/*
* Bitmap of bitmaps, where each layer is number-of-bits-per-word smaller than
* the previous. Hence an 'axmap', since we axe each previous layer into a
* much smaller piece. I swear, that is why it's named like that. It has
* nothing to do with anything remotely narcissistic.
*
* A set bit at layer N indicates a full word at layer N-1, and so forth. As
* the bitmap becomes progressively more full, checking for existence
* becomes cheaper (since fewer layers are walked, making it a lot more
* cache friendly) and locating the next free space likewise.
*
* Axmaps get pretty close to optimal (1 bit per block) space usage, since
* layers quickly diminish in size. Doing the size math is straight forward,
* since we have log64(blocks) layers of maps. For 20000 blocks, overhead
* is roughly 1.9%, or 1.019 bits per block. The number quickly converges
* towards 1.0158, or 1.58% of overhead.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "../arch/arch.h"
#include "axmap.h"
#include "../minmax.h"
#if BITS_PER_LONG == 64
#define UNIT_SHIFT 6
#elif BITS_PER_LONG == 32
#define UNIT_SHIFT 5
#else
#error "Number of arch bits unknown"
#endif
#define BLOCKS_PER_UNIT (1U << UNIT_SHIFT)
#define BLOCKS_PER_UNIT_MASK (BLOCKS_PER_UNIT - 1)
static const unsigned long bit_masks[] = {
0x0000000000000000, 0x0000000000000001, 0x0000000000000003, 0x0000000000000007,
0x000000000000000f, 0x000000000000001f, 0x000000000000003f, 0x000000000000007f,
0x00000000000000ff, 0x00000000000001ff, 0x00000000000003ff, 0x00000000000007ff,
0x0000000000000fff, 0x0000000000001fff, 0x0000000000003fff, 0x0000000000007fff,
0x000000000000ffff, 0x000000000001ffff, 0x000000000003ffff, 0x000000000007ffff,
0x00000000000fffff, 0x00000000001fffff, 0x00000000003fffff, 0x00000000007fffff,
0x0000000000ffffff, 0x0000000001ffffff, 0x0000000003ffffff, 0x0000000007ffffff,
0x000000000fffffff, 0x000000001fffffff, 0x000000003fffffff, 0x000000007fffffff,
0x00000000ffffffff,
#if BITS_PER_LONG == 64
0x00000001ffffffff, 0x00000003ffffffff, 0x00000007ffffffff, 0x0000000fffffffff,
0x0000001fffffffff, 0x0000003fffffffff, 0x0000007fffffffff, 0x000000ffffffffff,
0x000001ffffffffff, 0x000003ffffffffff, 0x000007ffffffffff, 0x00000fffffffffff,
0x00001fffffffffff, 0x00003fffffffffff, 0x00007fffffffffff, 0x0000ffffffffffff,
0x0001ffffffffffff, 0x0003ffffffffffff, 0x0007ffffffffffff, 0x000fffffffffffff,
0x001fffffffffffff, 0x003fffffffffffff, 0x007fffffffffffff, 0x00ffffffffffffff,
0x01ffffffffffffff, 0x03ffffffffffffff, 0x07ffffffffffffff, 0x0fffffffffffffff,
0x1fffffffffffffff, 0x3fffffffffffffff, 0x7fffffffffffffff, 0xffffffffffffffff
#endif
};
/**
* struct axmap_level - a bitmap used to implement struct axmap
* @level: Level index. Each map has at least one level with index zero. The
* higher the level index, the fewer bits a struct axmap_level contains.
* @map_size: Number of elements of the @map array.
* @map: A bitmap with @map_size elements.
*/
struct axmap_level {
int level;
unsigned long map_size;
unsigned long *map;
};
/**
* struct axmap - a set that can store numbers 0 .. @nr_bits - 1
* @nr_level: Number of elements of the @levels array.
* @levels: struct axmap_level array in which lower levels contain more bits
* than higher levels.
* @nr_bits: One more than the highest value stored in the set.
*/
struct axmap {
unsigned int nr_levels;
struct axmap_level *levels;
uint64_t nr_bits;
};
/* Remove all elements from the @axmap set */
void axmap_reset(struct axmap *axmap)
{
int i;
for (i = 0; i < axmap->nr_levels; i++) {
struct axmap_level *al = &axmap->levels[i];
memset(al->map, 0, al->map_size * sizeof(unsigned long));
}
}
void axmap_free(struct axmap *axmap)
{
unsigned int i;
if (!axmap)
return;
for (i = 0; i < axmap->nr_levels; i++)
free(axmap->levels[i].map);
free(axmap->levels);
free(axmap);
}
/* Allocate memory for a set that can store the numbers 0 .. @nr_bits - 1. */
struct axmap *axmap_new(uint64_t nr_bits)
{
struct axmap *axmap;
unsigned int i, levels;
axmap = malloc(sizeof(*axmap));
if (!axmap)
return NULL;
levels = 1;
i = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
while (i > 1) {
i = (i + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
levels++;
}
axmap->nr_levels = levels;
axmap->levels = calloc(axmap->nr_levels, sizeof(struct axmap_level));
if (!axmap->levels)
goto free_axmap;
axmap->nr_bits = nr_bits;
for (i = 0; i < axmap->nr_levels; i++) {
struct axmap_level *al = &axmap->levels[i];
nr_bits = (nr_bits + BLOCKS_PER_UNIT - 1) >> UNIT_SHIFT;
al->level = i;
al->map_size = nr_bits;
al->map = malloc(al->map_size * sizeof(unsigned long));
if (!al->map)
goto free_levels;
}
axmap_reset(axmap);
return axmap;
free_levels:
for (i = 0; i < axmap->nr_levels; i++)
free(axmap->levels[i].map);
free(axmap->levels);
free_axmap:
free(axmap);
return NULL;
}
/*
* Call @func for each level, starting at level zero, until a level is found
* for which @func returns true. Return false if none of the @func calls
* returns true.
*/
static bool axmap_handler(struct axmap *axmap, uint64_t bit_nr,
bool (*func)(struct axmap_level *, uint64_t, unsigned int,
void *), void *data)
{
struct axmap_level *al;
uint64_t index = bit_nr;
int i;
for (i = 0; i < axmap->nr_levels; i++) {
unsigned long offset = index >> UNIT_SHIFT;
unsigned int bit = index & BLOCKS_PER_UNIT_MASK;
al = &axmap->levels[i];
if (func(al, offset, bit, data))
return true;
if (index)
index >>= UNIT_SHIFT;
}
return false;
}
/*
* Call @func for each level, starting at the highest level, until a level is
* found for which @func returns true. Return false if none of the @func calls
* returns true.
*/
static bool axmap_handler_topdown(struct axmap *axmap, uint64_t bit_nr,
bool (*func)(struct axmap_level *, uint64_t, unsigned int, void *))
{
int i;
for (i = axmap->nr_levels - 1; i >= 0; i--) {
uint64_t index = bit_nr >> (UNIT_SHIFT * i);
unsigned long offset = index >> UNIT_SHIFT;
unsigned int bit = index & BLOCKS_PER_UNIT_MASK;
if (func(&axmap->levels[i], offset, bit, NULL))
return true;
}
return false;
}
struct axmap_set_data {
unsigned int nr_bits;
unsigned int set_bits;
};
/*
* Set at most @__data->nr_bits bits in @al at offset @offset. Do not exceed
* the boundary of the element at offset @offset. Return the number of bits
* that have been set in @__data->set_bits if @al->level == 0.
*/
static bool axmap_set_fn(struct axmap_level *al, uint64_t offset,
unsigned int bit, void *__data)
{
struct axmap_set_data *data = __data;
unsigned long mask, overlap;
unsigned int nr_bits;
nr_bits = min(data->nr_bits, BLOCKS_PER_UNIT - bit);
mask = bit_masks[nr_bits] << bit;
/*
* Mask off any potential overlap, only sets contig regions
*/
overlap = al->map[offset] & mask;
if (overlap == mask) {
data->set_bits = 0;
return true;
}
if (overlap) {
nr_bits = ffz(~overlap) - bit;
if (!nr_bits)
return true;
mask = bit_masks[nr_bits] << bit;
}
assert(mask);
assert(!(al->map[offset] & mask));
al->map[offset] |= mask;
if (!al->level)
data->set_bits = nr_bits;
/* For the next level */
data->nr_bits = 1;
return al->map[offset] != -1UL;
}
/*
* Set up to @data->nr_bits starting from @bit_nr in @axmap. Start at
* @bit_nr. If that bit has not yet been set then set it and continue until
* either @data->nr_bits have been set or a 1 bit is found. Store the number
* of bits that have been set in @data->set_bits. It is guaranteed that all
* bits that have been requested to set fit in the same unsigned long word of
* level 0 of @axmap.
*/
static void __axmap_set(struct axmap *axmap, uint64_t bit_nr,
struct axmap_set_data *data)
{
unsigned int nr_bits = data->nr_bits;
if (bit_nr > axmap->nr_bits)
return;
else if (bit_nr + nr_bits > axmap->nr_bits)
nr_bits = axmap->nr_bits - bit_nr;
assert(nr_bits <= BLOCKS_PER_UNIT);
axmap_handler(axmap, bit_nr, axmap_set_fn, data);
}
void axmap_set(struct axmap *axmap, uint64_t bit_nr)
{
struct axmap_set_data data = { .nr_bits = 1, };
__axmap_set(axmap, bit_nr, &data);
}
/*
* Set up to @nr_bits starting from @bit in @axmap. Start at @bit. If that
* bit has not yet been set then set it and continue until either @nr_bits
* have been set or a 1 bit is found. Return the number of bits that have been
* set.
*/
unsigned int axmap_set_nr(struct axmap *axmap, uint64_t bit_nr,
unsigned int nr_bits)
{
unsigned int set_bits = 0;
do {
struct axmap_set_data data = { .nr_bits = nr_bits, };
unsigned int max_bits, this_set;
max_bits = BLOCKS_PER_UNIT - (bit_nr & BLOCKS_PER_UNIT_MASK);
if (nr_bits > max_bits)
data.nr_bits = max_bits;
this_set = data.nr_bits;
__axmap_set(axmap, bit_nr, &data);
set_bits += data.set_bits;
if (data.set_bits != this_set)
break;
nr_bits -= data.set_bits;
bit_nr += data.set_bits;
} while (nr_bits);
return set_bits;
}
static bool axmap_isset_fn(struct axmap_level *al, uint64_t offset,
unsigned int bit, void *unused)
{
return (al->map[offset] & (1ULL << bit)) != 0;
}
bool axmap_isset(struct axmap *axmap, uint64_t bit_nr)
{
if (bit_nr <= axmap->nr_bits)
return axmap_handler_topdown(axmap, bit_nr, axmap_isset_fn);
return false;
}
/*
* Find the first free bit that is at least as large as bit_nr. Return
* -1 if no free bit is found before the end of the map.
*/
static uint64_t axmap_find_first_free(struct axmap *axmap, uint64_t bit_nr)
{
int i;
unsigned long temp;
unsigned int bit;
uint64_t offset, base_index, index;
struct axmap_level *al;
index = 0;
for (i = axmap->nr_levels - 1; i >= 0; i--) {
al = &axmap->levels[i];
/* Shift previously calculated index for next level */
index <<= UNIT_SHIFT;
/*
* Start from an index that's at least as large as the
* originally passed in bit number.
*/
base_index = bit_nr >> (UNIT_SHIFT * i);
if (index < base_index)
index = base_index;
/* Get the offset and bit for this level */
offset = index >> UNIT_SHIFT;
bit = index & BLOCKS_PER_UNIT_MASK;
/*
* If the previous level had unused bits in its last
* word, the offset could be bigger than the map at
* this level. That means no free bits exist before the
* end of the map, so return -1.
*/
if (offset >= al->map_size)
return -1ULL;
/* Check the first word starting with the specific bit */
temp = ~bit_masks[bit] & ~al->map[offset];
if (temp)
goto found;
/*
* No free bit in the first word, so iterate
* looking for a word with one or more free bits.
*/
for (offset++; offset < al->map_size; offset++) {
temp = ~al->map[offset];
if (temp)
goto found;
}
/* Did not find a free bit */
return -1ULL;
found:
/* Compute the index of the free bit just found */
index = (offset << UNIT_SHIFT) + ffz(~temp);
}
/* If found an unused bit in the last word of level 0, return -1 */
if (index >= axmap->nr_bits)
return -1ULL;
return index;
}
/*
* 'bit_nr' is already set. Find the next free bit after this one.
* Return -1 if no free bits found.
*/
uint64_t axmap_next_free(struct axmap *axmap, uint64_t bit_nr)
{
uint64_t ret;
uint64_t next_bit = bit_nr + 1;
unsigned long temp;
uint64_t offset;
unsigned int bit;
if (bit_nr >= axmap->nr_bits)
return -1ULL;
/* If at the end of the map, wrap-around */
if (next_bit == axmap->nr_bits)
next_bit = 0;
offset = next_bit >> UNIT_SHIFT;
bit = next_bit & BLOCKS_PER_UNIT_MASK;
/*
* As an optimization, do a quick check for a free bit
* in the current word at level 0. If not found, do
* a topdown search.
*/
temp = ~bit_masks[bit] & ~axmap->levels[0].map[offset];
if (temp) {
ret = (offset << UNIT_SHIFT) + ffz(~temp);
/* Might have found an unused bit at level 0 */
if (ret >= axmap->nr_bits)
ret = -1ULL;
} else
ret = axmap_find_first_free(axmap, next_bit);
/*
* If there are no free bits starting at next_bit and going
* to the end of the map, wrap around by searching again
* starting at bit 0.
*/
if (ret == -1ULL && next_bit != 0)
ret = axmap_find_first_free(axmap, 0);
return ret;
}