Adding upstream version 5.10.209.upstream/5.10.209upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 2086 insertions, 0 deletions

diff --git a/tools/testing/selftests/kvm/lib/sparsebit.c b/tools/testing/selftests/kvm/lib/sparsebit.c
new file mode 100644
index 000000000..031ba3c93
--- /dev/null
+++ b/tools/testing/selftests/kvm/lib/sparsebit.c
@@ -0,0 +1,2086 @@
+// SPDX-License-Identifier: GPL-2.0-only
+/*
+ * Sparse bit array
+ *
+ * Copyright (C) 2018, Google LLC.
+ * Copyright (C) 2018, Red Hat, Inc. (code style cleanup and fuzzing driver)
+ *
+ * This library provides functions to support a memory efficient bit array,
+ * with an index size of 2^64.  A sparsebit array is allocated through
+ * the use sparsebit_alloc() and free'd via sparsebit_free(),
+ * such as in the following:
+ *
+ *   struct sparsebit *s;
+ *   s = sparsebit_alloc();
+ *   sparsebit_free(&s);
+ *
+ * The struct sparsebit type resolves down to a struct sparsebit.
+ * Note that, sparsebit_free() takes a pointer to the sparsebit
+ * structure.  This is so that sparsebit_free() is able to poison
+ * the pointer (e.g. set it to NULL) to the struct sparsebit before
+ * returning to the caller.
+ *
+ * Between the return of sparsebit_alloc() and the call of
+ * sparsebit_free(), there are multiple query and modifying operations
+ * that can be performed on the allocated sparsebit array.  All of
+ * these operations take as a parameter the value returned from
+ * sparsebit_alloc() and most also take a bit index.  Frequently
+ * used routines include:
+ *
+ *  ---- Query Operations
+ *  sparsebit_is_set(s, idx)
+ *  sparsebit_is_clear(s, idx)
+ *  sparsebit_any_set(s)
+ *  sparsebit_first_set(s)
+ *  sparsebit_next_set(s, prev_idx)
+ *
+ *  ---- Modifying Operations
+ *  sparsebit_set(s, idx)
+ *  sparsebit_clear(s, idx)
+ *  sparsebit_set_num(s, idx, num);
+ *  sparsebit_clear_num(s, idx, num);
+ *
+ * A common operation, is to itterate over all the bits set in a test
+ * sparsebit array.  This can be done via code with the following structure:
+ *
+ *   sparsebit_idx_t idx;
+ *   if (sparsebit_any_set(s)) {
+ *     idx = sparsebit_first_set(s);
+ *     do {
+ *       ...
+ *       idx = sparsebit_next_set(s, idx);
+ *     } while (idx != 0);
+ *   }
+ *
+ * The index of the first bit set needs to be obtained via
+ * sparsebit_first_set(), because sparsebit_next_set(), needs
+ * the index of the previously set.  The sparsebit_idx_t type is
+ * unsigned, so there is no previous index before 0 that is available.
+ * Also, the call to sparsebit_first_set() is not made unless there
+ * is at least 1 bit in the array set.  This is because sparsebit_first_set()
+ * aborts if sparsebit_first_set() is called with no bits set.
+ * It is the callers responsibility to assure that the
+ * sparsebit array has at least a single bit set before calling
+ * sparsebit_first_set().
+ *
+ * ==== Implementation Overview ====
+ * For the most part the internal implementation of sparsebit is
+ * opaque to the caller.  One important implementation detail that the
+ * caller may need to be aware of is the spatial complexity of the
+ * implementation.  This implementation of a sparsebit array is not
+ * only sparse, in that it uses memory proportional to the number of bits
+ * set.  It is also efficient in memory usage when most of the bits are
+ * set.
+ *
+ * At a high-level the state of the bit settings are maintained through
+ * the use of a binary-search tree, where each node contains at least
+ * the following members:
+ *
+ *   typedef uint64_t sparsebit_idx_t;
+ *   typedef uint64_t sparsebit_num_t;
+ *
+ *   sparsebit_idx_t idx;
+ *   uint32_t mask;
+ *   sparsebit_num_t num_after;
+ *
+ * The idx member contains the bit index of the first bit described by this
+ * node, while the mask member stores the setting of the first 32-bits.
+ * The setting of the bit at idx + n, where 0 <= n < 32, is located in the
+ * mask member at 1 << n.
+ *
+ * Nodes are sorted by idx and the bits described by two nodes will never
+ * overlap. The idx member is always aligned to the mask size, i.e. a
+ * multiple of 32.
+ *
+ * Beyond a typical implementation, the nodes in this implementation also
+ * contains a member named num_after.  The num_after member holds the
+ * number of bits immediately after the mask bits that are contiguously set.
+ * The use of the num_after member allows this implementation to efficiently
+ * represent cases where most bits are set.  For example, the case of all
+ * but the last two bits set, is represented by the following two nodes:
+ *
+ *   node 0 - idx: 0x0 mask: 0xffffffff num_after: 0xffffffffffffffc0
+ *   node 1 - idx: 0xffffffffffffffe0 mask: 0x3fffffff num_after: 0
+ *
+ * ==== Invariants ====
+ * This implementation usses the following invariants:
+ *
+ *   + Node are only used to represent bits that are set.
+ *     Nodes with a mask of 0 and num_after of 0 are not allowed.
+ *
+ *   + Sum of bits set in all the nodes is equal to the value of
+ *     the struct sparsebit_pvt num_set member.
+ *
+ *   + The setting of at least one bit is always described in a nodes
+ *     mask (mask >= 1).
+ *
+ *   + A node with all mask bits set only occurs when the last bit
+ *     described by the previous node is not equal to this nodes
+ *     starting index - 1.  All such occurences of this condition are
+ *     avoided by moving the setting of the nodes mask bits into
+ *     the previous nodes num_after setting.
+ *
+ *   + Node starting index is evenly divisible by the number of bits
+ *     within a nodes mask member.
+ *
+ *   + Nodes never represent a range of bits that wrap around the
+ *     highest supported index.
+ *
+ *      (idx + MASK_BITS + num_after - 1) <= ((sparsebit_idx_t) 0) - 1)
+ *
+ *     As a consequence of the above, the num_after member of a node
+ *     will always be <=:
+ *
+ *       maximum_index - nodes_starting_index - number_of_mask_bits
+ *
+ *   + Nodes within the binary search tree are sorted based on each
+ *     nodes starting index.
+ *
+ *   + The range of bits described by any two nodes do not overlap.  The
+ *     range of bits described by a single node is:
+ *
+ *       start: node->idx
+ *       end (inclusive): node->idx + MASK_BITS + node->num_after - 1;
+ *
+ * Note, at times these invariants are temporarily violated for a
+ * specific portion of the code.  For example, when setting a mask
+ * bit, there is a small delay between when the mask bit is set and the
+ * value in the struct sparsebit_pvt num_set member is updated.  Other
+ * temporary violations occur when node_split() is called with a specified
+ * index and assures that a node where its mask represents the bit
+ * at the specified index exists.  At times to do this node_split()
+ * must split an existing node into two nodes or create a node that
+ * has no bits set.  Such temporary violations must be corrected before
+ * returning to the caller.  These corrections are typically performed
+ * by the local function node_reduce().
+ */
+
+#include "test_util.h"
+#include "sparsebit.h"
+#include <limits.h>
+#include <assert.h>
+
+#define DUMP_LINE_MAX 100 /* Does not include indent amount */
+
+typedef uint32_t mask_t;
+#define MASK_BITS (sizeof(mask_t) * CHAR_BIT)
+
+struct node {
+	struct node *parent;
+	struct node *left;
+	struct node *right;
+	sparsebit_idx_t idx; /* index of least-significant bit in mask */
+	sparsebit_num_t num_after; /* num contiguously set after mask */
+	mask_t mask;
+};
+
+struct sparsebit {
+	/*
+	 * Points to root node of the binary search
+	 * tree.  Equal to NULL when no bits are set in
+	 * the entire sparsebit array.
+	 */
+	struct node *root;
+
+	/*
+	 * A redundant count of the total number of bits set.  Used for
+	 * diagnostic purposes and to change the time complexity of
+	 * sparsebit_num_set() from O(n) to O(1).
+	 * Note: Due to overflow, a value of 0 means none or all set.
+	 */
+	sparsebit_num_t num_set;
+};
+
+/* Returns the number of set bits described by the settings
+ * of the node pointed to by nodep.
+ */
+static sparsebit_num_t node_num_set(struct node *nodep)
+{
+	return nodep->num_after + __builtin_popcount(nodep->mask);
+}
+
+/* Returns a pointer to the node that describes the
+ * lowest bit index.
+ */
+static struct node *node_first(struct sparsebit *s)
+{
+	struct node *nodep;
+
+	for (nodep = s->root; nodep && nodep->left; nodep = nodep->left)
+		;
+
+	return nodep;
+}
+
+/* Returns a pointer to the node that describes the
+ * lowest bit index > the index of the node pointed to by np.
+ * Returns NULL if no node with a higher index exists.
+ */
+static struct node *node_next(struct sparsebit *s, struct node *np)
+{
+	struct node *nodep = np;
+
+	/*
+	 * If current node has a right child, next node is the left-most
+	 * of the right child.
+	 */
+	if (nodep->right) {
+		for (nodep = nodep->right; nodep->left; nodep = nodep->left)
+			;
+		return nodep;
+	}
+
+	/*
+	 * No right child.  Go up until node is left child of a parent.
+	 * That parent is then the next node.
+	 */
+	while (nodep->parent && nodep == nodep->parent->right)
+		nodep = nodep->parent;
+
+	return nodep->parent;
+}
+
+/* Searches for and returns a pointer to the node that describes the
+ * highest index < the index of the node pointed to by np.
+ * Returns NULL if no node with a lower index exists.
+ */
+static struct node *node_prev(struct sparsebit *s, struct node *np)
+{
+	struct node *nodep = np;
+
+	/*
+	 * If current node has a left child, next node is the right-most
+	 * of the left child.
+	 */
+	if (nodep->left) {
+		for (nodep = nodep->left; nodep->right; nodep = nodep->right)
+			;
+		return (struct node *) nodep;
+	}
+
+	/*
+	 * No left child.  Go up until node is right child of a parent.
+	 * That parent is then the next node.
+	 */
+	while (nodep->parent && nodep == nodep->parent->left)
+		nodep = nodep->parent;
+
+	return (struct node *) nodep->parent;
+}
+
+
+/* Allocates space to hold a copy of the node sub-tree pointed to by
+ * subtree and duplicates the bit settings to the newly allocated nodes.
+ * Returns the newly allocated copy of subtree.
+ */
+static struct node *node_copy_subtree(struct node *subtree)
+{
+	struct node *root;
+
+	/* Duplicate the node at the root of the subtree */
+	root = calloc(1, sizeof(*root));
+	if (!root) {
+		perror("calloc");
+		abort();
+	}
+
+	root->idx = subtree->idx;
+	root->mask = subtree->mask;
+	root->num_after = subtree->num_after;
+
+	/* As needed, recursively duplicate the left and right subtrees */
+	if (subtree->left) {
+		root->left = node_copy_subtree(subtree->left);
+		root->left->parent = root;
+	}
+
+	if (subtree->right) {
+		root->right = node_copy_subtree(subtree->right);
+		root->right->parent = root;
+	}
+
+	return root;
+}
+
+/* Searches for and returns a pointer to the node that describes the setting
+ * of the bit given by idx.  A node describes the setting of a bit if its
+ * index is within the bits described by the mask bits or the number of
+ * contiguous bits set after the mask.  Returns NULL if there is no such node.
+ */
+static struct node *node_find(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep;
+
+	/* Find the node that describes the setting of the bit at idx */
+	for (nodep = s->root; nodep;
+	     nodep = nodep->idx > idx ? nodep->left : nodep->right) {
+		if (idx >= nodep->idx &&
+		    idx <= nodep->idx + MASK_BITS + nodep->num_after - 1)
+			break;
+	}
+
+	return nodep;
+}
+
+/* Entry Requirements:
+ *   + A node that describes the setting of idx is not already present.
+ *
+ * Adds a new node to describe the setting of the bit at the index given
+ * by idx.  Returns a pointer to the newly added node.
+ *
+ * TODO(lhuemill): Degenerate cases causes the tree to get unbalanced.
+ */
+static struct node *node_add(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep, *parentp, *prev;
+
+	/* Allocate and initialize the new node. */
+	nodep = calloc(1, sizeof(*nodep));
+	if (!nodep) {
+		perror("calloc");
+		abort();
+	}
+
+	nodep->idx = idx & -MASK_BITS;
+
+	/* If no nodes, set it up as the root node. */
+	if (!s->root) {
+		s->root = nodep;
+		return nodep;
+	}
+
+	/*
+	 * Find the parent where the new node should be attached
+	 * and add the node there.
+	 */
+	parentp = s->root;
+	while (true) {
+		if (idx < parentp->idx) {
+			if (!parentp->left) {
+				parentp->left = nodep;
+				nodep->parent = parentp;
+				break;
+			}
+			parentp = parentp->left;
+		} else {
+			assert(idx > parentp->idx + MASK_BITS + parentp->num_after - 1);
+			if (!parentp->right) {
+				parentp->right = nodep;
+				nodep->parent = parentp;
+				break;
+			}
+			parentp = parentp->right;
+		}
+	}
+
+	/*
+	 * Does num_after bits of previous node overlap with the mask
+	 * of the new node?  If so set the bits in the new nodes mask
+	 * and reduce the previous nodes num_after.
+	 */
+	prev = node_prev(s, nodep);
+	while (prev && prev->idx + MASK_BITS + prev->num_after - 1 >= nodep->idx) {
+		unsigned int n1 = (prev->idx + MASK_BITS + prev->num_after - 1)
+			- nodep->idx;
+		assert(prev->num_after > 0);
+		assert(n1 < MASK_BITS);
+		assert(!(nodep->mask & (1 << n1)));
+		nodep->mask |= (1 << n1);
+		prev->num_after--;
+	}
+
+	return nodep;
+}
+
+/* Returns whether all the bits in the sparsebit array are set.  */
+bool sparsebit_all_set(struct sparsebit *s)
+{
+	/*
+	 * If any nodes there must be at least one bit set.  Only case
+	 * where a bit is set and total num set is 0, is when all bits
+	 * are set.
+	 */
+	return s->root && s->num_set == 0;
+}
+
+/* Clears all bits described by the node pointed to by nodep, then
+ * removes the node.
+ */
+static void node_rm(struct sparsebit *s, struct node *nodep)
+{
+	struct node *tmp;
+	sparsebit_num_t num_set;
+
+	num_set = node_num_set(nodep);
+	assert(s->num_set >= num_set || sparsebit_all_set(s));
+	s->num_set -= node_num_set(nodep);
+
+	/* Have both left and right child */
+	if (nodep->left && nodep->right) {
+		/*
+		 * Move left children to the leftmost leaf node
+		 * of the right child.
+		 */
+		for (tmp = nodep->right; tmp->left; tmp = tmp->left)
+			;
+		tmp->left = nodep->left;
+		nodep->left = NULL;
+		tmp->left->parent = tmp;
+	}
+
+	/* Left only child */
+	if (nodep->left) {
+		if (!nodep->parent) {
+			s->root = nodep->left;
+			nodep->left->parent = NULL;
+		} else {
+			nodep->left->parent = nodep->parent;
+			if (nodep == nodep->parent->left)
+				nodep->parent->left = nodep->left;
+			else {
+				assert(nodep == nodep->parent->right);
+				nodep->parent->right = nodep->left;
+			}
+		}
+
+		nodep->parent = nodep->left = nodep->right = NULL;
+		free(nodep);
+
+		return;
+	}
+
+
+	/* Right only child */
+	if (nodep->right) {
+		if (!nodep->parent) {
+			s->root = nodep->right;
+			nodep->right->parent = NULL;
+		} else {
+			nodep->right->parent = nodep->parent;
+			if (nodep == nodep->parent->left)
+				nodep->parent->left = nodep->right;
+			else {
+				assert(nodep == nodep->parent->right);
+				nodep->parent->right = nodep->right;
+			}
+		}
+
+		nodep->parent = nodep->left = nodep->right = NULL;
+		free(nodep);
+
+		return;
+	}
+
+	/* Leaf Node */
+	if (!nodep->parent) {
+		s->root = NULL;
+	} else {
+		if (nodep->parent->left == nodep)
+			nodep->parent->left = NULL;
+		else {
+			assert(nodep == nodep->parent->right);
+			nodep->parent->right = NULL;
+		}
+	}
+
+	nodep->parent = nodep->left = nodep->right = NULL;
+	free(nodep);
+
+	return;
+}
+
+/* Splits the node containing the bit at idx so that there is a node
+ * that starts at the specified index.  If no such node exists, a new
+ * node at the specified index is created.  Returns the new node.
+ *
+ * idx must start of a mask boundary.
+ */
+static struct node *node_split(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep1, *nodep2;
+	sparsebit_idx_t offset;
+	sparsebit_num_t orig_num_after;
+
+	assert(!(idx % MASK_BITS));
+
+	/*
+	 * Is there a node that describes the setting of idx?
+	 * If not, add it.
+	 */
+	nodep1 = node_find(s, idx);
+	if (!nodep1)
+		return node_add(s, idx);
+
+	/*
+	 * All done if the starting index of the node is where the
+	 * split should occur.
+	 */
+	if (nodep1->idx == idx)
+		return nodep1;
+
+	/*
+	 * Split point not at start of mask, so it must be part of
+	 * bits described by num_after.
+	 */
+
+	/*
+	 * Calculate offset within num_after for where the split is
+	 * to occur.
+	 */
+	offset = idx - (nodep1->idx + MASK_BITS);
+	orig_num_after = nodep1->num_after;
+
+	/*
+	 * Add a new node to describe the bits starting at
+	 * the split point.
+	 */
+	nodep1->num_after = offset;
+	nodep2 = node_add(s, idx);
+
+	/* Move bits after the split point into the new node */
+	nodep2->num_after = orig_num_after - offset;
+	if (nodep2->num_after >= MASK_BITS) {
+		nodep2->mask = ~(mask_t) 0;
+		nodep2->num_after -= MASK_BITS;
+	} else {
+		nodep2->mask = (1 << nodep2->num_after) - 1;
+		nodep2->num_after = 0;
+	}
+
+	return nodep2;
+}
+
+/* Iteratively reduces the node pointed to by nodep and its adjacent
+ * nodes into a more compact form.  For example, a node with a mask with
+ * all bits set adjacent to a previous node, will get combined into a
+ * single node with an increased num_after setting.
+ *
+ * After each reduction, a further check is made to see if additional
+ * reductions are possible with the new previous and next nodes.  Note,
+ * a search for a reduction is only done across the nodes nearest nodep
+ * and those that became part of a reduction.  Reductions beyond nodep
+ * and the adjacent nodes that are reduced are not discovered.  It is the
+ * responsibility of the caller to pass a nodep that is within one node
+ * of each possible reduction.
+ *
+ * This function does not fix the temporary violation of all invariants.
+ * For example it does not fix the case where the bit settings described
+ * by two or more nodes overlap.  Such a violation introduces the potential
+ * complication of a bit setting for a specific index having different settings
+ * in different nodes.  This would then introduce the further complication
+ * of which node has the correct setting of the bit and thus such conditions
+ * are not allowed.
+ *
+ * This function is designed to fix invariant violations that are introduced
+ * by node_split() and by changes to the nodes mask or num_after members.
+ * For example, when setting a bit within a nodes mask, the function that
+ * sets the bit doesn't have to worry about whether the setting of that
+ * bit caused the mask to have leading only or trailing only bits set.
+ * Instead, the function can call node_reduce(), with nodep equal to the
+ * node address that it set a mask bit in, and node_reduce() will notice
+ * the cases of leading or trailing only bits and that there is an
+ * adjacent node that the bit settings could be merged into.
+ *
+ * This implementation specifically detects and corrects violation of the
+ * following invariants:
+ *
+ *   + Node are only used to represent bits that are set.
+ *     Nodes with a mask of 0 and num_after of 0 are not allowed.
+ *
+ *   + The setting of at least one bit is always described in a nodes
+ *     mask (mask >= 1).
+ *
+ *   + A node with all mask bits set only occurs when the last bit
+ *     described by the previous node is not equal to this nodes
+ *     starting index - 1.  All such occurences of this condition are
+ *     avoided by moving the setting of the nodes mask bits into
+ *     the previous nodes num_after setting.
+ */
+static void node_reduce(struct sparsebit *s, struct node *nodep)
+{
+	bool reduction_performed;
+
+	do {
+		reduction_performed = false;
+		struct node *prev, *next, *tmp;
+
+		/* 1) Potential reductions within the current node. */
+
+		/* Nodes with all bits cleared may be removed. */
+		if (nodep->mask == 0 && nodep->num_after == 0) {
+			/*
+			 * About to remove the node pointed to by
+			 * nodep, which normally would cause a problem
+			 * for the next pass through the reduction loop,
+			 * because the node at the starting point no longer
+			 * exists.  This potential problem is handled
+			 * by first remembering the location of the next
+			 * or previous nodes.  Doesn't matter which, because
+			 * once the node at nodep is removed, there will be
+			 * no other nodes between prev and next.
+			 *
+			 * Note, the checks performed on nodep against both
+			 * both prev and next both check for an adjacent
+			 * node that can be reduced into a single node.  As
+			 * such, after removing the node at nodep, doesn't
+			 * matter whether the nodep for the next pass
+			 * through the loop is equal to the previous pass
+			 * prev or next node.  Either way, on the next pass
+			 * the one not selected will become either the
+			 * prev or next node.
+			 */
+			tmp = node_next(s, nodep);
+			if (!tmp)
+				tmp = node_prev(s, nodep);
+
+			node_rm(s, nodep);
+			nodep = NULL;
+
+			nodep = tmp;
+			reduction_performed = true;
+			continue;
+		}
+
+		/*
+		 * When the mask is 0, can reduce the amount of num_after
+		 * bits by moving the initial num_after bits into the mask.
+		 */
+		if (nodep->mask == 0) {
+			assert(nodep->num_after != 0);
+			assert(nodep->idx + MASK_BITS > nodep->idx);
+
+			nodep->idx += MASK_BITS;
+
+			if (nodep->num_after >= MASK_BITS) {
+				nodep->mask = ~0;
+				nodep->num_after -= MASK_BITS;
+			} else {
+				nodep->mask = (1u << nodep->num_after) - 1;
+				nodep->num_after = 0;
+			}
+
+			reduction_performed = true;
+			continue;
+		}
+
+		/*
+		 * 2) Potential reductions between the current and
+		 * previous nodes.
+		 */
+		prev = node_prev(s, nodep);
+		if (prev) {
+			sparsebit_idx_t prev_highest_bit;
+
+			/* Nodes with no bits set can be removed. */
+			if (prev->mask == 0 && prev->num_after == 0) {
+				node_rm(s, prev);
+
+				reduction_performed = true;
+				continue;
+			}
+
+			/*
+			 * All mask bits set and previous node has
+			 * adjacent index.
+			 */
+			if (nodep->mask + 1 == 0 &&
+			    prev->idx + MASK_BITS == nodep->idx) {
+				prev->num_after += MASK_BITS + nodep->num_after;
+				nodep->mask = 0;
+				nodep->num_after = 0;
+
+				reduction_performed = true;
+				continue;
+			}
+
+			/*
+			 * Is node adjacent to previous node and the node
+			 * contains a single contiguous range of bits
+			 * starting from the beginning of the mask?
+			 */
+			prev_highest_bit = prev->idx + MASK_BITS - 1 + prev->num_after;
+			if (prev_highest_bit + 1 == nodep->idx &&
+			    (nodep->mask | (nodep->mask >> 1)) == nodep->mask) {
+				/*
+				 * How many contiguous bits are there?
+				 * Is equal to the total number of set
+				 * bits, due to an earlier check that
+				 * there is a single contiguous range of
+				 * set bits.
+				 */
+				unsigned int num_contiguous
+					= __builtin_popcount(nodep->mask);
+				assert((num_contiguous > 0) &&
+				       ((1ULL << num_contiguous) - 1) == nodep->mask);
+
+				prev->num_after += num_contiguous;
+				nodep->mask = 0;
+
+				/*
+				 * For predictable performance, handle special
+				 * case where all mask bits are set and there
+				 * is a non-zero num_after setting.  This code
+				 * is functionally correct without the following
+				 * conditionalized statements, but without them
+				 * the value of num_after is only reduced by
+				 * the number of mask bits per pass.  There are
+				 * cases where num_after can be close to 2^64.
+				 * Without this code it could take nearly
+				 * (2^64) / 32 passes to perform the full
+				 * reduction.
+				 */
+				if (num_contiguous == MASK_BITS) {
+					prev->num_after += nodep->num_after;
+					nodep->num_after = 0;
+				}
+
+				reduction_performed = true;
+				continue;
+			}
+		}
+
+		/*
+		 * 3) Potential reductions between the current and
+		 * next nodes.
+		 */
+		next = node_next(s, nodep);
+		if (next) {
+			/* Nodes with no bits set can be removed. */
+			if (next->mask == 0 && next->num_after == 0) {
+				node_rm(s, next);
+				reduction_performed = true;
+				continue;
+			}
+
+			/*
+			 * Is next node index adjacent to current node
+			 * and has a mask with all bits set?
+			 */
+			if (next->idx == nodep->idx + MASK_BITS + nodep->num_after &&
+			    next->mask == ~(mask_t) 0) {
+				nodep->num_after += MASK_BITS;
+				next->mask = 0;
+				nodep->num_after += next->num_after;
+				next->num_after = 0;
+
+				node_rm(s, next);
+				next = NULL;
+
+				reduction_performed = true;
+				continue;
+			}
+		}
+	} while (nodep && reduction_performed);
+}
+
+/* Returns whether the bit at the index given by idx, within the
+ * sparsebit array is set or not.
+ */
+bool sparsebit_is_set(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep;
+
+	/* Find the node that describes the setting of the bit at idx */
+	for (nodep = s->root; nodep;
+	     nodep = nodep->idx > idx ? nodep->left : nodep->right)
+		if (idx >= nodep->idx &&
+		    idx <= nodep->idx + MASK_BITS + nodep->num_after - 1)
+			goto have_node;
+
+	return false;
+
+have_node:
+	/* Bit is set if it is any of the bits described by num_after */
+	if (nodep->num_after && idx >= nodep->idx + MASK_BITS)
+		return true;
+
+	/* Is the corresponding mask bit set */
+	assert(idx >= nodep->idx && idx - nodep->idx < MASK_BITS);
+	return !!(nodep->mask & (1 << (idx - nodep->idx)));
+}
+
+/* Within the sparsebit array pointed to by s, sets the bit
+ * at the index given by idx.
+ */
+static void bit_set(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep;
+
+	/* Skip bits that are already set */
+	if (sparsebit_is_set(s, idx))
+		return;
+
+	/*
+	 * Get a node where the bit at idx is described by the mask.
+	 * The node_split will also create a node, if there isn't
+	 * already a node that describes the setting of bit.
+	 */
+	nodep = node_split(s, idx & -MASK_BITS);
+
+	/* Set the bit within the nodes mask */
+	assert(idx >= nodep->idx && idx <= nodep->idx + MASK_BITS - 1);
+	assert(!(nodep->mask & (1 << (idx - nodep->idx))));
+	nodep->mask |= 1 << (idx - nodep->idx);
+	s->num_set++;
+
+	node_reduce(s, nodep);
+}
+
+/* Within the sparsebit array pointed to by s, clears the bit
+ * at the index given by idx.
+ */
+static void bit_clear(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	struct node *nodep;
+
+	/* Skip bits that are already cleared */
+	if (!sparsebit_is_set(s, idx))
+		return;
+
+	/* Is there a node that describes the setting of this bit? */
+	nodep = node_find(s, idx);
+	if (!nodep)
+		return;
+
+	/*
+	 * If a num_after bit, split the node, so that the bit is
+	 * part of a node mask.
+	 */
+	if (idx >= nodep->idx + MASK_BITS)
+		nodep = node_split(s, idx & -MASK_BITS);
+
+	/*
+	 * After node_split above, bit at idx should be within the mask.
+	 * Clear that bit.
+	 */
+	assert(idx >= nodep->idx && idx <= nodep->idx + MASK_BITS - 1);
+	assert(nodep->mask & (1 << (idx - nodep->idx)));
+	nodep->mask &= ~(1 << (idx - nodep->idx));
+	assert(s->num_set > 0 || sparsebit_all_set(s));
+	s->num_set--;
+
+	node_reduce(s, nodep);
+}
+
+/* Recursively dumps to the FILE stream given by stream the contents
+ * of the sub-tree of nodes pointed to by nodep.  Each line of output
+ * is prefixed by the number of spaces given by indent.  On each
+ * recursion, the indent amount is increased by 2.  This causes nodes
+ * at each level deeper into the binary search tree to be displayed
+ * with a greater indent.
+ */
+static void dump_nodes(FILE *stream, struct node *nodep,
+	unsigned int indent)
+{
+	char *node_type;
+
+	/* Dump contents of node */
+	if (!nodep->parent)
+		node_type = "root";
+	else if (nodep == nodep->parent->left)
+		node_type = "left";
+	else {
+		assert(nodep == nodep->parent->right);
+		node_type = "right";
+	}
+	fprintf(stream, "%*s---- %s nodep: %p\n", indent, "", node_type, nodep);
+	fprintf(stream, "%*s  parent: %p left: %p right: %p\n", indent, "",
+		nodep->parent, nodep->left, nodep->right);
+	fprintf(stream, "%*s  idx: 0x%lx mask: 0x%x num_after: 0x%lx\n",
+		indent, "", nodep->idx, nodep->mask, nodep->num_after);
+
+	/* If present, dump contents of left child nodes */
+	if (nodep->left)
+		dump_nodes(stream, nodep->left, indent + 2);
+
+	/* If present, dump contents of right child nodes */
+	if (nodep->right)
+		dump_nodes(stream, nodep->right, indent + 2);
+}
+
+static inline sparsebit_idx_t node_first_set(struct node *nodep, int start)
+{
+	mask_t leading = (mask_t)1 << start;
+	int n1 = __builtin_ctz(nodep->mask & -leading);
+
+	return nodep->idx + n1;
+}
+
+static inline sparsebit_idx_t node_first_clear(struct node *nodep, int start)
+{
+	mask_t leading = (mask_t)1 << start;
+	int n1 = __builtin_ctz(~nodep->mask & -leading);
+
+	return nodep->idx + n1;
+}
+
+/* Dumps to the FILE stream specified by stream, the implementation dependent
+ * internal state of s.  Each line of output is prefixed with the number
+ * of spaces given by indent.  The output is completely implementation
+ * dependent and subject to change.  Output from this function should only
+ * be used for diagnostic purposes.  For example, this function can be
+ * used by test cases after they detect an unexpected condition, as a means
+ * to capture diagnostic information.
+ */
+static void sparsebit_dump_internal(FILE *stream, struct sparsebit *s,
+	unsigned int indent)
+{
+	/* Dump the contents of s */
+	fprintf(stream, "%*sroot: %p\n", indent, "", s->root);
+	fprintf(stream, "%*snum_set: 0x%lx\n", indent, "", s->num_set);
+
+	if (s->root)
+		dump_nodes(stream, s->root, indent);
+}
+
+/* Allocates and returns a new sparsebit array. The initial state
+ * of the newly allocated sparsebit array has all bits cleared.
+ */
+struct sparsebit *sparsebit_alloc(void)
+{
+	struct sparsebit *s;
+
+	/* Allocate top level structure. */
+	s = calloc(1, sizeof(*s));
+	if (!s) {
+		perror("calloc");
+		abort();
+	}
+
+	return s;
+}
+
+/* Frees the implementation dependent data for the sparsebit array
+ * pointed to by s and poisons the pointer to that data.
+ */
+void sparsebit_free(struct sparsebit **sbitp)
+{
+	struct sparsebit *s = *sbitp;
+
+	if (!s)
+		return;
+
+	sparsebit_clear_all(s);
+	free(s);
+	*sbitp = NULL;
+}
+
+/* Makes a copy of the sparsebit array given by s, to the sparsebit
+ * array given by d.  Note, d must have already been allocated via
+ * sparsebit_alloc().  It can though already have bits set, which
+ * if different from src will be cleared.
+ */
+void sparsebit_copy(struct sparsebit *d, struct sparsebit *s)
+{
+	/* First clear any bits already set in the destination */
+	sparsebit_clear_all(d);
+
+	if (s->root) {
+		d->root = node_copy_subtree(s->root);
+		d->num_set = s->num_set;
+	}
+}
+
+/* Returns whether num consecutive bits starting at idx are all set.  */
+bool sparsebit_is_set_num(struct sparsebit *s,
+	sparsebit_idx_t idx, sparsebit_num_t num)
+{
+	sparsebit_idx_t next_cleared;
+
+	assert(num > 0);
+	assert(idx + num - 1 >= idx);
+
+	/* With num > 0, the first bit must be set. */
+	if (!sparsebit_is_set(s, idx))
+		return false;
+
+	/* Find the next cleared bit */
+	next_cleared = sparsebit_next_clear(s, idx);
+
+	/*
+	 * If no cleared bits beyond idx, then there are at least num
+	 * set bits. idx + num doesn't wrap.  Otherwise check if
+	 * there are enough set bits between idx and the next cleared bit.
+	 */
+	return next_cleared == 0 || next_cleared - idx >= num;
+}
+
+/* Returns whether the bit at the index given by idx.  */
+bool sparsebit_is_clear(struct sparsebit *s,
+	sparsebit_idx_t idx)
+{
+	return !sparsebit_is_set(s, idx);
+}
+
+/* Returns whether num consecutive bits starting at idx are all cleared.  */
+bool sparsebit_is_clear_num(struct sparsebit *s,
+	sparsebit_idx_t idx, sparsebit_num_t num)
+{
+	sparsebit_idx_t next_set;
+
+	assert(num > 0);
+	assert(idx + num - 1 >= idx);
+
+	/* With num > 0, the first bit must be cleared. */
+	if (!sparsebit_is_clear(s, idx))
+		return false;
+
+	/* Find the next set bit */
+	next_set = sparsebit_next_set(s, idx);
+
+	/*
+	 * If no set bits beyond idx, then there are at least num
+	 * cleared bits. idx + num doesn't wrap.  Otherwise check if
+	 * there are enough cleared bits between idx and the next set bit.
+	 */
+	return next_set == 0 || next_set - idx >= num;
+}
+
+/* Returns the total number of bits set.  Note: 0 is also returned for
+ * the case of all bits set.  This is because with all bits set, there
+ * is 1 additional bit set beyond what can be represented in the return
+ * value.  Use sparsebit_any_set(), instead of sparsebit_num_set() > 0,
+ * to determine if the sparsebit array has any bits set.
+ */
+sparsebit_num_t sparsebit_num_set(struct sparsebit *s)
+{
+	return s->num_set;
+}
+
+/* Returns whether any bit is set in the sparsebit array.  */
+bool sparsebit_any_set(struct sparsebit *s)
+{
+	/*
+	 * Nodes only describe set bits.  If any nodes then there
+	 * is at least 1 bit set.
+	 */
+	if (!s->root)
+		return false;
+
+	/*
+	 * Every node should have a non-zero mask.  For now will
+	 * just assure that the root node has a non-zero mask,
+	 * which is a quick check that at least 1 bit is set.
+	 */
+	assert(s->root->mask != 0);
+	assert(s->num_set > 0 ||
+	       (s->root->num_after == ((sparsebit_num_t) 0) - MASK_BITS &&
+		s->root->mask == ~(mask_t) 0));
+
+	return true;
+}
+
+/* Returns whether all the bits in the sparsebit array are cleared.  */
+bool sparsebit_all_clear(struct sparsebit *s)
+{
+	return !sparsebit_any_set(s);
+}
+
+/* Returns whether all the bits in the sparsebit array are set.  */
+bool sparsebit_any_clear(struct sparsebit *s)
+{
+	return !sparsebit_all_set(s);
+}
+
+/* Returns the index of the first set bit.  Abort if no bits are set.
+ */
+sparsebit_idx_t sparsebit_first_set(struct sparsebit *s)
+{
+	struct node *nodep;
+
+	/* Validate at least 1 bit is set */
+	assert(sparsebit_any_set(s));
+
+	nodep = node_first(s);
+	return node_first_set(nodep, 0);
+}
+
+/* Returns the index of the first cleared bit.  Abort if
+ * no bits are cleared.
+ */
+sparsebit_idx_t sparsebit_first_clear(struct sparsebit *s)
+{
+	struct node *nodep1, *nodep2;
+
+	/* Validate at least 1 bit is cleared. */
+	assert(sparsebit_any_clear(s));
+
+	/* If no nodes or first node index > 0 then lowest cleared is 0 */
+	nodep1 = node_first(s);
+	if (!nodep1 || nodep1->idx > 0)
+		return 0;
+
+	/* Does the mask in the first node contain any cleared bits. */
+	if (nodep1->mask != ~(mask_t) 0)
+		return node_first_clear(nodep1, 0);
+
+	/*
+	 * All mask bits set in first node.  If there isn't a second node
+	 * then the first cleared bit is the first bit after the bits
+	 * described by the first node.
+	 */
+	nodep2 = node_next(s, nodep1);
+	if (!nodep2) {
+		/*
+		 * No second node.  First cleared bit is first bit beyond
+		 * bits described by first node.
+		 */
+		assert(nodep1->mask == ~(mask_t) 0);
+		assert(nodep1->idx + MASK_BITS + nodep1->num_after != (sparsebit_idx_t) 0);
+		return nodep1->idx + MASK_BITS + nodep1->num_after;
+	}
+
+	/*
+	 * There is a second node.
+	 * If it is not adjacent to the first node, then there is a gap
+	 * of cleared bits between the nodes, and the first cleared bit
+	 * is the first bit within the gap.
+	 */
+	if (nodep1->idx + MASK_BITS + nodep1->num_after != nodep2->idx)
+		return nodep1->idx + MASK_BITS + nodep1->num_after;
+
+	/*
+	 * Second node is adjacent to the first node.
+	 * Because it is adjacent, its mask should be non-zero.  If all
+	 * its mask bits are set, then with it being adjacent, it should
+	 * have had the mask bits moved into the num_after setting of the
+	 * previous node.
+	 */
+	return node_first_clear(nodep2, 0);
+}
+
+/* Returns index of next bit set within s after the index given by prev.
+ * Returns 0 if there are no bits after prev that are set.
+ */
+sparsebit_idx_t sparsebit_next_set(struct sparsebit *s,
+	sparsebit_idx_t prev)
+{
+	sparsebit_idx_t lowest_possible = prev + 1;
+	sparsebit_idx_t start;
+	struct node *nodep;
+
+	/* A bit after the highest index can't be set. */
+	if (lowest_possible == 0)
+		return 0;
+
+	/*
+	 * Find the leftmost 'candidate' overlapping or to the right
+	 * of lowest_possible.
+	 */
+	struct node *candidate = NULL;
+
+	/* True iff lowest_possible is within candidate */
+	bool contains = false;
+
+	/*
+	 * Find node that describes setting of bit at lowest_possible.
+	 * If such a node doesn't exist, find the node with the lowest
+	 * starting index that is > lowest_possible.
+	 */
+	for (nodep = s->root; nodep;) {
+		if ((nodep->idx + MASK_BITS + nodep->num_after - 1)
+			>= lowest_possible) {
+			candidate = nodep;
+			if (candidate->idx <= lowest_possible) {
+				contains = true;
+				break;
+			}
+			nodep = nodep->left;
+		} else {
+			nodep = nodep->right;
+		}
+	}
+	if (!candidate)
+		return 0;
+
+	assert(candidate->mask != 0);
+
+	/* Does the candidate node describe the setting of lowest_possible? */
+	if (!contains) {
+		/*
+		 * Candidate doesn't describe setting of bit at lowest_possible.
+		 * Candidate points to the first node with a starting index
+		 * > lowest_possible.
+		 */
+		assert(candidate->idx > lowest_possible);
+
+		return node_first_set(candidate, 0);
+	}
+
+	/*
+	 * Candidate describes setting of bit at lowest_possible.
+	 * Note: although the node describes the setting of the bit
+	 * at lowest_possible, its possible that its setting and the
+	 * setting of all latter bits described by this node are 0.
+	 * For now, just handle the cases where this node describes
+	 * a bit at or after an index of lowest_possible that is set.
+	 */
+	start = lowest_possible - candidate->idx;
+
+	if (start < MASK_BITS && candidate->mask >= (1 << start))
+		return node_first_set(candidate, start);
+
+	if (candidate->num_after) {
+		sparsebit_idx_t first_num_after_idx = candidate->idx + MASK_BITS;
+
+		return lowest_possible < first_num_after_idx
+			? first_num_after_idx : lowest_possible;
+	}
+
+	/*
+	 * Although candidate node describes setting of bit at
+	 * the index of lowest_possible, all bits at that index and
+	 * latter that are described by candidate are cleared.  With
+	 * this, the next bit is the first bit in the next node, if
+	 * such a node exists.  If a next node doesn't exist, then
+	 * there is no next set bit.
+	 */
+	candidate = node_next(s, candidate);
+	if (!candidate)
+		return 0;
+
+	return node_first_set(candidate, 0);
+}
+
+/* Returns index of next bit cleared within s after the index given by prev.
+ * Returns 0 if there are no bits after prev that are cleared.
+ */
+sparsebit_idx_t sparsebit_next_clear(struct sparsebit *s,
+	sparsebit_idx_t prev)
+{
+	sparsebit_idx_t lowest_possible = prev + 1;
+	sparsebit_idx_t idx;
+	struct node *nodep1, *nodep2;
+
+	/* A bit after the highest index can't be set. */
+	if (lowest_possible == 0)
+		return 0;
+
+	/*
+	 * Does a node describing the setting of lowest_possible exist?
+	 * If not, the bit at lowest_possible is cleared.
+	 */
+	nodep1 = node_find(s, lowest_possible);
+	if (!nodep1)
+		return lowest_possible;
+
+	/* Does a mask bit in node 1 describe the next cleared bit. */
+	for (idx = lowest_possible - nodep1->idx; idx < MASK_BITS; idx++)
+		if (!(nodep1->mask & (1 << idx)))
+			return nodep1->idx + idx;
+
+	/*
+	 * Next cleared bit is not described by node 1.  If there
+	 * isn't a next node, then next cleared bit is described
+	 * by bit after the bits described by the first node.
+	 */
+	nodep2 = node_next(s, nodep1);
+	if (!nodep2)
+		return nodep1->idx + MASK_BITS + nodep1->num_after;
+
+	/*
+	 * There is a second node.
+	 * If it is not adjacent to the first node, then there is a gap
+	 * of cleared bits between the nodes, and the next cleared bit
+	 * is the first bit within the gap.
+	 */
+	if (nodep1->idx + MASK_BITS + nodep1->num_after != nodep2->idx)
+		return nodep1->idx + MASK_BITS + nodep1->num_after;
+
+	/*
+	 * Second node is adjacent to the first node.
+	 * Because it is adjacent, its mask should be non-zero.  If all
+	 * its mask bits are set, then with it being adjacent, it should
+	 * have had the mask bits moved into the num_after setting of the
+	 * previous node.
+	 */
+	return node_first_clear(nodep2, 0);
+}
+
+/* Starting with the index 1 greater than the index given by start, finds
+ * and returns the index of the first sequence of num consecutively set
+ * bits.  Returns a value of 0 of no such sequence exists.
+ */
+sparsebit_idx_t sparsebit_next_set_num(struct sparsebit *s,
+	sparsebit_idx_t start, sparsebit_num_t num)
+{
+	sparsebit_idx_t idx;
+
+	assert(num >= 1);
+
+	for (idx = sparsebit_next_set(s, start);
+		idx != 0 && idx + num - 1 >= idx;
+		idx = sparsebit_next_set(s, idx)) {
+		assert(sparsebit_is_set(s, idx));
+
+		/*
+		 * Does the sequence of bits starting at idx consist of
+		 * num set bits?
+		 */
+		if (sparsebit_is_set_num(s, idx, num))
+			return idx;
+
+		/*
+		 * Sequence of set bits at idx isn't large enough.
+		 * Skip this entire sequence of set bits.
+		 */
+		idx = sparsebit_next_clear(s, idx);
+		if (idx == 0)
+			return 0;
+	}
+
+	return 0;
+}
+
+/* Starting with the index 1 greater than the index given by start, finds
+ * and returns the index of the first sequence of num consecutively cleared
+ * bits.  Returns a value of 0 of no such sequence exists.
+ */
+sparsebit_idx_t sparsebit_next_clear_num(struct sparsebit *s,
+	sparsebit_idx_t start, sparsebit_num_t num)
+{
+	sparsebit_idx_t idx;
+
+	assert(num >= 1);
+
+	for (idx = sparsebit_next_clear(s, start);
+		idx != 0 && idx + num - 1 >= idx;
+		idx = sparsebit_next_clear(s, idx)) {
+		assert(sparsebit_is_clear(s, idx));
+
+		/*
+		 * Does the sequence of bits starting at idx consist of
+		 * num cleared bits?
+		 */
+		if (sparsebit_is_clear_num(s, idx, num))
+			return idx;
+
+		/*
+		 * Sequence of cleared bits at idx isn't large enough.
+		 * Skip this entire sequence of cleared bits.
+		 */
+		idx = sparsebit_next_set(s, idx);
+		if (idx == 0)
+			return 0;
+	}
+
+	return 0;
+}
+
+/* Sets the bits * in the inclusive range idx through idx + num - 1.  */
+void sparsebit_set_num(struct sparsebit *s,
+	sparsebit_idx_t start, sparsebit_num_t num)
+{
+	struct node *nodep, *next;
+	unsigned int n1;
+	sparsebit_idx_t idx;
+	sparsebit_num_t n;
+	sparsebit_idx_t middle_start, middle_end;
+
+	assert(num > 0);
+	assert(start + num - 1 >= start);
+
+	/*
+	 * Leading - bits before first mask boundary.
+	 *
+	 * TODO(lhuemill): With some effort it may be possible to
+	 *   replace the following loop with a sequential sequence
+	 *   of statements.  High level sequence would be:
+	 *
+	 *     1. Use node_split() to force node that describes setting
+	 *        of idx to be within the mask portion of a node.
+	 *     2. Form mask of bits to be set.
+	 *     3. Determine number of mask bits already set in the node
+	 *        and store in a local variable named num_already_set.
+	 *     4. Set the appropriate mask bits within the node.
+	 *     5. Increment struct sparsebit_pvt num_set member
+	 *        by the number of bits that were actually set.
+	 *        Exclude from the counts bits that were already set.
+	 *     6. Before returning to the caller, use node_reduce() to
+	 *        handle the multiple corner cases that this method
+	 *        introduces.
+	 */
+	for (idx = start, n = num; n > 0 && idx % MASK_BITS != 0; idx++, n--)
+		bit_set(s, idx);
+
+	/* Middle - bits spanning one or more entire mask */
+	middle_start = idx;
+	middle_end = middle_start + (n & -MASK_BITS) - 1;
+	if (n >= MASK_BITS) {
+		nodep = node_split(s, middle_start);
+
+		/*
+		 * As needed, split just after end of middle bits.
+		 * No split needed if end of middle bits is at highest
+		 * supported bit index.
+		 */
+		if (middle_end + 1 > middle_end)
+			(void) node_split(s, middle_end + 1);
+
+		/* Delete nodes that only describe bits within the middle. */
+		for (next = node_next(s, nodep);
+			next && (next->idx < middle_end);
+			next = node_next(s, nodep)) {
+			assert(next->idx + MASK_BITS + next->num_after - 1 <= middle_end);
+			node_rm(s, next);
+			next = NULL;
+		}
+
+		/* As needed set each of the mask bits */
+		for (n1 = 0; n1 < MASK_BITS; n1++) {
+			if (!(nodep->mask & (1 << n1))) {
+				nodep->mask |= 1 << n1;
+				s->num_set++;
+			}
+		}
+
+		s->num_set -= nodep->num_after;
+		nodep->num_after = middle_end - middle_start + 1 - MASK_BITS;
+		s->num_set += nodep->num_after;
+
+		node_reduce(s, nodep);
+	}
+	idx = middle_end + 1;
+	n -= middle_end - middle_start + 1;
+
+	/* Trailing - bits at and beyond last mask boundary */
+	assert(n < MASK_BITS);
+	for (; n > 0; idx++, n--)
+		bit_set(s, idx);
+}
+
+/* Clears the bits * in the inclusive range idx through idx + num - 1.  */
+void sparsebit_clear_num(struct sparsebit *s,
+	sparsebit_idx_t start, sparsebit_num_t num)
+{
+	struct node *nodep, *next;
+	unsigned int n1;
+	sparsebit_idx_t idx;
+	sparsebit_num_t n;
+	sparsebit_idx_t middle_start, middle_end;
+
+	assert(num > 0);
+	assert(start + num - 1 >= start);
+
+	/* Leading - bits before first mask boundary */
+	for (idx = start, n = num; n > 0 && idx % MASK_BITS != 0; idx++, n--)
+		bit_clear(s, idx);
+
+	/* Middle - bits spanning one or more entire mask */
+	middle_start = idx;
+	middle_end = middle_start + (n & -MASK_BITS) - 1;
+	if (n >= MASK_BITS) {
+		nodep = node_split(s, middle_start);
+
+		/*
+		 * As needed, split just after end of middle bits.
+		 * No split needed if end of middle bits is at highest
+		 * supported bit index.
+		 */
+		if (middle_end + 1 > middle_end)
+			(void) node_split(s, middle_end + 1);
+
+		/* Delete nodes that only describe bits within the middle. */
+		for (next = node_next(s, nodep);
+			next && (next->idx < middle_end);
+			next = node_next(s, nodep)) {
+			assert(next->idx + MASK_BITS + next->num_after - 1 <= middle_end);
+			node_rm(s, next);
+			next = NULL;
+		}
+
+		/* As needed clear each of the mask bits */
+		for (n1 = 0; n1 < MASK_BITS; n1++) {
+			if (nodep->mask & (1 << n1)) {
+				nodep->mask &= ~(1 << n1);
+				s->num_set--;
+			}
+		}
+
+		/* Clear any bits described by num_after */
+		s->num_set -= nodep->num_after;
+		nodep->num_after = 0;
+
+		/*
+		 * Delete the node that describes the beginning of
+		 * the middle bits and perform any allowed reductions
+		 * with the nodes prev or next of nodep.
+		 */
+		node_reduce(s, nodep);
+		nodep = NULL;
+	}
+	idx = middle_end + 1;
+	n -= middle_end - middle_start + 1;
+
+	/* Trailing - bits at and beyond last mask boundary */
+	assert(n < MASK_BITS);
+	for (; n > 0; idx++, n--)
+		bit_clear(s, idx);
+}
+
+/* Sets the bit at the index given by idx.  */
+void sparsebit_set(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	sparsebit_set_num(s, idx, 1);
+}
+
+/* Clears the bit at the index given by idx.  */
+void sparsebit_clear(struct sparsebit *s, sparsebit_idx_t idx)
+{
+	sparsebit_clear_num(s, idx, 1);
+}
+
+/* Sets the bits in the entire addressable range of the sparsebit array.  */
+void sparsebit_set_all(struct sparsebit *s)
+{
+	sparsebit_set(s, 0);
+	sparsebit_set_num(s, 1, ~(sparsebit_idx_t) 0);
+	assert(sparsebit_all_set(s));
+}
+
+/* Clears the bits in the entire addressable range of the sparsebit array.  */
+void sparsebit_clear_all(struct sparsebit *s)
+{
+	sparsebit_clear(s, 0);
+	sparsebit_clear_num(s, 1, ~(sparsebit_idx_t) 0);
+	assert(!sparsebit_any_set(s));
+}
+
+static size_t display_range(FILE *stream, sparsebit_idx_t low,
+	sparsebit_idx_t high, bool prepend_comma_space)
+{
+	char *fmt_str;
+	size_t sz;
+
+	/* Determine the printf format string */
+	if (low == high)
+		fmt_str = prepend_comma_space ? ", 0x%lx" : "0x%lx";
+	else
+		fmt_str = prepend_comma_space ? ", 0x%lx:0x%lx" : "0x%lx:0x%lx";
+
+	/*
+	 * When stream is NULL, just determine the size of what would
+	 * have been printed, else print the range.
+	 */
+	if (!stream)
+		sz = snprintf(NULL, 0, fmt_str, low, high);
+	else
+		sz = fprintf(stream, fmt_str, low, high);
+
+	return sz;
+}
+
+
+/* Dumps to the FILE stream given by stream, the bit settings
+ * of s.  Each line of output is prefixed with the number of
+ * spaces given by indent.  The length of each line is implementation
+ * dependent and does not depend on the indent amount.  The following
+ * is an example output of a sparsebit array that has bits:
+ *
+ *   0x5, 0x8, 0xa:0xe, 0x12
+ *
+ * This corresponds to a sparsebit whose bits 5, 8, 10, 11, 12, 13, 14, 18
+ * are set.  Note that a ':', instead of a '-' is used to specify a range of
+ * contiguous bits.  This is done because '-' is used to specify command-line
+ * options, and sometimes ranges are specified as command-line arguments.
+ */
+void sparsebit_dump(FILE *stream, struct sparsebit *s,
+	unsigned int indent)
+{
+	size_t current_line_len = 0;
+	size_t sz;
+	struct node *nodep;
+
+	if (!sparsebit_any_set(s))
+		return;
+
+	/* Display initial indent */
+	fprintf(stream, "%*s", indent, "");
+
+	/* For each node */
+	for (nodep = node_first(s); nodep; nodep = node_next(s, nodep)) {
+		unsigned int n1;
+		sparsebit_idx_t low, high;
+
+		/* For each group of bits in the mask */
+		for (n1 = 0; n1 < MASK_BITS; n1++) {
+			if (nodep->mask & (1 << n1)) {
+				low = high = nodep->idx + n1;
+
+				for (; n1 < MASK_BITS; n1++) {
+					if (nodep->mask & (1 << n1))
+						high = nodep->idx + n1;
+					else
+						break;
+				}
+
+				if ((n1 == MASK_BITS) && nodep->num_after)
+					high += nodep->num_after;
+
+				/*
+				 * How much room will it take to display
+				 * this range.
+				 */
+				sz = display_range(NULL, low, high,
+					current_line_len != 0);
+
+				/*
+				 * If there is not enough room, display
+				 * a newline plus the indent of the next
+				 * line.
+				 */
+				if (current_line_len + sz > DUMP_LINE_MAX) {
+					fputs("\n", stream);
+					fprintf(stream, "%*s", indent, "");
+					current_line_len = 0;
+				}
+
+				/* Display the range */
+				sz = display_range(stream, low, high,
+					current_line_len != 0);
+				current_line_len += sz;
+			}
+		}
+
+		/*
+		 * If num_after and most significant-bit of mask is not
+		 * set, then still need to display a range for the bits
+		 * described by num_after.
+		 */
+		if (!(nodep->mask & (1 << (MASK_BITS - 1))) && nodep->num_after) {
+			low = nodep->idx + MASK_BITS;
+			high = nodep->idx + MASK_BITS + nodep->num_after - 1;
+
+			/*
+			 * How much room will it take to display
+			 * this range.
+			 */
+			sz = display_range(NULL, low, high,
+				current_line_len != 0);
+
+			/*
+			 * If there is not enough room, display
+			 * a newline plus the indent of the next
+			 * line.
+			 */
+			if (current_line_len + sz > DUMP_LINE_MAX) {
+				fputs("\n", stream);
+				fprintf(stream, "%*s", indent, "");
+				current_line_len = 0;
+			}
+
+			/* Display the range */
+			sz = display_range(stream, low, high,
+				current_line_len != 0);
+			current_line_len += sz;
+		}
+	}
+	fputs("\n", stream);
+}
+
+/* Validates the internal state of the sparsebit array given by
+ * s.  On error, diagnostic information is printed to stderr and
+ * abort is called.
+ */
+void sparsebit_validate_internal(struct sparsebit *s)
+{
+	bool error_detected = false;
+	struct node *nodep, *prev = NULL;
+	sparsebit_num_t total_bits_set = 0;
+	unsigned int n1;
+
+	/* For each node */
+	for (nodep = node_first(s); nodep;
+		prev = nodep, nodep = node_next(s, nodep)) {
+
+		/*
+		 * Increase total bits set by the number of bits set
+		 * in this node.
+		 */
+		for (n1 = 0; n1 < MASK_BITS; n1++)
+			if (nodep->mask & (1 << n1))
+				total_bits_set++;
+
+		total_bits_set += nodep->num_after;
+
+		/*
+		 * Arbitrary choice as to whether a mask of 0 is allowed
+		 * or not.  For diagnostic purposes it is beneficial to
+		 * have only one valid means to represent a set of bits.
+		 * To support this an arbitrary choice has been made
+		 * to not allow a mask of zero.
+		 */
+		if (nodep->mask == 0) {
+			fprintf(stderr, "Node mask of zero, "
+				"nodep: %p nodep->mask: 0x%x",
+				nodep, nodep->mask);
+			error_detected = true;
+			break;
+		}
+
+		/*
+		 * Validate num_after is not greater than the max index
+		 * - the number of mask bits.  The num_after member
+		 * uses 0-based indexing and thus has no value that
+		 * represents all bits set.  This limitation is handled
+		 * by requiring a non-zero mask.  With a non-zero mask,
+		 * MASK_BITS worth of bits are described by the mask,
+		 * which makes the largest needed num_after equal to:
+		 *
+		 *    (~(sparsebit_num_t) 0) - MASK_BITS + 1
+		 */
+		if (nodep->num_after
+			> (~(sparsebit_num_t) 0) - MASK_BITS + 1) {
+			fprintf(stderr, "num_after too large, "
+				"nodep: %p nodep->num_after: 0x%lx",
+				nodep, nodep->num_after);
+			error_detected = true;
+			break;
+		}
+
+		/* Validate node index is divisible by the mask size */
+		if (nodep->idx % MASK_BITS) {
+			fprintf(stderr, "Node index not divisible by "
+				"mask size,\n"
+				"  nodep: %p nodep->idx: 0x%lx "
+				"MASK_BITS: %lu\n",
+				nodep, nodep->idx, MASK_BITS);
+			error_detected = true;
+			break;
+		}
+
+		/*
+		 * Validate bits described by node don't wrap beyond the
+		 * highest supported index.
+		 */
+		if ((nodep->idx + MASK_BITS + nodep->num_after - 1) < nodep->idx) {
+			fprintf(stderr, "Bits described by node wrap "
+				"beyond highest supported index,\n"
+				"  nodep: %p nodep->idx: 0x%lx\n"
+				"  MASK_BITS: %lu nodep->num_after: 0x%lx",
+				nodep, nodep->idx, MASK_BITS, nodep->num_after);
+			error_detected = true;
+			break;
+		}
+
+		/* Check parent pointers. */
+		if (nodep->left) {
+			if (nodep->left->parent != nodep) {
+				fprintf(stderr, "Left child parent pointer "
+					"doesn't point to this node,\n"
+					"  nodep: %p nodep->left: %p "
+					"nodep->left->parent: %p",
+					nodep, nodep->left,
+					nodep->left->parent);
+				error_detected = true;
+				break;
+			}
+		}
+
+		if (nodep->right) {
+			if (nodep->right->parent != nodep) {
+				fprintf(stderr, "Right child parent pointer "
+					"doesn't point to this node,\n"
+					"  nodep: %p nodep->right: %p "
+					"nodep->right->parent: %p",
+					nodep, nodep->right,
+					nodep->right->parent);
+				error_detected = true;
+				break;
+			}
+		}
+
+		if (!nodep->parent) {
+			if (s->root != nodep) {
+				fprintf(stderr, "Unexpected root node, "
+					"s->root: %p nodep: %p",
+					s->root, nodep);
+				error_detected = true;
+				break;
+			}
+		}
+
+		if (prev) {
+			/*
+			 * Is index of previous node before index of
+			 * current node?
+			 */
+			if (prev->idx >= nodep->idx) {
+				fprintf(stderr, "Previous node index "
+					">= current node index,\n"
+					"  prev: %p prev->idx: 0x%lx\n"
+					"  nodep: %p nodep->idx: 0x%lx",
+					prev, prev->idx, nodep, nodep->idx);
+				error_detected = true;
+				break;
+			}
+
+			/*
+			 * Nodes occur in asscending order, based on each
+			 * nodes starting index.
+			 */
+			if ((prev->idx + MASK_BITS + prev->num_after - 1)
+				>= nodep->idx) {
+				fprintf(stderr, "Previous node bit range "
+					"overlap with current node bit range,\n"
+					"  prev: %p prev->idx: 0x%lx "
+					"prev->num_after: 0x%lx\n"
+					"  nodep: %p nodep->idx: 0x%lx "
+					"nodep->num_after: 0x%lx\n"
+					"  MASK_BITS: %lu",
+					prev, prev->idx, prev->num_after,
+					nodep, nodep->idx, nodep->num_after,
+					MASK_BITS);
+				error_detected = true;
+				break;
+			}
+
+			/*
+			 * When the node has all mask bits set, it shouldn't
+			 * be adjacent to the last bit described by the
+			 * previous node.
+			 */
+			if (nodep->mask == ~(mask_t) 0 &&
+			    prev->idx + MASK_BITS + prev->num_after == nodep->idx) {
+				fprintf(stderr, "Current node has mask with "
+					"all bits set and is adjacent to the "
+					"previous node,\n"
+					"  prev: %p prev->idx: 0x%lx "
+					"prev->num_after: 0x%lx\n"
+					"  nodep: %p nodep->idx: 0x%lx "
+					"nodep->num_after: 0x%lx\n"
+					"  MASK_BITS: %lu",
+					prev, prev->idx, prev->num_after,
+					nodep, nodep->idx, nodep->num_after,
+					MASK_BITS);
+
+				error_detected = true;
+				break;
+			}
+		}
+	}
+
+	if (!error_detected) {
+		/*
+		 * Is sum of bits set in each node equal to the count
+		 * of total bits set.
+		 */
+		if (s->num_set != total_bits_set) {
+			fprintf(stderr, "Number of bits set missmatch,\n"
+				"  s->num_set: 0x%lx total_bits_set: 0x%lx",
+				s->num_set, total_bits_set);
+
+			error_detected = true;
+		}
+	}
+
+	if (error_detected) {
+		fputs("  dump_internal:\n", stderr);
+		sparsebit_dump_internal(stderr, s, 4);
+		abort();
+	}
+}
+
+
+#ifdef FUZZ
+/* A simple but effective fuzzing driver.  Look for bugs with the help
+ * of some invariants and of a trivial representation of sparsebit.
+ * Just use 512 bytes of /dev/zero and /dev/urandom as inputs, and let
+ * afl-fuzz do the magic. :)
+ */
+
+#include <stdlib.h>
+#include <assert.h>
+
+struct range {
+	sparsebit_idx_t first, last;
+	bool set;
+};
+
+struct sparsebit *s;
+struct range ranges[1000];
+int num_ranges;
+
+static bool get_value(sparsebit_idx_t idx)
+{
+	int i;
+
+	for (i = num_ranges; --i >= 0; )
+		if (ranges[i].first <= idx && idx <= ranges[i].last)
+			return ranges[i].set;
+
+	return false;
+}
+
+static void operate(int code, sparsebit_idx_t first, sparsebit_idx_t last)
+{
+	sparsebit_num_t num;
+	sparsebit_idx_t next;
+
+	if (first < last) {
+		num = last - first + 1;
+	} else {
+		num = first - last + 1;
+		first = last;
+		last = first + num - 1;
+	}
+
+	switch (code) {
+	case 0:
+		sparsebit_set(s, first);
+		assert(sparsebit_is_set(s, first));
+		assert(!sparsebit_is_clear(s, first));
+		assert(sparsebit_any_set(s));
+		assert(!sparsebit_all_clear(s));
+		if (get_value(first))
+			return;
+		if (num_ranges == 1000)
+			exit(0);
+		ranges[num_ranges++] = (struct range)
+			{ .first = first, .last = first, .set = true };
+		break;
+	case 1:
+		sparsebit_clear(s, first);
+		assert(!sparsebit_is_set(s, first));
+		assert(sparsebit_is_clear(s, first));
+		assert(sparsebit_any_clear(s));
+		assert(!sparsebit_all_set(s));
+		if (!get_value(first))
+			return;
+		if (num_ranges == 1000)
+			exit(0);
+		ranges[num_ranges++] = (struct range)
+			{ .first = first, .last = first, .set = false };
+		break;
+	case 2:
+		assert(sparsebit_is_set(s, first) == get_value(first));
+		assert(sparsebit_is_clear(s, first) == !get_value(first));
+		break;
+	case 3:
+		if (sparsebit_any_set(s))
+			assert(get_value(sparsebit_first_set(s)));
+		if (sparsebit_any_clear(s))
+			assert(!get_value(sparsebit_first_clear(s)));
+		sparsebit_set_all(s);
+		assert(!sparsebit_any_clear(s));
+		assert(sparsebit_all_set(s));
+		num_ranges = 0;
+		ranges[num_ranges++] = (struct range)
+			{ .first = 0, .last = ~(sparsebit_idx_t)0, .set = true };
+		break;
+	case 4:
+		if (sparsebit_any_set(s))
+			assert(get_value(sparsebit_first_set(s)));
+		if (sparsebit_any_clear(s))
+			assert(!get_value(sparsebit_first_clear(s)));
+		sparsebit_clear_all(s);
+		assert(!sparsebit_any_set(s));
+		assert(sparsebit_all_clear(s));
+		num_ranges = 0;
+		break;
+	case 5:
+		next = sparsebit_next_set(s, first);
+		assert(next == 0 || next > first);
+		assert(next == 0 || get_value(next));
+		break;
+	case 6:
+		next = sparsebit_next_clear(s, first);
+		assert(next == 0 || next > first);
+		assert(next == 0 || !get_value(next));
+		break;
+	case 7:
+		next = sparsebit_next_clear(s, first);
+		if (sparsebit_is_set_num(s, first, num)) {
+			assert(next == 0 || next > last);
+			if (first)
+				next = sparsebit_next_set(s, first - 1);
+			else if (sparsebit_any_set(s))
+				next = sparsebit_first_set(s);
+			else
+				return;
+			assert(next == first);
+		} else {
+			assert(sparsebit_is_clear(s, first) || next <= last);
+		}
+		break;
+	case 8:
+		next = sparsebit_next_set(s, first);
+		if (sparsebit_is_clear_num(s, first, num)) {
+			assert(next == 0 || next > last);
+			if (first)
+				next = sparsebit_next_clear(s, first - 1);
+			else if (sparsebit_any_clear(s))
+				next = sparsebit_first_clear(s);
+			else
+				return;
+			assert(next == first);
+		} else {
+			assert(sparsebit_is_set(s, first) || next <= last);
+		}
+		break;
+	case 9:
+		sparsebit_set_num(s, first, num);
+		assert(sparsebit_is_set_num(s, first, num));
+		assert(!sparsebit_is_clear_num(s, first, num));
+		assert(sparsebit_any_set(s));
+		assert(!sparsebit_all_clear(s));
+		if (num_ranges == 1000)
+			exit(0);
+		ranges[num_ranges++] = (struct range)
+			{ .first = first, .last = last, .set = true };
+		break;
+	case 10:
+		sparsebit_clear_num(s, first, num);
+		assert(!sparsebit_is_set_num(s, first, num));
+		assert(sparsebit_is_clear_num(s, first, num));
+		assert(sparsebit_any_clear(s));
+		assert(!sparsebit_all_set(s));
+		if (num_ranges == 1000)
+			exit(0);
+		ranges[num_ranges++] = (struct range)
+			{ .first = first, .last = last, .set = false };
+		break;
+	case 11:
+		sparsebit_validate_internal(s);
+		break;
+	default:
+		break;
+	}
+}
+
+unsigned char get8(void)
+{
+	int ch;
+
+	ch = getchar();
+	if (ch == EOF)
+		exit(0);
+	return ch;
+}
+
+uint64_t get64(void)
+{
+	uint64_t x;
+
+	x = get8();
+	x = (x << 8) | get8();
+	x = (x << 8) | get8();
+	x = (x << 8) | get8();
+	x = (x << 8) | get8();
+	x = (x << 8) | get8();
+	x = (x << 8) | get8();
+	return (x << 8) | get8();
+}
+
+int main(void)
+{
+	s = sparsebit_alloc();
+	for (;;) {
+		uint8_t op = get8() & 0xf;
+		uint64_t first = get64();
+		uint64_t last = get64();
+
+		operate(op, first, last);
+	}
+}
+#endif