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libprobe.c
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libprobe.c
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#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>
#include <math.h>
#include <errno.h>
#include <time.h> /* For time(). */
#include <sys/time.h> /* For gettimeofday(). */
#include "libutils.h"
#include "libprobe.h"
static int write_blocks(struct device *dev,
uint64_t first_pos, uint64_t last_pos, uint64_t salt)
{
const int block_order = dev_get_block_order(dev);
const int block_size = dev_get_block_size(dev);
/* Aligning these pointers is necessary to directly read and write
* the block device.
* For the file device, this is superfluous.
*/
char stack[align_head(block_order) + BIG_BLOCK_SIZE_BYTE];
char *buffer = align_mem(stack, block_order);
char *stamp_blk = buffer;
char *flush_blk = buffer + BIG_BLOCK_SIZE_BYTE;
uint64_t offset = first_pos << block_order;
uint64_t pos, write_pos = first_pos;
for (pos = first_pos; pos <= last_pos; pos++) {
fill_buffer_with_block(stamp_blk, block_order, offset, salt);
stamp_blk += block_size;
offset += block_size;
if (stamp_blk == flush_blk || pos == last_pos) {
if (dev_write_blocks(dev, buffer, write_pos, pos) &&
dev_write_blocks(dev, buffer, write_pos, pos))
return true;
stamp_blk = buffer;
write_pos = pos + 1;
}
}
return false;
}
static int high_level_reset(struct device *dev, uint64_t start_pos,
uint64_t cache_size_block, int need_reset, uint64_t salt)
{
if (write_blocks(dev,
start_pos, start_pos + cache_size_block - 1, salt))
return true;
/* Reset. */
if (need_reset && dev_reset(dev) && dev_reset(dev))
return true;
return false;
}
/* Statistics used by bisect() in order to optimize the proportion
* between writes and resets.
*/
struct bisect_stats {
int write_count;
int reset_count;
uint64_t write_time_us;
uint64_t reset_time_us;
};
static void init_bisect_stats(struct bisect_stats *stats)
{
memset(stats, 0, sizeof(*stats));
}
#define MAX_N_BLOCK_ORDER 10
static uint64_t estimate_n_bisect_blocks(struct bisect_stats *pstats)
{
double t_w_us, t_2w_us, t_r_us;
uint64_t n_block_order;
if (pstats->write_count < 10 || pstats->reset_count < 1) {
/* There is not enough measurements. */
return (1 << 4) - 1;
}
/* Let 2^n be the total number of blocks on the drive.
* Let p be the total number of passes.
* Let w = (2^m - 1) be the number of blocks written on each pass,
* where m >= 1.
*
* A pass is an iteration of the loop in search_edge(), that is,
* a call to write_test_blocks(), dev_reset(), and probe_test_blocks().
*
* The reason to have w = (2^m - 1) instead of w = 2^m is because
* the former leads to a clean relationship between n, p, and m
* when m is constant: 2^n / (w + 1)^p = 1 => p = n/m
*
* Let Tr be the time to reset the device.
* Let Tw be the time to write a block to @dev.
* Let Tw' be the time to write a block to the underlying device
* of @dev, that is, without overhead due to chaining multiple
* struct device. For example, when struct safe_device is used
* Tw > Tw'.
* Let Trd be the time to read a block from @dev.
*
* Notice that each single-block pass reduces the search space in half,
* and that to reduce the search space in half writing blocks,
* one has to increase m of one.
*
* Thus, in order to be better writing more blocks than
* going for another pass, the following relation must be true:
*
* Tr + Tw + Tw' >= (w - 1)(Tw + Tw')
*
* The relation above assumes Trd = 0.
*
* The left side of the relation above is the time to do _another_
* pass writing a single block, whereas the right side is the time to
* stay in the same pass and write (w - 1) more blocks.
* In order words, if there is no advantage to write more blocks,
* we stick to single-block passes.
*
* Tw' is there to account for any operation that writes
* the blocks back (e.g. using struct safe_device), otherwise
* processing operations related per written blocks that is not
* being accounted for (e.g. reading the blocks back to test).
*
* Solving the relation for w: w <= Tr/(Tw + Tw') + 2
*
* However, we are not interested in any w, but only those of
* of the form (2^m - 1) to make sure that we are not better off
* calling another pass. Thus, solving the previous relation for m:
*
* m <= log_2(Tr/(Tw + Tw') + 3)
*
* We approximate Tw' making it equal to Tw.
*/
t_w_us = (double)pstats->write_time_us / pstats->write_count;
t_r_us = (double)pstats->reset_time_us / pstats->reset_count;
t_2w_us = t_w_us > 0. ? 2. * t_w_us : 1.; /* Avoid zero division. */
n_block_order = ilog2(round(t_r_us / t_2w_us + 3.));
/* Bound the maximum number of blocks per pass to limit
* the necessary amount of memory struct safe_device pre-allocates.
*/
if (n_block_order > MAX_N_BLOCK_ORDER)
n_block_order = MAX_N_BLOCK_ORDER;
return (1 << n_block_order) - 1;
}
/* Write blocks whose offsets are after @left_pos and before @right_pos. */
static int write_bisect_blocks(struct device *dev,
uint64_t left_pos, uint64_t right_pos, uint64_t n_blocks,
uint64_t salt, uint64_t *pa, uint64_t *pb, uint64_t *pmax_idx)
{
uint64_t pos, last_pos;
assert(n_blocks >= 1);
/* Find coefficients of function a*idx + b where idx <= max_idx. */
assert(left_pos < right_pos);
assert(right_pos - left_pos >= 2);
*pb = left_pos + 1;
*pa = round((right_pos - *pb - 1.) / (n_blocks + 1.));
*pa = !*pa ? 1ULL : *pa;
*pmax_idx = (right_pos - *pb - 1) / *pa;
if (*pmax_idx >= n_blocks) {
/* Shift the zero of the function to the right.
* This avoids picking the leftmost block when a more
* informative block to the right is available.
*/
*pb += *pa;
*pmax_idx = n_blocks - 1;
}
last_pos = *pa * *pmax_idx + *pb;
assert(last_pos < right_pos);
/* Write test blocks. */
for (pos = *pb; pos <= last_pos; pos += *pa)
if (write_blocks(dev, pos, pos, salt))
return true;
return false;
}
static int is_block_good(struct device *dev, uint64_t pos, int *pis_good,
uint64_t salt)
{
const int block_size = dev_get_block_size(dev);
const int block_order = dev_get_block_order(dev);
char stack[align_head(block_order) + block_size];
char *probe_blk = align_mem(stack, block_order);
uint64_t found_offset;
if (dev_read_blocks(dev, probe_blk, pos, pos) &&
dev_read_blocks(dev, probe_blk, pos, pos))
return true;
*pis_good = !validate_buffer_with_block(probe_blk, block_order,
&found_offset, salt) &&
found_offset == (pos << block_order);
return false;
}
static int probe_bisect_blocks(struct device *dev,
uint64_t *pleft_pos, uint64_t *pright_pos, uint64_t salt,
uint64_t a, uint64_t b, uint64_t max_idx)
{
/* Signed variables. */
int64_t left_idx = 0;
int64_t right_idx = max_idx;
while (left_idx <= right_idx) {
int64_t idx = (left_idx + right_idx) / 2;
uint64_t pos = a * idx + b;
int is_good;
if (is_block_good(dev, pos, &is_good, salt))
return true;
if (is_good) {
left_idx = idx + 1;
*pleft_pos = pos;
} else {
right_idx = idx - 1;
*pright_pos = pos;
}
}
return false;
}
/* This function assumes that the block at @left_pos is good, and
* that the block at @*pright_pos is bad.
*/
static int bisect(struct device *dev, struct bisect_stats *pstats,
uint64_t left_pos, uint64_t *pright_pos, uint64_t reset_pos,
uint64_t cache_size_block, int need_reset, uint64_t salt)
{
uint64_t gap = *pright_pos - left_pos;
struct timeval t1, t2;
assert(*pright_pos > left_pos);
while (gap >= 2) {
uint64_t a, b, max_idx;
uint64_t n_blocks = estimate_n_bisect_blocks(pstats);
assert(!gettimeofday(&t1, NULL));
if (write_bisect_blocks(dev, left_pos, *pright_pos, n_blocks,
salt, &a, &b, &max_idx))
return true;
assert(!gettimeofday(&t2, NULL));
pstats->write_count += max_idx + 1;
pstats->write_time_us += diff_timeval_us(&t1, &t2);
/* Reset. */
assert(!gettimeofday(&t1, NULL));
if (high_level_reset(dev, reset_pos,
cache_size_block, need_reset, salt))
return true;
assert(!gettimeofday(&t2, NULL));
pstats->reset_count++;
pstats->reset_time_us += diff_timeval_us(&t1, &t2);
if (probe_bisect_blocks(dev, &left_pos, pright_pos, salt,
a, b, max_idx))
return true;
gap = *pright_pos - left_pos;
}
assert(gap == 1);
return false;
}
static int count_good_blocks(struct device *dev, uint64_t *pcount,
uint64_t first_pos, uint64_t last_pos, uint64_t salt)
{
const int block_size = dev_get_block_size(dev);
const int block_order = dev_get_block_order(dev);
char stack[align_head(block_order) + BIG_BLOCK_SIZE_BYTE];
char *buffer = align_mem(stack, block_order);
uint64_t expected_sector_offset = first_pos << block_order;
uint64_t start_pos = first_pos;
uint64_t step = (BIG_BLOCK_SIZE_BYTE >> block_order) - 1;
uint64_t count = 0;
assert(BIG_BLOCK_SIZE_BYTE >= block_size);
while (start_pos <= last_pos) {
char *probe_blk = buffer;
uint64_t pos, next_pos = start_pos + step;
if (next_pos > last_pos)
next_pos = last_pos;
if (dev_read_blocks(dev, buffer, start_pos, next_pos) &&
dev_read_blocks(dev, buffer, start_pos, next_pos))
return true;
for (pos = start_pos; pos <= next_pos; pos++) {
uint64_t found_sector_offset;
if (!validate_buffer_with_block(probe_blk, block_order,
&found_sector_offset, salt) &&
expected_sector_offset == found_sector_offset)
count++;
expected_sector_offset += block_size;
probe_blk += block_size;
}
start_pos = next_pos + 1;
}
*pcount = count;
return false;
}
static int assess_reset_effect(struct device *dev,
uint64_t *pcache_size_block, int *pneed_reset, int *pdone,
uint64_t first_pos, uint64_t last_pos, uint64_t salt)
{
uint64_t write_target = (last_pos + 1) - first_pos;
uint64_t b4_reset_count_block, after_reset_count_block;
if (count_good_blocks(dev, &b4_reset_count_block,
first_pos, last_pos, salt))
return true;
if (!b4_reset_count_block) {
/* The drive has no cache whatsoever. */
*pcache_size_block = 0;
*pneed_reset = false;
*pdone = true;
return false;
}
/* Reset. */
if (dev_reset(dev) && dev_reset(dev))
return true;
if (count_good_blocks(dev, &after_reset_count_block,
first_pos, last_pos, salt))
return true;
/* Although unexpected, some fake cards do recover blocks after
* a reset! This behavior is not consistent, though.
* The first reported case is found here:
* https://github.com/AltraMayor/f3/issues/50
*/
if (b4_reset_count_block < write_target ||
after_reset_count_block < write_target) {
*pneed_reset = after_reset_count_block < b4_reset_count_block;
*pcache_size_block = *pneed_reset
? after_reset_count_block
: write_target;
*pdone = true;
return false;
}
*pdone = false;
return false;
}
static inline uint64_t uint64_rand(void)
{
return ((uint64_t)rand() << 32) | rand();
}
static uint64_t uint64_rand_range(uint64_t a, uint64_t b)
{
uint64_t r = uint64_rand();
assert(a <= b);
return a + (r % (b - a + 1));
}
#define N_BLOCK_SAMPLES 64
static int probabilistic_test(struct device *dev,
uint64_t first_pos, uint64_t last_pos, int *pfound_a_bad_block,
uint64_t salt)
{
uint64_t gap;
int i, n, is_linear;
if (first_pos > last_pos)
goto not_found;
/* Let g be the number of good blocks between
* @first_pos and @last_pos including them.
* Let b be the number of bad and overwritten blocks between
* @first_pos and @last_pos including them.
*
* The probability Pr_g of sampling a good block at random between
* @first_pos and @last_pos is Pr_g = g / (g + b), and
* the probability Pr_1b that among k block samples at least
* one block is bad is Pr_1b = 1 - Pr_g^k.
*
* Assuming Pr_g <= 95% and k = 64, Pr_1b >= 96.2%.
* That is, with high probability (i.e. Pr_1b),
* one can find at least a bad block with k samples
* when most blocks are good (Pr_g).
*/
/* Test @samples. */
gap = last_pos - first_pos + 1;
is_linear = gap <= N_BLOCK_SAMPLES;
n = is_linear ? gap : N_BLOCK_SAMPLES;
for (i = 0; i < n; i++) {
uint64_t sample_pos = is_linear
? first_pos + i
: uint64_rand_range(first_pos, last_pos);
int is_good;
if (is_block_good(dev, sample_pos, &is_good, salt))
return true;
if (!is_good) {
/* Found a bad block. */
*pfound_a_bad_block = true;
return false;
}
}
not_found:
*pfound_a_bad_block = false;
return false;
}
static int uint64_cmp(const void *pa, const void *pb)
{
const uint64_t *pia = pa;
const uint64_t *pib = pb;
return *pia - *pib;
}
static int find_a_bad_block(struct device *dev,
uint64_t left_pos, uint64_t *pright_pos, int *found_a_bad_block,
uint64_t reset_pos, uint64_t cache_size_block, int need_reset,
uint64_t salt)
{
/* We need to list all sampled blocks because
* we need a sorted array; read the code to find the why.
* If the sorted array were not needed, one could save the seed
* of the random sequence and repeat the sequence to read the blocks
* after writing them.
*/
uint64_t samples[N_BLOCK_SAMPLES];
uint64_t gap, prv_sample;
int n, i;
if (*pright_pos <= left_pos + 1)
goto not_found;
/* The code below relies on the same analytical result derived
* in probabilistic_test().
*/
/* Fill up @samples. */
gap = *pright_pos - left_pos - 1;
if (gap <= N_BLOCK_SAMPLES) {
n = gap;
for (i = 0; i < n; i++)
samples[i] = left_pos + 1 + i;
/* Write @samples. */
if (write_blocks(dev, left_pos + 1, *pright_pos - 1, salt))
return true;
} else {
n = N_BLOCK_SAMPLES;
for (i = 0; i < n; i++)
samples[i] = uint64_rand_range(left_pos + 1,
*pright_pos - 1);
/* Sort entries of @samples to minimize reads.
* As soon as one finds a bad block, one can stop and ignore
* the remaining blocks because the found bad block is
* the leftmost bad block.
*/
qsort(samples, n, sizeof(uint64_t), uint64_cmp);
/* Write @samples. */
prv_sample = left_pos;
for (i = 0; i < n; i++) {
if (samples[i] == prv_sample)
continue;
prv_sample = samples[i];
if (write_blocks(dev, prv_sample, prv_sample, salt))
return true;
}
}
/* Reset. */
if (high_level_reset(dev, reset_pos,
cache_size_block, need_reset, salt))
return true;
/* Test @samples. */
prv_sample = left_pos;
for (i = 0; i < n; i++) {
int is_good;
if (samples[i] == prv_sample)
continue;
prv_sample = samples[i];
if (is_block_good(dev, prv_sample, &is_good, salt))
return true;
if (!is_good) {
/* Found the leftmost bad block. */
*pright_pos = prv_sample;
*found_a_bad_block = true;
return false;
}
}
not_found:
*found_a_bad_block = false;
return false;
}
/* Both need to be a power of 2 and larger than, or equal to 2^block_order. */
#define MIN_CACHE_SIZE_BYTE (1ULL << 20)
#define MAX_CACHE_SIZE_BYTE (1ULL << 30)
static int find_cache_size(struct device *dev,
uint64_t left_pos, uint64_t *pright_pos, uint64_t *pcache_size_block,
int *pneed_reset, int *pgood_drive, const uint64_t salt)
{
const int block_order = dev_get_block_order(dev);
uint64_t write_target = MIN_CACHE_SIZE_BYTE >> block_order;
uint64_t final_write_target = MAX_CACHE_SIZE_BYTE >> block_order;
uint64_t first_pos, last_pos, end_pos;
int done;
/*
* Basis
*
* The key difference between the basis and the inductive step is
* the fact that the basis always calls assess_reset_effect().
* This difference is not for correctness, that is, one can remove it,
* and fold the basis into the inductive step.
* However, this difference is an important speedup because many
* fake drives do not have permanent cache.
*/
assert(write_target > 0);
assert(write_target < final_write_target);
last_pos = end_pos = *pright_pos - 1;
/* This convoluted test is needed because
* the variables are unsigned.
* In a simplified form, it tests the following:
* *pright_pos - write_target > left_pos
*/
if (*pright_pos > left_pos + write_target) {
first_pos = *pright_pos - write_target;
} else if (*pright_pos > left_pos + 1) {
/* There's no room to write @write_target blocks,
* so write what's possible.
*/
first_pos = left_pos + 1;
} else {
goto good;
}
if (write_blocks(dev, first_pos, last_pos, salt))
goto bad;
if (assess_reset_effect(dev, pcache_size_block,
pneed_reset, &done, first_pos, end_pos, salt))
goto bad;
if (done) {
*pright_pos = first_pos;
*pgood_drive = false;
return false;
}
/*
* Inductive step
*/
while (write_target < final_write_target) {
int found_a_bad_block;
write_target <<= 1;
last_pos = first_pos - 1;
if (first_pos > left_pos + write_target)
first_pos -= write_target;
else if (first_pos > left_pos + 1)
first_pos = left_pos + 1;
else
break; /* Cannot write any further. */
/* Write @write_target blocks before
* the previously written blocks.
*/
if (write_blocks(dev, first_pos, last_pos, salt))
goto bad;
if (probabilistic_test(dev, first_pos, end_pos,
&found_a_bad_block, salt))
goto bad;
if (found_a_bad_block) {
if (assess_reset_effect(dev, pcache_size_block,
pneed_reset, &done, first_pos, end_pos, salt))
goto bad;
assert(done);
*pright_pos = first_pos;
*pgood_drive = false;
return false;
}
}
good:
*pright_pos = end_pos + 1;
*pcache_size_block = 0;
*pneed_reset = false;
*pgood_drive = true;
return false;
bad:
/* *pright_pos does not change. */
*pcache_size_block = 0;
*pneed_reset = false;
*pgood_drive = false;
return true;
}
static int find_wrap(struct device *dev,
uint64_t left_pos, uint64_t *pright_pos,
uint64_t reset_pos, uint64_t cache_size_block, int need_reset,
uint64_t salt)
{
uint64_t offset, high_bit, pos = left_pos + 1;
int is_good, block_order;
/*
* Basis
*/
/* Make sure that there is at least a good block at the beginning
* of the drive.
*/
if (pos >= *pright_pos)
return false;
if (write_blocks(dev, pos, pos, salt) ||
high_level_reset(dev, reset_pos,
cache_size_block, need_reset, salt) ||
is_block_good(dev, pos, &is_good, salt) ||
!is_good)
return true;
/*
* Inductive step
*/
block_order = dev_get_block_order(dev);
offset = pos << block_order;
high_bit = clp2(pos);
if (high_bit <= pos)
high_bit <<= 1;
pos += high_bit;
while (pos < *pright_pos) {
char stack[align_head(block_order) + (1 << block_order)];
char *probe_blk = align_mem(stack, block_order);
uint64_t found_offset;
if (dev_read_blocks(dev, probe_blk, pos, pos) &&
dev_read_blocks(dev, probe_blk, pos, pos))
return true;
if (!validate_buffer_with_block(probe_blk, block_order,
&found_offset, salt) &&
found_offset == offset) {
*pright_pos = high_bit;
return false;
}
high_bit <<= 1;
pos = high_bit + left_pos + 1;
}
return false;
}
uint64_t probe_device_max_blocks(struct device *dev)
{
const int block_order = dev_get_block_order(dev);
uint64_t num_blocks = dev_get_size_byte(dev) >> block_order;
int n = ceiling_log2(num_blocks);
/* Make sure that there is no overflow in the formula below.
* The number 10 is arbitrary here, that is, it's not tight.
*/
assert(MAX_N_BLOCK_ORDER < 8*sizeof(int) - 10);
return
/* find_cache_size() */
(MAX_CACHE_SIZE_BYTE >> (block_order - 1)) +
/* find_wrap() */
1 +
/* The number below is just an educated guess. */
128 * (
/* bisect()
*
* The number of used blocks is (p * w); see comments
* in estimate_n_bisect_blocks() for the definition of
* the variables.
*
* p * w = n/m * (2^m - 1) < n/m * 2^m = n * (2^m / m)
*
* Let f(m) be 2^m / m. One can prove that
* f(m + 1) >= f(m) for all m >= 1.
* Therefore, the following bound is true.
*
* p * w < n * f(max_m)
*/
((n << MAX_N_BLOCK_ORDER) / MAX_N_BLOCK_ORDER) +
/* find_a_bad_block() */
N_BLOCK_SAMPLES
);
}
int probe_device(struct device *dev, uint64_t *preal_size_byte,
uint64_t *pannounced_size_byte, int *pwrap,
uint64_t *pcache_size_block, int *pneed_reset, int *pblock_order)
{
const uint64_t dev_size_byte = dev_get_size_byte(dev);
const int block_order = dev_get_block_order(dev);
struct bisect_stats stats;
uint64_t salt, cache_size_block;
uint64_t left_pos, right_pos, mid_drive_pos, reset_pos;
int need_reset, good_drive, wrap, found_a_bad_block;
assert(block_order <= 20);
/* @left_pos must point to a good block.
* We just point to the last block of the first 1MB of the card
* because this region is reserved for partition tables.
*
* Given that all writing is confined to the interval
* (@left_pos, @right_pos), we avoid losing the partition table.
*/
left_pos = (1ULL << (20 - block_order)) - 1;
/* @right_pos must point to a bad block.
* We just point to the block after the very last block.
*/
right_pos = dev_size_byte >> block_order;
/* @left_pos cannot be equal to @right_pos since
* @left_pos points to a good block, and @right_pos to a bad block.
*/
if (left_pos >= right_pos) {
cache_size_block = 0;
need_reset = false;
goto bad;
}
/* I, Michel Machado, define that any drive with less than
* this number of blocks is fake.
*/
mid_drive_pos = clp2(right_pos / 2);
assert(left_pos < mid_drive_pos);
assert(mid_drive_pos < right_pos);
/* This call is needed due to rand(). */
srand(time(NULL));
salt = uint64_rand();
if (find_cache_size(dev, mid_drive_pos - 1, &right_pos,
&cache_size_block, &need_reset, &good_drive, salt))
goto bad;
assert(mid_drive_pos <= right_pos);
reset_pos = right_pos;
if (find_wrap(dev, left_pos, &right_pos,
reset_pos, cache_size_block, need_reset, salt))
goto bad;
wrap = ceiling_log2(right_pos << block_order);
init_bisect_stats(&stats);
if (!good_drive) {
if (mid_drive_pos < right_pos)
right_pos = mid_drive_pos;
if (bisect(dev, &stats, left_pos, &right_pos,
reset_pos, cache_size_block, need_reset, salt))
goto bad;
}
do {
if (find_a_bad_block(dev, left_pos, &right_pos,
&found_a_bad_block, reset_pos, cache_size_block,
need_reset, salt))
goto bad;
if (found_a_bad_block &&
bisect(dev, &stats, left_pos, &right_pos,
reset_pos, cache_size_block, need_reset, salt))
goto bad;
} while (found_a_bad_block);
if (right_pos == left_pos + 1) {
/* Bad drive. */
right_pos = 0;
}
*preal_size_byte = right_pos << block_order;
*pwrap = wrap;
goto out;
bad:
*preal_size_byte = 0;
*pwrap = ceiling_log2(dev_size_byte);
out:
*pannounced_size_byte = dev_size_byte;
*pcache_size_block = cache_size_block;
*pneed_reset = need_reset;
*pblock_order = block_order;
return false;
}