nnn/src/qsort.h

/*
 * 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: */