/* $NetBSD: interval-tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */ /* $OpenBSD: interval-tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */ /* $FreeBSD$ */ /* This is a COPY of the in-tree tree.h modified to accomodate interval * tree operations */ /*- * 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_INTERVALTREE_H_ #define _SYS_INTERVALTREE_H_ #if defined(__clang_analyzer__) #define _T_ASSERT(a) assert((a)) #else #define _T_ASSERT(a) #endif /* * This file defines data structures for interval trees which are * implemented using red-black trees. * * A red-black tree is a binary search tree with the node color as an * extra attribute. It fulfills a set of conditions: * - every search path from the root to a leaf consists of the * same number of black nodes, * - each red node (except for the root) has a black parent, * - each leaf node is black. * * Every operation on a red-black tree is bounded as O(lg n). * The maximum height of a red-black tree is 2lg (n+1). */ /* Macros that define a red-black tree */ #define IRB_HEAD(name, type) \ struct name { \ struct type *rbh_root; /* root of the tree */ \ } #define IRB_INITIALIZER(root) \ { \ NULL \ } #define IRB_INIT(root) \ do { \ (root)->rbh_root = NULL; \ } while (/*CONSTCOND*/ 0) #define IRB_BLACK 0 #define IRB_RED 1 #define IRB_ENTRY(type) \ struct { \ struct type *rbe_left; /* left element */ \ struct type *rbe_right; /* right element */ \ struct type *rbe_parent; /* parent element */ \ int rbe_color; /* node color */ \ } #define IRB_LEFT(elm, field) (elm)->field.rbe_left #define IRB_RIGHT(elm, field) (elm)->field.rbe_right #define IRB_PARENT(elm, field) (elm)->field.rbe_parent #define IRB_COLOR(elm, field) (elm)->field.rbe_color #define IRB_ROOT(head) (head)->rbh_root #define IRB_EMPTY(head) (IRB_ROOT(head) == NULL) #define IRB_SET(elm, parent, field) \ do { \ IRB_PARENT(elm, field) = parent; \ IRB_LEFT(elm, field) = IRB_RIGHT(elm, field) = NULL; \ IRB_COLOR(elm, field) = IRB_RED; \ } while (/*CONSTCOND*/ 0) #define IRB_SET_BLACKRED(black, red, field) \ do { \ IRB_COLOR(black, field) = IRB_BLACK; \ IRB_COLOR(red, field) = IRB_RED; \ } while (/*CONSTCOND*/ 0) /* * The implementation of the following macro has been updated. * In order to incorporte it properly, the call sites of this * function have also been updated compared to the standard * Red Black tree implementation in tree.h of BSD */ #ifndef IRB_AUGMENT #define IRB_AUGMENT(x, field) \ do { \ if (x != NULL) { \ x->max = x->port2; \ if (IRB_LEFT(x, field) != NULL) { \ x->max = MAX(x->max, IRB_LEFT(x, field)->max); \ } \ if (IRB_RIGHT(x, field) != NULL) { \ x->max = MAX(x->max, IRB_RIGHT(x, field)->max); \ } \ } \ } while (0) #endif #define IRB_ROTATE_LEFT(head, elm, tmp, field) \ do { \ (tmp) = IRB_RIGHT(elm, field); \ if ((IRB_RIGHT(elm, field) = IRB_LEFT(tmp, field)) != NULL) { \ IRB_PARENT(IRB_LEFT(tmp, field), field) = (elm); \ } \ if ((IRB_PARENT(tmp, field) = IRB_PARENT(elm, field)) != NULL) { \ if ((elm) == IRB_LEFT(IRB_PARENT(elm, field), field)) \ IRB_LEFT(IRB_PARENT(elm, field), field) = (tmp); \ else \ IRB_RIGHT(IRB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ IRB_LEFT(tmp, field) = (elm); \ IRB_PARENT(elm, field) = (tmp); \ IRB_AUGMENT(elm, field); \ IRB_AUGMENT(tmp, field); \ if ((IRB_PARENT(tmp, field))) \ IRB_AUGMENT(IRB_PARENT(tmp, field), field); \ } while (/*CONSTCOND*/ 0) #define IRB_ROTATE_RIGHT(head, elm, tmp, field) \ do { \ (tmp) = IRB_LEFT(elm, field); \ if ((IRB_LEFT(elm, field) = IRB_RIGHT(tmp, field)) != NULL) { \ IRB_PARENT(IRB_RIGHT(tmp, field), field) = (elm); \ } \ if ((IRB_PARENT(tmp, field) = IRB_PARENT(elm, field)) != NULL) { \ if ((elm) == IRB_LEFT(IRB_PARENT(elm, field), field)) \ IRB_LEFT(IRB_PARENT(elm, field), field) = (tmp); \ else \ IRB_RIGHT(IRB_PARENT(elm, field), field) = (tmp); \ } else \ (head)->rbh_root = (tmp); \ IRB_RIGHT(tmp, field) = (elm); \ IRB_PARENT(elm, field) = (tmp); \ IRB_AUGMENT(elm, field); \ IRB_AUGMENT(tmp, field); \ if ((IRB_PARENT(tmp, field))) \ IRB_AUGMENT(IRB_PARENT(tmp, field), field); \ } while (/*CONSTCOND*/ 0) /* Generates prototypes and inline functions */ #define IRB_PROTOTYPE(name, type, field, cmp) IRB_PROTOTYPE_INTERNAL(name, type, field, cmp, ) #define IRB_PROTOTYPE_STATIC(name, type, field, cmp) \ IRB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) #define IRB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ IRB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ IRB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ IRB_PROTOTYPE_INSERT(name, type, attr); \ IRB_PROTOTYPE_REMOVE(name, type, attr); \ IRB_PROTOTYPE_FIND(name, type, attr); \ IRB_PROTOTYPE_NFIND(name, type, attr); \ IRB_PROTOTYPE_NEXT(name, type, attr); \ IRB_PROTOTYPE_PREV(name, type, attr); \ IRB_PROTOTYPE_MINMAX(name, type, attr); #define IRB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ attr void name##_IRB_INSERT_COLOR(struct name *, struct type *) #define IRB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ attr void name##_IRB_REMOVE_COLOR(struct name *, struct type *, struct type *) #define IRB_PROTOTYPE_REMOVE(name, type, attr) \ attr struct type *name##_IRB_REMOVE(struct name *, struct type *) #define IRB_PROTOTYPE_INSERT(name, type, attr) \ attr struct type *name##_IRB_INSERT(struct name *, struct type *) #define IRB_PROTOTYPE_FIND(name, type, attr) \ attr struct type *name##_IRB_FIND(struct name *, struct type *) #define IRB_PROTOTYPE_NFIND(name, type, attr) \ attr struct type *name##_IRB_NFIND(struct name *, struct type *) #define IRB_PROTOTYPE_NEXT(name, type, attr) attr struct type *name##_IRB_NEXT(struct type *) #define IRB_PROTOTYPE_PREV(name, type, attr) attr struct type *name##_IRB_PREV(struct type *) #define IRB_PROTOTYPE_MINMAX(name, type, attr) \ attr struct type *name##_IRB_MINMAX(struct name *, int) /* Main rb operation. * Moves node close to the key of elm to top */ #define IRB_GENERATE(name, type, field, cmp) IRB_GENERATE_INTERNAL(name, type, field, cmp, ) #define IRB_GENERATE_STATIC(name, type, field, cmp) \ IRB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) #define IRB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ IRB_GENERATE_INSERT_COLOR(name, type, field, attr) \ IRB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ IRB_GENERATE_INSERT(name, type, field, cmp, attr) \ IRB_GENERATE_REMOVE(name, type, field, attr) \ IRB_GENERATE_FIND(name, type, field, cmp, attr) \ IRB_GENERATE_NFIND(name, type, field, cmp, attr) \ IRB_GENERATE_NEXT(name, type, field, attr) \ IRB_GENERATE_PREV(name, type, field, attr) \ IRB_GENERATE_MINMAX(name, type, field, attr) #define IRB_GENERATE_INSERT_COLOR(name, type, field, attr) \ attr void name##_IRB_INSERT_COLOR(struct name *head, struct type *elm) \ { \ struct type *parent, *gparent, *tmp; \ while ((parent = IRB_PARENT(elm, field)) != NULL && IRB_COLOR(parent, field) == IRB_RED) { \ gparent = IRB_PARENT(parent, field); \ _T_ASSERT(gparent); \ if (parent == IRB_LEFT(gparent, field)) { \ tmp = IRB_RIGHT(gparent, field); \ if (tmp && IRB_COLOR(tmp, field) == IRB_RED) { \ IRB_COLOR(tmp, field) = IRB_BLACK; \ IRB_SET_BLACKRED(parent, gparent, field); \ elm = gparent; \ continue; \ } \ if (IRB_RIGHT(parent, field) == elm) { \ IRB_ROTATE_LEFT(head, parent, tmp, field); \ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ IRB_SET_BLACKRED(parent, gparent, field); \ IRB_ROTATE_RIGHT(head, gparent, tmp, field); \ } else { \ tmp = IRB_LEFT(gparent, field); \ if (tmp && IRB_COLOR(tmp, field) == IRB_RED) { \ IRB_COLOR(tmp, field) = IRB_BLACK; \ IRB_SET_BLACKRED(parent, gparent, field); \ elm = gparent; \ continue; \ } \ if (IRB_LEFT(parent, field) == elm) { \ IRB_ROTATE_RIGHT(head, parent, tmp, field); \ tmp = parent; \ parent = elm; \ elm = tmp; \ } \ IRB_SET_BLACKRED(parent, gparent, field); \ IRB_ROTATE_LEFT(head, gparent, tmp, field); \ } \ } \ IRB_COLOR(head->rbh_root, field) = IRB_BLACK; \ } #define IRB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ attr void name##_IRB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ { \ struct type *tmp; \ while ((elm == NULL || IRB_COLOR(elm, field) == IRB_BLACK) && elm != IRB_ROOT(head)) { \ if (IRB_LEFT(parent, field) == elm) { \ tmp = IRB_RIGHT(parent, field); \ if (IRB_COLOR(tmp, field) == IRB_RED) { \ IRB_SET_BLACKRED(tmp, parent, field); \ IRB_ROTATE_LEFT(head, parent, tmp, field); \ tmp = IRB_RIGHT(parent, field); \ } \ _T_ASSERT(tmp); \ if ((IRB_LEFT(tmp, field) == NULL || \ IRB_COLOR(IRB_LEFT(tmp, field), field) == IRB_BLACK) && \ (IRB_RIGHT(tmp, field) == NULL || \ IRB_COLOR(IRB_RIGHT(tmp, field), field) == IRB_BLACK)) { \ IRB_COLOR(tmp, field) = IRB_RED; \ elm = parent; \ parent = IRB_PARENT(elm, field); \ } else { \ if (IRB_RIGHT(tmp, field) == NULL || \ IRB_COLOR(IRB_RIGHT(tmp, field), field) == IRB_BLACK) { \ struct type *oleft; \ if ((oleft = IRB_LEFT(tmp, field)) != NULL) \ IRB_COLOR(oleft, field) = IRB_BLACK; \ IRB_COLOR(tmp, field) = IRB_RED; \ IRB_ROTATE_RIGHT(head, tmp, oleft, field); \ tmp = IRB_RIGHT(parent, field); \ } \ IRB_COLOR(tmp, field) = IRB_COLOR(parent, field); \ IRB_COLOR(parent, field) = IRB_BLACK; \ if (IRB_RIGHT(tmp, field)) \ IRB_COLOR(IRB_RIGHT(tmp, field), field) = IRB_BLACK; \ IRB_ROTATE_LEFT(head, parent, tmp, field); \ elm = IRB_ROOT(head); \ break; \ } \ } else { \ tmp = IRB_LEFT(parent, field); \ if (IRB_COLOR(tmp, field) == IRB_RED) { \ IRB_SET_BLACKRED(tmp, parent, field); \ IRB_ROTATE_RIGHT(head, parent, tmp, field); \ tmp = IRB_LEFT(parent, field); \ } \ _T_ASSERT(tmp); \ if ((IRB_LEFT(tmp, field) == NULL || \ IRB_COLOR(IRB_LEFT(tmp, field), field) == IRB_BLACK) && \ (IRB_RIGHT(tmp, field) == NULL || \ IRB_COLOR(IRB_RIGHT(tmp, field), field) == IRB_BLACK)) { \ IRB_COLOR(tmp, field) = IRB_RED; \ elm = parent; \ parent = IRB_PARENT(elm, field); \ } else { \ if (IRB_LEFT(tmp, field) == NULL || \ IRB_COLOR(IRB_LEFT(tmp, field), field) == IRB_BLACK) { \ struct type *oright; \ if ((oright = IRB_RIGHT(tmp, field)) != NULL) \ IRB_COLOR(oright, field) = IRB_BLACK; \ IRB_COLOR(tmp, field) = IRB_RED; \ IRB_ROTATE_LEFT(head, tmp, oright, field); \ tmp = IRB_LEFT(parent, field); \ } \ IRB_COLOR(tmp, field) = IRB_COLOR(parent, field); \ IRB_COLOR(parent, field) = IRB_BLACK; \ if (IRB_LEFT(tmp, field)) \ IRB_COLOR(IRB_LEFT(tmp, field), field) = IRB_BLACK; \ IRB_ROTATE_RIGHT(head, parent, tmp, field); \ elm = IRB_ROOT(head); \ break; \ } \ } \ } \ if (elm) \ IRB_COLOR(elm, field) = IRB_BLACK; \ } #define IRB_GENERATE_REMOVE(name, type, field, attr) \ attr struct type *name##_IRB_REMOVE(struct name *head, struct type *elm) \ { \ struct type *child, *parent, *old = elm; \ int color; \ if (IRB_LEFT(elm, field) == NULL) \ child = IRB_RIGHT(elm, field); \ else if (IRB_RIGHT(elm, field) == NULL) \ child = IRB_LEFT(elm, field); \ else { \ struct type *left; \ elm = IRB_RIGHT(elm, field); \ while ((left = IRB_LEFT(elm, field)) != NULL) \ elm = left; \ child = IRB_RIGHT(elm, field); \ parent = IRB_PARENT(elm, field); \ color = IRB_COLOR(elm, field); \ if (child) \ IRB_PARENT(child, field) = parent; \ if (parent) { \ if (IRB_LEFT(parent, field) == elm) \ IRB_LEFT(parent, field) = child; \ else \ IRB_RIGHT(parent, field) = child; \ IRB_AUGMENT(parent, field); \ } else \ IRB_ROOT(head) = child; \ if (IRB_PARENT(elm, field) == old) \ parent = elm; \ _T_ASSERT((old)); \ (elm)->field = (old)->field; \ if (IRB_PARENT(old, field)) { \ if (IRB_LEFT(IRB_PARENT(old, field), field) == old) \ IRB_LEFT(IRB_PARENT(old, field), field) = elm; \ else \ IRB_RIGHT(IRB_PARENT(old, field), field) = elm; \ IRB_AUGMENT(IRB_PARENT(old, field), field); \ } else \ IRB_ROOT(head) = elm; \ _T_ASSERT(old); \ _T_ASSERT(IRB_LEFT(old, field)); \ IRB_PARENT(IRB_LEFT(old, field), field) = elm; \ if (IRB_RIGHT(old, field)) \ IRB_PARENT(IRB_RIGHT(old, field), field) = elm; \ if (parent) { \ left = parent; \ do { \ IRB_AUGMENT(left, field); \ } while ((left = IRB_PARENT(left, field)) != NULL); \ } \ goto color; \ } \ parent = IRB_PARENT(elm, field); \ color = IRB_COLOR(elm, field); \ if (child) \ IRB_PARENT(child, field) = parent; \ if (parent) { \ if (IRB_LEFT(parent, field) == elm) \ IRB_LEFT(parent, field) = child; \ else \ IRB_RIGHT(parent, field) = child; \ IRB_AUGMENT(parent, field); \ } else \ IRB_ROOT(head) = child; \ color: \ if (color == IRB_BLACK) \ name##_IRB_REMOVE_COLOR(head, parent, child); \ return (old); \ } #define IRB_GENERATE_INSERT(name, type, field, cmp, attr) \ /* Inserts a node into the IRB tree */ \ attr struct type *name##_IRB_INSERT(struct name *head, struct type *elm) \ { \ struct type *tmp; \ struct type *parent = NULL; \ int comp = 0; \ tmp = IRB_ROOT(head); \ while (tmp) { \ parent = tmp; \ comp = (cmp)(elm, parent); \ if (comp < 0) { \ tmp = IRB_LEFT(tmp, field); \ } else if (comp > 0) { \ tmp = IRB_RIGHT(tmp, field); \ } else \ return (tmp); \ } \ IRB_SET(elm, parent, field); \ if (parent != NULL) { \ if (comp < 0) \ IRB_LEFT(parent, field) = elm; \ else \ IRB_RIGHT(parent, field) = elm; \ } else \ IRB_ROOT(head) = elm; \ IRB_AUGMENT(elm, field); \ name##_IRB_INSERT_COLOR(head, elm); \ return (NULL); \ } #define IRB_GENERATE_FIND(name, type, field, cmp, attr) \ /* Finds the node with the same key as elm */ \ attr struct type *name##_IRB_FIND(struct name *head, struct type *elm) \ { \ struct type *tmp = IRB_ROOT(head); \ int comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) \ tmp = IRB_LEFT(tmp, field); \ else if (comp > 0) \ tmp = IRB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (NULL); \ } #define IRB_GENERATE_NFIND(name, type, field, cmp, attr) \ /* Finds the first node greater than or equal to the search key */ \ attr struct type *name##_IRB_NFIND(struct name *head, struct type *elm) \ { \ struct type *tmp = IRB_ROOT(head); \ struct type *res = NULL; \ int comp; \ while (tmp) { \ comp = cmp(elm, tmp); \ if (comp < 0) { \ res = tmp; \ tmp = IRB_LEFT(tmp, field); \ } else if (comp > 0) \ tmp = IRB_RIGHT(tmp, field); \ else \ return (tmp); \ } \ return (res); \ } #define IRB_GENERATE_NEXT(name, type, field, attr) \ /* ARGSUSED */ \ attr struct type *name##_IRB_NEXT(struct type *elm) \ { \ if (IRB_RIGHT(elm, field)) { \ elm = IRB_RIGHT(elm, field); \ while (IRB_LEFT(elm, field)) \ elm = IRB_LEFT(elm, field); \ } else { \ if (IRB_PARENT(elm, field) && (elm == IRB_LEFT(IRB_PARENT(elm, field), field))) \ elm = IRB_PARENT(elm, field); \ else { \ while (IRB_PARENT(elm, field) && \ (elm == IRB_RIGHT(IRB_PARENT(elm, field), field))) \ elm = IRB_PARENT(elm, field); \ elm = IRB_PARENT(elm, field); \ } \ } \ return (elm); \ } #define IRB_GENERATE_PREV(name, type, field, attr) \ /* ARGSUSED */ \ attr struct type *name##_IRB_PREV(struct type *elm) \ { \ if (IRB_LEFT(elm, field)) { \ elm = IRB_LEFT(elm, field); \ while (IRB_RIGHT(elm, field)) \ elm = IRB_RIGHT(elm, field); \ } else { \ if (IRB_PARENT(elm, field) && (elm == IRB_RIGHT(IRB_PARENT(elm, field), field))) \ elm = IRB_PARENT(elm, field); \ else { \ while (IRB_PARENT(elm, field) && (elm == IRB_LEFT(IRB_PARENT(elm, field), field))) \ elm = IRB_PARENT(elm, field); \ elm = IRB_PARENT(elm, field); \ } \ } \ return (elm); \ } #define IRB_GENERATE_MINMAX(name, type, field, attr) \ attr struct type *name##_IRB_MINMAX(struct name *head, int val) \ { \ struct type *tmp = IRB_ROOT(head); \ struct type *parent = NULL; \ while (tmp) { \ parent = tmp; \ if (val < 0) \ tmp = IRB_LEFT(tmp, field); \ else \ tmp = IRB_RIGHT(tmp, field); \ } \ return (parent); \ } #define IRB_NEGINF -1 #define IRB_INF 1 #define IRB_INSERT(name, x, y) name##_IRB_INSERT(x, y) #define IRB_REMOVE(name, x, y) name##_IRB_REMOVE(x, y) #define IRB_FIND(name, x, y) name##_IRB_FIND(x, y) #define IRB_NFIND(name, x, y) name##_IRB_NFIND(x, y) #define IRB_NEXT(name, x, y) name##_IRB_NEXT(y) #define IRB_PREV(name, x, y) name##_IRB_PREV(y) #define IRB_MIN(name, x) name##_IRB_MINMAX(x, IRB_NEGINF) #define IRB_MAX(name, x) name##_IRB_MINMAX(x, IRB_INF) #define IRB_FOREACH(x, name, head) \ for ((x) = IRB_MIN(name, head); (x) != NULL; (x) = name##_IRB_NEXT(x)) #define IRB_FOREACH_FROM(x, name, y) \ for ((x) = (y); ((x) != NULL) && ((y) = name##_IRB_NEXT(x), (x) != NULL); (x) = (y)) #define IRB_FOREACH_SAFE(x, name, head, y) \ for ((x) = IRB_MIN(name, head); ((x) != NULL) && ((y) = name##_IRB_NEXT(x), (x) != NULL); \ (x) = (y)) #define IRB_FOREACH_REVERSE(x, name, head) \ for ((x) = IRB_MAX(name, head); (x) != NULL; (x) = name##_IRB_PREV(x)) #define IRB_FOREACH_REVERSE_FROM(x, name, y) \ for ((x) = (y); ((x) != NULL) && ((y) = name##_IRB_PREV(x), (x) != NULL); (x) = (y)) #define IRB_FOREACH_REVERSE_SAFE(x, name, head, y) \ for ((x) = IRB_MAX(name, head); ((x) != NULL) && ((y) = name##_IRB_PREV(x), (x) != NULL); \ (x) = (y)) #endif /* _SYS_INTERVALTREE_H_ */