TOMOYO Linux Cross Reference
Linux/tools/testing/selftests/kvm/lib/sparsebit.c

   // 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(const 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(const 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(const 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(const 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(const 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(const 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 = 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(const 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, const 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, const 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(const 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(const 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(const 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(const struct sparsebit *s)
 {
         return s->num_set;
 }
 
 /* Returns whether any bit is set in the sparsebit array.  */
 bool sparsebit_any_set(const 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(const struct sparsebit *s)
 {
         return !sparsebit_any_set(s);
 }
 
 /* Returns whether all the bits in the sparsebit array are set.  */
 bool sparsebit_any_clear(const 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(const 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(const 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(const 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(const 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(const 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(const 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, const 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(const 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 mismatch,\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>
 
 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
 

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