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 // 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 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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