first) / size >> 1);
332 Pivot(SWAP_nonaligned, size);
333 memcpy(pivot, mid, size);
336 Partition(SWAP_nonaligned, size);
337 /* Prepare to recurse/iterate. */
340 PreInsertion(SWAP_nonaligned, TRUNC_nonaligned, size);
341 Insertion(SWAP_nonaligned);
346 qsort_aligned(void *base, size_t nmemb, size_t size,
347 int (*compare) (const void *, const void *))
350 stack_entry stack[STACK_SIZE];
353 char *pivot = malloc(size);
354 size_t trunc = TRUNC_aligned * size;
357 first = (char *) base;
358 last = first + (nmemb - 1) * size;
360 if ((size_t) (last - first) > trunc) {
361 char *ffirst = first, *llast = last;
365 char *mid = first + size * ((last - first) / size >> 1);
366 Pivot(SWAP_aligned, size);
367 memcpy(pivot, mid, size);
370 Partition(SWAP_aligned, size);
371 /* Prepare to recurse/iterate. */
374 PreInsertion(SWAP_aligned, TRUNC_aligned, size);
375 Insertion(SWAP_aligned);
380 qsort_words(void *base, size_t nmemb,
381 int (*compare) (const void *, const void *))
384 stack_entry stack[STACK_SIZE];
387 char *pivot = malloc(WORD_BYTES);
390 first = (char *) base;
391 last = first + (nmemb - 1) * WORD_BYTES;
393 if (last - first > TRUNC_words) {
394 char *ffirst = first, *llast = last;
397 fprintf(stderr, "Doing %d:%d: ",
398 (first - (char *) base) / WORD_BYTES,
399 (last - (char *) base) / WORD_BYTES);
404 first + WORD_BYTES * ((last - first) / (2 * WORD_BYTES));
405 Pivot(SWAP_words, WORD_BYTES);
406 *(int *) pivot = *(int *) mid;
409 fprintf(stderr, "pivot=%d\n", *(int *) pivot);
412 Partition(SWAP_words, WORD_BYTES);
413 /* Prepare to recurse/iterate. */
414 Recurse(TRUNC_words)}
416 PreInsertion(SWAP_words, (TRUNC_words / WORD_BYTES), WORD_BYTES);
417 /* Now do insertion sort. */
418 last = ((char *) base) + nmemb * WORD_BYTES;
419 for (first = ((char *) base) + WORD_BYTES; first != last;
420 first += WORD_BYTES) {
421 /* Find the right place for |first|. My apologies for var reuse */
422 int *pl = (int *) (first - WORD_BYTES), *pr = (int *) first;
423 *(int *) pivot = *(int *) first;
424 for (; compare(pl, pivot) > 0; pr = pl, --pl) {
427 if (pr != (int *) first)
428 *pr = *(int *) pivot;
433 /* ---------------------------------------------------------------------- */
436 qsort(void *base, size_t nmemb, size_t size,
437 int (*compare) (const void *, const void *))
442 if (((uintptr_t) base | size) & (WORD_BYTES - 1))
443 qsort_nonaligned(base, nmemb, size, compare);
444 else if (size != WORD_BYTES)
445 qsort_aligned(base, nmemb, size, compare);
447 qsort_words(base, nmemb, compare);
450 #endif /* !HAVE_QSORT */
451 /* vi: set ts=4 sw=4 expandtab: */