add hierarchical bitmap data type and test cases

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.

Reviewed-by: Laszlo Ersek <lersek@redhat.com>
Reviewed-by: Eric Blake <eblake@redhat.com>
Signed-off-by: Paolo Bonzini <pbonzini@redhat.com>
Signed-off-by: Kevin Wolf <kwolf@redhat.com>

2 files changed, 401 insertions, 1 deletions

diff --git a/util/Makefile.objs b/util/Makefile.objs
index 5baeb53..495a178 100644
--- a/util/Makefile.objs
+++ b/util/Makefile.objs
@@ -2,7 +2,7 @@ util-obj-y = osdep.o cutils.o qemu-timer-common.o
 util-obj-$(CONFIG_WIN32) += oslib-win32.o qemu-thread-win32.o event_notifier-win32.o
 util-obj-$(CONFIG_POSIX) += oslib-posix.o qemu-thread-posix.o event_notifier-posix.o
 util-obj-y += envlist.o path.o host-utils.o cache-utils.o module.o
-util-obj-y += bitmap.o bitops.o
+util-obj-y += bitmap.o bitops.o hbitmap.o
 util-obj-y += acl.o
 util-obj-y += error.o qemu-error.o
 util-obj-$(CONFIG_POSIX) += compatfd.o
diff --git a/util/hbitmap.c b/util/hbitmap.c
new file mode 100644
index 0000000..fb7e01e
--- /dev/null
+++ b/util/hbitmap.c
@@ -0,0 +1,400 @@
+/*
+ * 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 <string.h>
+#include <glib.h>
+#include <assert.h>
+#include "qemu/osdep.h"
+#include "qemu/hbitmap.h"
+#include "qemu/host-utils.h"
+#include "trace.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 {
+    /* 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 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];
+};
+
+static inline int popcountl(unsigned long l)
+{
+    return BITS_PER_LONG == 32 ? ctpop32(l) : ctpop64(l);
+}
+
+/* Advance hbi to the next nonzero word and return it.  hbi->pos
+ * is updated.  Returns zero if we reach the end of the bitmap.
+ */
+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 {
+        cur = hbi->cur[--i];
+        pos >>= BITS_PER_LEVEL;
+    } 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.
+         */
+        pos = (pos << BITS_PER_LEVEL) + ffsl(cur) - 1;
+        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;
+}
+
+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;
+    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);
+        }
+    }
+}
+
+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;
+}
+
+/* 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 += popcountl(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 += popcountl(cur);
+    }
+
+    return count;
+}
+
+/* Setting starts at the last layer and propagates up if an element
+ * changes from zero to non-zero.
+ */
+static inline bool hb_set_elem(unsigned long *elem, uint64_t start, uint64_t last)
+{
+    unsigned long mask;
+    bool changed;
+
+    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));
+    changed = (*elem == 0);
+    *elem |= mask;
+    return changed;
+}
+
+/* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
+static void 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);
+    }
+}
+
+void hbitmap_set(HBitmap *hb, uint64_t start, uint64_t count)
+{
+    /* Compute range in the last layer.  */
+    uint64_t last = start + count - 1;
+
+    trace_hbitmap_set(hb, start, count,
+                      start >> hb->granularity, last >> hb->granularity);
+
+    start >>= hb->granularity;
+    last >>= hb->granularity;
+    count = last - start + 1;
+
+    hb->count += count - hb_count_between(hb, start, last);
+    hb_set_between(hb, HBITMAP_LEVELS - 1, start, last);
+}
+
+/* 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)... */
+static void 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);
+    }
+}
+
+void hbitmap_reset(HBitmap *hb, uint64_t start, uint64_t count)
+{
+    /* Compute range in the last layer.  */
+    uint64_t last = start + count - 1;
+
+    trace_hbitmap_reset(hb, start, count,
+                        start >> hb->granularity, last >> hb->granularity);
+
+    start >>= hb->granularity;
+    last >>= hb->granularity;
+
+    hb->count -= hb_count_between(hb, start, last);
+    hb_reset_between(hb, HBITMAP_LEVELS - 1, start, last);
+}
+
+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));
+
+    return (hb->levels[HBITMAP_LEVELS - 1][pos >> BITS_PER_LEVEL] & bit) != 0;
+}
+
+void hbitmap_free(HBitmap *hb)
+{
+    unsigned i;
+    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_malloc0(sizeof (struct HBitmap));
+    unsigned i;
+
+    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->levels[i] = g_malloc0(size * sizeof(unsigned long));
+    }
+
+    /* 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;
+}