/*
* 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 <glib.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];
/* 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.
*/
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.
*/
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;
}
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);
}
}
}
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 += 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 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);
}
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_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_new0(struct HBitmap, 1);
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->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;
/* 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 = QEMU_ALIGN_UP(num_elements, 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_realloc(hb->levels[i], size * sizeof(unsigned long));
if (!shrink) {
memset(&hb->levels[i][old], 0x00,
(size - old) * sizeof(*hb->levels[i]));
}
}
}
/**
* Given HBitmaps A and B, let A := A (BITOR) B.
* Bitmap B will not be modified.
*
* @return true if the merge was successful,
* false if it was not attempted.
*/
bool hbitmap_merge(HBitmap *a, const HBitmap *b)
{
int i;
uint64_t j;
if ((a->size != b->size) || (a->granularity != b->granularity)) {
return false;
}
if (hbitmap_count(b) == 0) {
return true;
}
/* 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.
*/
for (i = HBITMAP_LEVELS - 1; i >= 0; i--) {
for (j = 0; j < a->sizes[i]; j++) {
a->levels[i][j] |= b->levels[i][j];
}
}
return true;
}
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