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"
14 #include "qemu/hbitmap.h"
15 #include "qemu/host-utils.h"
18 /* HBitmaps provides an array of bits. The bits are stored as usual in an
19 * array of unsigned longs, but HBitmap is also optimized to provide fast
20 * iteration over set bits; going from one bit to the next is O(logB n)
21 * worst case, with B = sizeof(long) * CHAR_BIT: the result is low enough
22 * that the number of levels is in fact fixed.
24 * In order to do this, it stacks multiple bitmaps with progressively coarser
25 * granularity; in all levels except the last, bit N is set iff the N-th
26 * unsigned long is nonzero in the immediately next level. When iteration
27 * completes on the last level it can examine the 2nd-last level to quickly
28 * skip entire words, and even do so recursively to skip blocks of 64 words or
29 * powers thereof (32 on 32-bit machines).
31 * Given an index in the bitmap, it can be split in group of bits like
32 * this (for the 64-bit case):
34 * bits 0-57 => word in the last bitmap | bits 58-63 => bit in the word
35 * bits 0-51 => word in the 2nd-last bitmap | bits 52-57 => bit in the word
36 * bits 0-45 => word in the 3rd-last bitmap | bits 46-51 => bit in the word
38 * So it is easy to move up simply by shifting the index right by
39 * log2(BITS_PER_LONG) bits. To move down, you shift the index left
40 * similarly, and add the word index within the group. Iteration uses
41 * ffs (find first set bit) to find the next word to examine; this
42 * operation can be done in constant time in most current architectures.
44 * Setting or clearing a range of m bits on all levels, the work to perform
45 * is O(m + m/W + m/W^2 + ...), which is O(m) like on a regular bitmap.
47 * When iterating on a bitmap, each bit (on any level) is only visited
48 * once. Hence, The total cost of visiting a bitmap with m bits in it is
49 * the number of bits that are set in all bitmaps. Unless the bitmap is
50 * extremely sparse, this is also O(m + m/W + m/W^2 + ...), so the amortized
51 * cost of advancing from one bit to the next is usually constant (worst case
52 * O(logB n) as in the non-amortized complexity).
56 /* Number of total bits in the bottom level. */
59 /* Number of set bits in the bottom level. */
62 /* A scaling factor. Given a granularity of G, each bit in the bitmap will
63 * will actually represent a group of 2^G elements. Each operation on a
64 * range of bits first rounds the bits to determine which group they land
65 * in, and then affect the entire page; iteration will only visit the first
66 * bit of each group. Here is an example of operations in a size-16,
67 * granularity-1 HBitmap:
69 * initial state 00000000
70 * set(start=0, count=9) 11111000 (iter: 0, 2, 4, 6, 8)
71 * reset(start=1, count=3) 00111000 (iter: 4, 6, 8)
72 * set(start=9, count=2) 00111100 (iter: 4, 6, 8, 10)
73 * reset(start=5, count=5) 00000000
75 * From an implementation point of view, when setting or resetting bits,
76 * the bitmap will scale bit numbers right by this amount of bits. When
77 * iterating, the bitmap will scale bit numbers left by this amount of
82 /* A number of progressively less coarse bitmaps (i.e. level 0 is the
83 * coarsest). Each bit in level N represents a word in level N+1 that
84 * has a set bit, except the last level where each bit represents the
87 * Note that all bitmaps have the same number of levels. Even a 1-bit
88 * bitmap will still allocate HBITMAP_LEVELS arrays.
90 unsigned long *levels
[HBITMAP_LEVELS
];
92 /* The length of each levels[] array. */
93 uint64_t sizes
[HBITMAP_LEVELS
];
96 /* Advance hbi to the next nonzero word and return it. hbi->pos
97 * is updated. Returns zero if we reach the end of the bitmap.
99 unsigned long hbitmap_iter_skip_words(HBitmapIter
*hbi
)
101 size_t pos
= hbi
->pos
;
102 const HBitmap
*hb
= hbi
->hb
;
103 unsigned i
= HBITMAP_LEVELS
- 1;
108 pos
>>= BITS_PER_LEVEL
;
111 /* Check for end of iteration. We always use fewer than BITS_PER_LONG
112 * bits in the level 0 bitmap; thus we can repurpose the most significant
113 * bit as a sentinel. The sentinel is set in hbitmap_alloc and ensures
114 * that the above loop ends even without an explicit check on i.
117 if (i
== 0 && cur
== (1UL << (BITS_PER_LONG
- 1))) {
120 for (; i
< HBITMAP_LEVELS
- 1; i
++) {
121 /* Shift back pos to the left, matching the right shifts above.
122 * The index of this word's least significant set bit provides
123 * the low-order bits.
126 pos
= (pos
<< BITS_PER_LEVEL
) + ctzl(cur
);
127 hbi
->cur
[i
] = cur
& (cur
- 1);
129 /* Set up next level for iteration. */
130 cur
= hb
->levels
[i
+ 1][pos
];
134 trace_hbitmap_iter_skip_words(hbi
->hb
, hbi
, pos
, cur
);
140 void hbitmap_iter_init(HBitmapIter
*hbi
, const HBitmap
*hb
, uint64_t first
)
146 pos
= first
>> hb
->granularity
;
147 assert(pos
< hb
->size
);
148 hbi
->pos
= pos
>> BITS_PER_LEVEL
;
149 hbi
->granularity
= hb
->granularity
;
151 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
152 bit
= pos
& (BITS_PER_LONG
- 1);
153 pos
>>= BITS_PER_LEVEL
;
155 /* Drop bits representing items before first. */
156 hbi
->cur
[i
] = hb
->levels
[i
][pos
] & ~((1UL << bit
) - 1);
158 /* We have already added level i+1, so the lowest set bit has
159 * been processed. Clear it.
161 if (i
!= HBITMAP_LEVELS
- 1) {
162 hbi
->cur
[i
] &= ~(1UL << bit
);
167 bool hbitmap_empty(const HBitmap
*hb
)
169 return hb
->count
== 0;
172 int hbitmap_granularity(const HBitmap
*hb
)
174 return hb
->granularity
;
177 uint64_t hbitmap_count(const HBitmap
*hb
)
179 return hb
->count
<< hb
->granularity
;
182 /* Count the number of set bits between start and end, not accounting for
183 * the granularity. Also an example of how to use hbitmap_iter_next_word.
185 static uint64_t hb_count_between(HBitmap
*hb
, uint64_t start
, uint64_t last
)
189 uint64_t end
= last
+ 1;
193 hbitmap_iter_init(&hbi
, hb
, start
<< hb
->granularity
);
195 pos
= hbitmap_iter_next_word(&hbi
, &cur
);
196 if (pos
>= (end
>> BITS_PER_LEVEL
)) {
199 count
+= ctpopl(cur
);
202 if (pos
== (end
>> BITS_PER_LEVEL
)) {
203 /* Drop bits representing the END-th and subsequent items. */
204 int bit
= end
& (BITS_PER_LONG
- 1);
205 cur
&= (1UL << bit
) - 1;
206 count
+= ctpopl(cur
);
212 /* Setting starts at the last layer and propagates up if an element
213 * changes from zero to non-zero.
215 static inline bool hb_set_elem(unsigned long *elem
, uint64_t start
, uint64_t last
)
220 assert((last
>> BITS_PER_LEVEL
) == (start
>> BITS_PER_LEVEL
));
221 assert(start
<= last
);
223 mask
= 2UL << (last
& (BITS_PER_LONG
- 1));
224 mask
-= 1UL << (start
& (BITS_PER_LONG
- 1));
225 changed
= (*elem
== 0);
230 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
231 static void hb_set_between(HBitmap
*hb
, int level
, uint64_t start
, uint64_t last
)
233 size_t pos
= start
>> BITS_PER_LEVEL
;
234 size_t lastpos
= last
>> BITS_PER_LEVEL
;
235 bool changed
= false;
240 uint64_t next
= (start
| (BITS_PER_LONG
- 1)) + 1;
241 changed
|= hb_set_elem(&hb
->levels
[level
][i
], start
, next
- 1);
244 next
+= BITS_PER_LONG
;
245 if (++i
== lastpos
) {
248 changed
|= (hb
->levels
[level
][i
] == 0);
249 hb
->levels
[level
][i
] = ~0UL;
252 changed
|= hb_set_elem(&hb
->levels
[level
][i
], start
, last
);
254 /* If there was any change in this layer, we may have to update
257 if (level
> 0 && changed
) {
258 hb_set_between(hb
, level
- 1, pos
, lastpos
);
262 void hbitmap_set(HBitmap
*hb
, uint64_t start
, uint64_t count
)
264 /* Compute range in the last layer. */
265 uint64_t last
= start
+ count
- 1;
267 trace_hbitmap_set(hb
, start
, count
,
268 start
>> hb
->granularity
, last
>> hb
->granularity
);
270 start
>>= hb
->granularity
;
271 last
>>= hb
->granularity
;
272 count
= last
- start
+ 1;
274 hb
->count
+= count
- hb_count_between(hb
, start
, last
);
275 hb_set_between(hb
, HBITMAP_LEVELS
- 1, start
, last
);
278 /* Resetting works the other way round: propagate up if the new
281 static inline bool hb_reset_elem(unsigned long *elem
, uint64_t start
, uint64_t last
)
286 assert((last
>> BITS_PER_LEVEL
) == (start
>> BITS_PER_LEVEL
));
287 assert(start
<= last
);
289 mask
= 2UL << (last
& (BITS_PER_LONG
- 1));
290 mask
-= 1UL << (start
& (BITS_PER_LONG
- 1));
291 blanked
= *elem
!= 0 && ((*elem
& ~mask
) == 0);
296 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
297 static void hb_reset_between(HBitmap
*hb
, int level
, uint64_t start
, uint64_t last
)
299 size_t pos
= start
>> BITS_PER_LEVEL
;
300 size_t lastpos
= last
>> BITS_PER_LEVEL
;
301 bool changed
= false;
306 uint64_t next
= (start
| (BITS_PER_LONG
- 1)) + 1;
308 /* Here we need a more complex test than when setting bits. Even if
309 * something was changed, we must not blank bits in the upper level
310 * unless the lower-level word became entirely zero. So, remove pos
311 * from the upper-level range if bits remain set.
313 if (hb_reset_elem(&hb
->levels
[level
][i
], start
, next
- 1)) {
321 next
+= BITS_PER_LONG
;
322 if (++i
== lastpos
) {
325 changed
|= (hb
->levels
[level
][i
] != 0);
326 hb
->levels
[level
][i
] = 0UL;
330 /* Same as above, this time for lastpos. */
331 if (hb_reset_elem(&hb
->levels
[level
][i
], start
, last
)) {
337 if (level
> 0 && changed
) {
338 hb_reset_between(hb
, level
- 1, pos
, lastpos
);
342 void hbitmap_reset(HBitmap
*hb
, uint64_t start
, uint64_t count
)
344 /* Compute range in the last layer. */
345 uint64_t last
= start
+ count
- 1;
347 trace_hbitmap_reset(hb
, start
, count
,
348 start
>> hb
->granularity
, last
>> hb
->granularity
);
350 start
>>= hb
->granularity
;
351 last
>>= hb
->granularity
;
353 hb
->count
-= hb_count_between(hb
, start
, last
);
354 hb_reset_between(hb
, HBITMAP_LEVELS
- 1, start
, last
);
357 void hbitmap_reset_all(HBitmap
*hb
)
361 /* Same as hbitmap_alloc() except for memset() instead of malloc() */
362 for (i
= HBITMAP_LEVELS
; --i
>= 1; ) {
363 memset(hb
->levels
[i
], 0, hb
->sizes
[i
] * sizeof(unsigned long));
366 hb
->levels
[0][0] = 1UL << (BITS_PER_LONG
- 1);
370 bool hbitmap_get(const HBitmap
*hb
, uint64_t item
)
372 /* Compute position and bit in the last layer. */
373 uint64_t pos
= item
>> hb
->granularity
;
374 unsigned long bit
= 1UL << (pos
& (BITS_PER_LONG
- 1));
376 return (hb
->levels
[HBITMAP_LEVELS
- 1][pos
>> BITS_PER_LEVEL
] & bit
) != 0;
379 void hbitmap_free(HBitmap
*hb
)
382 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
383 g_free(hb
->levels
[i
]);
388 HBitmap
*hbitmap_alloc(uint64_t size
, int granularity
)
390 HBitmap
*hb
= g_new0(struct HBitmap
, 1);
393 assert(granularity
>= 0 && granularity
< 64);
394 size
= (size
+ (1ULL << granularity
) - 1) >> granularity
;
395 assert(size
<= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE
));
398 hb
->granularity
= granularity
;
399 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
400 size
= MAX((size
+ BITS_PER_LONG
- 1) >> BITS_PER_LEVEL
, 1);
402 hb
->levels
[i
] = g_new0(unsigned long, size
);
405 /* We necessarily have free bits in level 0 due to the definition
406 * of HBITMAP_LEVELS, so use one for a sentinel. This speeds up
407 * hbitmap_iter_skip_words.
410 hb
->levels
[0][0] |= 1UL << (BITS_PER_LONG
- 1);
414 void hbitmap_truncate(HBitmap
*hb
, uint64_t size
)
418 uint64_t num_elements
= size
;
421 /* Size comes in as logical elements, adjust for granularity. */
422 size
= (size
+ (1ULL << hb
->granularity
) - 1) >> hb
->granularity
;
423 assert(size
<= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE
));
424 shrink
= size
< hb
->size
;
426 /* bit sizes are identical; nothing to do. */
427 if (size
== hb
->size
) {
431 /* If we're losing bits, let's clear those bits before we invalidate all of
432 * our invariants. This helps keep the bitcount consistent, and will prevent
433 * us from carrying around garbage bits beyond the end of the map.
436 /* Don't clear partial granularity groups;
437 * start at the first full one. */
438 uint64_t start
= QEMU_ALIGN_UP(num_elements
, 1 << hb
->granularity
);
439 uint64_t fix_count
= (hb
->size
<< hb
->granularity
) - start
;
442 hbitmap_reset(hb
, start
, fix_count
);
446 for (i
= HBITMAP_LEVELS
; i
-- > 0; ) {
447 size
= MAX(BITS_TO_LONGS(size
), 1);
448 if (hb
->sizes
[i
] == size
) {
453 hb
->levels
[i
] = g_realloc(hb
->levels
[i
], size
* sizeof(unsigned long));
455 memset(&hb
->levels
[i
][old
], 0x00,
456 (size
- old
) * sizeof(*hb
->levels
[i
]));
463 * Given HBitmaps A and B, let A := A (BITOR) B.
464 * Bitmap B will not be modified.
466 * @return true if the merge was successful,
467 * false if it was not attempted.
469 bool hbitmap_merge(HBitmap
*a
, const HBitmap
*b
)
474 if ((a
->size
!= b
->size
) || (a
->granularity
!= b
->granularity
)) {
478 if (hbitmap_count(b
) == 0) {
482 /* This merge is O(size), as BITS_PER_LONG and HBITMAP_LEVELS are constant.
483 * It may be possible to improve running times for sparsely populated maps
484 * by using hbitmap_iter_next, but this is suboptimal for dense maps.
486 for (i
= HBITMAP_LEVELS
- 1; i
>= 0; i
--) {
487 for (j
= 0; j
< a
->sizes
[i
]; j
++) {
488 a
->levels
[i
][j
] |= b
->levels
[i
][j
];