2 * Bitmap of bitmaps, where each layer is number-of-bits-per-word smaller than
3 * the previous. Hence an 'axmap', since we axe each previous layer into a
4 * much smaller piece. I swear, that is why it's named like that. It has
5 * nothing to do with anything remotely narcissistic.
7 * A set bit at layer N indicates a full word at layer N-1, and so forth. As
8 * the bitmap becomes progressively more full, checking for existence
9 * becomes cheaper (since fewer layers are walked, making it a lot more
10 * cache friendly) and locating the next free space likewise.
12 * Axmaps get pretty close to optimal (1 bit per block) space usage, since
13 * layers quickly diminish in size. Doing the size math is straight forward,
14 * since we have log64(blocks) layers of maps. For 20000 blocks, overhead
15 * is roughly 1.9%, or 1.019 bits per block. The number quickly converges
16 * towards 1.0158, or 1.58% of overhead.
23 #include "../arch/arch.h"
25 #include "../minmax.h"
27 #if BITS_PER_LONG == 64
29 #elif BITS_PER_LONG == 32
32 #error "Number of arch bits unknown"
35 #define BLOCKS_PER_UNIT (1U << UNIT_SHIFT)
36 #define BLOCKS_PER_UNIT_MASK (BLOCKS_PER_UNIT - 1)
38 static const unsigned long bit_masks[] = {
39 0x0000000000000000, 0x0000000000000001, 0x0000000000000003, 0x0000000000000007,
40 0x000000000000000f, 0x000000000000001f, 0x000000000000003f, 0x000000000000007f,
41 0x00000000000000ff, 0x00000000000001ff, 0x00000000000003ff, 0x00000000000007ff,
42 0x0000000000000fff, 0x0000000000001fff, 0x0000000000003fff, 0x0000000000007fff,
43 0x000000000000ffff, 0x000000000001ffff, 0x000000000003ffff, 0x000000000007ffff,
44 0x00000000000fffff, 0x00000000001fffff, 0x00000000003fffff, 0x00000000007fffff,
45 0x0000000000ffffff, 0x0000000001ffffff, 0x0000000003ffffff, 0x0000000007ffffff,
46 0x000000000fffffff, 0x000000001fffffff, 0x000000003fffffff, 0x000000007fffffff,
48 #if BITS_PER_LONG == 64
49 0x00000001ffffffff, 0x00000003ffffffff, 0x00000007ffffffff, 0x0000000fffffffff,
50 0x0000001fffffffff, 0x0000003fffffffff, 0x0000007fffffffff, 0x000000ffffffffff,
51 0x000001ffffffffff, 0x000003ffffffffff, 0x000007ffffffffff, 0x00000fffffffffff,
52 0x00001fffffffffff, 0x00003fffffffffff, 0x00007fffffffffff, 0x0000ffffffffffff,
53 0x0001ffffffffffff, 0x0003ffffffffffff, 0x0007ffffffffffff, 0x000fffffffffffff,
54 0x001fffffffffffff, 0x003fffffffffffff, 0x007fffffffffffff, 0x00ffffffffffffff,
55 0x01ffffffffffffff, 0x03ffffffffffffff, 0x07ffffffffffffff, 0x0fffffffffffffff,
56 0x1fffffffffffffff, 0x3fffffffffffffff, 0x7fffffffffffffff, 0xffffffffffffffff
61 * struct axmap_level - a bitmap used to implement struct axmap
62 * @level: Level index. Each map has at least one level with index zero. The
63 * higher the level index, the fewer bits a struct axmap_level contains.
64 * @map_size: Number of elements of the @map array.
65 * @map: A bitmap with @map_size elements.
69 unsigned long map_size;
74 * struct axmap - a set that can store numbers 0 .. @nr_bits - 1
75 * @nr_level: Number of elements of the @levels array.
76 * @levels: struct axmap_level array in which lower levels contain more bits
78 * @nr_bits: One more than the highest value stored in the set.
81 unsigned int nr_levels;
82 struct axmap_level *levels;
86 /* Remove all elements from the @axmap set */
87 void axmap_reset(struct axmap *axmap)
91 for (i = 0; i < axmap->nr_levels; i++) {
92 struct axmap_level *al = &axmap->levels[i];
94 memset(al->map, 0, al->map_size * sizeof(unsigned long));
98 void axmap_free(struct axmap *axmap)
105 for (i = 0; i < axmap->nr_levels; i++)
106 free(axmap->levels[i].map);
112 /* Allocate memory for a set that can store the numbers 0 .. @nr_bits - 1. */
113 struct axmap *axmap_new(unsigned long nr_bits)
116 unsigned int i, levels;
118 axmap = malloc(sizeof(*axmap));
123 i = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
125 i = (i + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
129 axmap->nr_levels = levels;
130 axmap->levels = calloc(axmap->nr_levels, sizeof(struct axmap_level));
133 axmap->nr_bits = nr_bits;
135 for (i = 0; i < axmap->nr_levels; i++) {
136 struct axmap_level *al = &axmap->levels[i];
139 al->map_size = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
140 al->map = malloc(al->map_size * sizeof(unsigned long));
144 nr_bits = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
151 for (i = 0; i < axmap->nr_levels; i++)
152 free(axmap->levels[i].map);
162 * Call @func for each level, starting at level zero, until a level is found
163 * for which @func returns true. Return false if none of the @func calls
166 static bool axmap_handler(struct axmap *axmap, uint64_t bit_nr,
167 bool (*func)(struct axmap_level *, unsigned long, unsigned int,
170 struct axmap_level *al;
171 uint64_t index = bit_nr;
174 for (i = 0; i < axmap->nr_levels; i++) {
175 unsigned long offset = index >> UNIT_SHIFT;
176 unsigned int bit = index & BLOCKS_PER_UNIT_MASK;
178 al = &axmap->levels[i];
180 if (func(al, offset, bit, data))
184 index >>= UNIT_SHIFT;
191 * Call @func for each level, starting at the highest level, until a level is
192 * found for which @func returns true. Return false if none of the @func calls
195 static bool axmap_handler_topdown(struct axmap *axmap, uint64_t bit_nr,
196 bool (*func)(struct axmap_level *, unsigned long, unsigned int, void *))
200 for (i = axmap->nr_levels - 1; i >= 0; i--) {
201 unsigned long index = bit_nr >> (UNIT_SHIFT * i);
202 unsigned long offset = index >> UNIT_SHIFT;
203 unsigned int bit = index & BLOCKS_PER_UNIT_MASK;
205 if (func(&axmap->levels[i], offset, bit, NULL))
212 struct axmap_set_data {
213 unsigned int nr_bits;
214 unsigned int set_bits;
218 * Set at most @__data->nr_bits bits in @al at offset @offset. Do not exceed
219 * the boundary of the element at offset @offset. Return the number of bits
220 * that have been set in @__data->set_bits if @al->level == 0.
222 static bool axmap_set_fn(struct axmap_level *al, unsigned long offset,
223 unsigned int bit, void *__data)
225 struct axmap_set_data *data = __data;
226 unsigned long mask, overlap;
227 unsigned int nr_bits;
229 nr_bits = min(data->nr_bits, BLOCKS_PER_UNIT - bit);
231 mask = bit_masks[nr_bits] << bit;
234 * Mask off any potential overlap, only sets contig regions
236 overlap = al->map[offset] & mask;
237 if (overlap == mask) {
243 nr_bits = ffz(~overlap) - bit;
244 mask = bit_masks[nr_bits] << bit;
248 assert(!(al->map[offset] & mask));
249 al->map[offset] |= mask;
252 data->set_bits = nr_bits;
254 /* For the next level */
257 return al->map[offset] != -1UL;
261 * Set up to @data->nr_bits starting from @bit_nr in @axmap. Start at
262 * @bit_nr. If that bit has not yet been set then set it and continue until
263 * either @data->nr_bits have been set or a 1 bit is found. Store the number
264 * of bits that have been set in @data->set_bits. It is guaranteed that all
265 * bits that have been requested to set fit in the same unsigned long word of
268 static void __axmap_set(struct axmap *axmap, uint64_t bit_nr,
269 struct axmap_set_data *data)
271 unsigned int set_bits, nr_bits = data->nr_bits;
273 if (bit_nr > axmap->nr_bits)
275 else if (bit_nr + nr_bits > axmap->nr_bits)
276 nr_bits = axmap->nr_bits - bit_nr;
280 axmap_handler(axmap, bit_nr, axmap_set_fn, data);
281 set_bits += data->set_bits;
283 if (!data->set_bits ||
284 data->set_bits != (BLOCKS_PER_UNIT - nr_bits))
287 nr_bits -= data->set_bits;
288 bit_nr += data->set_bits;
290 data->nr_bits = nr_bits;
293 data->set_bits = set_bits;
296 void axmap_set(struct axmap *axmap, uint64_t bit_nr)
298 struct axmap_set_data data = { .nr_bits = 1, };
300 __axmap_set(axmap, bit_nr, &data);
304 * Set up to @nr_bits starting from @bit in @axmap. Start at @bit. If that
305 * bit has not yet been set then set it and continue until either @nr_bits
306 * have been set or a 1 bit is found. Return the number of bits that have been
309 unsigned int axmap_set_nr(struct axmap *axmap, uint64_t bit_nr,
310 unsigned int nr_bits)
312 unsigned int set_bits = 0;
315 struct axmap_set_data data = { .nr_bits = nr_bits, };
316 unsigned int max_bits, this_set;
318 max_bits = BLOCKS_PER_UNIT - (bit_nr & BLOCKS_PER_UNIT_MASK);
319 if (nr_bits > max_bits)
320 data.nr_bits = max_bits;
322 this_set = data.nr_bits;
323 __axmap_set(axmap, bit_nr, &data);
324 set_bits += data.set_bits;
325 if (data.set_bits != this_set)
328 nr_bits -= data.set_bits;
329 bit_nr += data.set_bits;
335 static bool axmap_isset_fn(struct axmap_level *al, unsigned long offset,
336 unsigned int bit, void *unused)
338 return (al->map[offset] & (1UL << bit)) != 0;
341 bool axmap_isset(struct axmap *axmap, uint64_t bit_nr)
343 if (bit_nr <= axmap->nr_bits)
344 return axmap_handler_topdown(axmap, bit_nr, axmap_isset_fn);
350 * Find the first free bit that is at least as large as bit_nr. Return
351 * -1 if no free bit is found before the end of the map.
353 static uint64_t axmap_find_first_free(struct axmap *axmap, uint64_t bit_nr)
358 uint64_t offset, base_index, index;
359 struct axmap_level *al;
362 for (i = axmap->nr_levels - 1; i >= 0; i--) {
363 al = &axmap->levels[i];
365 /* Shift previously calculated index for next level */
366 index <<= UNIT_SHIFT;
369 * Start from an index that's at least as large as the
370 * originally passed in bit number.
372 base_index = bit_nr >> (UNIT_SHIFT * i);
373 if (index < base_index)
376 /* Get the offset and bit for this level */
377 offset = index >> UNIT_SHIFT;
378 bit = index & BLOCKS_PER_UNIT_MASK;
381 * If the previous level had unused bits in its last
382 * word, the offset could be bigger than the map at
383 * this level. That means no free bits exist before the
384 * end of the map, so return -1.
386 if (offset >= al->map_size)
389 /* Check the first word starting with the specific bit */
390 temp = ~bit_masks[bit] & ~al->map[offset];
395 * No free bit in the first word, so iterate
396 * looking for a word with one or more free bits.
398 for (offset++; offset < al->map_size; offset++) {
399 temp = ~al->map[offset];
404 /* Did not find a free bit */
408 /* Compute the index of the free bit just found */
409 index = (offset << UNIT_SHIFT) + ffz(~temp);
412 /* If found an unused bit in the last word of level 0, return -1 */
413 if (index >= axmap->nr_bits)
420 * 'bit_nr' is already set. Find the next free bit after this one.
421 * Return -1 if no free bits found.
423 uint64_t axmap_next_free(struct axmap *axmap, uint64_t bit_nr)
426 uint64_t next_bit = bit_nr + 1;
431 if (bit_nr >= axmap->nr_bits)
434 /* If at the end of the map, wrap-around */
435 if (next_bit == axmap->nr_bits)
438 offset = next_bit >> UNIT_SHIFT;
439 bit = next_bit & BLOCKS_PER_UNIT_MASK;
442 * As an optimization, do a quick check for a free bit
443 * in the current word at level 0. If not found, do
446 temp = ~bit_masks[bit] & ~axmap->levels[0].map[offset];
448 ret = (offset << UNIT_SHIFT) + ffz(~temp);
450 /* Might have found an unused bit at level 0 */
451 if (ret >= axmap->nr_bits)
454 ret = axmap_find_first_free(axmap, next_bit);
457 * If there are no free bits starting at next_bit and going
458 * to the end of the map, wrap around by searching again
461 if (ret == -1ULL && next_bit != 0)
462 ret = axmap_find_first_free(axmap, 0);