summaryrefslogtreecommitdiffstats
path: root/util/hbitmap.c
blob: ab139717f57168b71119b0ce24ecfd076a4c06eb (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
/*
 * 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];
};

/* 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);
}

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->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;
}
OpenPOWER on IntegriCloud