/* qsort.c

  * (c) 1998 Gareth McCaughan

  *

  * This is a drop-in replacement for the C library's |qsort()| routine.

  *

  * Features:

  *   - Median-of-three pivoting (and more)

  *   - Truncation and final polishing by a single insertion sort

  *   - Early truncation when no swaps needed in pivoting step

  *   - Explicit recursion, guaranteed not to overflow

  *   - A few little wrinkles stolen from the GNU |qsort()|.

  *   - separate code for non-aligned / aligned / word-size objects

  *

  * This code may be reproduced freely provided

  *   - this file is retained unaltered apart from minor

  *     changes for portability and efficiency

  *   - no changes are made to this comment

  *   - any changes that *are* made are clearly flagged

  *   - the _ID string below is altered by inserting, after

  *     the date, the string " altered" followed at your option

  *     by other material. (Exceptions: you may change the name

  *     of the exported routine without changing the ID string.

  *     You may change the values of the macros TRUNC_* and

  *     PIVOT_THRESHOLD without changing the ID string, provided

  *     they remain constants with TRUNC_nonaligned, TRUNC_aligned

  *     and TRUNC_words/WORD_BYTES between 8 and 24, and

  *     PIVOT_THRESHOLD between 32 and 200.)

  *

  * You may use it in anything you like; you may make money

  * out of it; you may distribute it in object form or as

  * part of an executable without including source code;

  * you don't have to credit me. (But it would be nice if

  * you did.)

  *

  * If you find problems with this code, or find ways of

  * making it significantly faster, please let me know!

  * My e-mail address, valid as of early 1998 and certainly

  * OK for at least the next 18 months, is

  *    gjm11@dpmms.cam.ac.uk

  * Thanks!

  *

  * Gareth McCaughan   Peterhouse   Cambridge   1998

  */

 #include "SDL_config.h"

 /*

 #include <assert.h>

 #include <stdlib.h>

 #include <string.h>

 */

 #include "SDL_stdinc.h"

 #define assert(X)

 #define malloc	SDL_malloc

 #define free	SDL_free

 #define memcpy	SDL_memcpy

 #define memmove	SDL_memmove

 #define qsort	SDL_qsort

 #ifndef HAVE_QSORT

 static char _ID[] = "<qsort.c gjm 1.12 1998-03-19>";

 /* How many bytes are there per word? (Must be a power of 2,

  * and must in fact equal sizeof(int).)

  */

 #define WORD_BYTES sizeof(int)

 /* How big does our stack need to be? Answer: one entry per

  * bit in a |size_t|.

  */

 #define STACK_SIZE (8*sizeof(size_t))

 /* Different situations have slightly different requirements,

  * and we make life epsilon easier by using different truncation

  * points for the three different cases.

  * So far, I have tuned TRUNC_words and guessed that the same

  * value might work well for the other two cases. Of course

  * what works well on my machine might work badly on yours.

  */

 #define TRUNC_nonaligned	12

 #define TRUNC_aligned		12

 #define TRUNC_words		12*WORD_BYTES   /* nb different meaning */

 /* We use a simple pivoting algorithm for shortish sub-arrays

  * and a more complicated one for larger ones. The threshold

  * is PIVOT_THRESHOLD.

  */

 #define PIVOT_THRESHOLD 40

 typedef struct

 {

     char *first;

     char *last;

 } stack_entry;

 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}

 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}

 #define doLeft {first=ffirst;llast=last;continue;}

 #define doRight {ffirst=first;last=llast;continue;}

 #define pop {if (--stacktop<0) break;\

   first=ffirst=stack[stacktop].first;\

   last=llast=stack[stacktop].last;\

   continue;}

 /* Some comments on the implementation.

  * 1. When we finish partitioning the array into "low"

  *    and "high", we forget entirely about short subarrays,

  *    because they'll be done later by insertion sort.

  *    Doing lots of little insertion sorts might be a win

  *    on large datasets for locality-of-reference reasons,

  *    but it makes the code much nastier and increases

  *    bookkeeping overhead.

  * 2. We always save the shorter and get to work on the

  *    longer. This guarantees that every time we push

  *    an item onto the stack its size is <= 1/2 of that

  *    of its parent; so the stack can't need more than

  *    log_2(max-array-size) entries.

  * 3. We choose a pivot by looking at the first, last

  *    and middle elements. We arrange them into order

  *    because it's easy to do that in conjunction with

  *    choosing the pivot, and it makes things a little

  *    easier in the partitioning step. Anyway, the pivot

  *    is the middle of these three. It's still possible

  *    to construct datasets where the algorithm takes

  *    time of order n^2, but it simply never happens in

  *    practice.

  * 3' Newsflash: On further investigation I find that

  *    it's easy to construct datasets where median-of-3

  *    simply isn't good enough. So on large-ish subarrays

  *    we do a more sophisticated pivoting: we take three

  *    sets of 3 elements, find their medians, and then

  *    take the median of those.

  * 4. We copy the pivot element to a separate place

  *    because that way we can always do our comparisons

  *    directly against a pointer to that separate place,

  *    and don't have to wonder "did we move the pivot

  *    element?". This makes the inner loop better.

  * 5. It's possible to make the pivoting even more

  *    reliable by looking at more candidates when n

  *    is larger. (Taking this to its logical conclusion

  *    results in a variant of quicksort that doesn't

  *    have that n^2 worst case.) However, the overhead

  *    from the extra bookkeeping means that it's just

  *    not worth while.

  * 6. This is pretty clean and portable code. Here are

  *    all the potential portability pitfalls and problems

  *    I know of:

  *      - In one place (the insertion sort) I construct

  *        a pointer that points just past the end of the

  *        supplied array, and assume that (a) it won't

  *        compare equal to any pointer within the array,

  *        and (b) it will compare equal to a pointer

  *        obtained by stepping off the end of the array.

  *        These might fail on some segmented architectures.

  *      - I assume that there are 8 bits in a |char| when

  *        computing the size of stack needed. This would

  *        fail on machines with 9-bit or 16-bit bytes.

  *      - I assume that if |((int)base&(sizeof(int)-1))==0|

  *        and |(size&(sizeof(int)-1))==0| then it's safe to

  *        get at array elements via |int*|s, and that if

  *        actually |size==sizeof(int)| as well then it's

  *        safe to treat the elements as |int|s. This might

  *        fail on systems that convert pointers to integers

  *        in non-standard ways.

  *      - I assume that |8*sizeof(size_t)<=INT_MAX|. This

  *        would be false on a machine with 8-bit |char|s,

  *        16-bit |int|s and 4096-bit |size_t|s. :-)

  */

 /* The recursion logic is the same in each case: */

 #define Recurse(Trunc)				\

       { size_t l=last-ffirst,r=llast-first;	\

         if (l<Trunc) {				\

           if (r>=Trunc) doRight			\

           else pop				\

         }					\

         else if (l<=r) { pushLeft; doRight }	\

         else if (r>=Trunc) { pushRight; doLeft }\

         else doLeft				\

       }

 /* and so is the pivoting logic: */

 #define Pivot(swapper,sz)			\

   if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\

   else {	\

     if (compare(first,mid)<0) {			\

       if (compare(mid,last)>0) {		\

         swapper(mid,last);			\

         if (compare(first,mid)>0) swapper(first,mid);\

       }						\

     }						\

     else {					\

       if (compare(mid,last)>0) swapper(first,last)\

       else {					\

         swapper(first,mid);			\

         if (compare(mid,last)>0) swapper(mid,last);\

       }						\

     }						\

     first+=sz; last-=sz;			\

   }

 #ifdef DEBUG_QSORT

 #include <stdio.h>

 #endif

 /* and so is the partitioning logic: */

 #define Partition(swapper,sz) {			\

   int swapped=0;				\

   do {						\

     while (compare(first,pivot)<0) first+=sz;	\

     while (compare(pivot,last)<0) last-=sz;	\

     if (first<last) {				\

       swapper(first,last); swapped=1;		\

       first+=sz; last-=sz; }			\

     else if (first==last) { first+=sz; last-=sz; break; }\

   } while (first<=last);			\

   if (!swapped) pop				\

 }

 /* and so is the pre-insertion-sort operation of putting

  * the smallest element into place as a sentinel.

  * Doing this makes the inner loop nicer. I got this

  * idea from the GNU implementation of qsort().

  */

 #define PreInsertion(swapper,limit,sz)		\

   first=base;					\

   last=first + (nmemb>limit ? limit : nmemb-1)*sz;\

   while (last!=base) {				\

     if (compare(first,last)>0) first=last;	\

     last-=sz; }					\

   if (first!=base) swapper(first,(char*)base);

 /* and so is the insertion sort, in the first two cases: */

 #define Insertion(swapper)			\

   last=((char*)base)+nmemb*size;		\

   for (first=((char*)base)+size;first!=last;first+=size) {	\

     char *test;					\

     /* Find the right place for |first|.	\

      * My apologies for var reuse. */		\

     for (test=first-size;compare(test,first)>0;test-=size) ;	\

     test+=size;					\

     if (test!=first) {				\

       /* Shift everything in [test,first)	\

        * up by one, and place |first|		\

        * where |test| is. */			\

       memcpy(pivot,first,size);			\

       memmove(test+size,test,first-test);	\

       memcpy(test,pivot,size);			\

     }						\

   }

 #define SWAP_nonaligned(a,b) { \

   register char *aa=(a),*bb=(b); \

   register size_t sz=size; \

   do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }

 #define SWAP_aligned(a,b) { \

   register int *aa=(int*)(a),*bb=(int*)(b); \

   register size_t sz=size; \

   do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }

 #define SWAP_words(a,b) { \

   register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }

 /* ---------------------------------------------------------------------- */

 static char *

 pivot_big(char *first, char *mid, char *last, size_t size,

           int compare(const void *, const void *))

 {

     size_t d = (((last - first) / size) >> 3) * size;

     char *m1, *m2, *m3;

     {

         char *a = first, *b = first + d, *c = first + 2 * d;

 #ifdef DEBUG_QSORT

         fprintf(stderr, "< %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);

 #endif

         m1 = compare(a, b) < 0 ?

             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))

             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));

     }

     {

         char *a = mid - d, *b = mid, *c = mid + d;

 #ifdef DEBUG_QSORT

         fprintf(stderr, ". %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);

 #endif

         m2 = compare(a, b) < 0 ?

             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))

             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));

     }

     {

         char *a = last - 2 * d, *b = last - d, *c = last;

 #ifdef DEBUG_QSORT

         fprintf(stderr, "> %d %d %d\n", *(int *) a, *(int *) b, *(int *) c);

 #endif

         m3 = compare(a, b) < 0 ?

             (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))

             : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));

     }

 #ifdef DEBUG_QSORT

     fprintf(stderr, "-> %d %d %d\n", *(int *) m1, *(int *) m2, *(int *) m3);

 #endif

     return compare(m1, m2) < 0 ?

         (compare(m2, m3) < 0 ? m2 : (compare(m1, m3) < 0 ? m3 : m1))

         : (compare(m1, m3) < 0 ? m1 : (compare(m2, m3) < 0 ? m3 : m2));

 }

 /* ---------------------------------------------------------------------- */

 static void

 qsort_nonaligned(void *base, size_t nmemb, size_t size,

                  int (*compare) (const void *, const void *))

 {

     stack_entry stack[STACK_SIZE];

     int stacktop = 0;

     char *first, *last;

     char *pivot = malloc(size);

     size_t trunc = TRUNC_nonaligned * size;

     assert(pivot != 0);

     first = (char *) base;

     last = first + (nmemb - 1) * size;

     if ((size_t) (last - first) > trunc) {

         char *ffirst = first, *llast = last;

         while (1) {

             /* Select pivot */

             {

                 char *mid = first + size * ((last - first) / size >> 1);

                 Pivot(SWAP_nonaligned, size);

                 memcpy(pivot, mid, size);

             }

             /* Partition. */

             Partition(SWAP_nonaligned, size);

             /* Prepare to recurse/iterate. */

         Recurse(trunc)}

     }

     PreInsertion(SWAP_nonaligned, TRUNC_nonaligned, size);

     Insertion(SWAP_nonaligned);

     free(pivot);

 }

 static void

 qsort_aligned(void *base, size_t nmemb, size_t size,

               int (*compare) (const void *, const void *))

 {

     stack_entry stack[STACK_SIZE];

     int stacktop = 0;

     char *first, *last;

     char *pivot = malloc(size);

     size_t trunc = TRUNC_aligned * size;

     assert(pivot != 0);

     first = (char *) base;

     last = first + (nmemb - 1) * size;

     if ((size_t) (last - first) > trunc) {

         char *ffirst = first, *llast = last;

         while (1) {

             /* Select pivot */

             {

                 char *mid = first + size * ((last - first) / size >> 1);

                 Pivot(SWAP_aligned, size);

                 memcpy(pivot, mid, size);

             }

             /* Partition. */

             Partition(SWAP_aligned, size);

             /* Prepare to recurse/iterate. */

         Recurse(trunc)}

     }

     PreInsertion(SWAP_aligned, TRUNC_aligned, size);

     Insertion(SWAP_aligned);

     free(pivot);

 }

 static void

 qsort_words(void *base, size_t nmemb,

             int (*compare) (const void *, const void *))

 {

     stack_entry stack[STACK_SIZE];

     int stacktop = 0;

     char *first, *last;

     char *pivot = malloc(WORD_BYTES);

     assert(pivot != 0);

     first = (char *) base;

     last = first + (nmemb - 1) * WORD_BYTES;

     if (last - first > TRUNC_words) {

         char *ffirst = first, *llast = last;

         while (1) {

 #ifdef DEBUG_QSORT

             fprintf(stderr, "Doing %d:%d: ",

                     (first - (char *) base) / WORD_BYTES,

                     (last - (char *) base) / WORD_BYTES);

 #endif

             /* Select pivot */

             {

                 char *mid =

                     first + WORD_BYTES * ((last - first) / (2 * WORD_BYTES));

                 Pivot(SWAP_words, WORD_BYTES);

                 *(int *) pivot = *(int *) mid;

             }

 #ifdef DEBUG_QSORT

             fprintf(stderr, "pivot=%d\n", *(int *) pivot);

 #endif

             /* Partition. */

             Partition(SWAP_words, WORD_BYTES);

             /* Prepare to recurse/iterate. */

         Recurse(TRUNC_words)}

     }

     PreInsertion(SWAP_words, (TRUNC_words / WORD_BYTES), WORD_BYTES);

     /* Now do insertion sort. */

     last = ((char *) base) + nmemb * WORD_BYTES;

     for (first = ((char *) base) + WORD_BYTES; first != last;

          first += WORD_BYTES) {

         /* Find the right place for |first|. My apologies for var reuse */

         int *pl = (int *) (first - WORD_BYTES), *pr = (int *) first;

         *(int *) pivot = *(int *) first;

         for (; compare(pl, pivot) > 0; pr = pl, --pl) {

             *pr = *pl;

         }

         if (pr != (int *) first)

             *pr = *(int *) pivot;

     }

     free(pivot);

 }

 /* ---------------------------------------------------------------------- */

 void

 qsort(void *base, size_t nmemb, size_t size,

       int (*compare) (const void *, const void *))

 {

     if (nmemb <= 1)

         return;

     if (((uintptr_t) base | size) & (WORD_BYTES - 1))

         qsort_nonaligned(base, nmemb, size, compare);

     else if (size != WORD_BYTES)

         qsort_aligned(base, nmemb, size, compare);

     else

         qsort_words(base, nmemb, compare);

 }

 #endif /* !HAVE_QSORT */

 /* vi: set ts=4 sw=4 expandtab: */