From: Jarkko Hietaniemi Date: Fri, 1 Sep 2000 02:22:24 +0000 (+0000) Subject: Retract the mergesort code, way too incompatible licensing X-Git-Url: http://git.shadowcat.co.uk/gitweb/gitweb.cgi?a=commitdiff_plain;h=e35355fc86a8d4cbceeb314ff2c3d1b0d61b07d0;p=p5sagit%2Fp5-mst-13.2.git Retract the mergesort code, way too incompatible licensing and copyrights. p4raw-id: //depot/perl@6963 --- diff --git a/pod/perldelta.pod b/pod/perldelta.pod index 961ded3..d739204 100644 --- a/pod/perldelta.pod +++ b/pod/perldelta.pod @@ -290,17 +290,6 @@ distribution. map() that changes the size of the list should now work faster. -=item * - -sort() has been changed to use mergesort internally as opposed to the -earlier quicksort. For very small lists this may result in slightly -slower sorting times, but in general the speedup should be at least 20%. -Additional bonuses are that the worst case behaviour of sort() is now -better (in computer science terms it now runs in time O(N log N), as -opposed to quicksorts Theta(N**2) worst-case run time behaviour), and -that sort() is now stable (meaning that elements with identical keys -will stay ordered as they were before the sort). - =back =head1 Installation and Configuration Improvements diff --git a/pp_ctl.c b/pp_ctl.c index ac09d42..45f9a7e 100644 --- a/pp_ctl.c +++ b/pp_ctl.c @@ -3672,377 +3672,683 @@ S_doparseform(pTHX_ SV *sv) SvCOMPILED_on(sv); } - -#ifdef TESTHARNESS -#include -typedef void SV; -#define pTHXo_ -#define pTHX_ -#define STATIC -#define New(ID,VAR,N,TYPE) VAR=(TYPE *)malloc((N)*sizeof(TYPE)) -#define Safefree(VAR) free(VAR) -typedef int (*SVCOMPARE_t) (pTHXo_ SV*, SV*); -#endif /* TESTHARNESS */ - -typedef char * aptr; /* pointer for arithmetic on sizes */ -typedef SV * gptr; /* pointers in our lists */ - -/* - * The original author of the mergesort implementation included here - * is Peter M. McIlroy (see: Optimistic Merge Sort - * (SODA '92)), and the integrator of it to the Perl source code is - * John P. Linderman . - * - * Both Peter and John agree with the inclusion of their code in here - * and with their code being distributed under the same terms as Perl. - * - * Much of this code is original source code from BSD4.4, and is - * copyright (c) 1991 The Regents of the University of California. +/* + * The rest of this file was derived from source code contributed + * by Tom Horsley. * - * 1. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 2. Neither the name of the University nor the names of its contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. + * NOTE: this code was derived from Tom Horsley's qsort replacement + * and should not be confused with the original code. */ -/* Binary merge internal sort, with a few special mods -** for the special perl environment it now finds itself in. -** -** Things that were once options have been hotwired -** to values suitable for this use. In particular, we'll always -** initialize looking for natural runs, we'll always produce stable -** output, and we'll always do Peter McIlroy's binary merge. -*/ +/* Copyright (C) Tom Horsley, 1997. All rights reserved. -/* Pointer types for arithmetic and storage and convenience casts */ + Permission granted to distribute under the same terms as perl which are + (briefly): -#define APTR(P) ((aptr)(P)) -#define GPTP(P) ((gptr *)(P)) -#define GPPP(P) ((gptr **)(P)) + This program is free software; you can redistribute it and/or modify + it under the terms of either: + a) the GNU General Public License as published by the Free + Software Foundation; either version 1, or (at your option) any + later version, or -/* byte offset from pointer P to (larger) pointer Q */ -#define BYTEOFF(P, Q) (APTR(Q) - APTR(P)) + b) the "Artistic License" which comes with this Kit. -#define PSIZE sizeof(gptr) + Details on the perl license can be found in the perl source code which + may be located via the www.perl.com web page. -/* If PSIZE is power of 2, make PSHIFT that power, if that helps */ + This is the most wonderfulest possible qsort I can come up with (and + still be mostly portable) My (limited) tests indicate it consistently + does about 20% fewer calls to compare than does the qsort in the Visual + C++ library, other vendors may vary. -#ifdef PSHIFT -#define PNELEM(P, Q) (BYTEOFF(P,Q) >> (PSHIFT)) -#define PNBYTE(N) ((N) << (PSHIFT)) -#define PINDEX(P, N) (GPTP(APTR(P) + PNBYTE(N))) -#else -/* Leave optimization to compiler */ -#define PNELEM(P, Q) (GPTP(Q) - GPTP(P)) -#define PNBYTE(N) ((N) * (PSIZE)) -#define PINDEX(P, N) (GPTP(P) + (N)) -#endif + Some of the ideas in here can be found in "Algorithms" by Sedgewick, + others I invented myself (or more likely re-invented since they seemed + pretty obvious once I watched the algorithm operate for a while). -/* Pointer into other corresponding to pointer into this */ -#define POTHER(P, THIS, OTHER) GPTP(APTR(OTHER) + BYTEOFF(THIS,P)) + Most of this code was written while watching the Marlins sweep the Giants + in the 1997 National League Playoffs - no Braves fans allowed to use this + code (just kidding :-). -#define FROMTOUPTO(src, dst, lim) do *dst++ = *src++; while(src= 2 * PTHRESH. We only try to form long runs when -** PTHRESH adjacent pairs compare in the same way, suggesting overall order. -** -** Unless otherwise specified, pair pointers address the first of two elements. -** -** b and b+1 are a pair that compare with sense ``sense''. -** b is the ``bottom'' of adjacent pairs that might form a longer run. -** -** p2 parallels b in the list2 array, where runs are defined by -** a pointer chain. -** -** t represents the ``top'' of the adjacent pairs that might extend -** the run beginning at b. Usually, t addresses a pair -** that compares with opposite sense from (b,b+1). -** However, it may also address a singleton element at the end of list1, -** or it may be equal to ``last'', the first element beyond list1. -** -** r addresses the Nth pair following b. If this would be beyond t, -** we back it off to t. Only when r is less than t do we consider the -** run long enough to consider checking. -** -** q addresses a pair such that the pairs at b through q already form a run. -** Often, q will equal b, indicating we only are sure of the pair itself. -** However, a search on the previous cycle may have revealed a longer run, -** so q may be greater than b. -** -** p is used to work back from a candidate r, trying to reach q, -** which would mean b through r would be a run. If we discover such a run, -** we start q at r and try to push it further towards t. -** If b through r is NOT a run, we detect the wrong order at (p-1,p). -** In any event, after the check (if any), we have two main cases. -** -** 1) Short run. b <= q < p <= r <= t. -** b through q is a run (perhaps trivial) -** q through p are uninteresting pairs -** p through r is a run -** -** 2) Long run. b < r <= q < t. -** b through q is a run (of length >= 2 * PTHRESH) -** -** Note that degenerate cases are not only possible, but likely. -** For example, if the pair following b compares with opposite sense, -** then b == q < p == r == t. + Also note that there are very many highly architecture specific ways + these might be sped up, but this is simply the most generally portable + code I could think of. +*/ + +/* Return < 0 == 0 or > 0 as the value of elt1 is < elt2, == elt2, > elt2 */ +#define qsort_cmp(elt1, elt2) \ + ((*compare)(aTHXo_ array[elt1], array[elt2])) +#ifdef QSORT_ORDER_GUESS +#define QSORT_NOTICE_SWAP swapped++; +#else +#define QSORT_NOTICE_SWAP +#endif + +/* swaps contents of array elements elt1, elt2. +*/ +#define qsort_swap(elt1, elt2) \ + STMT_START { \ + QSORT_NOTICE_SWAP \ + temp = array[elt1]; \ + array[elt1] = array[elt2]; \ + array[elt2] = temp; \ + } STMT_END + +/* rotate contents of elt1, elt2, elt3 such that elt1 gets elt2, elt2 gets + elt3 and elt3 gets elt1. +*/ +#define qsort_rotate(elt1, elt2, elt3) \ + STMT_START { \ + QSORT_NOTICE_SWAP \ + temp = array[elt1]; \ + array[elt1] = array[elt2]; \ + array[elt2] = array[elt3]; \ + array[elt3] = temp; \ + } STMT_END + +/* ************************************************************ Debug stuff */ + +#ifdef QSORT_DEBUG static void -dynprep(pTHX_ gptr *list1, gptr *list2, size_t nmemb, SVCOMPARE_t cmp) +break_here() { - int sense; - register gptr *b, *p, *q, *t, *p2; - register gptr c, *last, *r; - gptr *savep; - - b = list1; - last = PINDEX(b, nmemb); - sense = (cmp(aTHX_ *b, *(b+1)) > 0); - for (p2 = list2; b < last; ) { - /* We just started, or just reversed sense. - ** Set t at end of pairs with the prevailing sense. - */ - for (p = b+2, t = p; ++p < last; t = ++p) { - if ((cmp(aTHX_ *t, *p) > 0) != sense) break; - } - q = b; - /* Having laid out the playing field, look for long runs */ - do { - p = r = b + (2 * PTHRESH); - if (r >= t) p = r = t; /* too short to care about */ - else { - while (((cmp(aTHX_ *(p-1), *p) > 0) == sense) && - ((p -= 2) > q)); - if (p <= q) { - /* b through r is a (long) run. - ** Extend it as far as possible. - */ - p = q = r; - while (((p += 2) < t) && - ((cmp(aTHX_ *(p-1), *p) > 0) == sense)) q = p; - r = p = q + 2; /* no simple pairs, no after-run */ - } - } - if (q > b) { /* run of greater than 2 at b */ - savep = p; - p = q += 2; - /* pick up singleton, if possible */ - if ((p == t) && - ((t + 1) == last) && - ((cmp(aTHX_ *(p-1), *p) > 0) == sense)) - savep = r = p = q = last; - p2 = NEXT(p2) = p2 + (p - b); - if (sense) while (b < --p) { - c = *b; - *b++ = *p; - *p = c; - } - p = savep; - } - while (q < p) { /* simple pairs */ - p2 = NEXT(p2) = p2 + 2; - if (sense) { - c = *q++; - *(q-1) = *q; - *q++ = c; - } else q += 2; - } - if (((b = p) == t) && ((t+1) == last)) { - NEXT(p2) = p2 + 1; - b++; - } - q = r; - } while (b < t); - sense = !sense; - } - return; + return; /* good place to set a breakpoint */ } +#define qsort_assert(t) (void)( (t) || (break_here(), 0) ) -/* Overview of bmerge variables: -** -** list1 and list2 address the main and auxiliary arrays. -** They swap identities after each merge pass. -** Base points to the original list1, so we can tell if -** the pointers ended up where they belonged (or must be copied). -** -** When we are merging two lists, f1 and f2 are the next elements -** on the respective lists. l1 and l2 mark the end of the lists. -** tp2 is the current location in the merged list. -** -** p1 records where f1 started. -** After the merge, a new descriptor is built there. -** -** p2 is a ``parallel'' pointer in (what starts as) descriptor space. -** It is used to identify and delimit the runs. -** -** In the heat of determining where q, the greater of the f1/f2 elements, -** belongs in the other list, b, t and p, represent bottom, top and probe -** locations, respectively, in the other list. -** They make convenient temporary pointers in other places. -*/ - -STATIC void -S_qsortsv(pTHX_ gptr *list1, size_t nmemb, SVCOMPARE_t cmp) +static void +doqsort_all_asserts( + void * array, + size_t num_elts, + size_t elt_size, + int (*compare)(const void * elt1, const void * elt2), + int pc_left, int pc_right, int u_left, int u_right) { - int i, run; - int sense; - register gptr *f1, *f2, *t, *b, *p, *tp2, *l1, *l2, *q; - gptr *aux, *list2, *p2, *last; - gptr *base = list1; - gptr *p1; - - if (nmemb <= 1) return; /* sorted trivially */ - New(799,list2,nmemb,gptr); /* allocate auxilliary array */ - aux = list2; - dynprep(aTHX_ list1, list2, nmemb, cmp); - last = PINDEX(list2, nmemb); - while (NEXT(list2) != last) { - /* More than one run remains. Do some merging to reduce runs. */ - l2 = p1 = list1; - for (tp2 = p2 = list2; p2 != last;) { - /* The new first run begins where the old second list ended. - ** Use the p2 ``parallel'' pointer to identify the end of the run. - */ - f1 = l2; - t = NEXT(p2); - f2 = l1 = POTHER(t, list2, list1); - if (t != last) t = NEXT(t); - l2 = POTHER(t, list2, list1); - p2 = t; - while (f1 < l1 && f2 < l2) { - /* If head 1 is larger than head 2, find ALL the elements - ** in list 2 strictly less than head1, write them all, - ** then head 1. Then compare the new heads, and repeat, - ** until one or both lists are exhausted. - ** - ** In all comparisons (after establishing - ** which head to merge) the item to merge - ** (at pointer q) is the first operand of - ** the comparison. When we want to know - ** if ``q is strictly less than the other'', - ** we can't just do - ** cmp(q, other) < 0 - ** because stability demands that we treat equality - ** as high when q comes from l2, and as low when - ** q was from l1. So we ask the question by doing - ** cmp(q, other) <= sense - ** and make sense == 0 when equality should look low, - ** and -1 when equality should look high. - */ - - - if (cmp(aTHX_ *f1, *f2) <= 0) { - q = f2; b = f1; t = l1; - sense = -1; - } else { - q = f1; b = f2; t = l2; - sense = 0; - } + int i; + + qsort_assert(pc_left <= pc_right); + qsort_assert(u_right < pc_left); + qsort_assert(pc_right < u_left); + for (i = u_right + 1; i < pc_left; ++i) { + qsort_assert(qsort_cmp(i, pc_left) < 0); + } + for (i = pc_left; i < pc_right; ++i) { + qsort_assert(qsort_cmp(i, pc_right) == 0); + } + for (i = pc_right + 1; i < u_left; ++i) { + qsort_assert(qsort_cmp(pc_right, i) < 0); + } +} +#define qsort_all_asserts(PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT) \ + doqsort_all_asserts(array, num_elts, elt_size, compare, \ + PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT) - /* ramp up - ** - ** Leave t at something strictly - ** greater than q (or at the end of the list), - ** and b at something strictly less than q. - */ - for (i = 1, run = 0 ;;) { - if ((p = PINDEX(b, i)) >= t) { - /* off the end */ - if (((p = PINDEX(t, -1)) > b) && - (cmp(aTHX_ *q, *p) <= sense)) - t = p; - else b = p; - break; - } else if (cmp(aTHX_ *q, *p) <= sense) { - t = p; - break; - } else b = p; - if (++run >= RTHRESH) i += i; - } +#else +#define qsort_assert(t) ((void)0) - /* q is known to follow b and must be inserted before t. - ** Increment b, so the range of possibilities is [b,t). - ** Round binary split down, to favor early appearance. - ** Adjust b and t until q belongs just before t. - */ +#define qsort_all_asserts(PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT) ((void)0) - b++; - while (b < t) { - p = PINDEX(b, (PNELEM(b, t) - 1) / 2); - if (cmp(aTHX_ *q, *p) <= sense) { - t = p; - } else b = p + 1; - } +#endif +/* ****************************************************************** qsort */ - /* Copy all the strictly low elements */ +STATIC void +S_qsortsv(pTHX_ SV ** array, size_t num_elts, SVCOMPARE_t compare) +{ + register SV * temp; - if (q == f1) { - FROMTOUPTO(f2, tp2, t); - *tp2++ = *f1++; - } else { - FROMTOUPTO(f1, tp2, t); - *tp2++ = *f2++; - } - } + struct partition_stack_entry partition_stack[QSORT_MAX_STACK]; + int next_stack_entry = 0; + int part_left; + int part_right; +#ifdef QSORT_ORDER_GUESS + int qsort_break_even; + int swapped; +#endif - /* Run out remaining list */ - if (f1 == l1) { - if (f2 < l2) FROMTOUPTO(f2, tp2, l2); - } else FROMTOUPTO(f1, tp2, l1); - p1 = NEXT(p1) = POTHER(tp2, list2, list1); - } - t = list1; - list1 = list2; - list2 = t; - last = PINDEX(list2, nmemb); - } - if (base == list2) { - last = PINDEX(list1, nmemb); - FROMTOUPTO(list1, list2, last); - } - Safefree(aux); - return; + /* Make sure we actually have work to do. + */ + if (num_elts <= 1) { + return; + } + + /* Setup the initial partition definition and fall into the sorting loop + */ + part_left = 0; + part_right = (int)(num_elts - 1); +#ifdef QSORT_ORDER_GUESS + qsort_break_even = QSORT_BREAK_EVEN; +#else +#define qsort_break_even QSORT_BREAK_EVEN +#endif + for ( ; ; ) { + if ((part_right - part_left) >= qsort_break_even) { + /* OK, this is gonna get hairy, so lets try to document all the + concepts and abbreviations and variables and what they keep + track of: + + pc: pivot chunk - the set of array elements we accumulate in the + middle of the partition, all equal in value to the original + pivot element selected. The pc is defined by: + + pc_left - the leftmost array index of the pc + pc_right - the rightmost array index of the pc + + we start with pc_left == pc_right and only one element + in the pivot chunk (but it can grow during the scan). + + u: uncompared elements - the set of elements in the partition + we have not yet compared to the pivot value. There are two + uncompared sets during the scan - one to the left of the pc + and one to the right. + + u_right - the rightmost index of the left side's uncompared set + u_left - the leftmost index of the right side's uncompared set + + The leftmost index of the left sides's uncompared set + doesn't need its own variable because it is always defined + by the leftmost edge of the whole partition (part_left). The + same goes for the rightmost edge of the right partition + (part_right). + + We know there are no uncompared elements on the left once we + get u_right < part_left and no uncompared elements on the + right once u_left > part_right. When both these conditions + are met, we have completed the scan of the partition. + + Any elements which are between the pivot chunk and the + uncompared elements should be less than the pivot value on + the left side and greater than the pivot value on the right + side (in fact, the goal of the whole algorithm is to arrange + for that to be true and make the groups of less-than and + greater-then elements into new partitions to sort again). + + As you marvel at the complexity of the code and wonder why it + has to be so confusing. Consider some of the things this level + of confusion brings: + + Once I do a compare, I squeeze every ounce of juice out of it. I + never do compare calls I don't have to do, and I certainly never + do redundant calls. + + I also never swap any elements unless I can prove there is a + good reason. Many sort algorithms will swap a known value with + an uncompared value just to get things in the right place (or + avoid complexity :-), but that uncompared value, once it gets + compared, may then have to be swapped again. A lot of the + complexity of this code is due to the fact that it never swaps + anything except compared values, and it only swaps them when the + compare shows they are out of position. + */ + int pc_left, pc_right; + int u_right, u_left; + + int s; + + pc_left = ((part_left + part_right) / 2); + pc_right = pc_left; + u_right = pc_left - 1; + u_left = pc_right + 1; + + /* Qsort works best when the pivot value is also the median value + in the partition (unfortunately you can't find the median value + without first sorting :-), so to give the algorithm a helping + hand, we pick 3 elements and sort them and use the median value + of that tiny set as the pivot value. + + Some versions of qsort like to use the left middle and right as + the 3 elements to sort so they can insure the ends of the + partition will contain values which will stop the scan in the + compare loop, but when you have to call an arbitrarily complex + routine to do a compare, its really better to just keep track of + array index values to know when you hit the edge of the + partition and avoid the extra compare. An even better reason to + avoid using a compare call is the fact that you can drop off the + edge of the array if someone foolishly provides you with an + unstable compare function that doesn't always provide consistent + results. + + So, since it is simpler for us to compare the three adjacent + elements in the middle of the partition, those are the ones we + pick here (conveniently pointed at by u_right, pc_left, and + u_left). The values of the left, center, and right elements + are refered to as l c and r in the following comments. + */ + +#ifdef QSORT_ORDER_GUESS + swapped = 0; +#endif + s = qsort_cmp(u_right, pc_left); + if (s < 0) { + /* l < c */ + s = qsort_cmp(pc_left, u_left); + /* if l < c, c < r - already in order - nothing to do */ + if (s == 0) { + /* l < c, c == r - already in order, pc grows */ + ++pc_right; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else if (s > 0) { + /* l < c, c > r - need to know more */ + s = qsort_cmp(u_right, u_left); + if (s < 0) { + /* l < c, c > r, l < r - swap c & r to get ordered */ + qsort_swap(pc_left, u_left); + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else if (s == 0) { + /* l < c, c > r, l == r - swap c&r, grow pc */ + qsort_swap(pc_left, u_left); + --pc_left; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else { + /* l < c, c > r, l > r - make lcr into rlc to get ordered */ + qsort_rotate(pc_left, u_right, u_left); + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } + } + } else if (s == 0) { + /* l == c */ + s = qsort_cmp(pc_left, u_left); + if (s < 0) { + /* l == c, c < r - already in order, grow pc */ + --pc_left; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else if (s == 0) { + /* l == c, c == r - already in order, grow pc both ways */ + --pc_left; + ++pc_right; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else { + /* l == c, c > r - swap l & r, grow pc */ + qsort_swap(u_right, u_left); + ++pc_right; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } + } else { + /* l > c */ + s = qsort_cmp(pc_left, u_left); + if (s < 0) { + /* l > c, c < r - need to know more */ + s = qsort_cmp(u_right, u_left); + if (s < 0) { + /* l > c, c < r, l < r - swap l & c to get ordered */ + qsort_swap(u_right, pc_left); + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else if (s == 0) { + /* l > c, c < r, l == r - swap l & c, grow pc */ + qsort_swap(u_right, pc_left); + ++pc_right; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else { + /* l > c, c < r, l > r - rotate lcr into crl to order */ + qsort_rotate(u_right, pc_left, u_left); + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } + } else if (s == 0) { + /* l > c, c == r - swap ends, grow pc */ + qsort_swap(u_right, u_left); + --pc_left; + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } else { + /* l > c, c > r - swap ends to get in order */ + qsort_swap(u_right, u_left); + qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1); + } + } + /* We now know the 3 middle elements have been compared and + arranged in the desired order, so we can shrink the uncompared + sets on both sides + */ + --u_right; + ++u_left; + qsort_all_asserts(pc_left, pc_right, u_left, u_right); + + /* The above massive nested if was the simple part :-). We now have + the middle 3 elements ordered and we need to scan through the + uncompared sets on either side, swapping elements that are on + the wrong side or simply shuffling equal elements around to get + all equal elements into the pivot chunk. + */ + + for ( ; ; ) { + int still_work_on_left; + int still_work_on_right; + + /* Scan the uncompared values on the left. If I find a value + equal to the pivot value, move it over so it is adjacent to + the pivot chunk and expand the pivot chunk. If I find a value + less than the pivot value, then just leave it - its already + on the correct side of the partition. If I find a greater + value, then stop the scan. + */ + while ((still_work_on_left = (u_right >= part_left))) { + s = qsort_cmp(u_right, pc_left); + if (s < 0) { + --u_right; + } else if (s == 0) { + --pc_left; + if (pc_left != u_right) { + qsort_swap(u_right, pc_left); + } + --u_right; + } else { + break; + } + qsort_assert(u_right < pc_left); + qsort_assert(pc_left <= pc_right); + qsort_assert(qsort_cmp(u_right + 1, pc_left) <= 0); + qsort_assert(qsort_cmp(pc_left, pc_right) == 0); + } + + /* Do a mirror image scan of uncompared values on the right + */ + while ((still_work_on_right = (u_left <= part_right))) { + s = qsort_cmp(pc_right, u_left); + if (s < 0) { + ++u_left; + } else if (s == 0) { + ++pc_right; + if (pc_right != u_left) { + qsort_swap(pc_right, u_left); + } + ++u_left; + } else { + break; + } + qsort_assert(u_left > pc_right); + qsort_assert(pc_left <= pc_right); + qsort_assert(qsort_cmp(pc_right, u_left - 1) <= 0); + qsort_assert(qsort_cmp(pc_left, pc_right) == 0); + } + + if (still_work_on_left) { + /* I know I have a value on the left side which needs to be + on the right side, but I need to know more to decide + exactly the best thing to do with it. + */ + if (still_work_on_right) { + /* I know I have values on both side which are out of + position. This is a big win because I kill two birds + with one swap (so to speak). I can advance the + uncompared pointers on both sides after swapping both + of them into the right place. + */ + qsort_swap(u_right, u_left); + --u_right; + ++u_left; + qsort_all_asserts(pc_left, pc_right, u_left, u_right); + } else { + /* I have an out of position value on the left, but the + right is fully scanned, so I "slide" the pivot chunk + and any less-than values left one to make room for the + greater value over on the right. If the out of position + value is immediately adjacent to the pivot chunk (there + are no less-than values), I can do that with a swap, + otherwise, I have to rotate one of the less than values + into the former position of the out of position value + and the right end of the pivot chunk into the left end + (got all that?). + */ + --pc_left; + if (pc_left == u_right) { + qsort_swap(u_right, pc_right); + qsort_all_asserts(pc_left, pc_right-1, u_left, u_right-1); + } else { + qsort_rotate(u_right, pc_left, pc_right); + qsort_all_asserts(pc_left, pc_right-1, u_left, u_right-1); + } + --pc_right; + --u_right; + } + } else if (still_work_on_right) { + /* Mirror image of complex case above: I have an out of + position value on the right, but the left is fully + scanned, so I need to shuffle things around to make room + for the right value on the left. + */ + ++pc_right; + if (pc_right == u_left) { + qsort_swap(u_left, pc_left); + qsort_all_asserts(pc_left+1, pc_right, u_left+1, u_right); + } else { + qsort_rotate(pc_right, pc_left, u_left); + qsort_all_asserts(pc_left+1, pc_right, u_left+1, u_right); + } + ++pc_left; + ++u_left; + } else { + /* No more scanning required on either side of partition, + break out of loop and figure out next set of partitions + */ + break; + } + } + + /* The elements in the pivot chunk are now in the right place. They + will never move or be compared again. All I have to do is decide + what to do with the stuff to the left and right of the pivot + chunk. + + Notes on the QSORT_ORDER_GUESS ifdef code: + + 1. If I just built these partitions without swapping any (or + very many) elements, there is a chance that the elements are + already ordered properly (being properly ordered will + certainly result in no swapping, but the converse can't be + proved :-). + + 2. A (properly written) insertion sort will run faster on + already ordered data than qsort will. + + 3. Perhaps there is some way to make a good guess about + switching to an insertion sort earlier than partition size 6 + (for instance - we could save the partition size on the stack + and increase the size each time we find we didn't swap, thus + switching to insertion sort earlier for partitions with a + history of not swapping). + + 4. Naturally, if I just switch right away, it will make + artificial benchmarks with pure ascending (or descending) + data look really good, but is that a good reason in general? + Hard to say... + */ + +#ifdef QSORT_ORDER_GUESS + if (swapped < 3) { +#if QSORT_ORDER_GUESS == 1 + qsort_break_even = (part_right - part_left) + 1; +#endif +#if QSORT_ORDER_GUESS == 2 + qsort_break_even *= 2; +#endif +#if QSORT_ORDER_GUESS == 3 + int prev_break = qsort_break_even; + qsort_break_even *= qsort_break_even; + if (qsort_break_even < prev_break) { + qsort_break_even = (part_right - part_left) + 1; + } +#endif + } else { + qsort_break_even = QSORT_BREAK_EVEN; + } +#endif + + if (part_left < pc_left) { + /* There are elements on the left which need more processing. + Check the right as well before deciding what to do. + */ + if (pc_right < part_right) { + /* We have two partitions to be sorted. Stack the biggest one + and process the smallest one on the next iteration. This + minimizes the stack height by insuring that any additional + stack entries must come from the smallest partition which + (because it is smallest) will have the fewest + opportunities to generate additional stack entries. + */ + if ((part_right - pc_right) > (pc_left - part_left)) { + /* stack the right partition, process the left */ + partition_stack[next_stack_entry].left = pc_right + 1; + partition_stack[next_stack_entry].right = part_right; +#ifdef QSORT_ORDER_GUESS + partition_stack[next_stack_entry].qsort_break_even = qsort_break_even; +#endif + part_right = pc_left - 1; + } else { + /* stack the left partition, process the right */ + partition_stack[next_stack_entry].left = part_left; + partition_stack[next_stack_entry].right = pc_left - 1; +#ifdef QSORT_ORDER_GUESS + partition_stack[next_stack_entry].qsort_break_even = qsort_break_even; +#endif + part_left = pc_right + 1; + } + qsort_assert(next_stack_entry < QSORT_MAX_STACK); + ++next_stack_entry; + } else { + /* The elements on the left are the only remaining elements + that need sorting, arrange for them to be processed as the + next partition. + */ + part_right = pc_left - 1; + } + } else if (pc_right < part_right) { + /* There is only one chunk on the right to be sorted, make it + the new partition and loop back around. + */ + part_left = pc_right + 1; + } else { + /* This whole partition wound up in the pivot chunk, so + we need to get a new partition off the stack. + */ + if (next_stack_entry == 0) { + /* the stack is empty - we are done */ + break; + } + --next_stack_entry; + part_left = partition_stack[next_stack_entry].left; + part_right = partition_stack[next_stack_entry].right; +#ifdef QSORT_ORDER_GUESS + qsort_break_even = partition_stack[next_stack_entry].qsort_break_even; +#endif + } + } else { + /* This partition is too small to fool with qsort complexity, just + do an ordinary insertion sort to minimize overhead. + */ + int i; + /* Assume 1st element is in right place already, and start checking + at 2nd element to see where it should be inserted. + */ + for (i = part_left + 1; i <= part_right; ++i) { + int j; + /* Scan (backwards - just in case 'i' is already in right place) + through the elements already sorted to see if the ith element + belongs ahead of one of them. + */ + for (j = i - 1; j >= part_left; --j) { + if (qsort_cmp(i, j) >= 0) { + /* i belongs right after j + */ + break; + } + } + ++j; + if (j != i) { + /* Looks like we really need to move some things + */ + int k; + temp = array[i]; + for (k = i - 1; k >= j; --k) + array[k + 1] = array[k]; + array[j] = temp; + } + } + + /* That partition is now sorted, grab the next one, or get out + of the loop if there aren't any more. + */ + + if (next_stack_entry == 0) { + /* the stack is empty - we are done */ + break; + } + --next_stack_entry; + part_left = partition_stack[next_stack_entry].left; + part_right = partition_stack[next_stack_entry].right; +#ifdef QSORT_ORDER_GUESS + qsort_break_even = partition_stack[next_stack_entry].qsort_break_even; +#endif + } + } + + /* Believe it or not, the array is sorted at this point! */ }