Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S261476AbUKODoc (ORCPT ); Sun, 14 Nov 2004 22:44:32 -0500 Received: (majordomo@vger.kernel.org) by vger.kernel.org id S261506AbUKODgI (ORCPT ); Sun, 14 Nov 2004 22:36:08 -0500 Received: from almesberger.net ([63.105.73.238]:57348 "EHLO host.almesberger.net") by vger.kernel.org with ESMTP id S261507AbUKOC7t (ORCPT ); Sun, 14 Nov 2004 21:59:49 -0500 Date: Sun, 14 Nov 2004 23:59:36 -0300 From: Werner Almesberger To: Rajesh Venkatasubramanian Cc: linux-kernel@vger.kernel.org Subject: Re: [RFC] Make MM use generalized prio_tree (2/3) Message-ID: <20041114235936.A23273@almesberger.net> References: <20041114235646.K28802@almesberger.net> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20041114235646.K28802@almesberger.net>; from werner@almesberger.net on Sun, Nov 14, 2004 at 11:56:46PM -0300 Sender: linux-kernel-owner@vger.kernel.org X-Mailing-List: linux-kernel@vger.kernel.org Content-Length: 13054 Lines: 478 The second part: make mm/prio_tree.c use lib/prio_tree.c - Werner ---------------------------------- cut here ----------------------------------- --- linux-2.6.9-orig/mm/prio_tree.c Mon Oct 18 18:55:28 2004 +++ linux-2.6.9/mm/prio_tree.c Sun Nov 14 21:32:50 2004 @@ -11,33 +11,12 @@ * 02Feb2004 Initial version */ -#include -#include #include #include /* - * A clever mix of heap and radix trees forms a radix priority search tree (PST) - * which is useful for storing intervals, e.g, we can consider a vma as a closed - * interval of file pages [offset_begin, offset_end], and store all vmas that - * map a file in a PST. Then, using the PST, we can answer a stabbing query, - * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a - * given input interval X (a set of consecutive file pages), in "O(log n + m)" - * time where 'log n' is the height of the PST, and 'm' is the number of stored - * intervals (vmas) that overlap (map) with the input interval X (the set of - * consecutive file pages). - * - * In our implementation, we store closed intervals of the form [radix_index, - * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST - * is designed for storing intervals with unique radix indices, i.e., each - * interval have different radix_index. However, this limitation can be easily - * overcome by using the size, i.e., heap_index - radix_index, as part of the - * index, so we index the tree using [(radix_index,size), heap_index]. - * - * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit - * machine, the maximum height of a PST can be 64. We can use a balanced version - * of the priority search tree to optimize the tree height, but the balanced - * tree proposed by McCreight is too complex and memory-hungry for our purpose. + * See ../lib/prio_tree.c for details on the general radix priority search tree + * code. */ /* @@ -62,422 +41,9 @@ GET_INDEX_VMA(__tmp, radix, heap); \ } while (0) -static unsigned long index_bits_to_maxindex[BITS_PER_LONG]; -void __init prio_tree_init(void) -{ - unsigned int i; +#include "../lib/prio_tree.c" - for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++) - index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1; - index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL; -} - -/* - * Maximum heap_index that can be stored in a PST with index_bits bits - */ -static inline unsigned long prio_tree_maxindex(unsigned int bits) -{ - return index_bits_to_maxindex[bits - 1]; -} - -static void prio_tree_remove(struct prio_tree_root *, struct prio_tree_node *); - -/* - * Extend a priority search tree so that it can store a node with heap_index - * max_heap_index. In the worst case, this algorithm takes O((log n)^2). - * However, this function is used rarely and the common case performance is - * not bad. - */ -static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root, - struct prio_tree_node *node, unsigned long max_heap_index) -{ - struct prio_tree_node *first = NULL, *prev, *last = NULL; - - if (max_heap_index > prio_tree_maxindex(root->index_bits)) - root->index_bits++; - - while (max_heap_index > prio_tree_maxindex(root->index_bits)) { - root->index_bits++; - - if (prio_tree_empty(root)) - continue; - - if (first == NULL) { - first = root->prio_tree_node; - prio_tree_remove(root, root->prio_tree_node); - INIT_PRIO_TREE_NODE(first); - last = first; - } else { - prev = last; - last = root->prio_tree_node; - prio_tree_remove(root, root->prio_tree_node); - INIT_PRIO_TREE_NODE(last); - prev->left = last; - last->parent = prev; - } - } - - INIT_PRIO_TREE_NODE(node); - - if (first) { - node->left = first; - first->parent = node; - } else - last = node; - - if (!prio_tree_empty(root)) { - last->left = root->prio_tree_node; - last->left->parent = last; - } - - root->prio_tree_node = node; - return node; -} - -/* - * Replace a prio_tree_node with a new node and return the old node - */ -static struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root, - struct prio_tree_node *old, struct prio_tree_node *node) -{ - INIT_PRIO_TREE_NODE(node); - - if (prio_tree_root(old)) { - BUG_ON(root->prio_tree_node != old); - /* - * We can reduce root->index_bits here. However, it is complex - * and does not help much to improve performance (IMO). - */ - node->parent = node; - root->prio_tree_node = node; - } else { - node->parent = old->parent; - if (old->parent->left == old) - old->parent->left = node; - else - old->parent->right = node; - } - - if (!prio_tree_left_empty(old)) { - node->left = old->left; - old->left->parent = node; - } - - if (!prio_tree_right_empty(old)) { - node->right = old->right; - old->right->parent = node; - } - - return old; -} - -/* - * Insert a prio_tree_node @node into a radix priority search tree @root. The - * algorithm typically takes O(log n) time where 'log n' is the number of bits - * required to represent the maximum heap_index. In the worst case, the algo - * can take O((log n)^2) - check prio_tree_expand. - * - * If a prior node with same radix_index and heap_index is already found in - * the tree, then returns the address of the prior node. Otherwise, inserts - * @node into the tree and returns @node. - */ -static struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root, - struct prio_tree_node *node) -{ - struct prio_tree_node *cur, *res = node; - unsigned long radix_index, heap_index; - unsigned long r_index, h_index, index, mask; - int size_flag = 0; - - GET_INDEX(node, radix_index, heap_index); - - if (prio_tree_empty(root) || - heap_index > prio_tree_maxindex(root->index_bits)) - return prio_tree_expand(root, node, heap_index); - - cur = root->prio_tree_node; - mask = 1UL << (root->index_bits - 1); - - while (mask) { - GET_INDEX(cur, r_index, h_index); - - if (r_index == radix_index && h_index == heap_index) - return cur; - - if (h_index < heap_index || - (h_index == heap_index && r_index > radix_index)) { - struct prio_tree_node *tmp = node; - node = prio_tree_replace(root, cur, node); - cur = tmp; - /* swap indices */ - index = r_index; - r_index = radix_index; - radix_index = index; - index = h_index; - h_index = heap_index; - heap_index = index; - } - - if (size_flag) - index = heap_index - radix_index; - else - index = radix_index; - - if (index & mask) { - if (prio_tree_right_empty(cur)) { - INIT_PRIO_TREE_NODE(node); - cur->right = node; - node->parent = cur; - return res; - } else - cur = cur->right; - } else { - if (prio_tree_left_empty(cur)) { - INIT_PRIO_TREE_NODE(node); - cur->left = node; - node->parent = cur; - return res; - } else - cur = cur->left; - } - - mask >>= 1; - - if (!mask) { - mask = 1UL << (root->index_bits - 1); - size_flag = 1; - } - } - /* Should not reach here */ - BUG(); - return NULL; -} - -/* - * Remove a prio_tree_node @node from a radix priority search tree @root. The - * algorithm takes O(log n) time where 'log n' is the number of bits required - * to represent the maximum heap_index. - */ -static void prio_tree_remove(struct prio_tree_root *root, - struct prio_tree_node *node) -{ - struct prio_tree_node *cur; - unsigned long r_index, h_index_right, h_index_left; - - cur = node; - - while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) { - if (!prio_tree_left_empty(cur)) - GET_INDEX(cur->left, r_index, h_index_left); - else { - cur = cur->right; - continue; - } - - if (!prio_tree_right_empty(cur)) - GET_INDEX(cur->right, r_index, h_index_right); - else { - cur = cur->left; - continue; - } - - /* both h_index_left and h_index_right cannot be 0 */ - if (h_index_left >= h_index_right) - cur = cur->left; - else - cur = cur->right; - } - - if (prio_tree_root(cur)) { - BUG_ON(root->prio_tree_node != cur); - INIT_PRIO_TREE_ROOT(root); - return; - } - - if (cur->parent->right == cur) - cur->parent->right = cur->parent; - else - cur->parent->left = cur->parent; - - while (cur != node) - cur = prio_tree_replace(root, cur->parent, cur); -} - -/* - * Following functions help to enumerate all prio_tree_nodes in the tree that - * overlap with the input interval X [radix_index, heap_index]. The enumeration - * takes O(log n + m) time where 'log n' is the height of the tree (which is - * proportional to # of bits required to represent the maximum heap_index) and - * 'm' is the number of prio_tree_nodes that overlap the interval X. - */ - -static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter, - unsigned long *r_index, unsigned long *h_index) -{ - if (prio_tree_left_empty(iter->cur)) - return NULL; - - GET_INDEX(iter->cur->left, *r_index, *h_index); - - if (iter->r_index <= *h_index) { - iter->cur = iter->cur->left; - iter->mask >>= 1; - if (iter->mask) { - if (iter->size_level) - iter->size_level++; - } else { - if (iter->size_level) { - BUG_ON(!prio_tree_left_empty(iter->cur)); - BUG_ON(!prio_tree_right_empty(iter->cur)); - iter->size_level++; - iter->mask = ULONG_MAX; - } else { - iter->size_level = 1; - iter->mask = 1UL << (iter->root->index_bits - 1); - } - } - return iter->cur; - } - - return NULL; -} - -static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter, - unsigned long *r_index, unsigned long *h_index) -{ - unsigned long value; - - if (prio_tree_right_empty(iter->cur)) - return NULL; - - if (iter->size_level) - value = iter->value; - else - value = iter->value | iter->mask; - - if (iter->h_index < value) - return NULL; - - GET_INDEX(iter->cur->right, *r_index, *h_index); - - if (iter->r_index <= *h_index) { - iter->cur = iter->cur->right; - iter->mask >>= 1; - iter->value = value; - if (iter->mask) { - if (iter->size_level) - iter->size_level++; - } else { - if (iter->size_level) { - BUG_ON(!prio_tree_left_empty(iter->cur)); - BUG_ON(!prio_tree_right_empty(iter->cur)); - iter->size_level++; - iter->mask = ULONG_MAX; - } else { - iter->size_level = 1; - iter->mask = 1UL << (iter->root->index_bits - 1); - } - } - return iter->cur; - } - - return NULL; -} - -static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter) -{ - iter->cur = iter->cur->parent; - if (iter->mask == ULONG_MAX) - iter->mask = 1UL; - else if (iter->size_level == 1) - iter->mask = 1UL; - else - iter->mask <<= 1; - if (iter->size_level) - iter->size_level--; - if (!iter->size_level && (iter->value & iter->mask)) - iter->value ^= iter->mask; - return iter->cur; -} - -static inline int overlap(struct prio_tree_iter *iter, - unsigned long r_index, unsigned long h_index) -{ - return iter->h_index >= r_index && iter->r_index <= h_index; -} - -/* - * prio_tree_first: - * - * Get the first prio_tree_node that overlaps with the interval [radix_index, - * heap_index]. Note that always radix_index <= heap_index. We do a pre-order - * traversal of the tree. - */ -static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter) -{ - struct prio_tree_root *root; - unsigned long r_index, h_index; - - INIT_PRIO_TREE_ITER(iter); - - root = iter->root; - if (prio_tree_empty(root)) - return NULL; - - GET_INDEX(root->prio_tree_node, r_index, h_index); - - if (iter->r_index > h_index) - return NULL; - - iter->mask = 1UL << (root->index_bits - 1); - iter->cur = root->prio_tree_node; - - while (1) { - if (overlap(iter, r_index, h_index)) - return iter->cur; - - if (prio_tree_left(iter, &r_index, &h_index)) - continue; - - if (prio_tree_right(iter, &r_index, &h_index)) - continue; - - break; - } - return NULL; -} - -/* - * prio_tree_next: - * - * Get the next prio_tree_node that overlaps with the input interval in iter - */ -static struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter) -{ - unsigned long r_index, h_index; - -repeat: - while (prio_tree_left(iter, &r_index, &h_index)) - if (overlap(iter, r_index, h_index)) - return iter->cur; - - while (!prio_tree_right(iter, &r_index, &h_index)) { - while (!prio_tree_root(iter->cur) && - iter->cur->parent->right == iter->cur) - prio_tree_parent(iter); - - if (prio_tree_root(iter->cur)) - return NULL; - - prio_tree_parent(iter); - } - - if (overlap(iter, r_index, h_index)) - return iter->cur; - - goto repeat; -} /* * Radix priority search tree for address_space->i_mmap -- _________________________________________________________________________ / Werner Almesberger, Buenos Aires, Argentina werner@almesberger.net / /_http://www.almesberger.net/____________________________________________/ - To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majordomo@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/