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