Date: Sun, 14 Nov 2004 23:59:36 -0300
From: Werner Almesberger <werner@almesberger.net>
To: Rajesh Venkatasubramanian <vrajesh@umich.edu>
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>
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In-Reply-To: <20041114235646.K28802@almesberger.net>; from werner@almesberger.net on Sun, Nov 14, 2004 at 11:56:46PM -0300
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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 <linux/init.h>
-#include <linux/module.h>
 #include <linux/mm.h>
 #include <linux/prio_tree.h>
 
 /*
- * 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/____________________________________________/
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