/* 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 */