util/hbitmap.c

   1 /*
   2  * Hierarchical Bitmap Data Type
   3  *
   4  * Copyright Red Hat, Inc., 2012
   5  *
   6  * Author: Paolo Bonzini <pbonzini@redhat.com>
   7  *
   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.
  10  */
  11
  12 #include <string.h>
  13 #include <glib.h>
  14 #include <assert.h>
  15 #include "qemu/osdep.h"
  16 #include "qemu/hbitmap.h"
  17 #include "qemu/host-utils.h"
  18 #include "trace.h"
  19
  20 /* HBitmaps provides an array of bits.  The bits are stored as usual in an
  21  * array of unsigned longs, but HBitmap is also optimized to provide fast
  22  * iteration over set bits; going from one bit to the next is O(logB n)
  23  * worst case, with B = sizeof(long) * CHAR_BIT: the result is low enough
  24  * that the number of levels is in fact fixed.
  25  *
  26  * In order to do this, it stacks multiple bitmaps with progressively coarser
  27  * granularity; in all levels except the last, bit N is set iff the N-th
  28  * unsigned long is nonzero in the immediately next level.  When iteration
  29  * completes on the last level it can examine the 2nd-last level to quickly
  30  * skip entire words, and even do so recursively to skip blocks of 64 words or
  31  * powers thereof (32 on 32-bit machines).
  32  *
  33  * Given an index in the bitmap, it can be split in group of bits like
  34  * this (for the 64-bit case):
  35  *
  36  *   bits 0-57 => word in the last bitmap     | bits 58-63 => bit in the word
  37  *   bits 0-51 => word in the 2nd-last bitmap | bits 52-57 => bit in the word
  38  *   bits 0-45 => word in the 3rd-last bitmap | bits 46-51 => bit in the word
  39  *
  40  * So it is easy to move up simply by shifting the index right by
  41  * log2(BITS_PER_LONG) bits.  To move down, you shift the index left
  42  * similarly, and add the word index within the group.  Iteration uses
  43  * ffs (find first set bit) to find the next word to examine; this
  44  * operation can be done in constant time in most current architectures.
  45  *
  46  * Setting or clearing a range of m bits on all levels, the work to perform
  47  * is O(m + m/W + m/W^2 + ...), which is O(m) like on a regular bitmap.
  48  *
  49  * When iterating on a bitmap, each bit (on any level) is only visited
  50  * once.  Hence, The total cost of visiting a bitmap with m bits in it is
  51  * the number of bits that are set in all bitmaps.  Unless the bitmap is
  52  * extremely sparse, this is also O(m + m/W + m/W^2 + ...), so the amortized
  53  * cost of advancing from one bit to the next is usually constant (worst case
  54  * O(logB n) as in the non-amortized complexity).
  55  */
  56
  57 struct HBitmap {
  58     /* Number of total bits in the bottom level.  */
  59     uint64_t size;
  60
  61     /* Number of set bits in the bottom level.  */
  62     uint64_t count;
  63
  64     /* A scaling factor.  Given a granularity of G, each bit in the bitmap will
  65      * will actually represent a group of 2^G elements.  Each operation on a
  66      * range of bits first rounds the bits to determine which group they land
  67      * in, and then affect the entire page; iteration will only visit the first
  68      * bit of each group.  Here is an example of operations in a size-16,
  69      * granularity-1 HBitmap:
  70      *
  71      *    initial state            00000000
  72      *    set(start=0, count=9)    11111000 (iter: 0, 2, 4, 6, 8)
  73      *    reset(start=1, count=3)  00111000 (iter: 4, 6, 8)
  74      *    set(start=9, count=2)    00111100 (iter: 4, 6, 8, 10)
  75      *    reset(start=5, count=5)  00000000
  76      *
  77      * From an implementation point of view, when setting or resetting bits,
  78      * the bitmap will scale bit numbers right by this amount of bits.  When
  79      * iterating, the bitmap will scale bit numbers left by this amount of
  80      * bits.
  81      */
  82     int granularity;
  83
  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
  87      * actual bitmap.
  88      *
  89      * Note that all bitmaps have the same number of levels.  Even a 1-bit
  90      * bitmap will still allocate HBITMAP_LEVELS arrays.
  91      */
  92     unsigned long *levels[HBITMAP_LEVELS];
  93 };
  94
  95 static inline int popcountl(unsigned long l)
  96 {
  97     return BITS_PER_LONG == 32 ? ctpop32(l) : ctpop64(l);
  98 }
  99
 100 /* Advance hbi to the next nonzero word and return it.  hbi->pos
 101  * is updated.  Returns zero if we reach the end of the bitmap.
 102  */
 103 unsigned long hbitmap_iter_skip_words(HBitmapIter *hbi)
 104 {
 105     size_t pos = hbi->pos;
 106     const HBitmap *hb = hbi->hb;
 107     unsigned i = HBITMAP_LEVELS - 1;
 108
 109     unsigned long cur;
 110     do {
 111         cur = hbi->cur[--i];
 112         pos >>= BITS_PER_LEVEL;
 113     } while (cur == 0);
 114
 115     /* Check for end of iteration.  We always use fewer than BITS_PER_LONG
 116      * bits in the level 0 bitmap; thus we can repurpose the most significant
 117      * bit as a sentinel.  The sentinel is set in hbitmap_alloc and ensures
 118      * that the above loop ends even without an explicit check on i.
 119      */
 120
 121     if (i == 0 && cur == (1UL << (BITS_PER_LONG - 1))) {
 122         return 0;
 123     }
 124     for (; i < HBITMAP_LEVELS - 1; i++) {
 125         /* Shift back pos to the left, matching the right shifts above.
 126          * The index of this word's least significant set bit provides
 127          * the low-order bits.
 128          */
 129         pos = (pos << BITS_PER_LEVEL) + ffsl(cur) - 1;
 130         hbi->cur[i] = cur & (cur - 1);
 131
 132         /* Set up next level for iteration.  */
 133         cur = hb->levels[i + 1][pos];
 134     }
 135
 136     hbi->pos = pos;
 137     trace_hbitmap_iter_skip_words(hbi->hb, hbi, pos, cur);
 138
 139     assert(cur);
 140     return cur;
 141 }
 142
 143 void hbitmap_iter_init(HBitmapIter *hbi, const HBitmap *hb, uint64_t first)
 144 {
 145     unsigned i, bit;
 146     uint64_t pos;
 147
 148     hbi->hb = hb;
 149     pos = first >> hb->granularity;
 150     assert(pos < hb->size);
 151     hbi->pos = pos >> BITS_PER_LEVEL;
 152     hbi->granularity = hb->granularity;
 153
 154     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 155         bit = pos & (BITS_PER_LONG - 1);
 156         pos >>= BITS_PER_LEVEL;
 157
 158         /* Drop bits representing items before first.  */
 159         hbi->cur[i] = hb->levels[i][pos] & ~((1UL << bit) - 1);
 160
 161         /* We have already added level i+1, so the lowest set bit has
 162          * been processed.  Clear it.
 163          */
 164         if (i != HBITMAP_LEVELS - 1) {
 165             hbi->cur[i] &= ~(1UL << bit);
 166         }
 167     }
 168 }
 169
 170 bool hbitmap_empty(const HBitmap *hb)
 171 {
 172     return hb->count == 0;
 173 }
 174
 175 int hbitmap_granularity(const HBitmap *hb)
 176 {
 177     return hb->granularity;
 178 }
 179
 180 uint64_t hbitmap_count(const HBitmap *hb)
 181 {
 182     return hb->count << hb->granularity;
 183 }
 184
 185 /* Count the number of set bits between start and end, not accounting for
 186  * the granularity.  Also an example of how to use hbitmap_iter_next_word.
 187  */
 188 static uint64_t hb_count_between(HBitmap *hb, uint64_t start, uint64_t last)
 189 {
 190     HBitmapIter hbi;
 191     uint64_t count = 0;
 192     uint64_t end = last + 1;
 193     unsigned long cur;
 194     size_t pos;
 195
 196     hbitmap_iter_init(&hbi, hb, start << hb->granularity);
 197     for (;;) {
 198         pos = hbitmap_iter_next_word(&hbi, &cur);
 199         if (pos >= (end >> BITS_PER_LEVEL)) {
 200             break;
 201         }
 202         count += popcountl(cur);
 203     }
 204
 205     if (pos == (end >> BITS_PER_LEVEL)) {
 206         /* Drop bits representing the END-th and subsequent items.  */
 207         int bit = end & (BITS_PER_LONG - 1);
 208         cur &= (1UL << bit) - 1;
 209         count += popcountl(cur);
 210     }
 211
 212     return count;
 213 }
 214
 215 /* Setting starts at the last layer and propagates up if an element
 216  * changes from zero to non-zero.
 217  */
 218 static inline bool hb_set_elem(unsigned long *elem, uint64_t start, uint64_t last)
 219 {
 220     unsigned long mask;
 221     bool changed;
 222
 223     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
 224     assert(start <= last);
 225
 226     mask = 2UL << (last & (BITS_PER_LONG - 1));
 227     mask -= 1UL << (start & (BITS_PER_LONG - 1));
 228     changed = (*elem == 0);
 229     *elem |= mask;
 230     return changed;
 231 }
 232
 233 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
 234 static void hb_set_between(HBitmap *hb, int level, uint64_t start, uint64_t last)
 235 {
 236     size_t pos = start >> BITS_PER_LEVEL;
 237     size_t lastpos = last >> BITS_PER_LEVEL;
 238     bool changed = false;
 239     size_t i;
 240
 241     i = pos;
 242     if (i < lastpos) {
 243         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
 244         changed |= hb_set_elem(&hb->levels[level][i], start, next - 1);
 245         for (;;) {
 246             start = next;
 247             next += BITS_PER_LONG;
 248             if (++i == lastpos) {
 249                 break;
 250             }
 251             changed |= (hb->levels[level][i] == 0);
 252             hb->levels[level][i] = ~0UL;
 253         }
 254     }
 255     changed |= hb_set_elem(&hb->levels[level][i], start, last);
 256
 257     /* If there was any change in this layer, we may have to update
 258      * the one above.
 259      */
 260     if (level > 0 && changed) {
 261         hb_set_between(hb, level - 1, pos, lastpos);
 262     }
 263 }
 264
 265 void hbitmap_set(HBitmap *hb, uint64_t start, uint64_t count)
 266 {
 267     /* Compute range in the last layer.  */
 268     uint64_t last = start + count - 1;
 269
 270     trace_hbitmap_set(hb, start, count,
 271                       start >> hb->granularity, last >> hb->granularity);
 272
 273     start >>= hb->granularity;
 274     last >>= hb->granularity;
 275     count = last - start + 1;
 276
 277     hb->count += count - hb_count_between(hb, start, last);
 278     hb_set_between(hb, HBITMAP_LEVELS - 1, start, last);
 279 }
 280
 281 /* Resetting works the other way round: propagate up if the new
 282  * value is zero.
 283  */
 284 static inline bool hb_reset_elem(unsigned long *elem, uint64_t start, uint64_t last)
 285 {
 286     unsigned long mask;
 287     bool blanked;
 288
 289     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
 290     assert(start <= last);
 291
 292     mask = 2UL << (last & (BITS_PER_LONG - 1));
 293     mask -= 1UL << (start & (BITS_PER_LONG - 1));
 294     blanked = *elem != 0 && ((*elem & ~mask) == 0);
 295     *elem &= ~mask;
 296     return blanked;
 297 }
 298
 299 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
 300 static void hb_reset_between(HBitmap *hb, int level, uint64_t start, uint64_t last)
 301 {
 302     size_t pos = start >> BITS_PER_LEVEL;
 303     size_t lastpos = last >> BITS_PER_LEVEL;
 304     bool changed = false;
 305     size_t i;
 306
 307     i = pos;
 308     if (i < lastpos) {
 309         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
 310
 311         /* Here we need a more complex test than when setting bits.  Even if
 312          * something was changed, we must not blank bits in the upper level
 313          * unless the lower-level word became entirely zero.  So, remove pos
 314          * from the upper-level range if bits remain set.
 315          */
 316         if (hb_reset_elem(&hb->levels[level][i], start, next - 1)) {
 317             changed = true;
 318         } else {
 319             pos++;
 320         }
 321
 322         for (;;) {
 323             start = next;
 324             next += BITS_PER_LONG;
 325             if (++i == lastpos) {
 326                 break;
 327             }
 328             changed |= (hb->levels[level][i] != 0);
 329             hb->levels[level][i] = 0UL;
 330         }
 331     }
 332
 333     /* Same as above, this time for lastpos.  */
 334     if (hb_reset_elem(&hb->levels[level][i], start, last)) {
 335         changed = true;
 336     } else {
 337         lastpos--;
 338     }
 339
 340     if (level > 0 && changed) {
 341         hb_reset_between(hb, level - 1, pos, lastpos);
 342     }
 343 }
 344
 345 void hbitmap_reset(HBitmap *hb, uint64_t start, uint64_t count)
 346 {
 347     /* Compute range in the last layer.  */
 348     uint64_t last = start + count - 1;
 349
 350     trace_hbitmap_reset(hb, start, count,
 351                         start >> hb->granularity, last >> hb->granularity);
 352
 353     start >>= hb->granularity;
 354     last >>= hb->granularity;
 355
 356     hb->count -= hb_count_between(hb, start, last);
 357     hb_reset_between(hb, HBITMAP_LEVELS - 1, start, last);
 358 }
 359
 360 bool hbitmap_get(const HBitmap *hb, uint64_t item)
 361 {
 362     /* Compute position and bit in the last layer.  */
 363     uint64_t pos = item >> hb->granularity;
 364     unsigned long bit = 1UL << (pos & (BITS_PER_LONG - 1));
 365
 366     return (hb->levels[HBITMAP_LEVELS - 1][pos >> BITS_PER_LEVEL] & bit) != 0;
 367 }
 368
 369 void hbitmap_free(HBitmap *hb)
 370 {
 371     unsigned i;
 372     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 373         g_free(hb->levels[i]);
 374     }
 375     g_free(hb);
 376 }
 377
 378 HBitmap *hbitmap_alloc(uint64_t size, int granularity)
 379 {
 380     HBitmap *hb = g_malloc0(sizeof (struct HBitmap));
 381     unsigned i;
 382
 383     assert(granularity >= 0 && granularity < 64);
 384     size = (size + (1ULL << granularity) - 1) >> granularity;
 385     assert(size <= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE));
 386
 387     hb->size = size;
 388     hb->granularity = granularity;
 389     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 390         size = MAX((size + BITS_PER_LONG - 1) >> BITS_PER_LEVEL, 1);
 391         hb->levels[i] = g_malloc0(size * sizeof(unsigned long));
 392     }
 393
 394     /* We necessarily have free bits in level 0 due to the definition
 395      * of HBITMAP_LEVELS, so use one for a sentinel.  This speeds up
 396      * hbitmap_iter_skip_words.
 397      */
 398     assert(size == 1);
 399     hb->levels[0][0] |= 1UL << (BITS_PER_LONG - 1);
 400     return hb;
 401 }