/* 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 #include #include */ #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[]=""; /* 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) 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 #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 (firstlimit ? 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 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 */