--- /dev/null
+/*
+ * 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].
+ */
+
+#ifndef QSORT_H
+#define QSORT_H
+
+/* 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(unsigned long, Q_N, Q_LESS, Q_SWAP); \
+} while (0)
+
+#endif
+
+/* ex:set ts=8 sts=4 sw=4 noet: */