[PATCH 3/3] prio_tree: move general code from mm/ to lib/

[Werner Almesberger <werner@almesberger.net>]

Last but not least, move the general prio_tree code from mm/
to lib/. This patch also duplicates some macros, which are used
in the VMA code for debugging purposes, so we can't properly
separate them yet.

Note that this patch conflicts with a patch in 2.6.10-rc3-mm1
(frv-better-mmap-support-in-uclinux.patch), which removes
mm/prio_tree in systems without an MMU. Not making that other
patch provide a dummy for prio_tree_init should resolve the
conflict. (That's just from reading the patch - I haven't
actually tried this.)

- Werner

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

Signed-off-by: Werner Almesberger <werner@almesberger.net>

--- linux-2.6.10-rc3-bk10/mm/prio_tree.c.gen	Fri Dec 17 01:24:01 2004
+++ linux-2.6.10-rc3-bk10/mm/prio_tree.c	Fri Dec 17 01:21:38 2004
@@ -11,477 +11,24 @@
  * 02Feb2004	Initial version
  */
 
-#include <linux/init.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.
  */
 
 /*
- * The following macros are used for implementing prio_tree for i_mmap
+ * The following #defines are mirrored from lib/prio_tree.c. They're only used
+ * for debugging, and should be removed (along with the debugging code using
+ * them) when switching also VMAs to the regular prio_tree code.
  */
 
 #define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
 #define VMA_SIZE(vma)	  (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
 /* avoid overflow */
-#define HEAP_INDEX(vma)	  ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
-
-
-static void get_index(const struct prio_tree_root *root,
-    const struct prio_tree_node *node,
-    unsigned long *radix, unsigned long *heap)
-{
-	if (root->raw) {
-		struct vm_area_struct *vma = prio_tree_entry(
-		    node, struct vm_area_struct, shared.prio_tree_node);
-
-		*radix = RADIX_INDEX(vma);
-		*heap = HEAP_INDEX(vma);
-	}
-	else {
-		*radix = node->start;
-		*heap = node->last;
-	}
-}
-
-static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
-
-void __init prio_tree_init(void)
-{
-	unsigned int i;
-
-	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];
-}
-
-/*
- * 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
- */
-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.
- */
-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(root, 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(root, 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 << (BITS_PER_LONG - 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.
- */
-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(root, cur->left, &r_index, &h_index_left);
-		else {
-			cur = cur->right;
-			continue;
-		}
-
-		if (!prio_tree_right_empty(cur))
-			get_index(root, 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, root->raw);
-		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->root, 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 << (BITS_PER_LONG - 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->root, 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 << (BITS_PER_LONG - 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, 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
- */
-struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
-{
-	unsigned long r_index, h_index;
-
-	if (iter->cur == NULL)
-		return prio_tree_first(iter);
-
-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;
-}
+#define HEAP_INDEX(vma)   ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
 
 /*
  * Radix priority search tree for address_space->i_mmap
--- linux-2.6.10-rc3-bk10/lib/Makefile.orig	Fri Dec 17 01:09:52 2004
+++ linux-2.6.10-rc3-bk10/lib/Makefile	Fri Dec 17 01:14:06 2004
@@ -5,7 +5,7 @@
 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 kobject_uevent.o
+	 bitmap.o extable.o kobject_uevent.o prio_tree.o
 
 ifeq ($(CONFIG_DEBUG_KOBJECT),y)
 CFLAGS_kobject.o += -DDEBUG
--- /dev/null	Wed Jun  9 20:31:45 2004
+++ linux-2.6.10-rc3-bk10/lib/prio_tree.c	Fri Dec 17 01:23:01 2004
@@ -0,0 +1,484 @@
+/*
+ * lib/prio_tree.c - priority search tree
+ *
+ * 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/init.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.
+ */
+
+/*
+ * The following macros are used for implementing prio_tree for i_mmap
+ */
+
+#define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
+#define VMA_SIZE(vma)	  (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
+/* avoid overflow */
+#define HEAP_INDEX(vma)	  ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
+
+
+static void get_index(const struct prio_tree_root *root,
+    const struct prio_tree_node *node,
+    unsigned long *radix, unsigned long *heap)
+{
+	if (root->raw) {
+		struct vm_area_struct *vma = prio_tree_entry(
+		    node, struct vm_area_struct, shared.prio_tree_node);
+
+		*radix = RADIX_INDEX(vma);
+		*heap = HEAP_INDEX(vma);
+	}
+	else {
+		*radix = node->start;
+		*heap = node->last;
+	}
+}
+
+static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
+
+void __init prio_tree_init(void)
+{
+	unsigned int i;
+
+	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];
+}
+
+/*
+ * 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
+ */
+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.
+ */
+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(root, 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(root, 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 << (BITS_PER_LONG - 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.
+ */
+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(root, cur->left, &r_index, &h_index_left);
+		else {
+			cur = cur->right;
+			continue;
+		}
+
+		if (!prio_tree_right_empty(cur))
+			get_index(root, 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, root->raw);
+		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->root, 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 << (BITS_PER_LONG - 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->root, 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 << (BITS_PER_LONG - 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, 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
+ */
+struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
+{
+	unsigned long r_index, h_index;
+
+	if (iter->cur == NULL)
+		return prio_tree_first(iter);
+
+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/____________________________________________/