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"
60 #define malloc SDL_malloc
68 #define memcpy SDL_memcpy
72 #define memmove SDL_memmove
76 #define qsort SDL_qsort
81 static char _ID[]="<qsort.c gjm 1.12 1998-03-19>";
83 /* How many bytes are there per word? (Must be a power of 2,
84 * and must in fact equal sizeof(int).)
86 #define WORD_BYTES sizeof(int)
88 /* How big does our stack need to be? Answer: one entry per
91 #define STACK_SIZE (8*sizeof(size_t))
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.
100 #define TRUNC_nonaligned 12
101 #define TRUNC_aligned 12
102 #define TRUNC_words 12*WORD_BYTES /* nb different meaning */
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.
108 #define PIVOT_THRESHOLD 40
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;\
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
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
160 * 6. This is pretty clean and portable code. Here are
161 * all the potential portability pitfalls and problems
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. :-)
185 /* The recursion logic is the same in each case: */
186 #define Recurse(Trunc) \
187 { size_t l=last-ffirst,r=llast-first; \
189 if (r>=Trunc) doRight \
192 else if (l<=r) { pushLeft; doRight } \
193 else if (r>=Trunc) { pushRight; doLeft }\
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);\
201 if (compare(first,mid)<0) { \
202 if (compare(mid,last)>0) { \
204 if (compare(first,mid)>0) swapper(first,mid);\
208 if (compare(mid,last)>0) swapper(first,last)\
210 swapper(first,mid); \
211 if (compare(mid,last)>0) swapper(mid,last);\
214 first+=sz; last-=sz; \
221 /* and so is the partitioning logic: */
222 #define Partition(swapper,sz) { \
225 while (compare(first,pivot)<0) first+=sz; \
226 while (compare(pivot,last)<0) last-=sz; \
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); \
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().
240 #define PreInsertion(swapper,limit,sz) \
242 last=first + (nmemb>limit ? limit : nmemb-1)*sz;\
243 while (last!=base) { \
244 if (compare(first,last)>0) first=last; \
246 if (first!=base) swapper(first,(char*)base);
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) { \
253 /* Find the right place for |first|. \
254 * My apologies for var reuse. */ \
255 for (test=first-size;compare(test,first)>0;test-=size) ; \
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); \
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); }
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); }
277 #define SWAP_words(a,b) { \
278 register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }
280 /* ---------------------------------------------------------------------- */
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;
286 { char *a=first, *b=first+d, *c=first+2*d;
288 fprintf(stderr,"< %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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));
294 { char *a=mid-d, *b=mid, *c=mid+d;
296 fprintf(stderr,". %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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));
302 { char *a=last-2*d, *b=last-d, *c=last;
304 fprintf(stderr,"> %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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));
311 fprintf(stderr,"-> %d %d %d\n",*(int*)m1,*(int*)m2,*(int*)m3);
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));
318 /* ---------------------------------------------------------------------- */
320 static void qsort_nonaligned(void *base, size_t nmemb, size_t size,
321 int (*compare)(const void *, const void *)) {
323 stack_entry stack[STACK_SIZE];
326 char *pivot=malloc(size);
327 size_t trunc=TRUNC_nonaligned*size;
330 first=(char*)base; last=first+(nmemb-1)*size;
332 if ((size_t)(last-first)>trunc) {
333 char *ffirst=first, *llast=last;
336 { char * mid=first+size*((last-first)/size >> 1);
337 Pivot(SWAP_nonaligned,size);
338 memcpy(pivot,mid,size);
341 Partition(SWAP_nonaligned,size);
342 /* Prepare to recurse/iterate. */
346 PreInsertion(SWAP_nonaligned,TRUNC_nonaligned,size);
347 Insertion(SWAP_nonaligned);
351 static void qsort_aligned(void *base, size_t nmemb, size_t size,
352 int (*compare)(const void *, const void *)) {
354 stack_entry stack[STACK_SIZE];
357 char *pivot=malloc(size);
358 size_t trunc=TRUNC_aligned*size;
361 first=(char*)base; last=first+(nmemb-1)*size;
363 if ((size_t)(last-first)>trunc) {
364 char *ffirst=first,*llast=last;
367 { char * mid=first+size*((last-first)/size >> 1);
368 Pivot(SWAP_aligned,size);
369 memcpy(pivot,mid,size);
372 Partition(SWAP_aligned,size);
373 /* Prepare to recurse/iterate. */
377 PreInsertion(SWAP_aligned,TRUNC_aligned,size);
378 Insertion(SWAP_aligned);
382 static void qsort_words(void *base, size_t nmemb,
383 int (*compare)(const void *, const void *)) {
385 stack_entry stack[STACK_SIZE];
388 char *pivot=malloc(WORD_BYTES);
391 first=(char*)base; 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);
402 { char * mid=first+WORD_BYTES*((last-first) / (2*WORD_BYTES));
403 Pivot(SWAP_words,WORD_BYTES);
404 *(int*)pivot=*(int*)mid;
407 fprintf(stderr,"pivot=%d\n",*(int*)pivot);
410 Partition(SWAP_words,WORD_BYTES);
411 /* Prepare to recurse/iterate. */
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) {
424 if (pr!=(int*)first) *pr=*(int*)pivot;
429 /* ---------------------------------------------------------------------- */
431 void qsort(void *base, size_t nmemb, size_t size,
432 int (*compare)(const void *, const void *)) {
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);
440 qsort_words(base,nmemb,compare);
443 #endif /* !HAVE_QSORT */