src/stdlib/SDL_qsort.c
author Sam Lantinga <slouken@libsdl.org>
Wed, 01 Mar 2006 09:43:47 +0000
changeset 1456 84de7511f79f
parent 1402 d910939febfa
child 1662 782fd950bd46
child 1895 c121d94672cb
child 4186 5bacec0933f5
permissions -rw-r--r--
Fixed a bunch of 64-bit compatibility problems
     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 #define assert(X)
    54 #define malloc	SDL_malloc
    55 #define free	SDL_free
    56 #define memcpy	SDL_memcpy
    57 #define memmove	SDL_memmove
    58 #define qsort	SDL_qsort
    59 
    60 
    61 #ifndef HAVE_QSORT
    62 
    63 static char _ID[]="<qsort.c gjm 1.12 1998-03-19>";
    64 
    65 /* How many bytes are there per word? (Must be a power of 2,
    66  * and must in fact equal sizeof(int).)
    67  */
    68 #define WORD_BYTES sizeof(int)
    69 
    70 /* How big does our stack need to be? Answer: one entry per
    71  * bit in a |size_t|.
    72  */
    73 #define STACK_SIZE (8*sizeof(size_t))
    74 
    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.
    81  */
    82 #define TRUNC_nonaligned	12
    83 #define TRUNC_aligned		12
    84 #define TRUNC_words		12*WORD_BYTES	/* nb different meaning */
    85 
    86 /* We use a simple pivoting algorithm for shortish sub-arrays
    87  * and a more complicated one for larger ones. The threshold
    88  * is PIVOT_THRESHOLD.
    89  */
    90 #define PIVOT_THRESHOLD 40
    91 
    92 typedef struct { char * first; char * last; } stack_entry;
    93 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}
    94 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}
    95 #define doLeft {first=ffirst;llast=last;continue;}
    96 #define doRight {ffirst=first;last=llast;continue;}
    97 #define pop {if (--stacktop<0) break;\
    98   first=ffirst=stack[stacktop].first;\
    99   last=llast=stack[stacktop].last;\
   100   continue;}
   101 
   102 /* Some comments on the implementation.
   103  * 1. When we finish partitioning the array into "low"
   104  *    and "high", we forget entirely about short subarrays,
   105  *    because they'll be done later by insertion sort.
   106  *    Doing lots of little insertion sorts might be a win
   107  *    on large datasets for locality-of-reference reasons,
   108  *    but it makes the code much nastier and increases
   109  *    bookkeeping overhead.
   110  * 2. We always save the shorter and get to work on the
   111  *    longer. This guarantees that every time we push
   112  *    an item onto the stack its size is <= 1/2 of that
   113  *    of its parent; so the stack can't need more than
   114  *    log_2(max-array-size) entries.
   115  * 3. We choose a pivot by looking at the first, last
   116  *    and middle elements. We arrange them into order
   117  *    because it's easy to do that in conjunction with
   118  *    choosing the pivot, and it makes things a little
   119  *    easier in the partitioning step. Anyway, the pivot
   120  *    is the middle of these three. It's still possible
   121  *    to construct datasets where the algorithm takes
   122  *    time of order n^2, but it simply never happens in
   123  *    practice.
   124  * 3' Newsflash: On further investigation I find that
   125  *    it's easy to construct datasets where median-of-3
   126  *    simply isn't good enough. So on large-ish subarrays
   127  *    we do a more sophisticated pivoting: we take three
   128  *    sets of 3 elements, find their medians, and then
   129  *    take the median of those.
   130  * 4. We copy the pivot element to a separate place
   131  *    because that way we can always do our comparisons
   132  *    directly against a pointer to that separate place,
   133  *    and don't have to wonder "did we move the pivot
   134  *    element?". This makes the inner loop better.
   135  * 5. It's possible to make the pivoting even more
   136  *    reliable by looking at more candidates when n
   137  *    is larger. (Taking this to its logical conclusion
   138  *    results in a variant of quicksort that doesn't
   139  *    have that n^2 worst case.) However, the overhead
   140  *    from the extra bookkeeping means that it's just
   141  *    not worth while.
   142  * 6. This is pretty clean and portable code. Here are
   143  *    all the potential portability pitfalls and problems
   144  *    I know of:
   145  *      - In one place (the insertion sort) I construct
   146  *        a pointer that points just past the end of the
   147  *        supplied array, and assume that (a) it won't
   148  *        compare equal to any pointer within the array,
   149  *        and (b) it will compare equal to a pointer
   150  *        obtained by stepping off the end of the array.
   151  *        These might fail on some segmented architectures.
   152  *      - I assume that there are 8 bits in a |char| when
   153  *        computing the size of stack needed. This would
   154  *        fail on machines with 9-bit or 16-bit bytes.
   155  *      - I assume that if |((int)base&(sizeof(int)-1))==0|
   156  *        and |(size&(sizeof(int)-1))==0| then it's safe to
   157  *        get at array elements via |int*|s, and that if
   158  *        actually |size==sizeof(int)| as well then it's
   159  *        safe to treat the elements as |int|s. This might
   160  *        fail on systems that convert pointers to integers
   161  *        in non-standard ways.
   162  *      - I assume that |8*sizeof(size_t)<=INT_MAX|. This
   163  *        would be false on a machine with 8-bit |char|s,
   164  *        16-bit |int|s and 4096-bit |size_t|s. :-)
   165  */
   166 
   167 /* The recursion logic is the same in each case: */
   168 #define Recurse(Trunc)				\
   169       { size_t l=last-ffirst,r=llast-first;	\
   170         if (l<Trunc) {				\
   171           if (r>=Trunc) doRight			\
   172           else pop				\
   173         }					\
   174         else if (l<=r) { pushLeft; doRight }	\
   175         else if (r>=Trunc) { pushRight; doLeft }\
   176         else doLeft				\
   177       }
   178 
   179 /* and so is the pivoting logic: */
   180 #define Pivot(swapper,sz)			\
   181   if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\
   182   else {	\
   183     if (compare(first,mid)<0) {			\
   184       if (compare(mid,last)>0) {		\
   185         swapper(mid,last);			\
   186         if (compare(first,mid)>0) swapper(first,mid);\
   187       }						\
   188     }						\
   189     else {					\
   190       if (compare(mid,last)>0) swapper(first,last)\
   191       else {					\
   192         swapper(first,mid);			\
   193         if (compare(mid,last)>0) swapper(mid,last);\
   194       }						\
   195     }						\
   196     first+=sz; last-=sz;			\
   197   }
   198 
   199 #ifdef DEBUG_QSORT
   200 #include <stdio.h>
   201 #endif
   202 
   203 /* and so is the partitioning logic: */
   204 #define Partition(swapper,sz) {			\
   205   int swapped=0;				\
   206   do {						\
   207     while (compare(first,pivot)<0) first+=sz;	\
   208     while (compare(pivot,last)<0) last-=sz;	\
   209     if (first<last) {				\
   210       swapper(first,last); swapped=1;		\
   211       first+=sz; last-=sz; }			\
   212     else if (first==last) { first+=sz; last-=sz; break; }\
   213   } while (first<=last);			\
   214   if (!swapped) pop				\
   215 }
   216 
   217 /* and so is the pre-insertion-sort operation of putting
   218  * the smallest element into place as a sentinel.
   219  * Doing this makes the inner loop nicer. I got this
   220  * idea from the GNU implementation of qsort().
   221  */
   222 #define PreInsertion(swapper,limit,sz)		\
   223   first=base;					\
   224   last=first + (nmemb>limit ? limit : nmemb-1)*sz;\
   225   while (last!=base) {				\
   226     if (compare(first,last)>0) first=last;	\
   227     last-=sz; }					\
   228   if (first!=base) swapper(first,(char*)base);
   229 
   230 /* and so is the insertion sort, in the first two cases: */
   231 #define Insertion(swapper)			\
   232   last=((char*)base)+nmemb*size;		\
   233   for (first=((char*)base)+size;first!=last;first+=size) {	\
   234     char *test;					\
   235     /* Find the right place for |first|.	\
   236      * My apologies for var reuse. */		\
   237     for (test=first-size;compare(test,first)>0;test-=size) ;	\
   238     test+=size;					\
   239     if (test!=first) {				\
   240       /* Shift everything in [test,first)	\
   241        * up by one, and place |first|		\
   242        * where |test| is. */			\
   243       memcpy(pivot,first,size);			\
   244       memmove(test+size,test,first-test);	\
   245       memcpy(test,pivot,size);			\
   246     }						\
   247   }
   248 
   249 #define SWAP_nonaligned(a,b) { \
   250   register char *aa=(a),*bb=(b); \
   251   register size_t sz=size; \
   252   do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }
   253 
   254 #define SWAP_aligned(a,b) { \
   255   register int *aa=(int*)(a),*bb=(int*)(b); \
   256   register size_t sz=size; \
   257   do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }
   258 
   259 #define SWAP_words(a,b) { \
   260   register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }
   261 
   262 /* ---------------------------------------------------------------------- */
   263 
   264 static char * pivot_big(char *first, char *mid, char *last, size_t size,
   265                         int compare(const void *, const void *)) {
   266   size_t d=(((last-first)/size)>>3)*size;
   267   char *m1,*m2,*m3;
   268   { char *a=first, *b=first+d, *c=first+2*d;
   269 #ifdef DEBUG_QSORT
   270 fprintf(stderr,"< %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
   271 #endif
   272     m1 = compare(a,b)<0 ?
   273            (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a))
   274          : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b));
   275   }
   276   { char *a=mid-d, *b=mid, *c=mid+d;
   277 #ifdef DEBUG_QSORT
   278 fprintf(stderr,". %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
   279 #endif
   280     m2 = compare(a,b)<0 ?
   281            (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a))
   282          : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b));
   283   }
   284   { char *a=last-2*d, *b=last-d, *c=last;
   285 #ifdef DEBUG_QSORT
   286 fprintf(stderr,"> %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
   287 #endif
   288     m3 = 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));
   291   }
   292 #ifdef DEBUG_QSORT
   293 fprintf(stderr,"-> %d %d %d\n",*(int*)m1,*(int*)m2,*(int*)m3);
   294 #endif
   295   return compare(m1,m2)<0 ?
   296            (compare(m2,m3)<0 ? m2 : (compare(m1,m3)<0 ? m3 : m1))
   297          : (compare(m1,m3)<0 ? m1 : (compare(m2,m3)<0 ? m3 : m2));
   298 }
   299 
   300 /* ---------------------------------------------------------------------- */
   301 
   302 static void qsort_nonaligned(void *base, size_t nmemb, size_t size,
   303            int (*compare)(const void *, const void *)) {
   304 
   305   stack_entry stack[STACK_SIZE];
   306   int stacktop=0;
   307   char *first,*last;
   308   char *pivot=malloc(size);
   309   size_t trunc=TRUNC_nonaligned*size;
   310   assert(pivot!=0);
   311 
   312   first=(char*)base; last=first+(nmemb-1)*size;
   313 
   314   if ((size_t)(last-first)>trunc) {
   315     char *ffirst=first, *llast=last;
   316     while (1) {
   317       /* Select pivot */
   318       { char * mid=first+size*((last-first)/size >> 1);
   319         Pivot(SWAP_nonaligned,size);
   320         memcpy(pivot,mid,size);
   321       }
   322       /* Partition. */
   323       Partition(SWAP_nonaligned,size);
   324       /* Prepare to recurse/iterate. */
   325       Recurse(trunc)
   326     }
   327   }
   328   PreInsertion(SWAP_nonaligned,TRUNC_nonaligned,size);
   329   Insertion(SWAP_nonaligned);
   330   free(pivot);
   331 }
   332 
   333 static void qsort_aligned(void *base, size_t nmemb, size_t size,
   334            int (*compare)(const void *, const void *)) {
   335 
   336   stack_entry stack[STACK_SIZE];
   337   int stacktop=0;
   338   char *first,*last;
   339   char *pivot=malloc(size);
   340   size_t trunc=TRUNC_aligned*size;
   341   assert(pivot!=0);
   342 
   343   first=(char*)base; last=first+(nmemb-1)*size;
   344 
   345   if ((size_t)(last-first)>trunc) {
   346     char *ffirst=first,*llast=last;
   347     while (1) {
   348       /* Select pivot */
   349       { char * mid=first+size*((last-first)/size >> 1);
   350         Pivot(SWAP_aligned,size);
   351         memcpy(pivot,mid,size);
   352       }
   353       /* Partition. */
   354       Partition(SWAP_aligned,size);
   355       /* Prepare to recurse/iterate. */
   356       Recurse(trunc)
   357     }
   358   }
   359   PreInsertion(SWAP_aligned,TRUNC_aligned,size);
   360   Insertion(SWAP_aligned);
   361   free(pivot);
   362 }
   363 
   364 static void qsort_words(void *base, size_t nmemb,
   365            int (*compare)(const void *, const void *)) {
   366 
   367   stack_entry stack[STACK_SIZE];
   368   int stacktop=0;
   369   char *first,*last;
   370   char *pivot=malloc(WORD_BYTES);
   371   assert(pivot!=0);
   372 
   373   first=(char*)base; last=first+(nmemb-1)*WORD_BYTES;
   374 
   375   if (last-first>TRUNC_words) {
   376     char *ffirst=first, *llast=last;
   377     while (1) {
   378 #ifdef DEBUG_QSORT
   379 fprintf(stderr,"Doing %d:%d: ",
   380         (first-(char*)base)/WORD_BYTES,
   381         (last-(char*)base)/WORD_BYTES);
   382 #endif
   383       /* Select pivot */
   384       { char * mid=first+WORD_BYTES*((last-first) / (2*WORD_BYTES));
   385         Pivot(SWAP_words,WORD_BYTES);
   386         *(int*)pivot=*(int*)mid;
   387       }
   388 #ifdef DEBUG_QSORT
   389 fprintf(stderr,"pivot=%d\n",*(int*)pivot);
   390 #endif
   391       /* Partition. */
   392       Partition(SWAP_words,WORD_BYTES);
   393       /* Prepare to recurse/iterate. */
   394       Recurse(TRUNC_words)
   395     }
   396   }
   397   PreInsertion(SWAP_words,(TRUNC_words/WORD_BYTES),WORD_BYTES);
   398   /* Now do insertion sort. */
   399   last=((char*)base)+nmemb*WORD_BYTES;
   400   for (first=((char*)base)+WORD_BYTES;first!=last;first+=WORD_BYTES) {
   401     /* Find the right place for |first|. My apologies for var reuse */
   402     int *pl=(int*)(first-WORD_BYTES),*pr=(int*)first;
   403     *(int*)pivot=*(int*)first;
   404     for (;compare(pl,pivot)>0;pr=pl,--pl) {
   405       *pr=*pl; }
   406     if (pr!=(int*)first) *pr=*(int*)pivot;
   407   }
   408   free(pivot);
   409 }
   410 
   411 /* ---------------------------------------------------------------------- */
   412 
   413 void qsort(void *base, size_t nmemb, size_t size,
   414            int (*compare)(const void *, const void *)) {
   415 
   416   if (nmemb<=1) return;
   417   if (((uintptr_t)base|size)&(WORD_BYTES-1))
   418     qsort_nonaligned(base,nmemb,size,compare);
   419   else if (size!=WORD_BYTES)
   420     qsort_aligned(base,nmemb,size,compare);
   421   else
   422     qsort_words(base,nmemb,compare);
   423 }
   424 
   425 #endif /* !HAVE_QSORT */