2 * Hierarchical Bitmap Data Type
4 * Copyright Red Hat, Inc., 2012
6 * Author: Paolo Bonzini <pbonzini@redhat.com>
8 * This work is licensed under the terms of the GNU GPL, version 2 or
9 * later. See the COPYING file in the top-level directory.
12 #include "qemu/osdep.h"
13 #include "qemu/hbitmap.h"
14 #include "qemu/host-utils.h"
17 /* HBitmaps provides an array of bits. The bits are stored as usual in an
18 * array of unsigned longs, but HBitmap is also optimized to provide fast
19 * iteration over set bits; going from one bit to the next is O(logB n)
20 * worst case, with B = sizeof(long) * CHAR_BIT: the result is low enough
21 * that the number of levels is in fact fixed.
23 * In order to do this, it stacks multiple bitmaps with progressively coarser
24 * granularity; in all levels except the last, bit N is set iff the N-th
25 * unsigned long is nonzero in the immediately next level. When iteration
26 * completes on the last level it can examine the 2nd-last level to quickly
27 * skip entire words, and even do so recursively to skip blocks of 64 words or
28 * powers thereof (32 on 32-bit machines).
30 * Given an index in the bitmap, it can be split in group of bits like
31 * this (for the 64-bit case):
33 * bits 0-57 => word in the last bitmap | bits 58-63 => bit in the word
34 * bits 0-51 => word in the 2nd-last bitmap | bits 52-57 => bit in the word
35 * bits 0-45 => word in the 3rd-last bitmap | bits 46-51 => bit in the word
37 * So it is easy to move up simply by shifting the index right by
38 * log2(BITS_PER_LONG) bits. To move down, you shift the index left
39 * similarly, and add the word index within the group. Iteration uses
40 * ffs (find first set bit) to find the next word to examine; this
41 * operation can be done in constant time in most current architectures.
43 * Setting or clearing a range of m bits on all levels, the work to perform
44 * is O(m + m/W + m/W^2 + ...), which is O(m) like on a regular bitmap.
46 * When iterating on a bitmap, each bit (on any level) is only visited
47 * once. Hence, The total cost of visiting a bitmap with m bits in it is
48 * the number of bits that are set in all bitmaps. Unless the bitmap is
49 * extremely sparse, this is also O(m + m/W + m/W^2 + ...), so the amortized
50 * cost of advancing from one bit to the next is usually constant (worst case
51 * O(logB n) as in the non-amortized complexity).
55 /* Number of total bits in the bottom level. */
58 /* Number of set bits in the bottom level. */
61 /* A scaling factor. Given a granularity of G, each bit in the bitmap will
62 * will actually represent a group of 2^G elements. Each operation on a
63 * range of bits first rounds the bits to determine which group they land
64 * in, and then affect the entire page; iteration will only visit the first
65 * bit of each group. Here is an example of operations in a size-16,
66 * granularity-1 HBitmap:
68 * initial state 00000000
69 * set(start=0, count=9) 11111000 (iter: 0, 2, 4, 6, 8)
70 * reset(start=1, count=3) 00111000 (iter: 4, 6, 8)
71 * set(start=9, count=2) 00111100 (iter: 4, 6, 8, 10)
72 * reset(start=5, count=5) 00000000
74 * From an implementation point of view, when setting or resetting bits,
75 * the bitmap will scale bit numbers right by this amount of bits. When
76 * iterating, the bitmap will scale bit numbers left by this amount of
81 /* A meta dirty bitmap to track the dirtiness of bits in this HBitmap. */
84 /* A number of progressively less coarse bitmaps (i.e. level 0 is the
85 * coarsest). Each bit in level N represents a word in level N+1 that
86 * has a set bit, except the last level where each bit represents the
89 * Note that all bitmaps have the same number of levels. Even a 1-bit
90 * bitmap will still allocate HBITMAP_LEVELS arrays.
92 unsigned long *levels
[HBITMAP_LEVELS
];
94 /* The length of each levels[] array. */
95 uint64_t sizes
[HBITMAP_LEVELS
];
98 /* Advance hbi to the next nonzero word and return it. hbi->pos
99 * is updated. Returns zero if we reach the end of the bitmap.
101 unsigned long hbitmap_iter_skip_words(HBitmapIter
*hbi
)
103 size_t pos
= hbi
->pos
;
104 const HBitmap
*hb
= hbi
->hb
;
105 unsigned i
= HBITMAP_LEVELS
- 1;
110 pos
>>= BITS_PER_LEVEL
;
113 /* Check for end of iteration. We always use fewer than BITS_PER_LONG
114 * bits in the level 0 bitmap; thus we can repurpose the most significant
115 * bit as a sentinel. The sentinel is set in hbitmap_alloc and ensures
116 * that the above loop ends even without an explicit check on i.
119 if (i
== 0 && cur
== (1UL << (BITS_PER_LONG
- 1))) {
122 for (; i
< HBITMAP_LEVELS
- 1; i
++) {
123 /* Shift back pos to the left, matching the right shifts above.
124 * The index of this word's least significant set bit provides
125 * the low-order bits.
128 pos
= (pos
<< BITS_PER_LEVEL
) + ctzl(cur
);
129 hbi
->cur
[i
] = cur
& (cur
- 1);
131 /* Set up next level for iteration. */
132 cur
= hb
->levels
[i
+ 1][pos
];
136 trace_hbitmap_iter_skip_words(hbi
->hb
, hbi
, pos
, cur
);
142 void hbitmap_iter_init(HBitmapIter
*hbi
, const HBitmap
*hb
, uint64_t first
)
148 pos
= first
>> hb
->granularity
;
149 assert(pos
< hb
->size
);
150 hbi
->pos
= pos
>> BITS_PER_LEVEL
;
151 hbi
->granularity
= hb
->granularity
;
153 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
154 bit
= pos
& (BITS_PER_LONG
- 1);
155 pos
>>= BITS_PER_LEVEL
;
157 /* Drop bits representing items before first. */
158 hbi
->cur
[i
] = hb
->levels
[i
][pos
] & ~((1UL << bit
) - 1);
160 /* We have already added level i+1, so the lowest set bit has
161 * been processed. Clear it.
163 if (i
!= HBITMAP_LEVELS
- 1) {
164 hbi
->cur
[i
] &= ~(1UL << bit
);
169 bool hbitmap_empty(const HBitmap
*hb
)
171 return hb
->count
== 0;
174 int hbitmap_granularity(const HBitmap
*hb
)
176 return hb
->granularity
;
179 uint64_t hbitmap_count(const HBitmap
*hb
)
181 return hb
->count
<< hb
->granularity
;
184 /* Count the number of set bits between start and end, not accounting for
185 * the granularity. Also an example of how to use hbitmap_iter_next_word.
187 static uint64_t hb_count_between(HBitmap
*hb
, uint64_t start
, uint64_t last
)
191 uint64_t end
= last
+ 1;
195 hbitmap_iter_init(&hbi
, hb
, start
<< hb
->granularity
);
197 pos
= hbitmap_iter_next_word(&hbi
, &cur
);
198 if (pos
>= (end
>> BITS_PER_LEVEL
)) {
201 count
+= ctpopl(cur
);
204 if (pos
== (end
>> BITS_PER_LEVEL
)) {
205 /* Drop bits representing the END-th and subsequent items. */
206 int bit
= end
& (BITS_PER_LONG
- 1);
207 cur
&= (1UL << bit
) - 1;
208 count
+= ctpopl(cur
);
214 /* Setting starts at the last layer and propagates up if an element
217 static inline bool hb_set_elem(unsigned long *elem
, uint64_t start
, uint64_t last
)
222 assert((last
>> BITS_PER_LEVEL
) == (start
>> BITS_PER_LEVEL
));
223 assert(start
<= last
);
225 mask
= 2UL << (last
& (BITS_PER_LONG
- 1));
226 mask
-= 1UL << (start
& (BITS_PER_LONG
- 1));
232 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)...
233 * Returns true if at least one bit is changed. */
234 static bool hb_set_between(HBitmap
*hb
, int level
, uint64_t start
,
237 size_t pos
= start
>> BITS_PER_LEVEL
;
238 size_t lastpos
= last
>> BITS_PER_LEVEL
;
239 bool changed
= false;
244 uint64_t next
= (start
| (BITS_PER_LONG
- 1)) + 1;
245 changed
|= hb_set_elem(&hb
->levels
[level
][i
], start
, next
- 1);
248 next
+= BITS_PER_LONG
;
249 if (++i
== lastpos
) {
252 changed
|= (hb
->levels
[level
][i
] == 0);
253 hb
->levels
[level
][i
] = ~0UL;
256 changed
|= hb_set_elem(&hb
->levels
[level
][i
], start
, last
);
258 /* If there was any change in this layer, we may have to update
261 if (level
> 0 && changed
) {
262 hb_set_between(hb
, level
- 1, pos
, lastpos
);
267 void hbitmap_set(HBitmap
*hb
, uint64_t start
, uint64_t count
)
269 /* Compute range in the last layer. */
271 uint64_t last
= start
+ count
- 1;
273 trace_hbitmap_set(hb
, start
, count
,
274 start
>> hb
->granularity
, last
>> hb
->granularity
);
276 first
= start
>> hb
->granularity
;
277 last
>>= hb
->granularity
;
278 assert(last
< hb
->size
);
279 n
= last
- first
+ 1;
281 hb
->count
+= n
- hb_count_between(hb
, first
, last
);
282 if (hb_set_between(hb
, HBITMAP_LEVELS
- 1, first
, last
) &&
284 hbitmap_set(hb
->meta
, start
, count
);
288 /* Resetting works the other way round: propagate up if the new
291 static inline bool hb_reset_elem(unsigned long *elem
, uint64_t start
, uint64_t last
)
296 assert((last
>> BITS_PER_LEVEL
) == (start
>> BITS_PER_LEVEL
));
297 assert(start
<= last
);
299 mask
= 2UL << (last
& (BITS_PER_LONG
- 1));
300 mask
-= 1UL << (start
& (BITS_PER_LONG
- 1));
301 blanked
= *elem
!= 0 && ((*elem
& ~mask
) == 0);
306 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)...
307 * Returns true if at least one bit is changed. */
308 static bool hb_reset_between(HBitmap
*hb
, int level
, uint64_t start
,
311 size_t pos
= start
>> BITS_PER_LEVEL
;
312 size_t lastpos
= last
>> BITS_PER_LEVEL
;
313 bool changed
= false;
318 uint64_t next
= (start
| (BITS_PER_LONG
- 1)) + 1;
320 /* Here we need a more complex test than when setting bits. Even if
321 * something was changed, we must not blank bits in the upper level
322 * unless the lower-level word became entirely zero. So, remove pos
323 * from the upper-level range if bits remain set.
325 if (hb_reset_elem(&hb
->levels
[level
][i
], start
, next
- 1)) {
333 next
+= BITS_PER_LONG
;
334 if (++i
== lastpos
) {
337 changed
|= (hb
->levels
[level
][i
] != 0);
338 hb
->levels
[level
][i
] = 0UL;
342 /* Same as above, this time for lastpos. */
343 if (hb_reset_elem(&hb
->levels
[level
][i
], start
, last
)) {
349 if (level
> 0 && changed
) {
350 hb_reset_between(hb
, level
- 1, pos
, lastpos
);
357 void hbitmap_reset(HBitmap
*hb
, uint64_t start
, uint64_t count
)
359 /* Compute range in the last layer. */
361 uint64_t last
= start
+ count
- 1;
363 trace_hbitmap_reset(hb
, start
, count
,
364 start
>> hb
->granularity
, last
>> hb
->granularity
);
366 first
= start
>> hb
->granularity
;
367 last
>>= hb
->granularity
;
368 assert(last
< hb
->size
);
370 hb
->count
-= hb_count_between(hb
, first
, last
);
371 if (hb_reset_between(hb
, HBITMAP_LEVELS
- 1, first
, last
) &&
373 hbitmap_set(hb
->meta
, start
, count
);
377 void hbitmap_reset_all(HBitmap
*hb
)
381 /* Same as hbitmap_alloc() except for memset() instead of malloc() */
382 for (i
= HBITMAP_LEVELS
; --i
>= 1; ) {
383 memset(hb
->levels
[i
], 0, hb
->sizes
[i
] * sizeof(unsigned long));
386 hb
->levels
[0][0] = 1UL << (BITS_PER_LONG
- 1);
390 bool hbitmap_get(const HBitmap
*hb
, uint64_t item
)
392 /* Compute position and bit in the last layer. */
393 uint64_t pos
= item
>> hb
->granularity
;
394 unsigned long bit
= 1UL << (pos
& (BITS_PER_LONG
- 1));
395 assert(pos
< hb
->size
);
397 return (hb
->levels
[HBITMAP_LEVELS
- 1][pos
>> BITS_PER_LEVEL
] & bit
) != 0;
400 uint64_t hbitmap_serialization_granularity(const HBitmap
*hb
)
402 /* Require at least 64 bit granularity to be safe on both 64 bit and 32 bit
404 return 64 << hb
->granularity
;
407 /* Start should be aligned to serialization granularity, chunk size should be
408 * aligned to serialization granularity too, except for last chunk.
410 static void serialization_chunk(const HBitmap
*hb
,
411 uint64_t start
, uint64_t count
,
412 unsigned long **first_el
, uint64_t *el_count
)
414 uint64_t last
= start
+ count
- 1;
415 uint64_t gran
= hbitmap_serialization_granularity(hb
);
417 assert((start
& (gran
- 1)) == 0);
418 assert((last
>> hb
->granularity
) < hb
->size
);
419 if ((last
>> hb
->granularity
) != hb
->size
- 1) {
420 assert((count
& (gran
- 1)) == 0);
423 start
= (start
>> hb
->granularity
) >> BITS_PER_LEVEL
;
424 last
= (last
>> hb
->granularity
) >> BITS_PER_LEVEL
;
426 *first_el
= &hb
->levels
[HBITMAP_LEVELS
- 1][start
];
427 *el_count
= last
- start
+ 1;
430 uint64_t hbitmap_serialization_size(const HBitmap
*hb
,
431 uint64_t start
, uint64_t count
)
439 serialization_chunk(hb
, start
, count
, &cur
, &el_count
);
441 return el_count
* sizeof(unsigned long);
444 void hbitmap_serialize_part(const HBitmap
*hb
, uint8_t *buf
,
445 uint64_t start
, uint64_t count
)
448 unsigned long *cur
, *end
;
453 serialization_chunk(hb
, start
, count
, &cur
, &el_count
);
454 end
= cur
+ el_count
;
458 (BITS_PER_LONG
== 32 ? cpu_to_le32(*cur
) : cpu_to_le64(*cur
));
460 memcpy(buf
, &el
, sizeof(el
));
466 void hbitmap_deserialize_part(HBitmap
*hb
, uint8_t *buf
,
467 uint64_t start
, uint64_t count
,
471 unsigned long *cur
, *end
;
476 serialization_chunk(hb
, start
, count
, &cur
, &el_count
);
477 end
= cur
+ el_count
;
480 memcpy(cur
, buf
, sizeof(*cur
));
482 if (BITS_PER_LONG
== 32) {
483 le32_to_cpus((uint32_t *)cur
);
485 le64_to_cpus((uint64_t *)cur
);
488 buf
+= sizeof(unsigned long);
492 hbitmap_deserialize_finish(hb
);
496 void hbitmap_deserialize_zeroes(HBitmap
*hb
, uint64_t start
, uint64_t count
,
500 unsigned long *first
;
505 serialization_chunk(hb
, start
, count
, &first
, &el_count
);
507 memset(first
, 0, el_count
* sizeof(unsigned long));
509 hbitmap_deserialize_finish(hb
);
513 void hbitmap_deserialize_finish(HBitmap
*bitmap
)
515 int64_t i
, size
, prev_size
;
518 /* restore levels starting from penultimate to zero level, assuming
519 * that the last level is ok */
520 size
= MAX((bitmap
->size
+ BITS_PER_LONG
- 1) >> BITS_PER_LEVEL
, 1);
521 for (lev
= HBITMAP_LEVELS
- 1; lev
-- > 0; ) {
523 size
= MAX((size
+ BITS_PER_LONG
- 1) >> BITS_PER_LEVEL
, 1);
524 memset(bitmap
->levels
[lev
], 0, size
* sizeof(unsigned long));
526 for (i
= 0; i
< prev_size
; ++i
) {
527 if (bitmap
->levels
[lev
+ 1][i
]) {
528 bitmap
->levels
[lev
][i
>> BITS_PER_LEVEL
] |=
529 1UL << (i
& (BITS_PER_LONG
- 1));
534 bitmap
->levels
[0][0] |= 1UL << (BITS_PER_LONG
- 1);
537 void hbitmap_free(HBitmap
*hb
)
541 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
542 g_free(hb
->levels
[i
]);
547 HBitmap
*hbitmap_alloc(uint64_t size
, int granularity
)
549 HBitmap
*hb
= g_new0(struct HBitmap
, 1);
552 assert(granularity
>= 0 && granularity
< 64);
553 size
= (size
+ (1ULL << granularity
) - 1) >> granularity
;
554 assert(size
<= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE
));
557 hb
->granularity
= granularity
;
558 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
559 size
= MAX((size
+ BITS_PER_LONG
- 1) >> BITS_PER_LEVEL
, 1);
561 hb
->levels
[i
] = g_new0(unsigned long, size
);
564 /* We necessarily have free bits in level 0 due to the definition
565 * of HBITMAP_LEVELS, so use one for a sentinel. This speeds up
566 * hbitmap_iter_skip_words.
569 hb
->levels
[0][0] |= 1UL << (BITS_PER_LONG
- 1);
573 void hbitmap_truncate(HBitmap
*hb
, uint64_t size
)
577 uint64_t num_elements
= size
;
580 /* Size comes in as logical elements, adjust for granularity. */
581 size
= (size
+ (1ULL << hb
->granularity
) - 1) >> hb
->granularity
;
582 assert(size
<= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE
));
583 shrink
= size
< hb
->size
;
585 /* bit sizes are identical; nothing to do. */
586 if (size
== hb
->size
) {
590 /* If we're losing bits, let's clear those bits before we invalidate all of
591 * our invariants. This helps keep the bitcount consistent, and will prevent
592 * us from carrying around garbage bits beyond the end of the map.
595 /* Don't clear partial granularity groups;
596 * start at the first full one. */
597 uint64_t start
= QEMU_ALIGN_UP(num_elements
, 1 << hb
->granularity
);
598 uint64_t fix_count
= (hb
->size
<< hb
->granularity
) - start
;
601 hbitmap_reset(hb
, start
, fix_count
);
605 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
606 size
= MAX(BITS_TO_LONGS(size
), 1);
607 if (hb
->sizes
[i
] == size
) {
612 hb
->levels
[i
] = g_realloc(hb
->levels
[i
], size
* sizeof(unsigned long));
614 memset(&hb
->levels
[i
][old
], 0x00,
615 (size
- old
) * sizeof(*hb
->levels
[i
]));
619 hbitmap_truncate(hb
->meta
, hb
->size
<< hb
->granularity
);
625 * Given HBitmaps A and B, let A := A (BITOR) B.
626 * Bitmap B will not be modified.
628 * @return true if the merge was successful,
629 * false if it was not attempted.
631 bool hbitmap_merge(HBitmap
*a
, const HBitmap
*b
)
636 if ((a
->size
!= b
->size
) || (a
->granularity
!= b
->granularity
)) {
640 if (hbitmap_count(b
) == 0) {
644 /* This merge is O(size), as BITS_PER_LONG and HBITMAP_LEVELS are constant.
645 * It may be possible to improve running times for sparsely populated maps
646 * by using hbitmap_iter_next, but this is suboptimal for dense maps.
648 for (i
= HBITMAP_LEVELS
- 1; i
>= 0; i
--) {
649 for (j
= 0; j
< a
->sizes
[i
]; j
++) {
650 a
->levels
[i
][j
] |= b
->levels
[i
][j
];
657 HBitmap
*hbitmap_create_meta(HBitmap
*hb
, int chunk_size
)
659 assert(!(chunk_size
& (chunk_size
- 1)));
661 hb
->meta
= hbitmap_alloc(hb
->size
<< hb
->granularity
,
662 hb
->granularity
+ ctz32(chunk_size
));
666 void hbitmap_free_meta(HBitmap
*hb
)
669 hbitmap_free(hb
->meta
);