--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/stdlib/SDL_qsort.c	Mon Feb 06 08:28:51 2006 +0000
@@ -0,0 +1,418 @@
+/* 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 <assert.h>
+#include <stdlib.h>
+#include <string.h>
+*/
+#define assert(X)
+#include "SDL_stdlib.h"
+#include "SDL_string.h"
+
+#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 *)) {
+  int 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 SDL_qsort(void *base, size_t nmemb, size_t size,
+           int (*compare)(const void *, const void *)) {
+
+  if (nmemb<=1) return;
+  if (((int)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 */
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