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Add <sys/queue_mergesort.h>

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Thie file provides macros for performing mergesorts and merging two
sorted lists implemented by <sys/queue.h>.  The mergesort operates
in guaranteed O(n log n) time and uses constant additional space:
3 or 4 pointers (depending on list type) and 4 size_t values.  The
merge operates in guaranteed O(n + m) time and uses constant
additional space: 3 pointers.

In memoriam:	hselasky
Reviewed by:	jhb (previous version)
Sponsored by:	https://www.patreon.com/cperciva
Differential Revision:	https://reviews.freebsd.org/D41073
This commit is contained in:
Colin Percival 2023-07-17 17:07:44 -07:00
parent 79fafc0974
commit 5f3587169a
1 changed files with 217 additions and 0 deletions
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/*-
* SPDX-License-Identifier: BSD-2-Clause
*
* Copyright (c) 2023 Colin Percival
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#ifndef _SYS_QUEUE_MERGESORT_H_
#define _SYS_QUEUE_MERGESORT_H_
/*
* This file defines macros for performing mergesorts on singly-linked lists,
* single-linked tail queues, lists, and tail queues as implemented in
* <sys/queue.h>.
*/
/*
* Shims to work around _CONCAT and _INSERT_AFTER taking different numbers of
* arguments for different types of linked lists.
*/
#define STAILQ_CONCAT_4(head1, head2, type, field) \
STAILQ_CONCAT(head1, head2)
#define TAILQ_CONCAT_4(head1, head2, type, field) \
TAILQ_CONCAT(head1, head2, field)
#define SLIST_INSERT_AFTER_4(head, slistelm, elm, field) \
SLIST_INSERT_AFTER(slistelm, elm, field)
#define LIST_INSERT_AFTER_4(head, slistelm, elm, field) \
LIST_INSERT_AFTER(slistelm, elm, field)
/*
* Generic macros which apply to all types of lists.
*/
#define SYSQUEUE_MERGE(sqms_list1, sqms_list2, thunk, sqms_cmp, TYPE, NAME, \
M_FIRST, M_INSERT_AFTER, M_INSERT_HEAD, M_NEXT, M_REMOVE_HEAD) \
do { \
struct TYPE *sqms_elm1; \
struct TYPE *sqms_elm1_prev; \
struct TYPE *sqms_elm2; \
\
/* Start at the beginning of list1; _prev is the previous node. */ \
sqms_elm1_prev = NULL; \
sqms_elm1 = M_FIRST(sqms_list1); \
\
/* Pull entries from list2 and insert them into list1. */ \
while ((sqms_elm2 = M_FIRST(sqms_list2)) != NULL) { \
/* Remove from list2. */ \
M_REMOVE_HEAD(sqms_list2, NAME); \
\
/* Advance until we find the right place to insert it. */ \
while ((sqms_elm1 != NULL) && \
(sqms_cmp)(sqms_elm2, sqms_elm1, thunk) >= 0) { \
sqms_elm1_prev = sqms_elm1; \
sqms_elm1 = M_NEXT(sqms_elm1, NAME); \
} \
\
/* Insert into list1. */ \
if (sqms_elm1_prev == NULL) \
M_INSERT_HEAD(sqms_list1, sqms_elm2, NAME); \
else \
M_INSERT_AFTER(sqms_list1, sqms_elm1_prev, \
sqms_elm2, NAME); \
sqms_elm1_prev = sqms_elm2; \
} \
} while (0)
#define SYSQUEUE_MERGE_SUBL(sqms_sorted, sqms_len1, sqms_len2, sqms_melm, \
sqms_mpos, thunk, sqms_cmp, TYPE, NAME, \
M_FIRST, M_NEXT, M_REMOVE_HEAD, M_INSERT_AFTER) \
do { \
struct TYPE *sqms_curelm; \
size_t sqms_i; \
\
/* Find the element before the start of the second sorted region. */ \
while ((sqms_mpos) < (sqms_len1)) { \
(sqms_melm) = M_NEXT((sqms_melm), NAME); \
(sqms_mpos)++; \
} \
\
/* Pull len1 entries off the list and insert in the right place. */ \
for (sqms_i = 0; sqms_i < (sqms_len1); sqms_i++) { \
/* Grab the first element. */ \
sqms_curelm = M_FIRST(&(sqms_sorted)); \
\
/* Advance until we find the right place to insert it. */ \
while (((sqms_mpos) < (sqms_len1) + (sqms_len2)) && \
((sqms_cmp)(sqms_curelm, M_NEXT((sqms_melm), NAME), \
thunk) >= 0)) { \
(sqms_melm) = M_NEXT((sqms_melm), NAME); \
(sqms_mpos)++; \
} \
\
/* Move the element in the right place if not already there. */ \
if (sqms_curelm != (sqms_melm)) { \
M_REMOVE_HEAD(&(sqms_sorted), NAME); \
M_INSERT_AFTER(&(sqms_sorted), (sqms_melm), \
sqms_curelm, NAME); \
(sqms_melm) = sqms_curelm; \
} \
} \
} while (0)
#define SYSQUEUE_MERGESORT(sqms_head, thunk, sqms_cmp, TYPE, NAME, M_HEAD, \
M_HEAD_INITIALIZER, M_EMPTY, M_FIRST, M_NEXT, M_INSERT_HEAD, \
M_INSERT_AFTER, M_CONCAT, M_REMOVE_HEAD) \
do { \
/* \
* Invariant: If sqms_slen = 2^a + 2^b + ... + 2^z with a < b < ... < z \
* then sqms_sorted is a sequence of 2^a sorted entries followed by a \
* list of 2^b sorted entries ... followed by a list of 2^z sorted \
* entries. \
*/ \
M_HEAD(, TYPE) sqms_sorted = M_HEAD_INITIALIZER(sqms_sorted); \
struct TYPE *sqms_elm; \
size_t sqms_slen = 0; \
size_t sqms_sortmask; \
size_t sqms_mpos; \
\
/* Move everything from the input list to sqms_sorted. */ \
while (!M_EMPTY(sqms_head)) { \
/* Pull the head off the input list. */ \
sqms_elm = M_FIRST(sqms_head); \
M_REMOVE_HEAD(sqms_head, NAME); \
\
/* Push it onto sqms_sorted. */ \
M_INSERT_HEAD(&sqms_sorted, sqms_elm, NAME); \
sqms_slen++; \
\
/* Restore sorting invariant. */ \
sqms_mpos = 1; \
for (sqms_sortmask = 1; \
sqms_sortmask & ~sqms_slen; \
sqms_sortmask <<= 1) \
SYSQUEUE_MERGE_SUBL(sqms_sorted, sqms_sortmask, \
sqms_sortmask, sqms_elm, sqms_mpos, thunk, sqms_cmp,\
TYPE, NAME, M_FIRST, M_NEXT, M_REMOVE_HEAD, \
M_INSERT_AFTER); \
} \
\
/* Merge the remaining sublists. */ \
sqms_elm = M_FIRST(&sqms_sorted); \
sqms_mpos = 1; \
for (sqms_sortmask = 2; \
sqms_sortmask < sqms_slen; \
sqms_sortmask <<= 1) \
if (sqms_slen & sqms_sortmask) \
SYSQUEUE_MERGE_SUBL(sqms_sorted, \
sqms_slen & (sqms_sortmask - 1), sqms_sortmask, \
sqms_elm, sqms_mpos, thunk, sqms_cmp, \
TYPE, NAME, M_FIRST, M_NEXT, M_REMOVE_HEAD, \
M_INSERT_AFTER); \
\
/* Move the sorted list back to the input list. */ \
M_CONCAT(sqms_head, &sqms_sorted, TYPE, NAME); \
} while (0)
/**
* Macros for each of the individual data types. They are all invoked as
* FOO_MERGESORT(head, thunk, compar, TYPE, NAME)
* and
* FOO_MERGE(list1, list2, thunk, compar, TYPE, NAME)
* where the compar function operates as in qsort_r, i.e. compar(a, b, thunk)
* returns an integer less than, equal to, or greater than zero if a is
* considered to be respectively less than, equal to, or greater than b.
*/
#define SLIST_MERGESORT(head, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGESORT((head), (thunk), (cmp), TYPE, NAME, SLIST_HEAD, \
SLIST_HEAD_INITIALIZER, SLIST_EMPTY, SLIST_FIRST, SLIST_NEXT, \
SLIST_INSERT_HEAD, SLIST_INSERT_AFTER_4, SLIST_CONCAT, SLIST_REMOVE_HEAD)
#define SLIST_MERGE(list1, list2, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGE((list1), (list2), (thunk), (cmp), TYPE, NAME, SLIST_FIRST, \
SLIST_INSERT_AFTER_4, SLIST_INSERT_HEAD, SLIST_NEXT, SLIST_REMOVE_HEAD)
#define LIST_MERGESORT(head, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGESORT((head), (thunk), (cmp), TYPE, NAME, LIST_HEAD, \
LIST_HEAD_INITIALIZER, LIST_EMPTY, LIST_FIRST, LIST_NEXT, \
LIST_INSERT_HEAD, LIST_INSERT_AFTER_4, LIST_CONCAT, LIST_REMOVE_HEAD)
#define LIST_MERGE(list1, list2, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGE((list1), (list2), (thunk), (cmp), TYPE, NAME, LIST_FIRST, \
LIST_INSERT_AFTER_4, LIST_INSERT_HEAD, LIST_NEXT, LIST_REMOVE_HEAD)
#define STAILQ_MERGESORT(head, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGESORT((head), (thunk), (cmp), TYPE, NAME, STAILQ_HEAD, \
STAILQ_HEAD_INITIALIZER, STAILQ_EMPTY, STAILQ_FIRST, STAILQ_NEXT, \
STAILQ_INSERT_HEAD, STAILQ_INSERT_AFTER, STAILQ_CONCAT_4, STAILQ_REMOVE_HEAD)
#define STAILQ_MERGE(list1, list2, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGE((list1), (list2), (thunk), (cmp), TYPE, NAME, STAILQ_FIRST, \
STAILQ_INSERT_AFTER, STAILQ_INSERT_HEAD, STAILQ_NEXT, STAILQ_REMOVE_HEAD)
#define TAILQ_MERGESORT(head, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGESORT((head), (thunk), (cmp), TYPE, NAME, TAILQ_HEAD, \
TAILQ_HEAD_INITIALIZER, TAILQ_EMPTY, TAILQ_FIRST, TAILQ_NEXT, \
TAILQ_INSERT_HEAD, TAILQ_INSERT_AFTER, TAILQ_CONCAT_4, TAILQ_REMOVE_HEAD)
#define TAILQ_MERGE(list1, list2, thunk, cmp, TYPE, NAME) \
SYSQUEUE_MERGE((list1), (list2), (thunk), (cmp), TYPE, NAME, TAILQ_FIRST, \
TAILQ_INSERT_AFTER, TAILQ_INSERT_HEAD, TAILQ_NEXT, TAILQ_REMOVE_HEAD)
#endif /* !_SYS_QUEUE_MERGESORT_H_ */