src/stdlib/SDL_qsort.c
author Ryan C. Gordon <icculus@icculus.org>
Sun, 24 Nov 2013 23:56:17 -0500
changeset 8093 b43765095a6f
parent 7351 668a3dc28361
child 9306 817656bd36ec
permissions -rw-r--r--
Make internal SDL sources include SDL_internal.h instead of SDL_config.h

The new header will include SDL_config.h, but allows for other global stuff.
     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_internal.h"
    45 
    46 /*
    47 #include <assert.h>
    48 #include <stdlib.h>
    49 #include <string.h>
    50 */
    51 #include "SDL_stdinc.h"
    52 #include "SDL_assert.h"
    53 
    54 #if defined(HAVE_QSORT)
    55 void
    56 SDL_qsort(void *base, size_t nmemb, size_t size, int (*compare) (const void *, const void *))
    57 {
    58     qsort(base, nmemb, size, compare);
    59 }
    60 #else
    61 
    62 #ifdef assert
    63 #undef assert
    64 #endif
    65 #define assert(X) SDL_assert(X)
    66 #ifdef malloc
    67 #undef malloc
    68 #endif
    69 #define malloc	SDL_malloc
    70 #ifdef free
    71 #undef free
    72 #endif
    73 #define free	SDL_free
    74 #ifdef memcpy
    75 #undef memcpy
    76 #endif
    77 #define memcpy	SDL_memcpy
    78 #ifdef memmove
    79 #undef memmove
    80 #endif
    81 #define memmove	SDL_memmove
    82 #ifdef qsort
    83 #undef qsort
    84 #endif
    85 #define qsort	SDL_qsort
    86 
    87 static const char _ID[] = "<qsort.c gjm 1.12 1998-03-19>";
    88 
    89 /* How many bytes are there per word? (Must be a power of 2,
    90  * and must in fact equal sizeof(int).)
    91  */
    92 #define WORD_BYTES sizeof(int)
    93 
    94 /* How big does our stack need to be? Answer: one entry per
    95  * bit in a |size_t|.
    96  */
    97 #define STACK_SIZE (8*sizeof(size_t))
    98 
    99 /* Different situations have slightly different requirements,
   100  * and we make life epsilon easier by using different truncation
   101  * points for the three different cases.
   102  * So far, I have tuned TRUNC_words and guessed that the same
   103  * value might work well for the other two cases. Of course
   104  * what works well on my machine might work badly on yours.
   105  */
   106 #define TRUNC_nonaligned	12
   107 #define TRUNC_aligned		12
   108 #define TRUNC_words		12*WORD_BYTES   /* nb different meaning */
   109 
   110 /* We use a simple pivoting algorithm for shortish sub-arrays
   111  * and a more complicated one for larger ones. The threshold
   112  * is PIVOT_THRESHOLD.
   113  */
   114 #define PIVOT_THRESHOLD 40
   115 
   116 typedef struct
   117 {
   118     char *first;
   119     char *last;
   120 } stack_entry;
   121 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}
   122 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}
   123 #define doLeft {first=ffirst;llast=last;continue;}
   124 #define doRight {ffirst=first;last=llast;continue;}
   125 #define pop {if (--stacktop<0) break;\
   126   first=ffirst=stack[stacktop].first;\
   127   last=llast=stack[stacktop].last;\
   128   continue;}
   129 
   130 /* Some comments on the implementation.
   131  * 1. When we finish partitioning the array into "low"
   132  *    and "high", we forget entirely about short subarrays,
   133  *    because they'll be done later by insertion sort.
   134  *    Doing lots of little insertion sorts might be a win
   135  *    on large datasets for locality-of-reference reasons,
   136  *    but it makes the code much nastier and increases
   137  *    bookkeeping overhead.
   138  * 2. We always save the shorter and get to work on the
   139  *    longer. This guarantees that every time we push
   140  *    an item onto the stack its size is <= 1/2 of that
   141  *    of its parent; so the stack can't need more than
   142  *    log_2(max-array-size) entries.
   143  * 3. We choose a pivot by looking at the first, last
   144  *    and middle elements. We arrange them into order
   145  *    because it's easy to do that in conjunction with
   146  *    choosing the pivot, and it makes things a little
   147  *    easier in the partitioning step. Anyway, the pivot
   148  *    is the middle of these three. It's still possible
   149  *    to construct datasets where the algorithm takes
   150  *    time of order n^2, but it simply never happens in
   151  *    practice.
   152  * 3' Newsflash: On further investigation I find that
   153  *    it's easy to construct datasets where median-of-3
   154  *    simply isn't good enough. So on large-ish subarrays
   155  *    we do a more sophisticated pivoting: we take three
   156  *    sets of 3 elements, find their medians, and then
   157  *    take the median of those.
   158  * 4. We copy the pivot element to a separate place
   159  *    because that way we can always do our comparisons
   160  *    directly against a pointer to that separate place,
   161  *    and don't have to wonder "did we move the pivot
   162  *    element?". This makes the inner loop better.
   163  * 5. It's possible to make the pivoting even more
   164  *    reliable by looking at more candidates when n
   165  *    is larger. (Taking this to its logical conclusion
   166  *    results in a variant of quicksort that doesn't
   167  *    have that n^2 worst case.) However, the overhead
   168  *    from the extra bookkeeping means that it's just
   169  *    not worth while.
   170  * 6. This is pretty clean and portable code. Here are
   171  *    all the potential portability pitfalls and problems
   172  *    I know of:
   173  *      - In one place (the insertion sort) I construct
   174  *        a pointer that points just past the end of the
   175  *        supplied array, and assume that (a) it won't
   176  *        compare equal to any pointer within the array,
   177  *        and (b) it will compare equal to a pointer
   178  *        obtained by stepping off the end of the array.
   179  *        These might fail on some segmented architectures.
   180  *      - I assume that there are 8 bits in a |char| when
   181  *        computing the size of stack needed. This would
   182  *        fail on machines with 9-bit or 16-bit bytes.
   183  *      - I assume that if |((int)base&(sizeof(int)-1))==0|
   184  *        and |(size&(sizeof(int)-1))==0| then it's safe to
   185  *        get at array elements via |int*|s, and that if
   186  *        actually |size==sizeof(int)| as well then it's
   187  *        safe to treat the elements as |int|s. This might
   188  *        fail on systems that convert pointers to integers
   189  *        in non-standard ways.
   190  *      - I assume that |8*sizeof(size_t)<=INT_MAX|. This
   191  *        would be false on a machine with 8-bit |char|s,
   192  *        16-bit |int|s and 4096-bit |size_t|s. :-)
   193  */
   194 
   195 /* The recursion logic is the same in each case: */
   196 #define Recurse(Trunc)				\
   197       { size_t l=last-ffirst,r=llast-first;	\
   198         if (l<Trunc) {				\
   199           if (r>=Trunc) doRight			\
   200           else pop				\
   201         }					\
   202         else if (l<=r) { pushLeft; doRight }	\
   203         else if (r>=Trunc) { pushRight; doLeft }\
   204         else doLeft				\
   205       }
   206 
   207 /* and so is the pivoting logic: */
   208 #define Pivot(swapper,sz)			\
   209   if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\
   210   else {	\
   211     if (compare(first,mid)<0) {			\
   212       if (compare(mid,last)>0) {		\
   213         swapper(mid,last);			\
   214         if (compare(first,mid)>0) swapper(first,mid);\
   215       }						\
   216     }						\
   217     else {					\
   218       if (compare(mid,last)>0) swapper(first,last)\
   219       else {					\
   220         swapper(first,mid);			\
   221         if (compare(mid,last)>0) swapper(mid,last);\
   222       }						\
   223     }						\
   224     first+=sz; last-=sz;			\
   225   }
   226 
   227 #ifdef DEBUG_QSORT
   228 #include <stdio.h>
   229 #endif
   230 
   231 /* and so is the partitioning logic: */
   232 #define Partition(swapper,sz) {			\
   233   int swapped=0;				\
   234   do {						\
   235     while (compare(first,pivot)<0) first+=sz;	\
   236     while (compare(pivot,last)<0) last-=sz;	\
   237     if (first<last) {				\
   238       swapper(first,last); swapped=1;		\
   239       first+=sz; last-=sz; }			\
   240     else if (first==last) { first+=sz; last-=sz; break; }\
   241   } while (first<=last);			\
   242   if (!swapped) pop				\
   243 }
   244 
   245 /* and so is the pre-insertion-sort operation of putting
   246  * the smallest element into place as a sentinel.
   247  * Doing this makes the inner loop nicer. I got this
   248  * idea from the GNU implementation of qsort().
   249  */
   250 #define PreInsertion(swapper,limit,sz)		\
   251   first=base;					\
   252   last=first + (nmemb>limit ? limit : nmemb-1)*sz;\
   253   while (last!=base) {				\
   254     if (compare(first,last)>0) first=last;	\
   255     last-=sz; }					\
   256   if (first!=base) swapper(first,(char*)base);
   257 
   258 /* and so is the insertion sort, in the first two cases: */
   259 #define Insertion(swapper)			\
   260   last=((char*)base)+nmemb*size;		\
   261   for (first=((char*)base)+size;first!=last;first+=size) {	\
   262     char *test;					\
   263     /* Find the right place for |first|.	\
   264      * My apologies for var reuse. */		\
   265     for (test=first-size;compare(test,first)>0;test-=size) ;	\
   266     test+=size;					\
   267     if (test!=first) {				\
   268       /* Shift everything in [test,first)	\
   269        * up by one, and place |first|		\
   270        * where |test| is. */			\
   271       memcpy(pivot,first,size);			\
   272       memmove(test+size,test,first-test);	\
   273       memcpy(test,pivot,size);			\
   274     }						\
   275   }
   276 
   277 #define SWAP_nonaligned(a,b) { \
   278   register char *aa=(a),*bb=(b); \
   279   register size_t sz=size; \
   280   do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }
   281 
   282 #define SWAP_aligned(a,b) { \
   283   register int *aa=(int*)(a),*bb=(int*)(b); \
   284   register size_t sz=size; \
   285   do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }
   286 
   287 #define SWAP_words(a,b) { \
   288   register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }
   289 
   290 /* ---------------------------------------------------------------------- */
   291 
   292 static char *
   293 pivot_big(char *first, char *mid, char *last, size_t size,
   294           int compare(const void *, const void *))
   295 {
   296     size_t d = (((last - first) / size) >> 3) * size;
   297     char *m1, *m2, *m3;
   298     {
   299         char *a = first, *b = first + d, *c = first + 2 * d;
   300 #ifdef DEBUG_QSORT
   301         fprintf(stderr, "< %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
   302 #endif
   303         m1 = compare(a, b) < 0 ?
   304             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))
   305             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));
   306     }
   307     {
   308         char *a = mid - d, *b = mid, *c = mid + d;
   309 #ifdef DEBUG_QSORT
   310         fprintf(stderr, ". %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
   311 #endif
   312         m2 = compare(a, b) < 0 ?
   313             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))
   314             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));
   315     }
   316     {
   317         char *a = last - 2 * d, *b = last - d, *c = last;
   318 #ifdef DEBUG_QSORT
   319         fprintf(stderr, "> %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);
   320 #endif
   321         m3 = compare(a, b) < 0 ?
   322             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))
   323             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));
   324     }
   325 #ifdef DEBUG_QSORT
   326     fprintf(stderr, "-> %d %d %d\n", *(int *) m1, *(int *) m2, *(int *) m3);
   327 #endif
   328     return compare(m1, m2) < 0 ?
   329         (compare(m2, m3) < 0 ? m2 : (compare(m1, m3) < 0 ? m3 : m1))
   330         : (compare(m1, m3) < 0 ? m1 : (compare(m2, m3) < 0 ? m3 : m2));
   331 }
   332 
   333 /* ---------------------------------------------------------------------- */
   334 
   335 static void
   336 qsort_nonaligned(void *base, size_t nmemb, size_t size,
   337                  int (*compare) (const void *, const void *))
   338 {
   339 
   340     stack_entry stack[STACK_SIZE];
   341     int stacktop = 0;
   342     char *first, *last;
   343     char *pivot = malloc(size);
   344     size_t trunc = TRUNC_nonaligned * size;
   345     assert(pivot != 0);
   346 
   347     first = (char *) base;
   348     last = first + (nmemb - 1) * size;
   349 
   350     if ((size_t) (last - first) > trunc) {
   351         char *ffirst = first, *llast = last;
   352         while (1) {
   353             /* Select pivot */
   354             {
   355                 char *mid = first + size * ((last - first) / size >> 1);
   356                 Pivot(SWAP_nonaligned, size);
   357                 memcpy(pivot, mid, size);
   358             }
   359             /* Partition. */
   360             Partition(SWAP_nonaligned, size);
   361             /* Prepare to recurse/iterate. */
   362         Recurse(trunc)}
   363     }
   364     PreInsertion(SWAP_nonaligned, TRUNC_nonaligned, size);
   365     Insertion(SWAP_nonaligned);
   366     free(pivot);
   367 }
   368 
   369 static void
   370 qsort_aligned(void *base, size_t nmemb, size_t size,
   371               int (*compare) (const void *, const void *))
   372 {
   373 
   374     stack_entry stack[STACK_SIZE];
   375     int stacktop = 0;
   376     char *first, *last;
   377     char *pivot = malloc(size);
   378     size_t trunc = TRUNC_aligned * size;
   379     assert(pivot != 0);
   380 
   381     first = (char *) base;
   382     last = first + (nmemb - 1) * size;
   383 
   384     if ((size_t) (last - first) > trunc) {
   385         char *ffirst = first, *llast = last;
   386         while (1) {
   387             /* Select pivot */
   388             {
   389                 char *mid = first + size * ((last - first) / size >> 1);
   390                 Pivot(SWAP_aligned, size);
   391                 memcpy(pivot, mid, size);
   392             }
   393             /* Partition. */
   394             Partition(SWAP_aligned, size);
   395             /* Prepare to recurse/iterate. */
   396         Recurse(trunc)}
   397     }
   398     PreInsertion(SWAP_aligned, TRUNC_aligned, size);
   399     Insertion(SWAP_aligned);
   400     free(pivot);
   401 }
   402 
   403 static void
   404 qsort_words(void *base, size_t nmemb,
   405             int (*compare) (const void *, const void *))
   406 {
   407 
   408     stack_entry stack[STACK_SIZE];
   409     int stacktop = 0;
   410     char *first, *last;
   411     char *pivot = malloc(WORD_BYTES);
   412     assert(pivot != 0);
   413 
   414     first = (char *) base;
   415     last = first + (nmemb - 1) * WORD_BYTES;
   416 
   417     if (last - first > TRUNC_words) {
   418         char *ffirst = first, *llast = last;
   419         while (1) {
   420 #ifdef DEBUG_QSORT
   421             fprintf(stderr, "Doing %d:%d: ",
   422                     (first - (char *) base) / WORD_BYTES,
   423                     (last - (char *) base) / WORD_BYTES);
   424 #endif
   425             /* Select pivot */
   426             {
   427                 char *mid =
   428                     first + WORD_BYTES * ((last - first) / (2 * WORD_BYTES));
   429                 Pivot(SWAP_words, WORD_BYTES);
   430                 *(int *) pivot = *(int *) mid;
   431             }
   432 #ifdef DEBUG_QSORT
   433             fprintf(stderr, "pivot=%d\n", *(int *) pivot);
   434 #endif
   435             /* Partition. */
   436             Partition(SWAP_words, WORD_BYTES);
   437             /* Prepare to recurse/iterate. */
   438         Recurse(TRUNC_words)}
   439     }
   440     PreInsertion(SWAP_words, (TRUNC_words / WORD_BYTES), WORD_BYTES);
   441     /* Now do insertion sort. */
   442     last = ((char *) base) + nmemb * WORD_BYTES;
   443     for (first = ((char *) base) + WORD_BYTES; first != last;
   444          first += WORD_BYTES) {
   445         /* Find the right place for |first|. My apologies for var reuse */
   446         int *pl = (int *) (first - WORD_BYTES), *pr = (int *) first;
   447         *(int *) pivot = *(int *) first;
   448         for (; compare(pl, pivot) > 0; pr = pl, --pl) {
   449             *pr = *pl;
   450         }
   451         if (pr != (int *) first)
   452             *pr = *(int *) pivot;
   453     }
   454     free(pivot);
   455 }
   456 
   457 /* ---------------------------------------------------------------------- */
   458 
   459 void
   460 qsort(void *base, size_t nmemb, size_t size,
   461       int (*compare) (const void *, const void *))
   462 {
   463 
   464     if (nmemb <= 1)
   465         return;
   466     if (((uintptr_t) base | size) & (WORD_BYTES - 1))
   467         qsort_nonaligned(base, nmemb, size, compare);
   468     else if (size != WORD_BYTES)
   469         qsort_aligned(base, nmemb, size, compare);
   470     else
   471         qsort_words(base, nmemb, compare);
   472 }
   473 
   474 #endif /* !SDL_qsort */
   475 
   476 /* vi: set ts=4 sw=4 expandtab: */