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| /* 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>
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 (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 (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 (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);
}
/* ---------------------------------------------------------------------- */
extern void qsortG(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);
} |
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