diff --git a/sys/sys/tree.h b/sys/sys/tree.h index 10f559f516d2..47cd14d6691b 100644 --- a/sys/sys/tree.h +++ b/sys/sys/tree.h @@ -1,989 +1,989 @@ /* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */ /* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */ /* $FreeBSD$ */ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright 2002 Niels Provos * All rights reserved. * * 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 ``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 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_TREE_H_ #define _SYS_TREE_H_ #include /* * This file defines data structures for different types of trees: * splay trees and rank-balanced trees. * * A splay tree is a self-organizing data structure. Every operation * on the tree causes a splay to happen. The splay moves the requested * node to the root of the tree and partly rebalances it. * * This has the benefit that request locality causes faster lookups as * the requested nodes move to the top of the tree. On the other hand, * every lookup causes memory writes. * * The Balance Theorem bounds the total access time for m operations * and n inserts on an initially empty tree as O((m + n)lg n). The * amortized cost for a sequence of m accesses to a splay tree is O(lg n); * * A rank-balanced tree is a binary search tree with an integer * rank-difference as an attribute of each pointer from parent to child. * The sum of the rank-differences on any path from a node down to null is * the same, and defines the rank of that node. The rank of the null node * is -1. * * Different additional conditions define different sorts of balanced trees, * including "red-black" and "AVL" trees. The set of conditions applied here * are the "weak-AVL" conditions of Haeupler, Sen and Tarjan presented in in * "Rank Balanced Trees", ACM Transactions on Algorithms Volume 11 Issue 4 June * 2015 Article No.: 30pp 1–26 https://doi.org/10.1145/2689412 (the HST paper): * - every rank-difference is 1 or 2. * - the rank of any leaf is 1. * * For historical reasons, rank differences that are even are associated * with the color red (Rank-Even-Difference), and the child that a red edge * points to is called a red child. * * Every operation on a rank-balanced tree is bounded as O(lg n). * The maximum height of a rank-balanced tree is 2lg (n+1). */ #define SPLAY_HEAD(name, type) \ struct name { \ struct type *sph_root; /* root of the tree */ \ } #define SPLAY_INITIALIZER(root) \ { NULL } #define SPLAY_INIT(root) do { \ (root)->sph_root = NULL; \ } while (/*CONSTCOND*/ 0) #define SPLAY_ENTRY(type) \ struct { \ struct type *spe_left; /* left element */ \ struct type *spe_right; /* right element */ \ } #define SPLAY_LEFT(elm, field) (elm)->field.spe_left #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right #define SPLAY_ROOT(head) (head)->sph_root #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL) /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */ #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ (head)->sph_root = tmp; \ } while (/*CONSTCOND*/ 0) #define SPLAY_LINKLEFT(head, tmp, field) do { \ SPLAY_LEFT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define SPLAY_LINKRIGHT(head, tmp, field) do { \ SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ tmp = (head)->sph_root; \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \ } while (/*CONSTCOND*/ 0) #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define SPLAY_PROTOTYPE(name, type, field, cmp) \ void name##_SPLAY(struct name *, struct type *); \ void name##_SPLAY_MINMAX(struct name *, int); \ struct type *name##_SPLAY_INSERT(struct name *, struct type *); \ struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ \ /* Finds the node with the same key as elm */ \ static __unused __inline struct type * \ name##_SPLAY_FIND(struct name *head, struct type *elm) \ { \ if (SPLAY_EMPTY(head)) \ return(NULL); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) \ return (head->sph_root); \ return (NULL); \ } \ \ static __unused __inline struct type * \ name##_SPLAY_NEXT(struct name *head, struct type *elm) \ { \ name##_SPLAY(head, elm); \ if (SPLAY_RIGHT(elm, field) != NULL) { \ elm = SPLAY_RIGHT(elm, field); \ while (SPLAY_LEFT(elm, field) != NULL) { \ elm = SPLAY_LEFT(elm, field); \ } \ } else \ elm = NULL; \ return (elm); \ } \ \ static __unused __inline struct type * \ name##_SPLAY_MIN_MAX(struct name *head, int val) \ { \ name##_SPLAY_MINMAX(head, val); \ return (SPLAY_ROOT(head)); \ } /* Main splay operation. * Moves node close to the key of elm to top */ #define SPLAY_GENERATE(name, type, field, cmp) \ struct type * \ name##_SPLAY_INSERT(struct name *head, struct type *elm) \ { \ if (SPLAY_EMPTY(head)) { \ SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \ } else { \ __typeof(cmp(NULL, NULL)) __comp; \ name##_SPLAY(head, elm); \ __comp = (cmp)(elm, (head)->sph_root); \ if(__comp < 0) { \ SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ SPLAY_RIGHT(elm, field) = (head)->sph_root; \ SPLAY_LEFT((head)->sph_root, field) = NULL; \ } else if (__comp > 0) { \ SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ SPLAY_LEFT(elm, field) = (head)->sph_root; \ SPLAY_RIGHT((head)->sph_root, field) = NULL; \ } else \ return ((head)->sph_root); \ } \ (head)->sph_root = (elm); \ return (NULL); \ } \ \ struct type * \ name##_SPLAY_REMOVE(struct name *head, struct type *elm) \ { \ struct type *__tmp; \ if (SPLAY_EMPTY(head)) \ return (NULL); \ name##_SPLAY(head, elm); \ if ((cmp)(elm, (head)->sph_root) == 0) { \ if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \ (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ } else { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ name##_SPLAY(head, elm); \ SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ } \ return (elm); \ } \ return (NULL); \ } \ \ void \ name##_SPLAY(struct name *head, struct type *elm) \ { \ struct type __node, *__left, *__right, *__tmp; \ __typeof(cmp(NULL, NULL)) __comp; \ \ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ __left = __right = &__node; \ \ while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if ((cmp)(elm, __tmp) < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if ((cmp)(elm, __tmp) > 0){ \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ } \ \ /* Splay with either the minimum or the maximum element \ * Used to find minimum or maximum element in tree. \ */ \ void name##_SPLAY_MINMAX(struct name *head, int __comp) \ { \ struct type __node, *__left, *__right, *__tmp; \ \ SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\ __left = __right = &__node; \ \ while (1) { \ if (__comp < 0) { \ __tmp = SPLAY_LEFT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if (__comp < 0){ \ SPLAY_ROTATE_RIGHT(head, __tmp, field); \ if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ break; \ } \ SPLAY_LINKLEFT(head, __right, field); \ } else if (__comp > 0) { \ __tmp = SPLAY_RIGHT((head)->sph_root, field); \ if (__tmp == NULL) \ break; \ if (__comp > 0) { \ SPLAY_ROTATE_LEFT(head, __tmp, field); \ if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ break; \ } \ SPLAY_LINKRIGHT(head, __left, field); \ } \ } \ SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ } #define SPLAY_NEGINF -1 #define SPLAY_INF 1 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y) #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y) #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y) #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y) #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \ : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF)) #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \ : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) #define SPLAY_FOREACH(x, name, head) \ for ((x) = SPLAY_MIN(name, head); \ (x) != NULL; \ (x) = SPLAY_NEXT(name, head, x)) /* Macros that define a rank-balanced tree */ #define RB_HEAD(name, type) \ struct name { \ struct type *rbh_root; /* root of the tree */ \ } #define RB_INITIALIZER(root) \ { NULL } #define RB_INIT(root) do { \ (root)->rbh_root = NULL; \ } while (/*CONSTCOND*/ 0) #define RB_ENTRY(type) \ struct { \ struct type *rbe_link[3]; \ } /* * With the expectation that any object of struct type has an * address that is a multiple of 4, and that therefore the * 2 least significant bits of a pointer to struct type are * always zero, this implementation sets those bits to indicate * that the left or right child of the tree node is "red". */ #define _RB_LINK(elm, dir, field) (elm)->field.rbe_link[dir] #define _RB_UP(elm, field) _RB_LINK(elm, 0, field) #define _RB_L ((__uintptr_t)1) #define _RB_R ((__uintptr_t)2) #define _RB_LR ((__uintptr_t)3) #define _RB_BITS(elm) (*(__uintptr_t *)&elm) #define _RB_BITSUP(elm, field) _RB_BITS(_RB_UP(elm, field)) #define _RB_PTR(elm) (__typeof(elm)) \ ((__uintptr_t)elm & ~_RB_LR) #define RB_PARENT(elm, field) _RB_PTR(_RB_UP(elm, field)) #define RB_LEFT(elm, field) _RB_LINK(elm, _RB_L, field) #define RB_RIGHT(elm, field) _RB_LINK(elm, _RB_R, field) #define RB_ROOT(head) (head)->rbh_root #define RB_EMPTY(head) (RB_ROOT(head) == NULL) #define RB_SET_PARENT(dst, src, field) do { \ _RB_BITSUP(dst, field) = (__uintptr_t)src | \ (_RB_BITSUP(dst, field) & _RB_LR); \ } while (/*CONSTCOND*/ 0) #define RB_SET(elm, parent, field) do { \ _RB_UP(elm, field) = parent; \ RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \ } while (/*CONSTCOND*/ 0) /* * Either RB_AUGMENT or RB_AUGMENT_CHECK is invoked in a loop at the root of * every modified subtree, from the bottom up to the root, to update augmented * node data. RB_AUGMENT_CHECK returns true only when the update changes the * node data, so that updating can be stopped short of the root when it returns * false. */ #ifndef RB_AUGMENT_CHECK #ifndef RB_AUGMENT #define RB_AUGMENT_CHECK(x) 0 #else #define RB_AUGMENT_CHECK(x) (RB_AUGMENT(x), 1) #endif #endif #define RB_UPDATE_AUGMENT(elm, field) do { \ __typeof(elm) rb_update_tmp = (elm); \ while (RB_AUGMENT_CHECK(rb_update_tmp) && \ (rb_update_tmp = RB_PARENT(rb_update_tmp, field)) != NULL) \ ; \ } while (0) #define RB_SWAP_CHILD(head, par, out, in, field) do { \ if (par == NULL) \ RB_ROOT(head) = (in); \ else if ((out) == RB_LEFT(par, field)) \ RB_LEFT(par, field) = (in); \ else \ RB_RIGHT(par, field) = (in); \ } while (/*CONSTCOND*/ 0) /* * RB_ROTATE macro partially restructures the tree to improve balance. In the * case when dir is _RB_L, tmp is a right child of elm. After rotation, elm * is a left child of tmp, and the subtree that represented the items between * them, which formerly hung to the left of tmp now hangs to the right of elm. * The parent-child relationship between elm and its former parent is not * changed; where this macro once updated those fields, that is now left to the * caller of RB_ROTATE to clean up, so that a pair of rotations does not twice * update the same pair of pointer fields with distinct values. */ #define RB_ROTATE(elm, tmp, dir, field) do { \ if ((_RB_LINK(elm, dir ^ _RB_LR, field) = \ _RB_LINK(tmp, dir, field)) != NULL) \ RB_SET_PARENT(_RB_LINK(tmp, dir, field), elm, field); \ _RB_LINK(tmp, dir, field) = (elm); \ RB_SET_PARENT(elm, tmp, field); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define RB_PROTOTYPE(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ RB_PROTOTYPE_RANK(name, type, attr) \ RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ RB_PROTOTYPE_INSERT(name, type, attr); \ RB_PROTOTYPE_REMOVE(name, type, attr); \ RB_PROTOTYPE_FIND(name, type, attr); \ RB_PROTOTYPE_NFIND(name, type, attr); \ RB_PROTOTYPE_NEXT(name, type, attr); \ RB_PROTOTYPE_PREV(name, type, attr); \ RB_PROTOTYPE_MINMAX(name, type, attr); \ RB_PROTOTYPE_REINSERT(name, type, attr); #ifdef _RB_DIAGNOSTIC #define RB_PROTOTYPE_RANK(name, type, attr) \ attr int name##_RB_RANK(struct type *); #else #define RB_PROTOTYPE_RANK(name, type, attr) #endif #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ attr struct type *name##_RB_INSERT_COLOR(struct name *, \ struct type *, struct type *) #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ attr struct type *name##_RB_REMOVE_COLOR(struct name *, \ struct type *, struct type *) #define RB_PROTOTYPE_REMOVE(name, type, attr) \ attr struct type *name##_RB_REMOVE(struct name *, struct type *) #define RB_PROTOTYPE_INSERT(name, type, attr) \ attr struct type *name##_RB_INSERT(struct name *, struct type *) #define RB_PROTOTYPE_FIND(name, type, attr) \ attr struct type *name##_RB_FIND(struct name *, struct type *) #define RB_PROTOTYPE_NFIND(name, type, attr) \ attr struct type *name##_RB_NFIND(struct name *, struct type *) #define RB_PROTOTYPE_NEXT(name, type, attr) \ attr struct type *name##_RB_NEXT(struct type *) #define RB_PROTOTYPE_PREV(name, type, attr) \ attr struct type *name##_RB_PREV(struct type *) #define RB_PROTOTYPE_MINMAX(name, type, attr) \ attr struct type *name##_RB_MINMAX(struct name *, int) #define RB_PROTOTYPE_REINSERT(name, type, attr) \ attr struct type *name##_RB_REINSERT(struct name *, struct type *) /* Main rb operation. * Moves node close to the key of elm to top */ #define RB_GENERATE(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp,) #define RB_GENERATE_STATIC(name, type, field, cmp) \ RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ RB_GENERATE_RANK(name, type, field, attr) \ RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ RB_GENERATE_INSERT(name, type, field, cmp, attr) \ RB_GENERATE_REMOVE(name, type, field, attr) \ RB_GENERATE_FIND(name, type, field, cmp, attr) \ RB_GENERATE_NFIND(name, type, field, cmp, attr) \ RB_GENERATE_NEXT(name, type, field, attr) \ RB_GENERATE_PREV(name, type, field, attr) \ RB_GENERATE_MINMAX(name, type, field, attr) \ RB_GENERATE_REINSERT(name, type, field, cmp, attr) #ifdef _RB_DIAGNOSTIC #ifndef RB_AUGMENT #define _RB_AUGMENT_VERIFY(x) RB_AUGMENT_CHECK(x) #else #define _RB_AUGMENT_VERIFY(x) 0 #endif #define RB_GENERATE_RANK(name, type, field, attr) \ /* \ * Return the rank of the subtree rooted at elm, or -1 if the subtree \ * is not rank-balanced, or has inconsistent augmentation data. */ \ attr int \ name##_RB_RANK(struct type *elm) \ { \ struct type *left, *right, *up; \ int left_rank, right_rank; \ \ if (elm == NULL) \ return (0); \ up = _RB_UP(elm, field); \ left = RB_LEFT(elm, field); \ left_rank = ((_RB_BITS(up) & _RB_L) ? 2 : 1) + \ name##_RB_RANK(left); \ right = RB_RIGHT(elm, field); \ right_rank = ((_RB_BITS(up) & _RB_R) ? 2 : 1) + \ name##_RB_RANK(right); \ if (left_rank != right_rank || \ (left_rank == 2 && left == NULL && right == NULL) || \ _RB_AUGMENT_VERIFY(elm)) \ return (-1); \ return (left_rank); \ } #else #define RB_GENERATE_RANK(name, type, field, attr) #endif #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ attr struct type * \ name##_RB_INSERT_COLOR(struct name *head, \ struct type *parent, struct type *elm) \ { \ /* \ * Initially, elm is a leaf. Either its parent was previously \ * a leaf, with two black null children, or an interior node \ * with a black non-null child and a red null child. The \ * balance criterion "the rank of any leaf is 1" precludes the \ * possibility of two red null children for the initial parent. \ * So the first loop iteration cannot lead to accessing an \ * uninitialized 'child', and a later iteration can only happen \ * when a value has been assigned to 'child' in the previous \ * one. \ */ \ struct type *child, *child_up, *gpar; \ __uintptr_t elmdir, sibdir; \ \ do { \ /* the rank of the tree rooted at elm grew */ \ gpar = _RB_UP(parent, field); \ elmdir = RB_RIGHT(parent, field) == elm ? _RB_R : _RB_L; \ if (_RB_BITS(gpar) & elmdir) { \ /* shorten the parent-elm edge to rebalance */ \ _RB_BITSUP(parent, field) ^= elmdir; \ return (NULL); \ } \ sibdir = elmdir ^ _RB_LR; \ /* the other edge must change length */ \ _RB_BITSUP(parent, field) ^= sibdir; \ if ((_RB_BITS(gpar) & _RB_LR) == 0) { \ /* both edges now short, retry from parent */ \ child = elm; \ elm = parent; \ continue; \ } \ _RB_UP(parent, field) = gpar = _RB_PTR(gpar); \ if (_RB_BITSUP(elm, field) & elmdir) { \ /* \ * Exactly one of the edges descending from elm \ * is long. The long one is in the same \ * direction as the edge from parent to elm, \ * so change that by rotation. The edge from \ * parent to z was shortened above. Shorten \ * the long edge down from elm, and adjust \ * other edge lengths based on the downward \ * edges from 'child'. \ * \ * par par \ * / \ / \ \ * elm z / z \ * / \ child \ * / child / \ \ * / / \ elm \ \ * w / \ / \ y \ * x y w \ \ * x \ */ \ RB_ROTATE(elm, child, elmdir, field); \ child_up = _RB_UP(child, field); \ if (_RB_BITS(child_up) & sibdir) \ _RB_BITSUP(parent, field) ^= elmdir; \ if (_RB_BITS(child_up) & elmdir) \ _RB_BITSUP(elm, field) ^= _RB_LR; \ else \ _RB_BITSUP(elm, field) ^= elmdir; \ /* if child is a leaf, don't augment elm, \ * since it is restored to be a leaf again. */ \ if ((_RB_BITS(child_up) & _RB_LR) == 0) \ elm = child; \ } else \ child = elm; \ \ /* \ * The long edge descending from 'child' points back \ * in the direction of 'parent'. Rotate to make \ * 'parent' a child of 'child', then make both edges \ * of 'child' short to rebalance. \ * \ * par child \ * / \ / \ \ * / z x par \ * child / \ \ * / \ / z \ * x \ y \ * y \ */ \ RB_ROTATE(parent, child, sibdir, field); \ _RB_UP(child, field) = gpar; \ RB_SWAP_CHILD(head, gpar, parent, child, field); \ /* \ * Elements rotated down have new, smaller subtrees, \ * so update augmentation for them. \ */ \ if (elm != child) \ - RB_AUGMENT_CHECK(elm); \ - RB_AUGMENT_CHECK(parent); \ + (void)RB_AUGMENT_CHECK(elm); \ + (void)RB_AUGMENT_CHECK(parent); \ return (child); \ } while ((parent = gpar) != NULL); \ return (NULL); \ } #ifndef RB_STRICT_HST /* * In REMOVE_COLOR, the HST paper, in figure 3, in the single-rotate case, has * 'parent' with one higher rank, and then reduces its rank if 'parent' has * become a leaf. This implementation always has the parent in its new position * with lower rank, to avoid the leaf check. Define RB_STRICT_HST to 1 to get * the behavior that HST describes. */ #define RB_STRICT_HST 0 #endif #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ attr struct type * \ name##_RB_REMOVE_COLOR(struct name *head, \ struct type *parent, struct type *elm) \ { \ struct type *gpar, *sib, *up; \ __uintptr_t elmdir, sibdir; \ \ if (RB_RIGHT(parent, field) == elm && \ RB_LEFT(parent, field) == elm) { \ /* Deleting a leaf that is an only-child creates a \ * rank-2 leaf. Demote that leaf. */ \ _RB_UP(parent, field) = _RB_PTR(_RB_UP(parent, field)); \ elm = parent; \ if ((parent = _RB_UP(elm, field)) == NULL) \ return (NULL); \ } \ do { \ /* the rank of the tree rooted at elm shrank */ \ gpar = _RB_UP(parent, field); \ elmdir = RB_RIGHT(parent, field) == elm ? _RB_R : _RB_L; \ _RB_BITS(gpar) ^= elmdir; \ if (_RB_BITS(gpar) & elmdir) { \ /* lengthen the parent-elm edge to rebalance */ \ _RB_UP(parent, field) = gpar; \ return (NULL); \ } \ if (_RB_BITS(gpar) & _RB_LR) { \ /* shorten other edge, retry from parent */ \ _RB_BITS(gpar) ^= _RB_LR; \ _RB_UP(parent, field) = gpar; \ gpar = _RB_PTR(gpar); \ continue; \ } \ sibdir = elmdir ^ _RB_LR; \ sib = _RB_LINK(parent, sibdir, field); \ up = _RB_UP(sib, field); \ _RB_BITS(up) ^= _RB_LR; \ if ((_RB_BITS(up) & _RB_LR) == 0) { \ /* shorten edges descending from sib, retry */ \ _RB_UP(sib, field) = up; \ continue; \ } \ if ((_RB_BITS(up) & sibdir) == 0) { \ /* \ * The edge descending from 'sib' away from \ * 'parent' is long. The short edge descending \ * from 'sib' toward 'parent' points to 'elm*' \ * Rotate to make 'sib' a child of 'elm*' \ * then adjust the lengths of the edges \ * descending from 'sib' and 'elm*'. \ * \ * par par \ * / \ / \ \ * / sib elm \ \ * / / \ elm* \ * elm elm* \ / \ \ * / \ \ / \ \ * / \ z / \ \ * x y x sib \ * / \ \ * / z \ * y \ */ \ elm = _RB_LINK(sib, elmdir, field); \ /* elm is a 1-child. First rotate at elm. */ \ RB_ROTATE(sib, elm, sibdir, field); \ up = _RB_UP(elm, field); \ _RB_BITSUP(parent, field) ^= \ (_RB_BITS(up) & elmdir) ? _RB_LR : elmdir; \ _RB_BITSUP(sib, field) ^= \ (_RB_BITS(up) & sibdir) ? _RB_LR : sibdir; \ _RB_BITSUP(elm, field) |= _RB_LR; \ } else { \ if ((_RB_BITS(up) & elmdir) == 0 && \ RB_STRICT_HST && elm != NULL) { \ /* if parent does not become a leaf, \ do not demote parent yet. */ \ _RB_BITSUP(parent, field) ^= sibdir; \ _RB_BITSUP(sib, field) ^= _RB_LR; \ } else if ((_RB_BITS(up) & elmdir) == 0) { \ /* demote parent. */ \ _RB_BITSUP(parent, field) ^= elmdir; \ _RB_BITSUP(sib, field) ^= sibdir; \ } else \ _RB_BITSUP(sib, field) ^= sibdir; \ elm = sib; \ } \ \ /* \ * The edge descending from 'elm' away from 'parent' \ * is short. Rotate to make 'parent' a child of 'elm', \ * then lengthen the short edges descending from \ * 'parent' and 'elm' to rebalance. \ * \ * par elm \ * / \ / \ \ * e \ / \ \ * elm / \ \ * / \ par s \ * / \ / \ \ * / \ e \ \ * x s x \ */ \ RB_ROTATE(parent, elm, elmdir, field); \ RB_SET_PARENT(elm, gpar, field); \ RB_SWAP_CHILD(head, gpar, parent, elm, field); \ /* \ * An element rotated down, but not into the search \ * path has a new, smaller subtree, so update \ * augmentation for it. \ */ \ if (sib != elm) \ - RB_AUGMENT_CHECK(sib); \ + (void)RB_AUGMENT_CHECK(sib); \ return (parent); \ } while (elm = parent, (parent = gpar) != NULL); \ return (NULL); \ } #define _RB_AUGMENT_WALK(elm, match, field) \ do { \ if (match == elm) \ match = NULL; \ } while (RB_AUGMENT_CHECK(elm) && \ (elm = RB_PARENT(elm, field)) != NULL) #define RB_GENERATE_REMOVE(name, type, field, attr) \ attr struct type * \ name##_RB_REMOVE(struct name *head, struct type *out) \ { \ struct type *child, *in, *opar, *parent; \ \ child = RB_LEFT(out, field); \ in = RB_RIGHT(out, field); \ opar = _RB_UP(out, field); \ if (in == NULL || child == NULL) { \ in = child = in == NULL ? child : in; \ parent = opar = _RB_PTR(opar); \ } else { \ parent = in; \ while (RB_LEFT(in, field)) \ in = RB_LEFT(in, field); \ RB_SET_PARENT(child, in, field); \ RB_LEFT(in, field) = child; \ child = RB_RIGHT(in, field); \ if (parent != in) { \ RB_SET_PARENT(parent, in, field); \ RB_RIGHT(in, field) = parent; \ parent = RB_PARENT(in, field); \ RB_LEFT(parent, field) = child; \ } \ _RB_UP(in, field) = opar; \ opar = _RB_PTR(opar); \ } \ RB_SWAP_CHILD(head, opar, out, in, field); \ if (child != NULL) \ _RB_UP(child, field) = parent; \ if (parent != NULL) { \ opar = name##_RB_REMOVE_COLOR(head, parent, child); \ /* if rotation has made 'parent' the root of the same \ * subtree as before, don't re-augment it. */ \ if (parent == in && RB_LEFT(parent, field) == NULL) { \ opar = NULL; \ parent = RB_PARENT(parent, field); \ } \ _RB_AUGMENT_WALK(parent, opar, field); \ if (opar != NULL) { \ /* \ * Elements rotated into the search path have \ * changed subtrees, so update augmentation for \ * them if AUGMENT_WALK didn't. \ */ \ - RB_AUGMENT_CHECK(opar); \ - RB_AUGMENT_CHECK(RB_PARENT(opar, field)); \ + (void)RB_AUGMENT_CHECK(opar); \ + (void)RB_AUGMENT_CHECK(RB_PARENT(opar, field)); \ } \ } \ return (out); \ } #define RB_GENERATE_INSERT(name, type, field, cmp, attr) \ /* Inserts a node into the RB tree */ \ attr struct type * \ name##_RB_INSERT(struct name *head, struct type *elm) \ { \ struct type *tmp; \ struct type **tmpp = &RB_ROOT(head); \ struct type *parent = NULL; \ \ while ((tmp = *tmpp) != NULL) { \ parent = tmp; \ __typeof(cmp(NULL, NULL)) comp = (cmp)(elm, parent); \ if (comp < 0) \ tmpp = &RB_LEFT(parent, field); \ else if (comp > 0) \ tmpp = &RB_RIGHT(parent, field); \ else \ return (parent); \ } \ RB_SET(elm, parent, field); \ *tmpp = elm; \ if (parent != NULL) \ tmp = name##_RB_INSERT_COLOR(head, parent, elm); \ _RB_AUGMENT_WALK(elm, tmp, field); \ if (tmp != NULL) \ /* \ * An element rotated into the search path has a \ * changed subtree, so update augmentation for it if \ * AUGMENT_WALK didn't. \ */ \ - RB_AUGMENT_CHECK(tmp); \ + (void)RB_AUGMENT_CHECK(tmp); \ return (NULL); \ } #define RB_GENERATE_FIND(name, type, field, cmp, attr) \ /* Finds the node with the same key as elm */ \ attr struct type * \ name##_RB_FIND(struct name *head, struct type *elm) \ { \ struct type *tmp = RB_ROOT(head); \ __typeof(cmp(NULL, NULL)) comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) \ tmp = RB_LEFT(tmp, field); \ else if (comp > 0) \ tmp = RB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (NULL); \ } #define RB_GENERATE_NFIND(name, type, field, cmp, attr) \ /* Finds the first node greater than or equal to the search key */ \ attr struct type * \ name##_RB_NFIND(struct name *head, struct type *elm) \ { \ struct type *tmp = RB_ROOT(head); \ struct type *res = NULL; \ __typeof(cmp(NULL, NULL)) comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) { \ res = tmp; \ tmp = RB_LEFT(tmp, field); \ } \ else if (comp > 0) \ tmp = RB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (res); \ } #define RB_GENERATE_NEXT(name, type, field, attr) \ /* ARGSUSED */ \ attr struct type * \ name##_RB_NEXT(struct type *elm) \ { \ if (RB_RIGHT(elm, field)) { \ elm = RB_RIGHT(elm, field); \ while (RB_LEFT(elm, field)) \ elm = RB_LEFT(elm, field); \ } else { \ while (RB_PARENT(elm, field) && \ (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ elm = RB_PARENT(elm, field); \ elm = RB_PARENT(elm, field); \ } \ return (elm); \ } #define RB_GENERATE_PREV(name, type, field, attr) \ /* ARGSUSED */ \ attr struct type * \ name##_RB_PREV(struct type *elm) \ { \ if (RB_LEFT(elm, field)) { \ elm = RB_LEFT(elm, field); \ while (RB_RIGHT(elm, field)) \ elm = RB_RIGHT(elm, field); \ } else { \ while (RB_PARENT(elm, field) && \ (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ elm = RB_PARENT(elm, field); \ elm = RB_PARENT(elm, field); \ } \ return (elm); \ } #define RB_GENERATE_MINMAX(name, type, field, attr) \ attr struct type * \ name##_RB_MINMAX(struct name *head, int val) \ { \ struct type *tmp = RB_ROOT(head); \ struct type *parent = NULL; \ while (tmp) { \ parent = tmp; \ if (val < 0) \ tmp = RB_LEFT(tmp, field); \ else \ tmp = RB_RIGHT(tmp, field); \ } \ return (parent); \ } #define RB_GENERATE_REINSERT(name, type, field, cmp, attr) \ attr struct type * \ name##_RB_REINSERT(struct name *head, struct type *elm) \ { \ struct type *cmpelm; \ if (((cmpelm = RB_PREV(name, head, elm)) != NULL && \ cmp(cmpelm, elm) >= 0) || \ ((cmpelm = RB_NEXT(name, head, elm)) != NULL && \ cmp(elm, cmpelm) >= 0)) { \ /* XXXLAS: Remove/insert is heavy handed. */ \ RB_REMOVE(name, head, elm); \ return (RB_INSERT(name, head, elm)); \ } \ return (NULL); \ } \ #define RB_NEGINF -1 #define RB_INF 1 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) #define RB_FIND(name, x, y) name##_RB_FIND(x, y) #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) #define RB_NEXT(name, x, y) name##_RB_NEXT(y) #define RB_PREV(name, x, y) name##_RB_PREV(y) #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y) #define RB_FOREACH(x, name, head) \ for ((x) = RB_MIN(name, head); \ (x) != NULL; \ (x) = name##_RB_NEXT(x)) #define RB_FOREACH_FROM(x, name, y) \ for ((x) = (y); \ ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ (x) = (y)) #define RB_FOREACH_SAFE(x, name, head, y) \ for ((x) = RB_MIN(name, head); \ ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ (x) = (y)) #define RB_FOREACH_REVERSE(x, name, head) \ for ((x) = RB_MAX(name, head); \ (x) != NULL; \ (x) = name##_RB_PREV(x)) #define RB_FOREACH_REVERSE_FROM(x, name, y) \ for ((x) = (y); \ ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ (x) = (y)) #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ for ((x) = RB_MAX(name, head); \ ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ (x) = (y)) #endif /* _SYS_TREE_H_ */