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 /* Advance hbi to the next nonzero word and return it.  hbi->pos
  96  * is updated.  Returns zero if we reach the end of the bitmap.
  97  */
  98 unsigned long hbitmap_iter_skip_words(HBitmapIter *hbi)
  99 {
 100     size_t pos = hbi->pos;
 101     const HBitmap *hb = hbi->hb;
 102     unsigned i = HBITMAP_LEVELS - 1;
 103
 104     unsigned long cur;
 105     do {
 106         cur = hbi->cur[--i];
 107         pos >>= BITS_PER_LEVEL;
 108     } while (cur == 0);
 109
 110     /* Check for end of iteration.  We always use fewer than BITS_PER_LONG
 111      * bits in the level 0 bitmap; thus we can repurpose the most significant
 112      * bit as a sentinel.  The sentinel is set in hbitmap_alloc and ensures
 113      * that the above loop ends even without an explicit check on i.
 114      */
 115
 116     if (i == 0 && cur == (1UL << (BITS_PER_LONG - 1))) {
 117         return 0;
 118     }
 119     for (; i < HBITMAP_LEVELS - 1; i++) {
 120         /* Shift back pos to the left, matching the right shifts above.
 121          * The index of this word's least significant set bit provides
 122          * the low-order bits.
 123          */
 124         assert(cur);
 125         pos = (pos << BITS_PER_LEVEL) + ctzl(cur);
 126         hbi->cur[i] = cur & (cur - 1);
 127
 128         /* Set up next level for iteration.  */
 129         cur = hb->levels[i + 1][pos];
 130     }
 131
 132     hbi->pos = pos;
 133     trace_hbitmap_iter_skip_words(hbi->hb, hbi, pos, cur);
 134
 135     assert(cur);
 136     return cur;
 137 }
 138
 139 void hbitmap_iter_init(HBitmapIter *hbi, const HBitmap *hb, uint64_t first)
 140 {
 141     unsigned i, bit;
 142     uint64_t pos;
 143
 144     hbi->hb = hb;
 145     pos = first >> hb->granularity;
 146     assert(pos < hb->size);
 147     hbi->pos = pos >> BITS_PER_LEVEL;
 148     hbi->granularity = hb->granularity;
 149
 150     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 151         bit = pos & (BITS_PER_LONG - 1);
 152         pos >>= BITS_PER_LEVEL;
 153
 154         /* Drop bits representing items before first.  */
 155         hbi->cur[i] = hb->levels[i][pos] & ~((1UL << bit) - 1);
 156
 157         /* We have already added level i+1, so the lowest set bit has
 158          * been processed.  Clear it.
 159          */
 160         if (i != HBITMAP_LEVELS - 1) {
 161             hbi->cur[i] &= ~(1UL << bit);
 162         }
 163     }
 164 }
 165
 166 bool hbitmap_empty(const HBitmap *hb)
 167 {
 168     return hb->count == 0;
 169 }
 170
 171 int hbitmap_granularity(const HBitmap *hb)
 172 {
 173     return hb->granularity;
 174 }
 175
 176 uint64_t hbitmap_count(const HBitmap *hb)
 177 {
 178     return hb->count << hb->granularity;
 179 }
 180
 181 /* Count the number of set bits between start and end, not accounting for
 182  * the granularity.  Also an example of how to use hbitmap_iter_next_word.
 183  */
 184 static uint64_t hb_count_between(HBitmap *hb, uint64_t start, uint64_t last)
 185 {
 186     HBitmapIter hbi;
 187     uint64_t count = 0;
 188     uint64_t end = last + 1;
 189     unsigned long cur;
 190     size_t pos;
 191
 192     hbitmap_iter_init(&hbi, hb, start << hb->granularity);
 193     for (;;) {
 194         pos = hbitmap_iter_next_word(&hbi, &cur);
 195         if (pos >= (end >> BITS_PER_LEVEL)) {
 196             break;
 197         }
 198         count += ctpopl(cur);
 199     }
 200
 201     if (pos == (end >> BITS_PER_LEVEL)) {
 202         /* Drop bits representing the END-th and subsequent items.  */
 203         int bit = end & (BITS_PER_LONG - 1);
 204         cur &= (1UL << bit) - 1;
 205         count += ctpopl(cur);
 206     }
 207
 208     return count;
 209 }
 210
 211 /* Setting starts at the last layer and propagates up if an element
 212  * changes from zero to non-zero.
 213  */
 214 static inline bool hb_set_elem(unsigned long *elem, uint64_t start, uint64_t last)
 215 {
 216     unsigned long mask;
 217     bool changed;
 218
 219     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
 220     assert(start <= last);
 221
 222     mask = 2UL << (last & (BITS_PER_LONG - 1));
 223     mask -= 1UL << (start & (BITS_PER_LONG - 1));
 224     changed = (*elem == 0);
 225     *elem |= mask;
 226     return changed;
 227 }
 228
 229 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
 230 static void hb_set_between(HBitmap *hb, int level, uint64_t start, uint64_t last)
 231 {
 232     size_t pos = start >> BITS_PER_LEVEL;
 233     size_t lastpos = last >> BITS_PER_LEVEL;
 234     bool changed = false;
 235     size_t i;
 236
 237     i = pos;
 238     if (i < lastpos) {
 239         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
 240         changed |= hb_set_elem(&hb->levels[level][i], start, next - 1);
 241         for (;;) {
 242             start = next;
 243             next += BITS_PER_LONG;
 244             if (++i == lastpos) {
 245                 break;
 246             }
 247             changed |= (hb->levels[level][i] == 0);
 248             hb->levels[level][i] = ~0UL;
 249         }
 250     }
 251     changed |= hb_set_elem(&hb->levels[level][i], start, last);
 252
 253     /* If there was any change in this layer, we may have to update
 254      * the one above.
 255      */
 256     if (level > 0 && changed) {
 257         hb_set_between(hb, level - 1, pos, lastpos);
 258     }
 259 }
 260
 261 void hbitmap_set(HBitmap *hb, uint64_t start, uint64_t count)
 262 {
 263     /* Compute range in the last layer.  */
 264     uint64_t last = start + count - 1;
 265
 266     trace_hbitmap_set(hb, start, count,
 267                       start >> hb->granularity, last >> hb->granularity);
 268
 269     start >>= hb->granularity;
 270     last >>= hb->granularity;
 271     count = last - start + 1;
 272
 273     hb->count += count - hb_count_between(hb, start, last);
 274     hb_set_between(hb, HBITMAP_LEVELS - 1, start, last);
 275 }
 276
 277 /* Resetting works the other way round: propagate up if the new
 278  * value is zero.
 279  */
 280 static inline bool hb_reset_elem(unsigned long *elem, uint64_t start, uint64_t last)
 281 {
 282     unsigned long mask;
 283     bool blanked;
 284
 285     assert((last >> BITS_PER_LEVEL) == (start >> BITS_PER_LEVEL));
 286     assert(start <= last);
 287
 288     mask = 2UL << (last & (BITS_PER_LONG - 1));
 289     mask -= 1UL << (start & (BITS_PER_LONG - 1));
 290     blanked = *elem != 0 && ((*elem & ~mask) == 0);
 291     *elem &= ~mask;
 292     return blanked;
 293 }
 294
 295 /* The recursive workhorse (the depth is limited to HBITMAP_LEVELS)... */
 296 static void hb_reset_between(HBitmap *hb, int level, uint64_t start, uint64_t last)
 297 {
 298     size_t pos = start >> BITS_PER_LEVEL;
 299     size_t lastpos = last >> BITS_PER_LEVEL;
 300     bool changed = false;
 301     size_t i;
 302
 303     i = pos;
 304     if (i < lastpos) {
 305         uint64_t next = (start | (BITS_PER_LONG - 1)) + 1;
 306
 307         /* Here we need a more complex test than when setting bits.  Even if
 308          * something was changed, we must not blank bits in the upper level
 309          * unless the lower-level word became entirely zero.  So, remove pos
 310          * from the upper-level range if bits remain set.
 311          */
 312         if (hb_reset_elem(&hb->levels[level][i], start, next - 1)) {
 313             changed = true;
 314         } else {
 315             pos++;
 316         }
 317
 318         for (;;) {
 319             start = next;
 320             next += BITS_PER_LONG;
 321             if (++i == lastpos) {
 322                 break;
 323             }
 324             changed |= (hb->levels[level][i] != 0);
 325             hb->levels[level][i] = 0UL;
 326         }
 327     }
 328
 329     /* Same as above, this time for lastpos.  */
 330     if (hb_reset_elem(&hb->levels[level][i], start, last)) {
 331         changed = true;
 332     } else {
 333         lastpos--;
 334     }
 335
 336     if (level > 0 && changed) {
 337         hb_reset_between(hb, level - 1, pos, lastpos);
 338     }
 339 }
 340
 341 void hbitmap_reset(HBitmap *hb, uint64_t start, uint64_t count)
 342 {
 343     /* Compute range in the last layer.  */
 344     uint64_t last = start + count - 1;
 345
 346     trace_hbitmap_reset(hb, start, count,
 347                         start >> hb->granularity, last >> hb->granularity);
 348
 349     start >>= hb->granularity;
 350     last >>= hb->granularity;
 351
 352     hb->count -= hb_count_between(hb, start, last);
 353     hb_reset_between(hb, HBITMAP_LEVELS - 1, start, last);
 354 }
 355
 356 bool hbitmap_get(const HBitmap *hb, uint64_t item)
 357 {
 358     /* Compute position and bit in the last layer.  */
 359     uint64_t pos = item >> hb->granularity;
 360     unsigned long bit = 1UL << (pos & (BITS_PER_LONG - 1));
 361
 362     return (hb->levels[HBITMAP_LEVELS - 1][pos >> BITS_PER_LEVEL] & bit) != 0;
 363 }
 364
 365 void hbitmap_free(HBitmap *hb)
 366 {
 367     unsigned i;
 368     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 369         g_free(hb->levels[i]);
 370     }
 371     g_free(hb);
 372 }
 373
 374 HBitmap *hbitmap_alloc(uint64_t size, int granularity)
 375 {
 376     HBitmap *hb = g_new0(struct HBitmap, 1);
 377     unsigned i;
 378
 379     assert(granularity >= 0 && granularity < 64);
 380     size = (size + (1ULL << granularity) - 1) >> granularity;
 381     assert(size <= ((uint64_t)1 << HBITMAP_LOG_MAX_SIZE));
 382
 383     hb->size = size;
 384     hb->granularity = granularity;
 385     for (i = HBITMAP_LEVELS; i-- > 0; ) {
 386         size = MAX((size + BITS_PER_LONG - 1) >> BITS_PER_LEVEL, 1);
 387         hb->levels[i] = g_new0(unsigned long, size);
 388     }
 389
 390     /* We necessarily have free bits in level 0 due to the definition
 391      * of HBITMAP_LEVELS, so use one for a sentinel.  This speeds up
 392      * hbitmap_iter_skip_words.
 393      */
 394     assert(size == 1);
 395     hb->levels[0][0] |= 1UL << (BITS_PER_LONG - 1);
 396     return hb;
 397 }