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/*
* Copyright (c) 2013, 2017 Alexey Tourbin
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
/*
* This is a traditional Quicksort implementation which mostly follows
* [Sedgewick 1978]. Sorting is performed entirely on array indices,
* while actual access to the array elements is abstracted out with the
* user-defined `LESS` and `SWAP` primitives.
*
* Synopsis:
* QSORT(N, LESS, SWAP);
* where
* N - the number of elements in A[];
* LESS(i, j) - compares A[i] to A[j];
* SWAP(i, j) - exchanges A[i] with A[j].
*/
#pragma once
/* Sort 3 elements. */
#define Q_SORT3(q_a1, q_a2, q_a3, Q_LESS, Q_SWAP) \
do { \
if (Q_LESS(q_a2, q_a1)) { \
if (Q_LESS(q_a3, q_a2)) \
Q_SWAP(q_a1, q_a3); \
else { \
Q_SWAP(q_a1, q_a2); \
if (Q_LESS(q_a3, q_a2)) \
Q_SWAP(q_a2, q_a3); \
} \
} \
else if (Q_LESS(q_a3, q_a2)) { \
Q_SWAP(q_a2, q_a3); \
if (Q_LESS(q_a2, q_a1)) \
Q_SWAP(q_a1, q_a2); \
} \
} while (0)
/* Partition [q_l,q_r] around a pivot. After partitioning,
* [q_l,q_j] are the elements that are less than or equal to the pivot,
* while [q_i,q_r] are the elements greater than or equal to the pivot. */
#define Q_PARTITION(q_l, q_r, q_i, q_j, Q_UINT, Q_LESS, Q_SWAP) \
do { \
/* The middle element, not to be confused with the median. */ \
Q_UINT q_m = q_l + ((q_r - q_l) >> 1); \
/* Reorder the second, the middle, and the last items. \
* As [Edelkamp Weiss 2016] explain, using the second element \
* instead of the first one helps avoid bad behaviour for \
* decreasingly sorted arrays. This method is used in recent \
* versions of gcc's std::sort, see gcc bug 58437#c13, although \
* the details are somewhat different (cf. #c14). */ \
Q_SORT3(q_l + 1, q_m, q_r, Q_LESS, Q_SWAP); \
/* Place the median at the beginning. */ \
Q_SWAP(q_l, q_m); \
/* Partition [q_l+2, q_r-1] around the median which is in q_l. \
* q_i and q_j are initially off by one, they get decremented \
* in the do-while loops. */ \
q_i = q_l + 1; q_j = q_r; \
while (1) { \
do q_i++; while (Q_LESS(q_i, q_l)); \
do q_j--; while (Q_LESS(q_l, q_j)); \
if (q_i >= q_j) break; /* Sedgewick says "until j < i" */ \
Q_SWAP(q_i, q_j); \
} \
/* Compensate for the i==j case. */ \
q_i = q_j + 1; \
/* Put the median to its final place. */ \
Q_SWAP(q_l, q_j); \
/* The median is not part of the left subfile. */ \
q_j--; \
} while (0)
/* Insertion sort is applied to small subfiles - this is contrary to
* Sedgewick's suggestion to run a separate insertion sort pass after
* the partitioning is done. The reason I don't like a separate pass
* is that it triggers extra comparisons, because it can't see that the
* medians are already in their final positions and need not be rechecked.
* Since I do not assume that comparisons are cheap, I also do not try
* to eliminate the (q_j > q_l) boundary check. */
#define Q_INSERTION_SORT(q_l, q_r, Q_UINT, Q_LESS, Q_SWAP) \
do { \
Q_UINT q_i, q_j; \
/* For each item starting with the second... */ \
for (q_i = q_l + 1; q_i <= q_r; q_i++) \
/* move it down the array so that the first part is sorted. */ \
for (q_j = q_i; q_j > q_l && (Q_LESS(q_j, q_j - 1)); q_j--) \
Q_SWAP(q_j, q_j - 1); \
} while (0)
/* When the size of [q_l,q_r], i.e. q_r-q_l+1, is greater than or equal to
* Q_THRESH, the algorithm performs recursive partitioning. When the size
* drops below Q_THRESH, the algorithm switches to insertion sort.
* The minimum valid value is probably 5 (with 5 items, the second and
* the middle items, the middle itself being rounded down, are distinct). */
#define Q_THRESH 16
/* The main loop. */
#define Q_LOOP(Q_UINT, Q_N, Q_LESS, Q_SWAP) \
do { \
Q_UINT q_l = 0; \
Q_UINT q_r = (Q_N) - 1; \
Q_UINT q_sp = 0; /* the number of frames pushed to the stack */ \
struct { Q_UINT q_l, q_r; } \
/* On 32-bit platforms, to sort a "char[3GB+]" array, \
* it may take full 32 stack frames. On 64-bit CPUs, \
* though, the address space is limited to 48 bits. \
* The usage is further reduced if Q_N has a 32-bit type. */ \
q_st[sizeof(Q_UINT) > 4 && sizeof(Q_N) > 4 ? 48 : 32]; \
while (1) { \
if (q_r - q_l + 1 >= Q_THRESH) { \
Q_UINT q_i, q_j; \
Q_PARTITION(q_l, q_r, q_i, q_j, Q_UINT, Q_LESS, Q_SWAP); \
/* Now have two subfiles: [q_l,q_j] and [q_i,q_r]. \
* Dealing with them depends on which one is bigger. */ \
if (q_j - q_l >= q_r - q_i) \
Q_SUBFILES(q_l, q_j, q_i, q_r); \
else \
Q_SUBFILES(q_i, q_r, q_l, q_j); \
} \
else { \
Q_INSERTION_SORT(q_l, q_r, Q_UINT, Q_LESS, Q_SWAP); \
/* Pop subfiles from the stack, until it gets empty. */ \
if (q_sp == 0) break; \
q_sp--; \
q_l = q_st[q_sp].q_l; \
q_r = q_st[q_sp].q_r; \
} \
} \
} while (0)
/* The missing part: dealing with subfiles.
* Assumes that the first subfile is not smaller than the second. */
#define Q_SUBFILES(q_l1, q_r1, q_l2, q_r2) \
do { \
/* If the second subfile is only a single element, it needs \
* no further processing. The first subfile will be processed \
* on the next iteration (both subfiles cannot be only a single \
* element, due to Q_THRESH). */ \
if (q_l2 == q_r2) { \
q_l = q_l1; \
q_r = q_r1; \
} \
else { \
/* Otherwise, both subfiles need processing. \
* Push the larger subfile onto the stack. */ \
q_st[q_sp].q_l = q_l1; \
q_st[q_sp].q_r = q_r1; \
q_sp++; \
/* Process the smaller subfile on the next iteration. */ \
q_l = q_l2; \
q_r = q_r2; \
} \
} while (0)
/* And now, ladies and gentlemen, may I proudly present to you... */
#define QSORT(Q_N, Q_LESS, Q_SWAP) \
do { \
if ((Q_N) > 1) \
/* We could check sizeof(Q_N) and use "unsigned", but at least \
* on x86_64, this has the performance penalty of up to 5%. */ \
Q_LOOP(ulong, Q_N, Q_LESS, Q_SWAP); \
} while (0)
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