qemu

hbitmap.c (27864B)

---

 /*
  * Hierarchical Bitmap Data Type
  *
  * Copyright Red Hat, Inc., 2012
  *
  * Author: Paolo Bonzini <pbonzini@redhat.com>
  *
  * This work is licensed under the terms of the GNU GPL, version 2 or
  * later.  See the COPYING file in the top-level directory.
  */
 
 #include "qemu/osdep.h"
 #include "qemu/hbitmap.h"
 #include "qemu/host-utils.h"
 #include "trace.h"
 #include "crypto/hash.h"
 
 /* HBitmaps provides an array of bits.  The bits are stored as usual in an
  * array of unsigned longs, but HBitmap is also optimized to provide fast
  * iteration over set bits; going from one bit to the next is O(logB n)
  * worst case, with B = sizeof(long) * CHAR_BIT: the result is low enough
  * that the number of levels is in fact fixed.
  *
  * In order to do this, it stacks multiple bitmaps with progressively coarser
  * granularity; in all levels except the last, bit N is set iff the N-th
  * unsigned long is nonzero in the immediately next level.  When iteration
  * completes on the last level it can examine the 2nd-last level to quickly
  * skip entire words, and even do so recursively to skip blocks of 64 words or
  * powers thereof (32 on 32-bit machines).
  *
  * Given an index in the bitmap, it can be split in group of bits like
  * this (for the 64-bit case):
  *
  *   bits 0-57 => word in the last bitmap     | bits 58-63 => bit in the word
  *   bits 0-51 => word in the 2nd-last bitmap | bits 52-57 => bit in the word
  *   bits 0-45 => word in the 3rd-last bitmap | bits 46-51 => bit in the word
  *
  * So it is easy to move up simply by shifting the index right by
  * log2(BITS_PER_LONG) bits.  To move down, you shift the index left
  * similarly, and add the word index within the group.  Iteration uses
  * ffs (find first set bit) to find the next word to examine; this
  * operation can be done in constant time in most current architectures.
  *
  * Setting or clearing a range of m bits on all levels, the work to perform
  * is O(m + m/W + m/W^2 + ...), which is O(m) like on a regular bitmap.
  *
  * When iterating on a bitmap, each bit (on any level) is only visited
  * once.  Hence, The total cost of visiting a bitmap with m bits in it is
  * the number of bits that are set in all bitmaps.  Unless the bitmap is
  * extremely sparse, this is also O(m + m/W + m/W^2 + ...), so the amortized
  * cost of advancing from one bit to the next is usually constant (worst case
  * O(logB n) as in the non-amortized complexity).
  */
 
 struct HBitmap {
     /*
      * Size of the bitmap, as requested in hbitmap_alloc or in hbitmap_truncate.
      */
     uint64_t orig_size;
 
     /* Number of total bits in the bottom level.  */
     uint64_t size;
 
     /* Number of set bits in the bottom level.  */
     uint64_t count;
 
     /* A scaling factor.  Given a granularity of G, each bit in the bitmap will
      * will actually represent a group of 2^G elements.  Each operation on a
      * range of bits first rounds the bits to determine which group they land
      * in, and then affect the entire page; iteration will only visit the first
      * bit of each group.  Here is an example of operations in a size-16,
      * granularity-1 HBitmap:
      *
      *    initial state            00000000
      *    set(start=0, count=9)    11111000 (iter: 0, 2, 4, 6, 8)
      *    reset(start=1, count=3)  00111000 (iter: 4, 6, 8)
      *    set(start=9, count=2)    00111100 (iter: 4, 6, 8, 10)
      *    reset(start=5, count=5)  00000000
      *
      * From an implementation point of view, when setting or resetting bits,
      * the bitmap will scale bit numbers right by this amount of bits.  When
      * iterating, the bitmap will scale bit numbers left by this amount of
      * bits.
      */
     int granularity;
 
     /* A meta dirty bitmap to track the dirtiness of bits in this HBitmap. */
     HBitmap *meta;
 
     /* A number of progressively less coarse bitmaps (i.e. level 0 is the
      * coarsest).  Each bit in level N represents a word in level N+1 that
      * has a set bit, except the last level where each bit represents the
      * actual bitmap.
      *
      * Note that all bitmaps have the same number of levels.  Even a 1-bit
      * bitmap will still allocate HBITMAP_LEVELS arrays.
      */
     unsigned long *levels[HBITMAP_LEVELS];
 
     /* The length of each levels[] array. */
     uint64_t sizes[HBITMAP_LEVELS];
 };
 
 /* Advance hbi to the next nonzero word and return it.  hbi->pos
  * is updated.  Returns zero if we reach the end of the bitmap.
  */
 static unsigned long hbitmap_iter_skip_words(HBitmapIter *hbi)
 {
     size_t pos = hbi->pos;
     const HBitmap *hb = hbi->hb;
     unsigned i = HBITMAP_LEVELS - 1;
 
     unsigned long cur;
     do {
         i--;
         pos >>= BITS_PER_LEVEL;
         cur = hbi->cur[i] & hb->levels[i][pos];
     } while (cur == 0);
 
     /* Check for end of iteration.  We always use fewer than BITS_PER_LONG
      * bits in the level 0 bitmap; thus we can repurpose the most significant
      * bit as a sentinel.  The sentinel is set in hbitmap_alloc and ensures
      * that the above loop ends even without an explicit check on i.
      */
 
     if (i == 0 && cur == (1UL << (BITS_PER_LONG - 1))) {
         return 0;
     }
     for (; i < HBITMAP_LEVELS - 1; i++) {
         /* Shift back pos to the left, matching the right shifts above.
          * The index of this word's least significant set bit provides
          * the low-order bits.
          */
         assert(cur);
         pos = (pos << BITS_PER_LEVEL) + ctzl(cur);
         hbi->cur[i] = cur & (cur - 1);
 
         /* Set up next level for iteration.  */
         cur = hb->levels[i + 1][pos];
     }
 
     hbi->pos = pos;
     trace_hbitmap_iter_skip_words(hbi->hb, hbi, pos, cur);
 
     assert(cur);
     return cur;
 }
 
 int64_t hbitmap_iter_next(HBitmapIter *hbi)
 {
     unsigned long cur = hbi->cur[HBITMAP_LEVELS - 1] &
             hbi->hb->levels[HBITMAP_LEVELS - 1][hbi->pos];
     int64_t item;
 
     if (cur == 0) {
         cur = hbitmap_iter_skip_words(hbi);
         if (cur == 0) {
             return -1;
         }
     }
 
     /* The next call will resume work from the next bit.  */
     hbi->cur[HBITMAP_LEVELS - 1] = cur & (cur - 1);
     item = ((uint64_t)hbi->pos << BITS_PER_LEVEL) + ctzl(cur);
 
     return item << hbi->granularity;
 }
 
 void hbitmap_iter_init(HBitmapIter *hbi, const HBitmap *hb, uint64_t first)
 {
     unsigned i, bit;
     uint64_t pos;
 
     hbi->hb = hb;
     pos = first >> hb->granularity;
     assert(pos < hb->size);
     hbi->pos = pos >> BITS_PER_LEVEL;
     hbi->granularity = hb->granularity;
 
     for (i = HBITMAP_LEVELS; i-- > 0; ) {
         bit = pos & (BITS_PER_LONG - 1);
         pos >>= BITS_PER_LEVEL;
 
         /* Drop bits representing items before first.  */
         hbi->cur[i] = hb->levels[i][pos] & ~((1UL << bit) - 1);
 
         /* We have already added level i+1, so the lowest set bit has
          * been processed.  Clear it.
          */
         if (i != HBITMAP_LEVELS - 1) {
             hbi->cur[i] &= ~(1UL << bit);
         }
     }
 }
 
 int64_t hbitmap_next_dirty(const HBitmap *hb, int64_t start, int64_t count)
 {
     HBitmapIter hbi;
     int64_t first_dirty_off;
     uint64_t end;
 
     assert(start >= 0 && count >= 0);
 
     if (start >= hb->orig_size || count == 0) {
         return -1;
     }
 
     end = count > hb->orig_size - start ? hb->orig_size : start + count;
 
     hbitmap_iter_init(&hbi, hb, start);
     first_dirty_off = hbitmap_iter_next(&hbi);
 
     if (first_dirty_off < 0 || first_dirty_off >= end) {
         return -1;
     }
 
     return MAX(start, first_dirty_off);
 }
 
 int64_t hbitmap_next_zero(const HBitmap *hb, int64_t start, int64_t count)
 {
     size_t pos = (start >> hb->granularity) >> BITS_PER_LEVEL;
     unsigned long *last_lev = hb->levels[HBITMAP_LEVELS - 1];
     unsigned long cur = last_lev[pos];
     unsigned start_bit_offset;
     uint64_t end_bit, sz;
     int64_t res;
 
     assert(start >= 0 && count >= 0);
 
     if (start >= hb->orig_size || count == 0) {
         return -1;
     }
 
     end_bit = count > hb->orig_size - start ?
                 hb->size :
                 ((start + count - 1) >> hb->granularity) + 1;
     sz = (end_bit + BITS_PER_LONG - 1) >> BITS_PER_LEVEL;
 
     /* There may be some zero bits in @cur before @start. We are not interested
      * in them, let's set them.
      */
     start_bit_offset = (start >> hb->granularity) & (BITS_PER_LONG - 1);
     cur |= (1UL << start_bit_offset) - 1;
     assert((start >> hb->granularity) < hb->size);
 
     if (cur == (unsigned long)-1) {
         do {
             pos++;
         } while (pos < sz && last_lev[pos] == (unsigned long)-1);
 
         if (pos >= sz) {
             return -1;
         }
 
         cur = last_lev[pos];
     }
 
     res = (pos << BITS_PER_LEVEL) + ctol(cur);
     if (res >= end_bit) {
         return -1;
     }
 
     res = res << hb->granularity;
     if (res < start) {
         assert(((start - res) >> hb->granularity) == 0);
         return start;
     }
 
     return res;
 }
 
 bool hbitmap_next_dirty_area(const HBitmap *hb, int64_t start, int64_t end,
                              int64_t max_dirty_count,
                              int64_t *dirty_start, int64_t *dirty_count)
 {
     int64_t next_zero;
 
     assert(start >= 0 && end >= 0 && max_dirty_count > 0);
 
     end = MIN(end, hb->orig_size);
     if (start >= end) {
         return false;
     }
 
     start = hbitmap_next_dirty(hb, start, end - start);
     if (start < 0) {
         return false;
     }
 
     end = start + MIN(end - start, max_dirty_count);
 
     next_zero = hbitmap_next_zero(hb, start, end - start);
     if (next_zero >= 0) {
         end = next_zero;
     }
 
     *dirty_start = start;
     *dirty_count = end - start;
 
     return true;
 }
 
 bool hbitmap_status(const HBitmap *hb, int64_t start, int64_t count,
                     int64_t *pnum)
 {
     int64_t next_dirty, next_zero;
 
     assert(start >= 0);
     assert(count > 0);
     assert(start + count <= hb->orig_size);
 
     next_dirty = hbitmap_next_dirty(hb, start, count);
     if (next_dirty == -1) {
         *pnum = count;
         return false;
     }
 
     if (next_dirty > start) {
         *pnum = next_dirty - start;
         return false;
     }
 
     assert(next_dirty == start);
 
     next_zero = hbitmap_next_zero(hb, start, count);
     if (next_zero == -1) {
         *pnum = count;
         return true;
     }
 
     assert(next_zero > start);
     *pnum = next_zero - start;
     return false;
 }
 
 bool hbitmap_empty(const HBitmap *hb)
 {
     return hb->count == 0;
 }
 
 int hbitmap_granularity(const HBitmap *hb)
 {
     return hb->granularity;
 }
 
 uint64_t hbitmap_count(const HBitmap *hb)
 {
     return hb->count << hb->granularity;
 }
 
 /**
  * hbitmap_iter_next_word:
  * @hbi: HBitmapIter to operate on.
  * @p_cur: Location where to store the next non-zero word.
  *
  * Return the index of the next nonzero word that is set in @hbi's
  * associated HBitmap, and set *p_cur to the content of that word
  * (bits before the index that was passed to hbitmap_iter_init are
  * trimmed on the first call).  Return -1, and set *p_cur to zero,
  * if all remaining words are zero.
  */
 static size_t hbitmap_iter_next_word(HBitmapIter *hbi, unsigned long *p_cur)
 {
     unsigned long cur = hbi->cur[HBITMAP_LEVELS - 1];
 
     if (cur == 0) {
         cur = hbitmap_iter_skip_words(hbi);
         if (cur == 0) {
             *p_cur = 0;
             return -1;
         }
     }
 
     /* The next call will resume work from the next word.  */
     hbi->cur[HBITMAP_LEVELS - 1] = 0;
     *p_cur = cur;
     return hbi->pos;
 }
 
 /* Count the number of set bits between start and end, not accounting for
  * the granularity.  Also an example of how to use hbitmap_iter_next_word.
  */
 static uint64_t hb_count_between(HBitmap *hb, uint64_t start, uint64_t last)
 {
     HBitmapIter hbi;
     uint64_t count = 0;
     uint64_t end = last + 1;
     unsigned long cur;
     size_t pos;
 
     hbitmap_iter_init(&hbi, hb, start << hb->granularity);
     for (;;) {
         pos = hbitmap_iter_next_word(&hbi, &cur);
         if (pos >= (end >> BITS_PER_LEVEL)) {
             break;
         }
         count += ctpopl(cur);
     }
 
     if (pos == (end >> BITS_PER_LEVEL)) {
         /* Drop bits representing the END-th and subsequent items.  */
         int bit = end & (BITS_PER_LONG - 1);
         cur &= (1UL << bit) - 1;
         count += ctpopl(cur);
     }
 
     return count;
 }
 
 /* Setting starts at the last layer and propagates up if an element
  * changes.
  */
 static inline bool hb_set_elem(unsigned long *elem, uint64_t start, uint64_t last)
 {
     unsigned long mask;
     unsigned long old;
 
     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
     assert(start <= last);
 
     mask = 2UL << (last & (BITS_PER_LONG - 1));
     mask -= 1UL << (start & (BITS_PER_LONG - 1));
     old = *elem;
     *elem |= mask;
     return old != *elem;
 }
 
 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)...
  * Returns true if at least one bit is changed. */
 static bool hb_set_between(HBitmap *hb, int level, uint64_t start,
                            uint64_t last)
 {
     size_t pos = start >> BITS_PER_LEVEL;
     size_t lastpos = last >> BITS_PER_LEVEL;
     bool changed = false;
     size_t i;
 
     i = pos;
     if (i < lastpos) {
         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
         changed |= hb_set_elem(&hb->levels[level][i], start, next - 1);
         for (;;) {
             start = next;
             next += BITS_PER_LONG;
             if (++i == lastpos) {
                 break;
             }
             changed |= (hb->levels[level][i] == 0);
             hb->levels[level][i] = ~0UL;
         }
     }
     changed |= hb_set_elem(&hb->levels[level][i], start, last);
 
     /* If there was any change in this layer, we may have to update
      * the one above.
      */
     if (level > 0 && changed) {
         hb_set_between(hb, level - 1, pos, lastpos);
     }
     return changed;
 }
 
 void hbitmap_set(HBitmap *hb, uint64_t start, uint64_t count)
 {
     /* Compute range in the last layer.  */
     uint64_t first, n;
     uint64_t last = start + count - 1;
 
     if (count == 0) {
         return;
     }
 
     trace_hbitmap_set(hb, start, count,
                       start >> hb->granularity, last >> hb->granularity);
 
     first = start >> hb->granularity;
     last >>= hb->granularity;
     assert(last < hb->size);
     n = last - first + 1;
 
     hb->count += n - hb_count_between(hb, first, last);
     if (hb_set_between(hb, HBITMAP_LEVELS - 1, first, last) &&
         hb->meta) {
         hbitmap_set(hb->meta, start, count);
     }
 }
 
 /* Resetting works the other way round: propagate up if the new
  * value is zero.
  */
 static inline bool hb_reset_elem(unsigned long *elem, uint64_t start, uint64_t last)
 {
     unsigned long mask;
     bool blanked;
 
     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
     assert(start <= last);
 
     mask = 2UL << (last & (BITS_PER_LONG - 1));
     mask -= 1UL << (start & (BITS_PER_LONG - 1));
     blanked = *elem != 0 && ((*elem & ~mask) == 0);
     *elem &= ~mask;
     return blanked;
 }
 
 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)...
  * Returns true if at least one bit is changed. */
 static bool hb_reset_between(HBitmap *hb, int level, uint64_t start,
                              uint64_t last)
 {
     size_t pos = start >> BITS_PER_LEVEL;
     size_t lastpos = last >> BITS_PER_LEVEL;
     bool changed = false;
     size_t i;
 
     i = pos;
     if (i < lastpos) {
         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
 
         /* Here we need a more complex test than when setting bits.  Even if
          * something was changed, we must not blank bits in the upper level
          * unless the lower-level word became entirely zero.  So, remove pos
          * from the upper-level range if bits remain set.
          */
         if (hb_reset_elem(&hb->levels[level][i], start, next - 1)) {
             changed = true;
         } else {
             pos++;
         }
 
         for (;;) {
             start = next;
             next += BITS_PER_LONG;
             if (++i == lastpos) {
                 break;
             }
             changed |= (hb->levels[level][i] != 0);
             hb->levels[level][i] = 0UL;
         }
     }
 
     /* Same as above, this time for lastpos.  */
     if (hb_reset_elem(&hb->levels[level][i], start, last)) {
         changed = true;
     } else {
         lastpos--;
     }
 
     if (level > 0 && changed) {
         hb_reset_between(hb, level - 1, pos, lastpos);
     }
 
     return changed;
 
 }
 
 void hbitmap_reset(HBitmap *hb, uint64_t start, uint64_t count)
 {
     /* Compute range in the last layer.  */
     uint64_t first;
     uint64_t last = start + count - 1;
     uint64_t gran = 1ULL << hb->granularity;
 
     if (count == 0) {
         return;
     }
 
     assert(QEMU_IS_ALIGNED(start, gran));
     assert(QEMU_IS_ALIGNED(count, gran) || (start + count == hb->orig_size));
 
     trace_hbitmap_reset(hb, start, count,
                         start >> hb->granularity, last >> hb->granularity);
 
     first = start >> hb->granularity;
     last >>= hb->granularity;
     assert(last < hb->size);
 
     hb->count -= hb_count_between(hb, first, last);
     if (hb_reset_between(hb, HBITMAP_LEVELS - 1, first, last) &&
         hb->meta) {
         hbitmap_set(hb->meta, start, count);
     }
 }
 
 void hbitmap_reset_all(HBitmap *hb)
 {
     unsigned int i;
 
     /* Same as hbitmap_alloc() except for memset() instead of malloc() */
     for (i = HBITMAP_LEVELS; --i >= 1; ) {
         memset(hb->levels[i], 0, hb->sizes[i] * sizeof(unsigned long));
     }
 
     hb->levels[0][0] = 1UL << (BITS_PER_LONG - 1);
     hb->count = 0;
 }
 
 bool hbitmap_is_serializable(const HBitmap *hb)
 {
     /* Every serialized chunk must be aligned to 64 bits so that endianness
      * requirements can be fulfilled on both 64 bit and 32 bit hosts.
      * We have hbitmap_serialization_align() which converts this
      * alignment requirement from bitmap bits to items covered (e.g. sectors).
      * That value is:
      *    64 << hb->granularity
      * Since this value must not exceed UINT64_MAX, hb->granularity must be
      * less than 58 (== 64 - 6, where 6 is ld(64), i.e. 1 << 6 == 64).
      *
      * In order for hbitmap_serialization_align() to always return a
      * meaningful value, bitmaps that are to be serialized must have a
      * granularity of less than 58. */
 
     return hb->granularity < 58;
 }
 
 bool hbitmap_get(const HBitmap *hb, uint64_t item)
 {
     /* Compute position and bit in the last layer.  */
     uint64_t pos = item >> hb->granularity;
     unsigned long bit = 1UL << (pos & (BITS_PER_LONG - 1));
     assert(pos < hb->size);
 
     return (hb->levels[HBITMAP_LEVELS - 1][pos >> BITS_PER_LEVEL] & bit) != 0;
 }
 
 uint64_t hbitmap_serialization_align(const HBitmap *hb)
 {
     assert(hbitmap_is_serializable(hb));
 
     /* Require at least 64 bit granularity to be safe on both 64 bit and 32 bit
      * hosts. */
     return UINT64_C(64) << hb->granularity;
 }
 
 /* Start should be aligned to serialization granularity, chunk size should be
  * aligned to serialization granularity too, except for last chunk.
  */
 static void serialization_chunk(const HBitmap *hb,
                                 uint64_t start, uint64_t count,
                                 unsigned long **first_el, uint64_t *el_count)
 {
     uint64_t last = start + count - 1;
     uint64_t gran = hbitmap_serialization_align(hb);
 
     assert((start & (gran - 1)) == 0);
     assert((last >> hb->granularity) < hb->size);
     if ((last >> hb->granularity) != hb->size - 1) {
         assert((count & (gran - 1)) == 0);
     }
 
     start = (start >> hb->granularity) >> BITS_PER_LEVEL;
     last = (last >> hb->granularity) >> BITS_PER_LEVEL;
 
     *first_el = &hb->levels[HBITMAP_LEVELS - 1][start];
     *el_count = last - start + 1;
 }
 
 uint64_t hbitmap_serialization_size(const HBitmap *hb,
                                     uint64_t start, uint64_t count)
 {
     uint64_t el_count;
     unsigned long *cur;
 
     if (!count) {
         return 0;
     }
     serialization_chunk(hb, start, count, &cur, &el_count);
 
     return el_count * sizeof(unsigned long);
 }
 
 void hbitmap_serialize_part(const HBitmap *hb, uint8_t *buf,
                             uint64_t start, uint64_t count)
 {
     uint64_t el_count;
     unsigned long *cur, *end;
 
     if (!count) {
         return;
     }
     serialization_chunk(hb, start, count, &cur, &el_count);
     end = cur + el_count;
 
     while (cur != end) {
         unsigned long el =
             (BITS_PER_LONG == 32 ? cpu_to_le32(*cur) : cpu_to_le64(*cur));
 
         memcpy(buf, &el, sizeof(el));
         buf += sizeof(el);
         cur++;
     }
 }
 
 void hbitmap_deserialize_part(HBitmap *hb, uint8_t *buf,
                               uint64_t start, uint64_t count,
                               bool finish)
 {
     uint64_t el_count;
     unsigned long *cur, *end;
 
     if (!count) {
         return;
     }
     serialization_chunk(hb, start, count, &cur, &el_count);
     end = cur + el_count;
 
     while (cur != end) {
         memcpy(cur, buf, sizeof(*cur));
 
         if (BITS_PER_LONG == 32) {
             le32_to_cpus((uint32_t *)cur);
         } else {
             le64_to_cpus((uint64_t *)cur);
         }
 
         buf += sizeof(unsigned long);
         cur++;
     }
     if (finish) {
         hbitmap_deserialize_finish(hb);
     }
 }
 
 void hbitmap_deserialize_zeroes(HBitmap *hb, uint64_t start, uint64_t count,
                                 bool finish)
 {
     uint64_t el_count;
     unsigned long *first;
 
     if (!count) {
         return;
     }
     serialization_chunk(hb, start, count, &first, &el_count);
 
     memset(first, 0, el_count * sizeof(unsigned long));
     if (finish) {
         hbitmap_deserialize_finish(hb);
     }
 }
 
 void hbitmap_deserialize_ones(HBitmap *hb, uint64_t start, uint64_t count,
                               bool finish)
 {
     uint64_t el_count;
     unsigned long *first;
 
     if (!count) {
         return;
     }
     serialization_chunk(hb, start, count, &first, &el_count);
 
     memset(first, 0xff, el_count * sizeof(unsigned long));
     if (finish) {
         hbitmap_deserialize_finish(hb);
     }
 }
 
 void hbitmap_deserialize_finish(HBitmap *bitmap)
 {
     int64_t i, size, prev_size;
     int lev;
 
     /* restore levels starting from penultimate to zero level, assuming
      * that the last level is ok */
     size = MAX((bitmap->size + BITS_PER_LONG - 1) >> BITS_PER_LEVEL, 1);
     for (lev = HBITMAP_LEVELS - 1; lev-- > 0; ) {
         prev_size = size;
         size = MAX((size + BITS_PER_LONG - 1) >> BITS_PER_LEVEL, 1);
         memset(bitmap->levels[lev], 0, size * sizeof(unsigned long));
 
         for (i = 0; i < prev_size; ++i) {
             if (bitmap->levels[lev + 1][i]) {
                 bitmap->levels[lev][i >> BITS_PER_LEVEL] |=
                     1UL << (i & (BITS_PER_LONG - 1));
             }
         }
     }
 
     bitmap->levels[0][0] |= 1UL << (BITS_PER_LONG - 1);
     bitmap->count = hb_count_between(bitmap, 0, bitmap->size - 1);
 }
 
 void hbitmap_free(HBitmap *hb)
 {
     unsigned i;
     assert(!hb->meta);
     for (i = HBITMAP_LEVELS; i-- > 0; ) {
         g_free(hb->levels[i]);
     }
     g_free(hb);
 }
 
 HBitmap *hbitmap_alloc(uint64_t size, int granularity)
 {
     HBitmap *hb = g_new0(struct HBitmap, 1);
     unsigned i;
 
     assert(size <= INT64_MAX);
     hb->orig_size = size;
 
     assert(granularity >= 0 && granularity < 64);
     size = (size + (1ULL << granularity) - 1) >> granularity;
     assert(size <= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE));
 
     hb->size = size;
     hb->granularity = granularity;
     for (i = HBITMAP_LEVELS; i-- > 0; ) {
         size = MAX((size + BITS_PER_LONG - 1) >> BITS_PER_LEVEL, 1);
         hb->sizes[i] = size;
         hb->levels[i] = g_new0(unsigned long, size);
     }
 
     /* We necessarily have free bits in level 0 due to the definition
      * of HBITMAP_LEVELS, so use one for a sentinel.  This speeds up
      * hbitmap_iter_skip_words.
      */
     assert(size == 1);
     hb->levels[0][0] |= 1UL << (BITS_PER_LONG - 1);
     return hb;
 }
 
 void hbitmap_truncate(HBitmap *hb, uint64_t size)
 {
     bool shrink;
     unsigned i;
     uint64_t num_elements = size;
     uint64_t old;
 
     assert(size <= INT64_MAX);
     hb->orig_size = size;
 
     /* Size comes in as logical elements, adjust for granularity. */
     size = (size + (1ULL << hb->granularity) - 1) >> hb->granularity;
     assert(size <= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE));
     shrink = size < hb->size;
 
     /* bit sizes are identical; nothing to do. */
     if (size == hb->size) {
         return;
     }
 
     /* If we're losing bits, let's clear those bits before we invalidate all of
      * our invariants. This helps keep the bitcount consistent, and will prevent
      * us from carrying around garbage bits beyond the end of the map.
      */
     if (shrink) {
         /* Don't clear partial granularity groups;
          * start at the first full one. */
         uint64_t start = ROUND_UP(num_elements, UINT64_C(1) << hb->granularity);
         uint64_t fix_count = (hb->size << hb->granularity) - start;
 
         assert(fix_count);
         hbitmap_reset(hb, start, fix_count);
     }
 
     hb->size = size;
     for (i = HBITMAP_LEVELS; i-- > 0; ) {
         size = MAX(BITS_TO_LONGS(size), 1);
         if (hb->sizes[i] == size) {
             break;
         }
         old = hb->sizes[i];
         hb->sizes[i] = size;
         hb->levels[i] = g_renew(unsigned long, hb->levels[i], size);
         if (!shrink) {
             memset(&hb->levels[i][old], 0x00,
                    (size - old) * sizeof(*hb->levels[i]));
         }
     }
     if (hb->meta) {
         hbitmap_truncate(hb->meta, hb->size << hb->granularity);
     }
 }
 
 /**
  * hbitmap_sparse_merge: performs dst = dst | src
  * works with differing granularities.
  * best used when src is sparsely populated.
  */
 static void hbitmap_sparse_merge(HBitmap *dst, const HBitmap *src)
 {
     int64_t offset;
     int64_t count;
 
     for (offset = 0;
          hbitmap_next_dirty_area(src, offset, src->orig_size, INT64_MAX,
                                  &offset, &count);
          offset += count)
     {
         hbitmap_set(dst, offset, count);
     }
 }
 
 /**
  * Given HBitmaps A and B, let R := A (BITOR) B.
  * Bitmaps A and B will not be modified,
  *     except when bitmap R is an alias of A or B.
  * Bitmaps must have same size.
  */
 void hbitmap_merge(const HBitmap *a, const HBitmap *b, HBitmap *result)
 {
     int i;
     uint64_t j;
 
     assert(a->orig_size == result->orig_size);
     assert(b->orig_size == result->orig_size);
 
     if ((!hbitmap_count(a) && result == b) ||
         (!hbitmap_count(b) && result == a)) {
         return;
     }
 
     if (!hbitmap_count(a) && !hbitmap_count(b)) {
         hbitmap_reset_all(result);
         return;
     }
 
     if (a->granularity != b->granularity) {
         if ((a != result) && (b != result)) {
             hbitmap_reset_all(result);
         }
         if (a != result) {
             hbitmap_sparse_merge(result, a);
         }
         if (b != result) {
             hbitmap_sparse_merge(result, b);
         }
         return;
     }
 
     /* This merge is O(size), as BITS_PER_LONG and HBITMAP_LEVELS are constant.
      * It may be possible to improve running times for sparsely populated maps
      * by using hbitmap_iter_next, but this is suboptimal for dense maps.
      */
     assert(a->size == b->size);
     for (i = HBITMAP_LEVELS - 1; i >= 0; i--) {
         for (j = 0; j < a->sizes[i]; j++) {
             result->levels[i][j] = a->levels[i][j] | b->levels[i][j];
         }
     }
 
     /* Recompute the dirty count */
     result->count = hb_count_between(result, 0, result->size - 1);
 }
 
 char *hbitmap_sha256(const HBitmap *bitmap, Error **errp)
 {
     size_t size = bitmap->sizes[HBITMAP_LEVELS - 1] * sizeof(unsigned long);
     char *data = (char *)bitmap->levels[HBITMAP_LEVELS - 1];
     char *hash = NULL;
     qcrypto_hash_digest(QCRYPTO_HASH_ALG_SHA256, data, size, &hash, errp);
 
     return hash;
 }