/* 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"

#include "SDL_assert.h"

#ifdef SDL_qsort

#undef SDL_qsort

void

SDL_qsort(void *base, size_t nmemb, size_t size, int (*compare) (const void *, const void *))

{

SDL_qsort_inline(base, nmemb, size, compare);

}

#else

#ifdef assert

#undef assert

#endif

#define assert(X) SDL_assert(X)

#ifdef malloc

#undef malloc

#endif

#define malloc SDL_malloc

#ifdef free

#undef free

#endif

#define free SDL_free

#ifdef memcpy

#undef memcpy

#endif

#define memcpy SDL_memcpy

#ifdef memmove

#undef memmove

#endif

#define memmove SDL_memmove

#ifdef qsort

#undef qsort

#endif

#define qsort SDL_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 /* !SDL_qsort */