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Merge pull request #172 from ia0/v2_lib

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Add format helpers for new store
This commit is contained in:
Julien Cretin
2020-10-27 14:13:33 +01:00
committed by GitHub
parent 1f0f2d16e3 71815cad09
commit 55ceec2a21
3 changed files with 1312 additions and 19 deletions
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libraries/persistent_store/src/bitfield.rs
+22 -19
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@@ -13,8 +13,6 @@
// limitations under the License.
//! Helps manipulate bit fields in 32-bits words.
// TODO(ia0): Remove when the module is used.
#![cfg_attr(not(test), allow(dead_code, unused_macros))]
use crate::{StoreError, StoreResult};
@@ -180,24 +178,29 @@ macro_rules! bitfield_impl {
// - Input are bit field descriptors
// - Position is the number of bits used by prior bit fields
// - Output are the bit field definitions
([$($output: tt)*]{ pos: $pos: expr }[$name: ident: Bit, $($input: tt)*]) => {
([$($output: tt)*]{ pos: $pos: expr }
[$(#[$meta: meta])* $name: ident: Bit, $($input: tt)*]) => {
bitfield_impl! {
[$($output)* const $name: Bit = Bit { pos: $pos };]
[$($output)* $(#[$meta])* const $name: Bit = Bit { pos: $pos };]
{ pos: $pos + 1 }
[$($input)*]
}
};
([$($output: tt)*]{ pos: $pos: expr }[$name: ident: Field <= $max: expr, $($input: tt)*]) => {
([$($output: tt)*]{ pos: $pos: expr }
[$(#[$meta: meta])* $name: ident: Field <= $max: expr, $($input: tt)*]) => {
bitfield_impl! {
[$($output)* const $name: Field = Field { pos: $pos, len: num_bits($max) };]
[$($output)* $(#[$meta])* const $name: Field = Field {
pos: $pos,
len: num_bits($max),
};]
{ pos: $pos + $name.len }
[$($input)*]
}
};
([$($output: tt)*]{ pos: $pos: expr }
[$name: ident: Checksum <= $max: expr, $($input: tt)*]) => {
[$(#[$meta: meta])* $name: ident: Checksum <= $max: expr, $($input: tt)*]) => {
bitfield_impl! {
[$($output)* const $name: Checksum = Checksum {
[$($output)* $(#[$meta])* const $name: Checksum = Checksum {
field: Field { pos: $pos, len: num_bits($max) }
};]
{ pos: $pos + $name.field.len }
@@ -213,9 +216,9 @@ macro_rules! bitfield_impl {
}
};
([$($output: tt)*]{ pos: $pos: expr }
[$name: ident: ConstField = $bits: tt, $($input: tt)*]) => {
[$(#[$meta: meta])* $name: ident: ConstField = $bits: tt, $($input: tt)*]) => {
bitfield_impl! {
Reverse $name []$bits
Reverse $(#[$meta])* $name []$bits
[$($output)*]{ pos: $pos }[$($input)*]
}
};
@@ -224,17 +227,17 @@ macro_rules! bitfield_impl {
// Auxiliary rules for constant bit fields:
// - Input is a sequence of bits
// - Output is the reversed sequence of bits
(Reverse $name: ident [$($output_bits: tt)*] [$bit: tt $($input_bits: tt)*]
(Reverse $(#[$meta: meta])* $name: ident [$($output_bits: tt)*] [$bit: tt $($input_bits: tt)*]
[$($output: tt)*]{ pos: $pos: expr }[$($input: tt)*]) => {
bitfield_impl! {
Reverse $name [$bit $($output_bits)*][$($input_bits)*]
Reverse $(#[$meta])* $name [$bit $($output_bits)*][$($input_bits)*]
[$($output)*]{ pos: $pos }[$($input)*]
}
};
(Reverse $name: ident $bits: tt []
(Reverse $(#[$meta: meta])* $name: ident $bits: tt []
[$($output: tt)*]{ pos: $pos: expr }[$($input: tt)*]) => {
bitfield_impl! {
ConstField $name { len: 0, val: 0 }$bits
ConstField $(#[$meta])* $name { len: 0, val: 0 }$bits
[$($output)*]{ pos: $pos }[$($input)*]
}
};
@@ -242,10 +245,10 @@ macro_rules! bitfield_impl {
// Auxiliary rules for constant bit fields:
// - Input is a sequence of bits in reversed order
// - Output is the constant bit field definition with the sequence of bits as value
(ConstField $name: ident { len: $len: expr, val: $val: expr }[]
(ConstField $(#[$meta: meta])* $name: ident { len: $len: expr, val: $val: expr }[]
[$($output: tt)*]{ pos: $pos: expr }[$($input: tt)*]) => {
bitfield_impl! {
[$($output)* const $name: ConstField = ConstField {
[$($output)* $(#[$meta])* const $name: ConstField = ConstField {
field: Field { pos: $pos, len: $len },
value: $val,
};]
@@ -253,10 +256,10 @@ macro_rules! bitfield_impl {
[$($input)*]
}
};
(ConstField $name: ident { len: $len: expr, val: $val: expr }[$bit: tt $($bits: tt)*]
[$($output: tt)*]{ pos: $pos: expr }[$($input: tt)*]) => {
(ConstField $(#[$meta: meta])* $name: ident { len: $len: expr, val: $val: expr }
[$bit: tt $($bits: tt)*][$($output: tt)*]{ pos: $pos: expr }[$($input: tt)*]) => {
bitfield_impl! {
ConstField $name { len: $len + 1, val: $val * 2 + $bit }[$($bits)*]
ConstField $(#[$meta])* $name { len: $len + 1, val: $val * 2 + $bit }[$($bits)*]
[$($output)*]{ pos: $pos }[$($input)*]
}
};
libraries/persistent_store/src/format.rs
+957
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File diff suppressed because it is too large Load Diff
libraries/persistent_store/src/lib.rs
+333
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@@ -12,13 +12,346 @@
// See the License for the specific language governing permissions and
// limitations under the License.
// TODO(ia0): Add links once the code is complete.
//! Store abstraction for flash storage
//!
//! # Specification
//!
//! The store provides a partial function from keys to values on top of a storage
//! interface. The store total capacity depends on the size of the storage. Store
//! updates may be bundled in transactions. Mutable operations are atomic, including
//! when interrupted.
//!
//! The store is flash-efficient in the sense that it uses the storage lifetime
//! efficiently. For each page, all words are written at least once between erase
//! cycles and all erase cycles are used. However, not all written words are user
//! content: lifetime is also consumed with metadata and compaction.
//!
//! The store is extendable with other entries than key-values. It is essentially a
//! framework providing access to the storage lifetime. The partial function is
//! simply the most common usage and can be used to encode other usages.
//!
//! ## Definitions
//!
//! An _entry_ is a pair of a key and a value. A _key_ is a number between 0
//! and 4095. A _value_ is a byte slice with a length between 0 and 1023 bytes (for
//! large enough pages).
//!
//! The store provides the following _updates_:
//! - Given a key and a value, `Insert` updates the store such that the value is
//! associated with the key. The values for other keys are left unchanged.
//! - Given a key, `Remove` updates the store such that no value is associated with
//! the key. The values for other keys are left unchanged. Additionally, if there
//! was a value associated with the key, the value is wiped from the storage
//! (all its bits are set to 0).
//!
//! The store provides the following _read-only operations_:
//! - `Iter` iterates through the store returning all entries exactly once. The
//! iteration order is not specified but stable between mutable operations.
//! - `Capacity` returns how many words can be stored before the store is full.
//! - `Lifetime` returns how many words can be written before the storage lifetime
//! is consumed.
//!
//! The store provides the following _mutable operations_:
//! - Given a set of independent updates, `Transaction` applies the sequence of
//! updates.
//! - Given a threshold, `Clear` removes all entries with a key greater or equal
//! to the threshold.
//! - Given a length in words, `Prepare` makes one step of compaction unless that
//! many words can be written without compaction. This operation has no effect
//! on the store but may still mutate its storage. In particular, the store has
//! the same capacity but a possibly reduced lifetime.
//!
//! A mutable operation is _atomic_ if, when power is lost during the operation, the
//! store is either updated (as if the operation succeeded) or left unchanged (as if
//! the operation did not occur). If the store is left unchanged, lifetime may still
//! be consumed.
//!
//! The store relies on the following _storage interface_:
//! - It is possible to read a byte slice. The slice won't span multiple pages.
//! - It is possible to write a word slice. The slice won't span multiple pages.
//! - It is possible to erase a page.
//! - The pages are sequentially indexed from 0. If the actual underlying storage
//! is segmented, then the storage layer should translate those indices to
//! actual page addresses.
//!
//! The store has a _total capacity_ of `C = (N - 1) * (P - 4) - M - 1` words, where
//! `P` is the number of words per page, `N` is the number of pages, and `M` is the
//! maximum length in words of a value (256 for large enough pages). The capacity
//! used by each mutable operation is given below (a transient word only uses
//! capacity during the operation):
//! - `Insert` uses `1 + ceil(len / 4)` words where `len` is the length of the
//! value in bytes. If an entry was replaced, the words used by its insertion
//! are freed.
//! - `Remove` doesn't use capacity if alone in the transaction and 1 transient
//! word otherwise. If an entry was deleted, the words used by its insertion are
//! freed.
//! - `Transaction` uses 1 transient word. In addition, the updates of the
//! transaction use and free words as described above.
//! - `Clear` doesn't use capacity and frees the words used by the insertion of
//! the deleted entries.
//! - `Prepare` doesn't use capacity.
//!
//! The _total lifetime_ of the store is below `L = ((E + 1) * N - 1) * (P - 2)` and
//! above `L - M` words, where `E` is the maximum number of erase cycles. The
//! lifetime is used when capacity is used, including transiently, as well as when
//! compaction occurs. Compaction frequency and lifetime consumption are positively
//! correlated to the store load factor (the ratio of used capacity to total capacity).
//!
//! It is possible to approximate the cost of transient words in terms of capacity:
//! `L` transient words are equivalent to `C - x` words of capacity where `x` is the
//! average capacity (including transient) of operations.
//!
//! ## Preconditions
//!
//! The following assumptions need to hold, or the store may behave in unexpected ways:
//! - A word can be written twice between erase cycles.
//! - A page can be erased `E` times after the first boot of the store.
//! - When power is lost while writing a slice or erasing a page, the next read
//! returns a slice where a subset (possibly none or all) of the bits that
//! should have been modified have been modified.
//! - Reading a slice is deterministic. When power is lost while writing a slice
//! or erasing a slice (erasing a page containing that slice), reading that
//! slice repeatedly returns the same result (until it is overwritten or its
//! page is erased).
//! - To decide whether a page has been erased, it is enough to test if all its
//! bits are equal to 1.
//! - When power is lost while writing a slice or erasing a page, that operation
//! does not count towards the limits. However, completing that write or erase
//! operation would count towards the limits, as if the number of writes per
//! word and number of erase cycles could be fractional.
//! - The storage is only modified by the store. Note that completely erasing the
//! storage is supported, essentially losing all content and lifetime tracking.
//! It is preferred to use `Clear` with a threshold of 0 to keep the lifetime
//! tracking.
//!
//! The store properties may still hold outside some of those assumptions, but with
//! an increasing chance of failure.
//!
//! # Implementation
//!
//! We define the following constants:
//! - `E < 65536` the number of times a page can be erased.
//! - `3 <= N < 64` the number of pages in the storage.
//! - `8 <= P <= 1024` the number of words in a page.
//! - `Q = P - 2` the number of words in a virtual page.
//! - `K = 4096` the maximum number of keys.
//! - `M = min(Q - 1, 256)` the maximum length in words of a value.
//! - `V = (N - 1) * (Q - 1) - M` the virtual capacity.
//! - `C = V - N` the user capacity.
//!
//! We build a virtual storage from the physical storage using the first 2 words of
//! each page:
//! - The first word contains the number of times the page has been erased.
//! - The second word contains the starting word to which this page is being moved
//! during compaction.
//!
//! The virtual storage has a length of `(E + 1) * N * Q` words and represents the
//! lifetime of the store. (We reserve the last `Q + M` words to support adding
//! emergency lifetime.) This virtual storage has a linear address space.
//!
//! We define a set of overlapping windows of `N * Q` words at each `Q`-aligned
//! boundary. We call `i` the window spanning from `i * Q` to `(i + N) * Q`. Only
//! those windows actually exist in the underlying storage. We use compaction to
//! shift the current window from `i` to `i + 1`, preserving the content of the
//! store.
//!
//! For a given state of the virtual storage, we define `h_i` as the position of the
//! first entry of the window `i`. We call it the head of the window `i`. Because
//! entries are at most `M + 1` words, they can overlap on the next page only by `M`
//! words. So we have `i * Q <= h_i <= i * Q + M` . Since there are no entries
//! before the first page, we have `h_0 = 0`.
//!
//! We define `t_i` as one past the last entry of the window `i`. If there are no
//! entries in that window, we have `t_i = h_i`. We call `t_i` the tail of the
//! window `i`. We define the compaction invariant as `t_i - h_i <= V`.
//!
//! We define `|x|` as the capacity used before position `x`. We have `|x| <= x`. We
//! define the capacity invariant as `|t_i| - |h_i| <= C`.
//!
//! Using this virtual storage, entries are appended to the tail as long as there is
//! both virtual capacity to preserve the compaction invariant and capacity to
//! preserve the capacity invariant. When virtual capacity runs out, the first page
//! of the window is compacted and the window is shifted.
//!
//! Entries are identified by a prefix of bits. The prefix has to contain at least
//! one bit set to zero to differentiate from the tail. Entries can be one of:
//! - Padding: A word whose first bit is set to zero. The rest is arbitrary. This
//! entry is used to mark words partially written after an interrupted operation
//! as padding such that they are ignored by future operations.
//! - Header: A word whose second bit is set to zero. It contains the following fields:
//! - A bit indicating whether the entry is deleted.
//! - A bit indicating whether the value is word-aligned and has all bits set
//! to 1 in its last word. The last word of an entry is used to detect that
//! an entry has been fully written. As such it must contain at least one
//! bit equal to zero.
//! - The key of the entry.
//! - The length in bytes of the value. The value follows the header. The
//! entry is word-aligned if the value is not.
//! - The checksum of the first and last word of the entry.
//! - Erase: A word used during compaction. It contains the page to be erased and
//! a checksum.
//! - Clear: A word used during the `Clear` operation. It contains the threshold
//! and a checksum.
//! - Marker: A word used during the `Transaction` operation. It contains the
//! number of updates following the marker and a checksum.
//! - Remove: A word used during the `Transaction` operation. It contains the key
//! of the entry to be removed and a checksum.
//!
//! Checksums are the number of bits equal to 0.
//!
//! # Proofs
//!
//! ## Compaction
//!
//! It should always be possible to fully compact the store, after what the
//! remaining capacity should be available in the current window (restoring the
//! compaction invariant). We consider all notations on the virtual storage after
//! the full compaction. We will use the `|x|` notation although we update the state
//! of the virtual storage. This is fine because compaction doesn't change the
//! status of an existing word.
//!
//! We want to show that the next `N - 1` compactions won't move the tail past the
//! last page of their window, with `I` the initial window:
//!
//! ```text
//! forall 1 <= i <= N - 1, t_{I + i} <= (I + i + N - 1) * Q
//! ```
//!
//! We assume `i` between `1` and `N - 1`.
//!
//! One step of compaction advances the tail by how many words were used in the
//! first page of the window with the last entry possibly overlapping on the next
//! page.
//!
//! ```text
//! forall j, t_{j + 1} = t_j + |h_{j + 1}| - |h_j| + 1
//! ```
//!
//! By induction, we have:
//!
//! ```text
//! t_{I + i} <= t_I + |h_{I + i}| - |h_I| + i
//! ```
//!
//! We have the following properties:
//!
//! ```text
//! t_I <= h_I + V
//! |h_{I + i}| - |h_I| <= h_{I + i} - h_I
//! h_{I + i} <= (I + i) * Q + M
//! ```
//!
//! Replacing into our previous equality, we can conclude:
//!
//! ```text
//! t_{I + i} = t_I + |h_{I + i}| - |h_I| + i
//! <= h_I + V + (I + i) * Q + M - h_I + i
//! = (N - 1) * (Q - 1) - M + (I + i) * Q + M + i
//! = (N - 1) * (Q - 1) + (I + i) * Q + i
//! = (I + i + N - 1) * Q + i - (N - 1)
//! <= (I + i + N - 1) * Q
//! ```
//!
//! We also want to show that after `N - 1` compactions, the remaining capacity is
//! available without compaction.
//!
//! ```text
//! V - (t_{I + N - 1} - h_{I + N - 1}) >= // The available words in the window.
//! C - (|t_{I + N - 1}| - |h_{I + N - 1}|) // The remaining capacity.
//! + 1 // Reserved for Clear.
//! ```
//!
//! We can replace the definition of `C` and simplify:
//!
//! ```text
//! V - (t_{I + N - 1} - h_{I + N - 1}) >= V - N - (|t_{I + N - 1}| - |h_{I + N - 1}|) + 1
//! iff t_{I + N - 1} - h_{I + N - 1} <= |t_{I + N - 1}| - |h_{I + N - 1}| + N - 1
//! ```
//!
//! We have the following properties:
//!
//! ```text
//! t_{I + N - 1} = t_I + |h_{I + N - 1}| - |h_I| + N - 1
//! |t_{I + N - 1}| - |h_{I + N - 1}| = |t_I| - |h_I| // Compaction preserves capacity.
//! |h_{I + N - 1}| - |t_I| <= h_{I + N - 1} - t_I
//! ```
//!
//! From which we conclude:
//!
//! ```text
//! t_{I + N - 1} - h_{I + N - 1} <= |t_{I + N - 1}| - |h_{I + N - 1}| + N - 1
//! iff t_I + |h_{I + N - 1}| - |h_I| + N - 1 - h_{I + N - 1} <= |t_I| - |h_I| + N - 1
//! iff t_I + |h_{I + N - 1}| - h_{I + N - 1} <= |t_I|
//! iff |h_{I + N - 1}| - |t_I| <= h_{I + N - 1} - t_I
//! ```
//!
//!
//! ## Checksum
//!
//! The main property we want is that all partially written/erased words are either
//! the initial word, the final word, or invalid.
//!
//! We say that a bit sequence `TARGET` is reachable from a bit sequence `SOURCE` if
//! both have the same length and `SOURCE & TARGET == TARGET` where `&` is the
//! bitwise AND operation on bit sequences of that length. In other words, when
//! `SOURCE` has a bit equal to 0 then `TARGET` also has that bit equal to 0.
//!
//! The only written entries start with `101` or `110` and are written from an
//! erased word. Marking an entry as padding or deleted is a single bit operation,
//! so the property trivially holds. For those cases, the proof relies on the fact
//! that there is exactly one bit equal to 0 in the 3 first bits. Either the 3 first
//! bits are still `111` in which case we expect the remaining bits to be equal
//! to 1. Otherwise we can use the checksum of the given type of entry because those
//! 2 types of entries are not reachable from each other. Here is a visualization of
//! the partitioning based on the first 3 bits:
//!
//! | First 3 bits | Description | How to check |
//! | ------------:| ------------------ | ---------------------------- |
//! | `111` | Erased word | All bits set to `1` |
//! | `101` | User entry | Contains a checksum |
//! | `110` | Internal entry | Contains a checksum |
//! | `100` | Deleted user entry | No check, atomically written |
//! | `0??` | Padding entry | No check, atomically written |
//!
//! To show that valid entries of a given type are not reachable from each other, we
//! show 3 lemmas:
//!
//! 1. A bit sequence is not reachable from another if its number of bits equal to
//! 0 is smaller.
//!
//! 2. A bit sequence is not reachable from another if they have the same number of
//! bits equals to 0 and are different.
//!
//! 3. A bit sequence is not reachable from another if it is bigger when they are
//! interpreted as numbers in binary representation.
//!
//! From those lemmas we consider the 2 cases. If both entries have the same number
//! of bits equal to 0, they are either equal or not reachable from each other
//! because of the second lemma. If they don't have the same number of bits equal to
//! 0, then the one with less bits equal to 0 is not reachable from the other
//! because of the first lemma and the one with more bits equal to 0 is not
//! reachable from the other because of the third lemma and the definition of the
//! checksum.
//!
//! # Fuzzing
//!
//! For any sequence of operations and interruptions starting from an erased
//! storage, the store is checked against its model and some internal invariant at
//! each step.
//!
//! For any sequence of operations and interruptions starting from an arbitrary
//! storage, the store is checked not to crash.
#![cfg_attr(not(feature = "std"), no_std)]
#[macro_use]
extern crate alloc;
#[macro_use]
mod bitfield;
mod buffer;
mod format;
mod storage;
mod store;