src/stdlib/SDL_qsort.c
author Ryan C. Gordon <icculus@icculus.org>
Sat, 12 Sep 2009 13:15:27 +0000
branchSDL-1.2
changeset 4186 5bacec0933f5
parent 1456 84de7511f79f
child 10086 2e3396e62aa6
permissions -rw-r--r--
Fixed compiler warnings on Mac OS X 10.6 SDK.
     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 */