Date: Sun, 14 Nov 2004 23:56:46 -0300
From: Werner Almesberger <werner@almesberger.net>
To: Rajesh Venkatasubramanian <vrajesh@umich.edu>
Cc: linux-kernel@vger.kernel.org
Subject: [RFC] Generalize prio_tree (1/3)
Message-ID: <20041114235646.K28802@almesberger.net>
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Disposition: inline
Sender: linux-kernel-owner@vger.kernel.org
Content-Length: 15287
Lines: 539

Hi Rajesh,

perhaps you remember me posting a long time ago about generalizing
prio_tree. Now I finally got to make that patch. In fact, there are
three parts:

 - the prio_tree "core" in lib/
 - switching mm/prio_tree.c to use the "core"
 - some debugging extensions

The reason for wanting this generalization is that we'll also need
radix priority search trees for healthier barrier handling in the
IO scheduler (aka disk elevator).

Since this rearranges fairly crucial code, I think a first round
for review is approproate. If nothing major turns up, I'll make
another patch for merging into mainline when the next version is
out.

The patch below puts an includeable version of prio_tree to lib/.
This should be included similar to how inflate.c is used.

The only real change is that index_bits_to_maxindex is now called
prio_tree_index_bits_to_maxindex, and is globally shard.

- Werner

---------------------------------- cut here -----------------------------------

--- linux-2.6.9-orig/include/linux/prio_tree.h	Mon Oct 18 18:54:08 2004
+++ linux-2.6.9/include/linux/prio_tree.h	Sun Nov 14 21:29:29 2004
@@ -73,4 +73,6 @@
 	return node->right == node;
 }
 
+extern unsigned long prio_tree_index_bits_to_maxindex[];
+
 #endif /* _LINUX_PRIO_TREE_H */
--- linux-2.6.9-orig/lib/Makefile	Mon Oct 18 18:53:08 2004
+++ linux-2.6.9/lib/Makefile	Sun Nov 14 21:33:17 2004
@@ -6,7 +6,7 @@
 lib-y := errno.o ctype.o string.o vsprintf.o cmdline.o \
 	 bust_spinlocks.o rbtree.o radix-tree.o dump_stack.o \
 	 kobject.o kref.o idr.o div64.o parser.o int_sqrt.o \
-	 bitmap.o extable.o
+	 bitmap.o extable.o prio_tree_init.o
 
 lib-$(CONFIG_RWSEM_GENERIC_SPINLOCK) += rwsem-spinlock.o
 lib-$(CONFIG_RWSEM_XCHGADD_ALGORITHM) += rwsem.o
--- /dev/null	Wed Jun  9 20:31:45 2004
+++ linux-2.6.9/lib/prio_tree_init.c	Sun Nov 14 21:54:27 2004
@@ -0,0 +1,29 @@
+/*
+ * lib/prio_tree_init.c - priority search tree: initialization
+ *
+ * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
+ *
+ * This file is released under the GPL v2.
+ *
+ * Based on the radix priority search tree proposed by Edward M. McCreight
+ * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
+ *
+ * 02Feb2004	Initial version
+ */
+
+#include <linux/kernel.h>
+#include <linux/init.h>
+#include <linux/prio_tree.h>
+
+
+unsigned long prio_tree_index_bits_to_maxindex[BITS_PER_LONG];
+
+void __init prio_tree_init(void)
+{
+	unsigned int i;
+
+	for (i = 0; i < ARRAY_SIZE(prio_tree_index_bits_to_maxindex) - 1; i++)
+		prio_tree_index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
+	prio_tree_index_bits_to_maxindex
+	    [ARRAY_SIZE(prio_tree_index_bits_to_maxindex) - 1] = ~0UL;
+}
--- /dev/null	Wed Jun  9 20:31:45 2004
+++ linux-2.6.9/lib/prio_tree.c	Sun Nov 14 23:00:57 2004
@@ -0,0 +1,445 @@
+/*
+ * lib/prio_tree.c - priority search tree: common code
+ *
+ * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
+ *
+ * This file is released under the GPL v2.
+ *
+ * Based on the radix priority search tree proposed by Edward M. McCreight
+ * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
+ *
+ * 02Feb2004	Initial version
+ */
+
+/* Includer will have included linux/prio_tree.h for us */
+
+/*
+ * 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.
+ */
+
+
+/*
+ * 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 prio_tree_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;
+}

-- 
  _________________________________________________________________________
 / 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/