src/stdlib/SDL_qsort.c
author Sam Lantinga <slouken@libsdl.org>
Tue, 21 Feb 2006 08:46:50 +0000
changeset 1402 d910939febfa
parent 1354 22f39393668a
child 1456 84de7511f79f
permissions -rw-r--r--
Use consistent identifiers for the various platforms we support.
Make sure every source file includes SDL_config.h, so the proper system
headers are chosen.
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/* qsort.c
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 * (c) 1998 Gareth McCaughan
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 *
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 * This is a drop-in replacement for the C library's |qsort()| routine.
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 *
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 * Features:
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 *   - Median-of-three pivoting (and more)
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 *   - Truncation and final polishing by a single insertion sort
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 *   - Early truncation when no swaps needed in pivoting step
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 *   - Explicit recursion, guaranteed not to overflow
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 *   - A few little wrinkles stolen from the GNU |qsort()|.
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 *   - separate code for non-aligned / aligned / word-size objects
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 *
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 * This code may be reproduced freely provided
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 *   - this file is retained unaltered apart from minor
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 *     changes for portability and efficiency
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 *   - no changes are made to this comment
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 *   - any changes that *are* made are clearly flagged
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 *   - the _ID string below is altered by inserting, after
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 *     the date, the string " altered" followed at your option
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 *     by other material. (Exceptions: you may change the name
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 *     of the exported routine without changing the ID string.
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 *     You may change the values of the macros TRUNC_* and
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 *     PIVOT_THRESHOLD without changing the ID string, provided
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 *     they remain constants with TRUNC_nonaligned, TRUNC_aligned
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 *     and TRUNC_words/WORD_BYTES between 8 and 24, and
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 *     PIVOT_THRESHOLD between 32 and 200.)
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 *
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 * You may use it in anything you like; you may make money
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 * out of it; you may distribute it in object form or as
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 * part of an executable without including source code;
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 * you don't have to credit me. (But it would be nice if
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 * you did.)
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 *
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 * If you find problems with this code, or find ways of
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 * making it significantly faster, please let me know!
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 * My e-mail address, valid as of early 1998 and certainly
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 * OK for at least the next 18 months, is
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 *    gjm11@dpmms.cam.ac.uk
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 * Thanks!
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 *
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 * Gareth McCaughan   Peterhouse   Cambridge   1998
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 */
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#include "SDL_config.h"
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/*
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#include <assert.h>
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#include <stdlib.h>
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#include <string.h>
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*/
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#include "SDL_stdinc.h"
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#define assert(X)
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#define malloc	SDL_malloc
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#define free	SDL_free
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#define memcpy	SDL_memcpy
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#define memmove	SDL_memmove
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#define qsort	SDL_qsort
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#ifndef HAVE_QSORT
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static char _ID[]="<qsort.c gjm 1.12 1998-03-19>";
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/* How many bytes are there per word? (Must be a power of 2,
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 * and must in fact equal sizeof(int).)
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 */
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#define WORD_BYTES sizeof(int)
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/* How big does our stack need to be? Answer: one entry per
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 * bit in a |size_t|.
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 */
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#define STACK_SIZE (8*sizeof(size_t))
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/* Different situations have slightly different requirements,
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 * and we make life epsilon easier by using different truncation
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 * points for the three different cases.
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 * So far, I have tuned TRUNC_words and guessed that the same
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 * value might work well for the other two cases. Of course
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 * what works well on my machine might work badly on yours.
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 */
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#define TRUNC_nonaligned	12
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#define TRUNC_aligned		12
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#define TRUNC_words		12*WORD_BYTES	/* nb different meaning */
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/* We use a simple pivoting algorithm for shortish sub-arrays
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 * and a more complicated one for larger ones. The threshold
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 * is PIVOT_THRESHOLD.
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 */
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#define PIVOT_THRESHOLD 40
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typedef struct { char * first; char * last; } stack_entry;
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#define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}
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#define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}
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#define doLeft {first=ffirst;llast=last;continue;}
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#define doRight {ffirst=first;last=llast;continue;}
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#define pop {if (--stacktop<0) break;\
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  first=ffirst=stack[stacktop].first;\
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  last=llast=stack[stacktop].last;\
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  continue;}
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/* Some comments on the implementation.
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 * 1. When we finish partitioning the array into "low"
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 *    and "high", we forget entirely about short subarrays,
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 *    because they'll be done later by insertion sort.
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 *    Doing lots of little insertion sorts might be a win
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 *    on large datasets for locality-of-reference reasons,
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 *    but it makes the code much nastier and increases
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 *    bookkeeping overhead.
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 * 2. We always save the shorter and get to work on the
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 *    longer. This guarantees that every time we push
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 *    an item onto the stack its size is <= 1/2 of that
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 *    of its parent; so the stack can't need more than
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 *    log_2(max-array-size) entries.
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 * 3. We choose a pivot by looking at the first, last
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 *    and middle elements. We arrange them into order
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 *    because it's easy to do that in conjunction with
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 *    choosing the pivot, and it makes things a little
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 *    easier in the partitioning step. Anyway, the pivot
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 *    is the middle of these three. It's still possible
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 *    to construct datasets where the algorithm takes
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 *    time of order n^2, but it simply never happens in
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 *    practice.
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 * 3' Newsflash: On further investigation I find that
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 *    it's easy to construct datasets where median-of-3
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 *    simply isn't good enough. So on large-ish subarrays
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 *    we do a more sophisticated pivoting: we take three
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 *    sets of 3 elements, find their medians, and then
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 *    take the median of those.
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 * 4. We copy the pivot element to a separate place
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 *    because that way we can always do our comparisons
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 *    directly against a pointer to that separate place,
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 *    and don't have to wonder "did we move the pivot
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 *    element?". This makes the inner loop better.
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 * 5. It's possible to make the pivoting even more
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 *    reliable by looking at more candidates when n
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 *    is larger. (Taking this to its logical conclusion
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 *    results in a variant of quicksort that doesn't
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 *    have that n^2 worst case.) However, the overhead
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 *    from the extra bookkeeping means that it's just
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 *    not worth while.
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 * 6. This is pretty clean and portable code. Here are
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 *    all the potential portability pitfalls and problems
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 *    I know of:
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 *      - In one place (the insertion sort) I construct
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 *        a pointer that points just past the end of the
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 *        supplied array, and assume that (a) it won't
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 *        compare equal to any pointer within the array,
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 *        and (b) it will compare equal to a pointer
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 *        obtained by stepping off the end of the array.
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 *        These might fail on some segmented architectures.
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 *      - I assume that there are 8 bits in a |char| when
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 *        computing the size of stack needed. This would
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 *        fail on machines with 9-bit or 16-bit bytes.
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 *      - I assume that if |((int)base&(sizeof(int)-1))==0|
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 *        and |(size&(sizeof(int)-1))==0| then it's safe to
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 *        get at array elements via |int*|s, and that if
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 *        actually |size==sizeof(int)| as well then it's
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 *        safe to treat the elements as |int|s. This might
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 *        fail on systems that convert pointers to integers
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 *        in non-standard ways.
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 *      - I assume that |8*sizeof(size_t)<=INT_MAX|. This
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 *        would be false on a machine with 8-bit |char|s,
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 *        16-bit |int|s and 4096-bit |size_t|s. :-)
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 */
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/* The recursion logic is the same in each case: */
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#define Recurse(Trunc)				\
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      { size_t l=last-ffirst,r=llast-first;	\
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        if (l<Trunc) {				\
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          if (r>=Trunc) doRight			\
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          else pop				\
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        }					\
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        else if (l<=r) { pushLeft; doRight }	\
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        else if (r>=Trunc) { pushRight; doLeft }\
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        else doLeft				\
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      }
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/* and so is the pivoting logic: */
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#define Pivot(swapper,sz)			\
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  if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\
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  else {	\
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    if (compare(first,mid)<0) {			\
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      if (compare(mid,last)>0) {		\
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        swapper(mid,last);			\
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        if (compare(first,mid)>0) swapper(first,mid);\
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      }						\
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    }						\
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    else {					\
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      if (compare(mid,last)>0) swapper(first,last)\
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      else {					\
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        swapper(first,mid);			\
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        if (compare(mid,last)>0) swapper(mid,last);\
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      }						\
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    }						\
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    first+=sz; last-=sz;			\
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  }
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#ifdef DEBUG_QSORT
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#include <stdio.h>
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#endif
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/* and so is the partitioning logic: */
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#define Partition(swapper,sz) {			\
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  int swapped=0;				\
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  do {						\
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    while (compare(first,pivot)<0) first+=sz;	\
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    while (compare(pivot,last)<0) last-=sz;	\
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    if (first<last) {				\
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      swapper(first,last); swapped=1;		\
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      first+=sz; last-=sz; }			\
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    else if (first==last) { first+=sz; last-=sz; break; }\
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  } while (first<=last);			\
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  if (!swapped) pop				\
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}
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/* and so is the pre-insertion-sort operation of putting
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 * the smallest element into place as a sentinel.
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 * Doing this makes the inner loop nicer. I got this
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 * idea from the GNU implementation of qsort().
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 */
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#define PreInsertion(swapper,limit,sz)		\
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  first=base;					\
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  last=first + (nmemb>limit ? limit : nmemb-1)*sz;\
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  while (last!=base) {				\
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    if (compare(first,last)>0) first=last;	\
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    last-=sz; }					\
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  if (first!=base) swapper(first,(char*)base);
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/* and so is the insertion sort, in the first two cases: */
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#define Insertion(swapper)			\
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  last=((char*)base)+nmemb*size;		\
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  for (first=((char*)base)+size;first!=last;first+=size) {	\
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    char *test;					\
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    /* Find the right place for |first|.	\
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     * My apologies for var reuse. */		\
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    for (test=first-size;compare(test,first)>0;test-=size) ;	\
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    test+=size;					\
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    if (test!=first) {				\
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      /* Shift everything in [test,first)	\
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       * up by one, and place |first|		\
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       * where |test| is. */			\
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      memcpy(pivot,first,size);			\
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      memmove(test+size,test,first-test);	\
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      memcpy(test,pivot,size);			\
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    }						\
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  }
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#define SWAP_nonaligned(a,b) { \
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  register char *aa=(a),*bb=(b); \
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  register size_t sz=size; \
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  do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }
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#define SWAP_aligned(a,b) { \
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  register int *aa=(int*)(a),*bb=(int*)(b); \
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  register size_t sz=size; \
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  do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }
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#define SWAP_words(a,b) { \
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  register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }
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/* ---------------------------------------------------------------------- */
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static char * pivot_big(char *first, char *mid, char *last, size_t size,
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                        int compare(const void *, const void *)) {
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  int d=(((last-first)/size)>>3)*size;
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  char *m1,*m2,*m3;
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  { char *a=first, *b=first+d, *c=first+2*d;
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#ifdef DEBUG_QSORT
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fprintf(stderr,"< %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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#endif
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    m1 = compare(a,b)<0 ?
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           (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a))
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         : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b));
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  }
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  { char *a=mid-d, *b=mid, *c=mid+d;
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#ifdef DEBUG_QSORT
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fprintf(stderr,". %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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#endif
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    m2 = compare(a,b)<0 ?
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           (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a))
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         : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b));
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  }
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  { char *a=last-2*d, *b=last-d, *c=last;
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#ifdef DEBUG_QSORT
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fprintf(stderr,"> %d %d %d\n",*(int*)a,*(int*)b,*(int*)c);
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#endif
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    m3 = compare(a,b)<0 ?
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           (compare(b,c)<0 ? b : (compare(a,c)<0 ? c : a))
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         : (compare(a,c)<0 ? a : (compare(b,c)<0 ? c : b));
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  }
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#ifdef DEBUG_QSORT
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fprintf(stderr,"-> %d %d %d\n",*(int*)m1,*(int*)m2,*(int*)m3);
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#endif
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  return compare(m1,m2)<0 ?
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           (compare(m2,m3)<0 ? m2 : (compare(m1,m3)<0 ? m3 : m1))
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         : (compare(m1,m3)<0 ? m1 : (compare(m2,m3)<0 ? m3 : m2));
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}
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/* ---------------------------------------------------------------------- */
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static void qsort_nonaligned(void *base, size_t nmemb, size_t size,
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           int (*compare)(const void *, const void *)) {
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  stack_entry stack[STACK_SIZE];
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  int stacktop=0;
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  char *first,*last;
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  char *pivot=malloc(size);
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  size_t trunc=TRUNC_nonaligned*size;
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  assert(pivot!=0);
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  first=(char*)base; last=first+(nmemb-1)*size;
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  if ((size_t)(last-first)>trunc) {
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    char *ffirst=first, *llast=last;
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    while (1) {
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      /* Select pivot */
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      { char * mid=first+size*((last-first)/size >> 1);
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        Pivot(SWAP_nonaligned,size);
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        memcpy(pivot,mid,size);
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      }
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   322
      /* Partition. */
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   323
      Partition(SWAP_nonaligned,size);
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   324
      /* Prepare to recurse/iterate. */
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   325
      Recurse(trunc)
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   326
    }
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   327
  }
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   328
  PreInsertion(SWAP_nonaligned,TRUNC_nonaligned,size);
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   329
  Insertion(SWAP_nonaligned);
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   330
  free(pivot);
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   331
}
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   332
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   333
static void qsort_aligned(void *base, size_t nmemb, size_t size,
slouken@1330
   334
           int (*compare)(const void *, const void *)) {
slouken@1330
   335
slouken@1330
   336
  stack_entry stack[STACK_SIZE];
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   337
  int stacktop=0;
slouken@1330
   338
  char *first,*last;
slouken@1337
   339
  char *pivot=malloc(size);
slouken@1330
   340
  size_t trunc=TRUNC_aligned*size;
slouken@1330
   341
  assert(pivot!=0);
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   342
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   343
  first=(char*)base; last=first+(nmemb-1)*size;
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   344
slouken@1330
   345
  if ((size_t)(last-first)>trunc) {
slouken@1330
   346
    char *ffirst=first,*llast=last;
slouken@1330
   347
    while (1) {
slouken@1330
   348
      /* Select pivot */
slouken@1330
   349
      { char * mid=first+size*((last-first)/size >> 1);
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   350
        Pivot(SWAP_aligned,size);
slouken@1337
   351
        memcpy(pivot,mid,size);
slouken@1330
   352
      }
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   353
      /* Partition. */
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   354
      Partition(SWAP_aligned,size);
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   355
      /* Prepare to recurse/iterate. */
slouken@1330
   356
      Recurse(trunc)
slouken@1330
   357
    }
slouken@1330
   358
  }
slouken@1330
   359
  PreInsertion(SWAP_aligned,TRUNC_aligned,size);
slouken@1330
   360
  Insertion(SWAP_aligned);
slouken@1337
   361
  free(pivot);
slouken@1330
   362
}
slouken@1330
   363
slouken@1330
   364
static void qsort_words(void *base, size_t nmemb,
slouken@1330
   365
           int (*compare)(const void *, const void *)) {
slouken@1330
   366
slouken@1330
   367
  stack_entry stack[STACK_SIZE];
slouken@1330
   368
  int stacktop=0;
slouken@1330
   369
  char *first,*last;
slouken@1337
   370
  char *pivot=malloc(WORD_BYTES);
slouken@1330
   371
  assert(pivot!=0);
slouken@1330
   372
slouken@1330
   373
  first=(char*)base; last=first+(nmemb-1)*WORD_BYTES;
slouken@1330
   374
slouken@1330
   375
  if (last-first>TRUNC_words) {
slouken@1330
   376
    char *ffirst=first, *llast=last;
slouken@1330
   377
    while (1) {
slouken@1330
   378
#ifdef DEBUG_QSORT
slouken@1330
   379
fprintf(stderr,"Doing %d:%d: ",
slouken@1330
   380
        (first-(char*)base)/WORD_BYTES,
slouken@1330
   381
        (last-(char*)base)/WORD_BYTES);
slouken@1330
   382
#endif
slouken@1330
   383
      /* Select pivot */
slouken@1330
   384
      { char * mid=first+WORD_BYTES*((last-first) / (2*WORD_BYTES));
slouken@1330
   385
        Pivot(SWAP_words,WORD_BYTES);
slouken@1330
   386
        *(int*)pivot=*(int*)mid;
slouken@1330
   387
      }
slouken@1330
   388
#ifdef DEBUG_QSORT
slouken@1330
   389
fprintf(stderr,"pivot=%d\n",*(int*)pivot);
slouken@1330
   390
#endif
slouken@1330
   391
      /* Partition. */
slouken@1330
   392
      Partition(SWAP_words,WORD_BYTES);
slouken@1330
   393
      /* Prepare to recurse/iterate. */
slouken@1330
   394
      Recurse(TRUNC_words)
slouken@1330
   395
    }
slouken@1330
   396
  }
slouken@1330
   397
  PreInsertion(SWAP_words,(TRUNC_words/WORD_BYTES),WORD_BYTES);
slouken@1330
   398
  /* Now do insertion sort. */
slouken@1330
   399
  last=((char*)base)+nmemb*WORD_BYTES;
slouken@1330
   400
  for (first=((char*)base)+WORD_BYTES;first!=last;first+=WORD_BYTES) {
slouken@1330
   401
    /* Find the right place for |first|. My apologies for var reuse */
slouken@1330
   402
    int *pl=(int*)(first-WORD_BYTES),*pr=(int*)first;
slouken@1330
   403
    *(int*)pivot=*(int*)first;
slouken@1330
   404
    for (;compare(pl,pivot)>0;pr=pl,--pl) {
slouken@1330
   405
      *pr=*pl; }
slouken@1330
   406
    if (pr!=(int*)first) *pr=*(int*)pivot;
slouken@1330
   407
  }
slouken@1337
   408
  free(pivot);
slouken@1330
   409
}
slouken@1330
   410
slouken@1330
   411
/* ---------------------------------------------------------------------- */
slouken@1330
   412
slouken@1337
   413
void qsort(void *base, size_t nmemb, size_t size,
slouken@1330
   414
           int (*compare)(const void *, const void *)) {
slouken@1330
   415
slouken@1330
   416
  if (nmemb<=1) return;
slouken@1330
   417
  if (((int)base|size)&(WORD_BYTES-1))
slouken@1330
   418
    qsort_nonaligned(base,nmemb,size,compare);
slouken@1330
   419
  else if (size!=WORD_BYTES)
slouken@1330
   420
    qsort_aligned(base,nmemb,size,compare);
slouken@1330
   421
  else
slouken@1330
   422
    qsort_words(base,nmemb,compare);
slouken@1330
   423
}
slouken@1330
   424
slouken@1331
   425
#endif /* !HAVE_QSORT */