| 1 | /* |
| 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. |
| 6 | * |
| 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. |
| 11 | * |
| 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. |
| 17 | */ |
| 18 | #include <stdio.h> |
| 19 | #include <stdlib.h> |
| 20 | #include <string.h> |
| 21 | #include <assert.h> |
| 22 | |
| 23 | #include "../arch/arch.h" |
| 24 | #include "axmap.h" |
| 25 | #include "../minmax.h" |
| 26 | |
| 27 | #if BITS_PER_LONG == 64 |
| 28 | #define UNIT_SHIFT 6 |
| 29 | #elif BITS_PER_LONG == 32 |
| 30 | #define UNIT_SHIFT 5 |
| 31 | #else |
| 32 | #error "Number of arch bits unknown" |
| 33 | #endif |
| 34 | |
| 35 | #define BLOCKS_PER_UNIT (1U << UNIT_SHIFT) |
| 36 | #define BLOCKS_PER_UNIT_MASK (BLOCKS_PER_UNIT - 1) |
| 37 | |
| 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, |
| 47 | 0x00000000ffffffff, |
| 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 |
| 57 | #endif |
| 58 | }; |
| 59 | |
| 60 | /** |
| 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. |
| 66 | */ |
| 67 | struct axmap_level { |
| 68 | int level; |
| 69 | unsigned long map_size; |
| 70 | unsigned long *map; |
| 71 | }; |
| 72 | |
| 73 | /** |
| 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 |
| 77 | * than higher levels. |
| 78 | * @nr_bits: One more than the highest value stored in the set. |
| 79 | */ |
| 80 | struct axmap { |
| 81 | unsigned int nr_levels; |
| 82 | struct axmap_level *levels; |
| 83 | uint64_t nr_bits; |
| 84 | }; |
| 85 | |
| 86 | /* Remove all elements from the @axmap set */ |
| 87 | void axmap_reset(struct axmap *axmap) |
| 88 | { |
| 89 | int i; |
| 90 | |
| 91 | for (i = 0; i < axmap->nr_levels; i++) { |
| 92 | struct axmap_level *al = &axmap->levels[i]; |
| 93 | |
| 94 | memset(al->map, 0, al->map_size * sizeof(unsigned long)); |
| 95 | } |
| 96 | } |
| 97 | |
| 98 | void axmap_free(struct axmap *axmap) |
| 99 | { |
| 100 | unsigned int i; |
| 101 | |
| 102 | if (!axmap) |
| 103 | return; |
| 104 | |
| 105 | for (i = 0; i < axmap->nr_levels; i++) |
| 106 | free(axmap->levels[i].map); |
| 107 | |
| 108 | free(axmap->levels); |
| 109 | free(axmap); |
| 110 | } |
| 111 | |
| 112 | /* Allocate memory for a set that can store the numbers 0 .. @nr_bits - 1. */ |
| 113 | struct axmap *axmap_new(unsigned long nr_bits) |
| 114 | { |
| 115 | struct axmap *axmap; |
| 116 | unsigned int i, levels; |
| 117 | |
| 118 | axmap = malloc(sizeof(*axmap)); |
| 119 | if (!axmap) |
| 120 | return NULL; |
| 121 | |
| 122 | levels = 1; |
| 123 | i = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT; |
| 124 | while (i > 1) { |
| 125 | i = (i + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT; |
| 126 | levels++; |
| 127 | } |
| 128 | |
| 129 | axmap->nr_levels = levels; |
| 130 | axmap->levels = calloc(axmap->nr_levels, sizeof(struct axmap_level)); |
| 131 | if (!axmap->levels) |
| 132 | goto free_axmap; |
| 133 | axmap->nr_bits = nr_bits; |
| 134 | |
| 135 | for (i = 0; i < axmap->nr_levels; i++) { |
| 136 | struct axmap_level *al = &axmap->levels[i]; |
| 137 | |
| 138 | al->level = i; |
| 139 | al->map_size = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT; |
| 140 | al->map = malloc(al->map_size * sizeof(unsigned long)); |
| 141 | if (!al->map) |
| 142 | goto free_levels; |
| 143 | |
| 144 | nr_bits = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT; |
| 145 | } |
| 146 | |
| 147 | axmap_reset(axmap); |
| 148 | return axmap; |
| 149 | |
| 150 | free_levels: |
| 151 | for (i = 0; i < axmap->nr_levels; i++) |
| 152 | free(axmap->levels[i].map); |
| 153 | |
| 154 | free(axmap->levels); |
| 155 | |
| 156 | free_axmap: |
| 157 | free(axmap); |
| 158 | return NULL; |
| 159 | } |
| 160 | |
| 161 | /* |
| 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 |
| 164 | * returns true. |
| 165 | */ |
| 166 | static bool axmap_handler(struct axmap *axmap, uint64_t bit_nr, |
| 167 | bool (*func)(struct axmap_level *, unsigned long, unsigned int, |
| 168 | void *), void *data) |
| 169 | { |
| 170 | struct axmap_level *al; |
| 171 | uint64_t index = bit_nr; |
| 172 | int i; |
| 173 | |
| 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; |
| 177 | |
| 178 | al = &axmap->levels[i]; |
| 179 | |
| 180 | if (func(al, offset, bit, data)) |
| 181 | return true; |
| 182 | |
| 183 | if (index) |
| 184 | index >>= UNIT_SHIFT; |
| 185 | } |
| 186 | |
| 187 | return false; |
| 188 | } |
| 189 | |
| 190 | /* |
| 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 |
| 193 | * returns true. |
| 194 | */ |
| 195 | static bool axmap_handler_topdown(struct axmap *axmap, uint64_t bit_nr, |
| 196 | bool (*func)(struct axmap_level *, unsigned long, unsigned int, void *)) |
| 197 | { |
| 198 | int i; |
| 199 | |
| 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; |
| 204 | |
| 205 | if (func(&axmap->levels[i], offset, bit, NULL)) |
| 206 | return true; |
| 207 | } |
| 208 | |
| 209 | return false; |
| 210 | } |
| 211 | |
| 212 | struct axmap_set_data { |
| 213 | unsigned int nr_bits; |
| 214 | unsigned int set_bits; |
| 215 | }; |
| 216 | |
| 217 | /* |
| 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. |
| 221 | */ |
| 222 | static bool axmap_set_fn(struct axmap_level *al, unsigned long offset, |
| 223 | unsigned int bit, void *__data) |
| 224 | { |
| 225 | struct axmap_set_data *data = __data; |
| 226 | unsigned long mask, overlap; |
| 227 | unsigned int nr_bits; |
| 228 | |
| 229 | nr_bits = min(data->nr_bits, BLOCKS_PER_UNIT - bit); |
| 230 | |
| 231 | mask = bit_masks[nr_bits] << bit; |
| 232 | |
| 233 | /* |
| 234 | * Mask off any potential overlap, only sets contig regions |
| 235 | */ |
| 236 | overlap = al->map[offset] & mask; |
| 237 | if (overlap == mask) { |
| 238 | data->set_bits = 0; |
| 239 | return true; |
| 240 | } |
| 241 | |
| 242 | if (overlap) { |
| 243 | nr_bits = ffz(~overlap) - bit; |
| 244 | mask = bit_masks[nr_bits] << bit; |
| 245 | } |
| 246 | |
| 247 | assert(mask); |
| 248 | assert(!(al->map[offset] & mask)); |
| 249 | al->map[offset] |= mask; |
| 250 | |
| 251 | if (!al->level) |
| 252 | data->set_bits = nr_bits; |
| 253 | |
| 254 | /* For the next level */ |
| 255 | data->nr_bits = 1; |
| 256 | |
| 257 | return al->map[offset] != -1UL; |
| 258 | } |
| 259 | |
| 260 | /* |
| 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 |
| 266 | * level 0 of @axmap. |
| 267 | */ |
| 268 | static void __axmap_set(struct axmap *axmap, uint64_t bit_nr, |
| 269 | struct axmap_set_data *data) |
| 270 | { |
| 271 | unsigned int nr_bits = data->nr_bits; |
| 272 | |
| 273 | if (bit_nr > axmap->nr_bits) |
| 274 | return; |
| 275 | else if (bit_nr + nr_bits > axmap->nr_bits) |
| 276 | nr_bits = axmap->nr_bits - bit_nr; |
| 277 | |
| 278 | assert(nr_bits <= BLOCKS_PER_UNIT); |
| 279 | |
| 280 | axmap_handler(axmap, bit_nr, axmap_set_fn, data); |
| 281 | } |
| 282 | |
| 283 | void axmap_set(struct axmap *axmap, uint64_t bit_nr) |
| 284 | { |
| 285 | struct axmap_set_data data = { .nr_bits = 1, }; |
| 286 | |
| 287 | __axmap_set(axmap, bit_nr, &data); |
| 288 | } |
| 289 | |
| 290 | /* |
| 291 | * Set up to @nr_bits starting from @bit in @axmap. Start at @bit. If that |
| 292 | * bit has not yet been set then set it and continue until either @nr_bits |
| 293 | * have been set or a 1 bit is found. Return the number of bits that have been |
| 294 | * set. |
| 295 | */ |
| 296 | unsigned int axmap_set_nr(struct axmap *axmap, uint64_t bit_nr, |
| 297 | unsigned int nr_bits) |
| 298 | { |
| 299 | unsigned int set_bits = 0; |
| 300 | |
| 301 | do { |
| 302 | struct axmap_set_data data = { .nr_bits = nr_bits, }; |
| 303 | unsigned int max_bits, this_set; |
| 304 | |
| 305 | max_bits = BLOCKS_PER_UNIT - (bit_nr & BLOCKS_PER_UNIT_MASK); |
| 306 | if (nr_bits > max_bits) |
| 307 | data.nr_bits = max_bits; |
| 308 | |
| 309 | this_set = data.nr_bits; |
| 310 | __axmap_set(axmap, bit_nr, &data); |
| 311 | set_bits += data.set_bits; |
| 312 | if (data.set_bits != this_set) |
| 313 | break; |
| 314 | |
| 315 | nr_bits -= data.set_bits; |
| 316 | bit_nr += data.set_bits; |
| 317 | } while (nr_bits); |
| 318 | |
| 319 | return set_bits; |
| 320 | } |
| 321 | |
| 322 | static bool axmap_isset_fn(struct axmap_level *al, unsigned long offset, |
| 323 | unsigned int bit, void *unused) |
| 324 | { |
| 325 | return (al->map[offset] & (1UL << bit)) != 0; |
| 326 | } |
| 327 | |
| 328 | bool axmap_isset(struct axmap *axmap, uint64_t bit_nr) |
| 329 | { |
| 330 | if (bit_nr <= axmap->nr_bits) |
| 331 | return axmap_handler_topdown(axmap, bit_nr, axmap_isset_fn); |
| 332 | |
| 333 | return false; |
| 334 | } |
| 335 | |
| 336 | /* |
| 337 | * Find the first free bit that is at least as large as bit_nr. Return |
| 338 | * -1 if no free bit is found before the end of the map. |
| 339 | */ |
| 340 | static uint64_t axmap_find_first_free(struct axmap *axmap, uint64_t bit_nr) |
| 341 | { |
| 342 | int i; |
| 343 | unsigned long temp; |
| 344 | unsigned int bit; |
| 345 | uint64_t offset, base_index, index; |
| 346 | struct axmap_level *al; |
| 347 | |
| 348 | index = 0; |
| 349 | for (i = axmap->nr_levels - 1; i >= 0; i--) { |
| 350 | al = &axmap->levels[i]; |
| 351 | |
| 352 | /* Shift previously calculated index for next level */ |
| 353 | index <<= UNIT_SHIFT; |
| 354 | |
| 355 | /* |
| 356 | * Start from an index that's at least as large as the |
| 357 | * originally passed in bit number. |
| 358 | */ |
| 359 | base_index = bit_nr >> (UNIT_SHIFT * i); |
| 360 | if (index < base_index) |
| 361 | index = base_index; |
| 362 | |
| 363 | /* Get the offset and bit for this level */ |
| 364 | offset = index >> UNIT_SHIFT; |
| 365 | bit = index & BLOCKS_PER_UNIT_MASK; |
| 366 | |
| 367 | /* |
| 368 | * If the previous level had unused bits in its last |
| 369 | * word, the offset could be bigger than the map at |
| 370 | * this level. That means no free bits exist before the |
| 371 | * end of the map, so return -1. |
| 372 | */ |
| 373 | if (offset >= al->map_size) |
| 374 | return -1ULL; |
| 375 | |
| 376 | /* Check the first word starting with the specific bit */ |
| 377 | temp = ~bit_masks[bit] & ~al->map[offset]; |
| 378 | if (temp) |
| 379 | goto found; |
| 380 | |
| 381 | /* |
| 382 | * No free bit in the first word, so iterate |
| 383 | * looking for a word with one or more free bits. |
| 384 | */ |
| 385 | for (offset++; offset < al->map_size; offset++) { |
| 386 | temp = ~al->map[offset]; |
| 387 | if (temp) |
| 388 | goto found; |
| 389 | } |
| 390 | |
| 391 | /* Did not find a free bit */ |
| 392 | return -1ULL; |
| 393 | |
| 394 | found: |
| 395 | /* Compute the index of the free bit just found */ |
| 396 | index = (offset << UNIT_SHIFT) + ffz(~temp); |
| 397 | } |
| 398 | |
| 399 | /* If found an unused bit in the last word of level 0, return -1 */ |
| 400 | if (index >= axmap->nr_bits) |
| 401 | return -1ULL; |
| 402 | |
| 403 | return index; |
| 404 | } |
| 405 | |
| 406 | /* |
| 407 | * 'bit_nr' is already set. Find the next free bit after this one. |
| 408 | * Return -1 if no free bits found. |
| 409 | */ |
| 410 | uint64_t axmap_next_free(struct axmap *axmap, uint64_t bit_nr) |
| 411 | { |
| 412 | uint64_t ret; |
| 413 | uint64_t next_bit = bit_nr + 1; |
| 414 | unsigned long temp; |
| 415 | uint64_t offset; |
| 416 | unsigned int bit; |
| 417 | |
| 418 | if (bit_nr >= axmap->nr_bits) |
| 419 | return -1ULL; |
| 420 | |
| 421 | /* If at the end of the map, wrap-around */ |
| 422 | if (next_bit == axmap->nr_bits) |
| 423 | next_bit = 0; |
| 424 | |
| 425 | offset = next_bit >> UNIT_SHIFT; |
| 426 | bit = next_bit & BLOCKS_PER_UNIT_MASK; |
| 427 | |
| 428 | /* |
| 429 | * As an optimization, do a quick check for a free bit |
| 430 | * in the current word at level 0. If not found, do |
| 431 | * a topdown search. |
| 432 | */ |
| 433 | temp = ~bit_masks[bit] & ~axmap->levels[0].map[offset]; |
| 434 | if (temp) { |
| 435 | ret = (offset << UNIT_SHIFT) + ffz(~temp); |
| 436 | |
| 437 | /* Might have found an unused bit at level 0 */ |
| 438 | if (ret >= axmap->nr_bits) |
| 439 | ret = -1ULL; |
| 440 | } else |
| 441 | ret = axmap_find_first_free(axmap, next_bit); |
| 442 | |
| 443 | /* |
| 444 | * If there are no free bits starting at next_bit and going |
| 445 | * to the end of the map, wrap around by searching again |
| 446 | * starting at bit 0. |
| 447 | */ |
| 448 | if (ret == -1ULL && next_bit != 0) |
| 449 | ret = axmap_find_first_free(axmap, 0); |
| 450 | return ret; |
| 451 | } |