/* * 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]; }; static inline int popcountl(unsigned long l) { return BITS_PER_LONG == 32 ? ctpop32(l) : ctpop64(l); } /* 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 += popcountl(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 += popcountl(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_malloc0(sizeof (struct HBitmap)); 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_malloc0(size * sizeof(unsigned long)); } /* 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; }