/* 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 const 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: */