From d0ad46b868f361559ed3dd2afe9411be87198c91 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 30 Sep 2020 10:34:35 +0200 Subject: [PATCH 01/15] Add format helpers for new store --- libraries/persistent_store/src/bitfield.rs | 41 +- libraries/persistent_store/src/format.rs | 907 +++++++++++++++++++++ libraries/persistent_store/src/lib.rs | 326 ++++++++ 3 files changed, 1255 insertions(+), 19 deletions(-) create mode 100644 libraries/persistent_store/src/format.rs diff --git a/libraries/persistent_store/src/bitfield.rs b/libraries/persistent_store/src/bitfield.rs index a2760c2..09e0ad7 100644 --- a/libraries/persistent_store/src/bitfield.rs +++ b/libraries/persistent_store/src/bitfield.rs @@ -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)*] } }; diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs new file mode 100644 index 0000000..21f4abc --- /dev/null +++ b/libraries/persistent_store/src/format.rs @@ -0,0 +1,907 @@ +// Copyright 2019-2020 Google LLC +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// TODO(ia0): Remove when the module is used. +#![allow(dead_code)] + +use crate::bitfield::*; +use crate::{Storage, StorageIndex, StoreError, StoreResult}; +use alloc::vec::Vec; +use core::cmp::min; +use core::convert::TryFrom; + +type WORD = u32; + +/// Size of a word in bytes. +const WORD_SIZE: usize = core::mem::size_of::(); + +/// Maximum size of a page in bytes. +const MAX_PAGE_SIZE: usize = 4096; + +/// Maximum number of erase cycles. +const MAX_CYCLE: usize = 65535; + +/// Maximum page index. +/// +/// Thus the maximum number of pages in one more than this number. +const MAX_PAGE: usize = 63; + +/// Maximum number of keys. +const MAX_KEY: usize = 4095; + +/// Maximum length in bytes of a user payload. +const MAX_VALUE_LEN: usize = 1023; + +/// Maximum number of updates per transaction. +const MAX_UPDATES: usize = 31; + +/// Maximum number of words per virtual page. +const MAX_VIRT_PAGE_SIZE: usize = div_ceil(MAX_PAGE_SIZE, WORD_SIZE) - CONTENT_WORD; + +/// Word with all bits set to one. +const ERASED_WORD: u32 = 0xffffffff; + +/// Helpers for a given storage configuration. +#[derive(Clone, Debug)] +pub struct Format { + /// The size in bytes of a page in the storage. + page_size: usize, + + /// The number of pages in the storage. + num_pages: usize, + + /// The maximum number of times a page can be erased. + max_page_erases: usize, +} + +impl Format { + /// Extracts the format from a storage. + /// + /// Returns `None` if the storage is not [supported]. + /// + /// [supported]: struct.Format.html#method.is_storage_supported + pub fn new(storage: &S) -> Option { + if Format::is_storage_supported(storage) { + Some(Format { + page_size: storage.page_size(), + num_pages: storage.num_pages(), + max_page_erases: storage.max_page_erases(), + }) + } else { + None + } + } + + /// Returns whether a storage is supported. + /// + /// A storage is supported if the following conditions hold: + /// - The size of a word is 4 bytes. + /// - The size of a word evenly divides the size of a page. + /// - A page contains at least 8 words. + /// - A page contains at most [`MAX_PAGE_SIZE`] bytes. + /// - There is at least 3 pages. + /// - There is at most [`MAX_PAGE`]` + 1` pages. + /// - A word can be written at least twice between erase cycles. + /// - A page can be erased at most [`MAX_CYCLE`] times. + /// + /// [`MAX_PAGE_SIZE`]: constant.MAX_PAGE_SIZE.html + /// [`MAX_PAGE`]: constant.MAX_PAGE.html + /// [`MAX_CYCLE`]: constant.MAX_CYCLE.html + fn is_storage_supported(storage: &S) -> bool { + let word_size = storage.word_size(); + let page_size = storage.page_size(); + let num_pages = storage.num_pages(); + let max_word_writes = storage.max_word_writes(); + let max_page_erases = storage.max_page_erases(); + word_size == 4 + && page_size % word_size == 0 + && (8 * word_size <= page_size && page_size <= MAX_PAGE_SIZE) + && (3 <= num_pages && num_pages <= MAX_PAGE + 1) + && max_word_writes >= 2 + && max_page_erases <= MAX_CYCLE + } + + /// The size of a word in bytes. + pub fn word_size(&self) -> usize { + WORD_SIZE + } + + /// The size of a page in bytes. + /// + /// We have `32 <= self.page_size() <= MAX_PAGE_SIZE`. + pub fn page_size(&self) -> usize { + self.page_size + } + + /// The number of pages in the storage. + /// + /// Notation: `N`. We have `3 <= N <= MAX_PAGE + 1`. + pub fn num_pages(&self) -> usize { + self.num_pages + } + + /// The maximum page index. + /// + /// We have `2 <= self.max_page() <= MAX_PAGE`. + pub fn max_page(&self) -> usize { + self.num_pages - 1 + } + + /// The maximum number of times a page can be erased. + /// + /// Notation: `E`. We have `E <= MAX_CYCLE`. + pub fn max_page_erases(&self) -> usize { + self.max_page_erases + } + + /// The maximum key. + pub fn max_key(&self) -> usize { + MAX_KEY + } + + /// The maximum number of updates per transaction. + pub fn max_updates(&self) -> usize { + MAX_UPDATES + } + + /// The size of a virtual page in words. + /// + /// A virtual page is stored in a physical page after the page header. + /// + /// Notation: `Q`. We have `6 <= Q <= MAX_VIRT_PAGE_SIZE`. + pub fn virt_page_size(&self) -> usize { + self.page_size() / self.word_size() - CONTENT_WORD + } + + /// The maximum length in bytes of a user payload. + /// + /// We have `20 <= self.max_value_len() <= MAX_VALUE_LEN`. + pub fn max_value_len(&self) -> usize { + min( + (self.virt_page_size() - 1) * self.word_size(), + MAX_VALUE_LEN, + ) + } + + /// The maximum prefix length in words. + /// + /// A prefix is the first words of a virtual page that belong to the last entry of the previous + /// virtual page. This happens because entries may overlap up to 2 virtual pages. + /// + /// Notation: `M`. We have `5 <= M < Q`. + pub fn max_prefix_len(&self) -> usize { + self.bytes_to_words(self.max_value_len()) + } + + /// The total virtual capacity in words. + /// + /// Notation: `V`. We have `V = (N - 1) * (Q - 1) - M`. + pub fn virt_size(&self) -> usize { + (self.num_pages() - 1) * (self.virt_page_size() - 1) - self.max_prefix_len() + } + + /// The total user capacity in words. + /// + /// Notation: `C`. We have `C = V - N = (N - 1) * (Q - 2) - M - 1`. + pub fn total_capacity(&self) -> usize { + // From the virtual capacity, we reserve N - 1 words for `Erase` entries and 1 word for a + // `Clear` entry. + self.virt_size() - self.num_pages() + } + + /// The total virtual lifetime in words. + /// + /// Notation: `L`. We have `L = (E * N + N - 1) * Q`. + pub fn total_lifetime(&self) -> Position { + Position::new(self, self.max_page_erases(), self.num_pages() - 1, 0) + } + + /// Returns the word position of the first entry of a page. + /// + /// The init info of the page must be provided to know where the first entry of the page + /// starts. + pub fn page_head(&self, init: InitInfo, page: usize) -> Position { + Position::new(self, init.cycle, page, init.prefix) + } + + /// Returns the storage index of the init info of a page. + pub fn index_init(&self, page: usize) -> StorageIndex { + let byte = INIT_WORD * self.word_size(); + StorageIndex { page, byte } + } + + /// Parses the init info of a page from its storage representation. + pub fn parse_init(&self, word: &[u8]) -> StoreResult> { + let word = slice_to_word(word); + Ok(if word == ERASED_WORD { + WordState::Erased + } else if WORD_CHECKSUM.get(word)? != 0 { + WordState::Partial + } else { + let cycle = INIT_CYCLE.get(word); + let prefix = INIT_PREFIX.get(word); + if cycle > self.max_page_erases() || prefix > self.max_prefix_len() { + return Err(StoreError::InvalidStorage); + } + WordState::Valid(InitInfo { cycle, prefix }) + }) + } + + /// Builds the storage representation of an init info. + pub fn build_init(&self, init: InitInfo) -> [u8; WORD_SIZE] { + let mut word = ERASED_WORD; + INIT_CYCLE.set(&mut word, init.cycle); + INIT_PREFIX.set(&mut word, init.prefix); + WORD_CHECKSUM.set(&mut word, 0); + word.to_ne_bytes() + } + + /// Returns the storage index of the compact info of a page. + pub fn index_compact(&self, page: usize) -> StorageIndex { + let byte = COMPACT_WORD * self.word_size(); + StorageIndex { page, byte } + } + + /// Parses the compact info of a page from its storage representation. + pub fn parse_compact(&self, word: &[u8]) -> StoreResult> { + let word = slice_to_word(word); + Ok(if word == ERASED_WORD { + WordState::Erased + } else if WORD_CHECKSUM.get(word)? != 0 { + WordState::Partial + } else { + let tail = COMPACT_TAIL.get(word); + if tail > self.virt_size() + self.max_prefix_len() { + return Err(StoreError::InvalidStorage); + } + WordState::Valid(CompactInfo { tail }) + }) + } + + /// Builds the storage representation of a compact info. + pub fn build_compact(&self, compact: CompactInfo) -> [u8; WORD_SIZE] { + let mut word = ERASED_WORD; + COMPACT_TAIL.set(&mut word, compact.tail); + WORD_CHECKSUM.set(&mut word, 0); + word.to_ne_bytes() + } + + /// Builds the storage representation of an internal entry. + pub fn build_internal(&self, internal: Internal) -> [u8; WORD_SIZE] { + let mut word = ERASED_WORD; + match internal { + Internal::Erase { page } => { + ID_ERASE.set(&mut word); + ERASE_PAGE.set(&mut word, page); + } + Internal::Clear { min_key } => { + ID_CLEAR.set(&mut word); + CLEAR_MIN_KEY.set(&mut word, min_key); + } + Internal::Marker { count } => { + ID_MARKER.set(&mut word); + MARKER_COUNT.set(&mut word, count); + } + Internal::Remove { key } => { + ID_REMOVE.set(&mut word); + REMOVE_KEY.set(&mut word, key); + } + } + WORD_CHECKSUM.set(&mut word, 0); + word.to_ne_bytes() + } + + /// Parses the first word of an entry from its storage representation. + pub fn parse_word(&self, word: &[u8]) -> StoreResult> { + let word = slice_to_word(word); + let valid = if ID_PADDING.check(word) { + ParsedWord::Padding(Padding { length: 0 }) + } else if ID_HEADER.check(word) { + if HEADER_DELETED.get(word) { + let length = HEADER_LENGTH.get(word); + if length > self.max_value_len() { + return Err(StoreError::InvalidStorage); + } + let length = self.bytes_to_words(length); + ParsedWord::Padding(Padding { length }) + } else { + let flipped = HEADER_FLIPPED.get(word); + let length = HEADER_LENGTH.get(word); + let key = HEADER_KEY.get(word); + let checksum = HEADER_CHECKSUM.get(word)?; + ParsedWord::Header(Header { + flipped, + length, + key, + checksum, + }) + } + } else if ID_ERASE.check(word) { + let page = ERASE_PAGE.get(word); + ParsedWord::Internal(Internal::Erase { page }) + } else if ID_CLEAR.check(word) { + let min_key = CLEAR_MIN_KEY.get(word); + ParsedWord::Internal(Internal::Clear { min_key }) + } else if ID_MARKER.check(word) { + let count = MARKER_COUNT.get(word); + ParsedWord::Internal(Internal::Marker { count }) + } else if ID_REMOVE.check(word) { + let key = REMOVE_KEY.get(word); + ParsedWord::Internal(Internal::Remove { key }) + } else if word == ERASED_WORD { + return Ok(WordState::Erased); + } else { + return Ok(WordState::Partial); + }; + if let ParsedWord::Internal(internal) = &valid { + if WORD_CHECKSUM.get(word)? != 0 { + return Ok(WordState::Partial); + } + let invalid = match internal { + Internal::Erase { page } => *page > self.max_page(), + Internal::Clear { min_key } => *min_key > self.max_key(), + Internal::Marker { count } => *count > MAX_UPDATES, + Internal::Remove { key } => *key > self.max_key(), + }; + if invalid { + return Err(StoreError::InvalidStorage); + } + } + Ok(WordState::Valid(valid)) + } + + /// Builds the storage representation of a user entry. + pub fn build_user(&self, key: usize, value: &[u8]) -> Vec { + let length = value.len(); + let word_size = self.word_size(); + let footer = self.bytes_to_words(length); + let mut result = vec![0xff; (1 + footer) * word_size]; + result[word_size..][..length].copy_from_slice(value); + let mut word = ERASED_WORD; + ID_HEADER.set(&mut word); + if footer > 0 && is_erased(&result[footer * word_size..]) { + HEADER_FLIPPED.set(&mut word); + *result.last_mut().unwrap() = 0x7f; + } + HEADER_LENGTH.set(&mut word, length); + HEADER_KEY.set(&mut word, key); + HEADER_CHECKSUM.set(&mut word, count_zeros(&result[footer * word_size..])); + result[..word_size].copy_from_slice(&word.to_ne_bytes()); + result + } + + /// Sets the padding bit in the first word of a user entry. + /// + /// The word is taken as a slice for convenience. + /// + /// # Panics + /// + /// Panics if `slice.len() != WORD_SIZE`. + pub fn set_padding(&self, slice: &mut [u8]) { + let mut word = slice_to_word(slice); + ID_PADDING.set(&mut word); + slice.copy_from_slice(&word.to_ne_bytes()); + } + + /// Sets the deleted bit in the first word of a user entry. + /// + /// The word is taken as a slice for convenience. + /// + /// # Panics + /// + /// Panics if `slice.len() != WORD_SIZE`. + pub fn set_deleted(&self, slice: &mut [u8]) { + let mut word = slice_to_word(slice); + HEADER_DELETED.set(&mut word); + slice.copy_from_slice(&word.to_ne_bytes()); + } + + /// Returns the minimum number of words to represent a given number of bytes. + pub fn bytes_to_words(&self, bytes: usize) -> usize { + div_ceil(bytes, self.word_size()) + } +} + +/// The word index of the init info in a page. +const INIT_WORD: usize = 0; + +/// The word index of the compact info in a page. +const COMPACT_WORD: usize = 1; + +/// The word index of the content of a page. +const CONTENT_WORD: usize = 2; + +/// The checksum for a single word. +/// +/// It needs 5 bits to store numbers between 0 and 27. +const WORD_CHECKSUM: Checksum = Checksum { + field: Field { pos: 27, len: 5 }, +}; + +// The fields of the init info of a page. +bitfield! { + /// The number of times the page has been erased. + INIT_CYCLE: Field <= MAX_CYCLE, + + /// The word index of the first entry in this virtual page. + INIT_PREFIX: Field <= div_ceil(MAX_VALUE_LEN, WORD_SIZE), + + #[cfg(test)] + LEN_INIT: Length, +} + +// The fields of the compact info of a page. +bitfield! { + /// The distance in words between head and tail at compaction. + /// + /// In particular, compaction copies non-deleted user entries from the head to the tail as long + /// as entries span the page to be compacted. + COMPACT_TAIL: Field <= MAX_VIRT_PAGE_SIZE * MAX_PAGE, + + #[cfg(test)] + LEN_COMPACT: Length, +} + +// Overview of the first word of the different kind of entries: +// +// 0123456789abcdef0123456789abcdef +// padding 0 +// header 10.............................. +// erase 11000........... +// clear 11001................. +// marker 11010.......... +// remove 11011................. +// +// NOTE: We could pad the internal entries to the right. + +// The fields of a padding entry. +bitfield! { + /// The identifier for padding entries. + ID_PADDING: ConstField = [0], +} + +// The fields of a user entry. +bitfield! { + /// The identifier for user entries. + ID_HEADER: ConstField = [1 0], + + /// Whether the user entry is deleted. + HEADER_DELETED: Bit, + + /// Whether the last bit of the user data is flipped. + HEADER_FLIPPED: Bit, + + /// The length in bytes of the user data. + // NOTE: It is possible to support values of length 1024 by having a separate kind of entries + // when the value is empty. We could then subtract one from the length here. + HEADER_LENGTH: Field <= MAX_VALUE_LEN, + + /// The key of the user entry. + HEADER_KEY: Field <= MAX_KEY, + + /// The checksum of the user entry. + /// + /// This counts the number of bits set to zero in both the first and last words of the user + /// entry, except in the checksum itself. So it needs 6 bits to store numbers between 0 and 58. + // NOTE: It may be possible to save one bit by storing: + // - the footer checksum (as a field) if the value is not empty + // - the header checksum (as a checksum) if the value is empty + HEADER_CHECKSUM: Checksum <= 58, + + #[cfg(test)] + LEN_HEADER: Length, +} + +// The fields of an erase entry. +bitfield! { + /// The identifier for erase entries. + ID_ERASE: ConstField = [1 1 0 0 0], + + /// The page to be erased. + ERASE_PAGE: Field <= MAX_PAGE, + + #[cfg(test)] + LEN_ERASE: Length, +} + +// The fields of a clear entry. +bitfield! { + /// The identifier for clear entries. + ID_CLEAR: ConstField = [1 1 0 0 1], + + /// The minimum key to be cleared. + /// + /// All entries with a key below this limit are not cleared. All other entries are deleted. + CLEAR_MIN_KEY: Field <= MAX_KEY, + + #[cfg(test)] + LEN_CLEAR: Length, +} + +// The fields of a marker entry. +bitfield! { + /// The identifier for marker entries. + ID_MARKER: ConstField = [1 1 0 1 0], + + /// The number of updates in this transaction. + /// + /// The update entries follow this marker entry. + MARKER_COUNT: Field <= MAX_UPDATES, + + #[cfg(test)] + LEN_MARKER: Length, +} + +// The fields of a remove entry. +bitfield! { + /// The identifier for remove entries. + ID_REMOVE: ConstField = [1 1 0 1 1], + + /// The key of the user entry to be removed. + REMOVE_KEY: Field <= MAX_KEY, + + #[cfg(test)] + LEN_REMOVE: Length, +} + +/// The position of a word in the virtual storage. +/// +/// With the notations defined in `Format`, let: +/// - `w` a virtual word offset in a page which is between `0` and `Q - 1` +/// - `p` a page offset which is between `0` and `N - 1` +/// - `c` the number of erase cycles of a page which is between `0` and `E` +/// +/// Then the position of a word is `(c*N + p)*Q + w`. This position monotonically increases and +/// represents the consumed lifetime of the storage. +#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord)] +pub struct Position(usize); + +impl core::ops::Add for Position { + type Output = Position; + + fn add(self, delta: usize) -> Position { + Position(self.0 + delta) + } +} + +impl core::ops::Sub for Position { + type Output = usize; + + fn sub(self, base: Position) -> usize { + self.0 - base.0 + } +} + +impl core::ops::AddAssign for Position { + fn add_assign(&mut self, delta: usize) { + self.0 += delta; + } +} + +impl Position { + /// Create a word position given its coordinates. + /// + /// The coordinates of a word are: + /// - Its word index in its page. + /// - Its page index in the storage. + /// - The number of times that page was erased. + pub fn new(format: &Format, cycle: usize, page: usize, word: usize) -> Position { + Position((cycle * format.num_pages() + page) * format.virt_page_size() + word) + } + + /// Accesses the underlying position as a natural number. + pub fn get(self) -> usize { + self.0 + } + + /// Returns the associated storage index. + pub fn index(self, format: &Format) -> StorageIndex { + let page = self.page(format); + let word = CONTENT_WORD + self.word(format); + let byte = word * format.word_size(); + StorageIndex { page, byte } + } + + /// Returns the beginning of the current virtual page. + pub fn page_begin(self, format: &Format) -> Position { + let virt_page_size = format.virt_page_size(); + Position((self.0 / virt_page_size) * virt_page_size) + } + + /// Returns the beginning of the next virtual page. + pub fn next_page(self, format: &Format) -> Position { + let virt_page_size = format.virt_page_size(); + Position((self.0 / virt_page_size + 1) * virt_page_size) + } + + /// Returns the number of times the current page was erased. + pub fn cycle(self, format: &Format) -> usize { + (self.0 / format.virt_page_size()) / format.num_pages() + } + + /// Returns the current page index. + pub fn page(self, format: &Format) -> usize { + (self.0 / format.virt_page_size()) % format.num_pages() + } + + /// Returns the current word index in the page. + pub fn word(self, format: &Format) -> usize { + self.0 % format.virt_page_size() + } +} + +/// Possible states of some storage representation as a word. +pub enum WordState { + /// The word is still erased. + Erased, + + /// The word is partially written. + Partial, + + /// Holds the decoded version of a valid word. + Valid(T), +} + +/// Information for an initialized page. +pub struct InitInfo { + /// The number of times this page has been erased. + pub cycle: usize, + + /// The word index of the first entry in this virtual page. + pub prefix: usize, +} + +/// Information for a page being compacted. +pub struct CompactInfo { + /// The distance in words between head and tail at compaction. + pub tail: usize, +} + +/// The first word of an entry. +#[derive(Debug)] +pub enum ParsedWord { + /// Padding entry. + Padding(Padding), + + /// Header of a user entry. + Header(Header), + + /// Internal entry. + Internal(Internal), +} + +/// Padding entry. +#[derive(Debug)] +pub struct Padding { + /// The number of following padding words after the first word of the padding entry. + pub length: usize, +} + +/// Header of a user entry. +#[derive(Debug)] +pub struct Header { + /// Whether the last bit of the user data is flipped. + pub flipped: bool, + + /// The length in bytes of the user data. + pub length: usize, + + /// The key of the user entry. + pub key: usize, + + /// The checksum of the user entry. + pub checksum: usize, +} + +impl Header { + /// Checks the validity of a user entry. + /// + /// If the user entry has no payload, the `footer` must be set to `None`. Otherwise it should be + /// the last word of the entry. + pub fn check(&self, footer: Option<&[u8]>) -> bool { + footer.map_or(0, |x| count_zeros(x)) == self.checksum + } +} + +/// Internal entry. +#[derive(Debug)] +pub enum Internal { + /// Indicates that a page should be erased. + Erase { + /// The page to be erased. + page: usize, + }, + + /// Indicates that user entries with high key should be deleted. + Clear { + /// The minimum key a user entry should have to be deleted. + min_key: usize, + }, + + /// Marks the start of a transaction. + /// + /// The marker is followed by a given number of updates, which are either user entries or remove + /// entries. + Marker { + /// The number of updates in the transaction. + count: usize, + }, + + /// Indicates that a user entry should be removed. + /// + /// This is only useful (and valid) as part of a transaction, since removing a single entry is + /// already atomic. + Remove { + /// The key of the user entry to be removed. + key: usize, + }, +} + +/// Returns whether a slice has all bits equal to one. +pub fn is_erased(slice: &[u8]) -> bool { + slice.iter().all(|&x| x == 0xff) +} + +/// Converts a word slice into a word. +/// +/// # Panics +/// +/// Panics if `word.len() != WORD_SIZE`. +fn slice_to_word(word: &[u8]) -> WORD { + u32::from_ne_bytes(<[u8; WORD_SIZE]>::try_from(word).unwrap()) +} + +/// Divides then takes ceiling. +/// +/// Returns `ceil(x / m)` with mathematical notations. +pub const fn div_ceil(x: usize, m: usize) -> usize { + (x + m - 1) / m +} + +#[cfg(test)] +mod tests { + use super::*; + + #[test] + fn size_of_format() { + assert_eq!(std::mem::size_of::(), 24); + } + + #[test] + fn checksum_ok() { + let Field { pos, len } = WORD_CHECKSUM.field; + // There is enough bits to represents the number of zeros preceding the checksum. + assert_eq!(len, num_bits(pos)); + // The checksum is the last field of a word. + assert_eq!(pos + len, 8 * WORD_SIZE); + // The data of words using the checksum don't overlap the checksum. + let words = &[ + &LEN_INIT, + &LEN_COMPACT, + &LEN_ERASE, + &LEN_CLEAR, + &LEN_MARKER, + &LEN_REMOVE, + ]; + for word in words { + assert!(word.pos < pos); + } + } + + #[test] + fn init_ok() { + assert_eq!(INIT_CYCLE.pos, 0); + assert_eq!(INIT_CYCLE.len, 16); + assert_eq!(INIT_PREFIX.pos, 16); + assert_eq!(INIT_PREFIX.len, 9); + assert_eq!(LEN_INIT.pos, 25); + } + + #[test] + fn compact_ok() { + assert_eq!(COMPACT_TAIL.pos, 0); + assert_eq!(COMPACT_TAIL.len, 16); + assert_eq!(LEN_COMPACT.pos, 16); + } + + #[test] + fn header_ok() { + assert_eq!(ID_HEADER.field.pos, 0); + assert_eq!(ID_HEADER.field.len, 2); + assert_eq!(ID_HEADER.value, 0b01); + assert_eq!(HEADER_DELETED.pos, 2); + assert_eq!(HEADER_FLIPPED.pos, 3); + assert_eq!(HEADER_LENGTH.pos, 4); + assert_eq!(HEADER_LENGTH.len, 10); + assert_eq!(HEADER_KEY.pos, 14); + assert_eq!(HEADER_KEY.len, 12); + assert_eq!(HEADER_CHECKSUM.field.pos, 26); + assert_eq!(HEADER_CHECKSUM.field.len, 6); + assert_eq!(LEN_HEADER.pos, 32); + } + + #[test] + fn erase_ok() { + assert_eq!(ID_ERASE.field.pos, 0); + assert_eq!(ID_ERASE.field.len, 5); + assert_eq!(ID_ERASE.value, 0b00011); + assert_eq!(ERASE_PAGE.pos, 5); + assert_eq!(ERASE_PAGE.len, 6); + assert_eq!(LEN_ERASE.pos, 11); + } + + #[test] + fn clear_ok() { + assert_eq!(ID_CLEAR.field.pos, 0); + assert_eq!(ID_CLEAR.field.len, 5); + assert_eq!(ID_CLEAR.value, 0b10011); + assert_eq!(CLEAR_MIN_KEY.pos, 5); + assert_eq!(CLEAR_MIN_KEY.len, 12); + assert_eq!(LEN_CLEAR.pos, 17); + } + + #[test] + fn marker_ok() { + assert_eq!(ID_MARKER.field.pos, 0); + assert_eq!(ID_MARKER.field.len, 5); + assert_eq!(ID_MARKER.value, 0b01011); + assert_eq!(MARKER_COUNT.pos, 5); + assert_eq!(MARKER_COUNT.len, 5); + assert_eq!(LEN_MARKER.pos, 10); + } + + #[test] + fn remove_ok() { + assert_eq!(ID_REMOVE.field.pos, 0); + assert_eq!(ID_REMOVE.field.len, 5); + assert_eq!(ID_REMOVE.value, 0b11011); + assert_eq!(REMOVE_KEY.pos, 5); + assert_eq!(REMOVE_KEY.len, 12); + assert_eq!(LEN_REMOVE.pos, 17); + } + + #[test] + fn is_erased_ok() { + assert!(is_erased(&[])); + assert!(is_erased(&[0xff])); + assert!(is_erased(&[0xff, 0xff])); + assert!(!is_erased(&[0x00])); + assert!(!is_erased(&[0xff, 0xfe])); + assert!(!is_erased(&[0x7f, 0xff])); + } + + #[test] + fn slice_to_word_ok() { + // We write test with little-endian in mind, but use this helper function to test regardless + // of endianness. + fn test(slice: &[u8], word: u32) { + #[cfg(target_endian = "little")] + let word = word.swap_bytes(); + assert_eq!(slice_to_word(slice), word); + } + test(&[0x01, 0x02, 0x03, 0x04], 0x01020304); + test(&[0xf0, 0x78, 0x3c, 0x1e], 0xf0783c1e); + } + + #[test] + fn div_ceil_ok() { + assert_eq!(div_ceil(0, 1), 0); + assert_eq!(div_ceil(1, 1), 1); + assert_eq!(div_ceil(2, 1), 2); + assert_eq!(div_ceil(0, 2), 0); + assert_eq!(div_ceil(1, 2), 1); + assert_eq!(div_ceil(2, 2), 1); + assert_eq!(div_ceil(3, 2), 2); + } +} diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index 954e66f..242a218 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -12,10 +12,336 @@ // 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 value for other keys are left unchanged. +//! - Given a key, `Remove` updates the store such that no value is associated for +//! the key. The value 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. The more the store is loaded (few remaining words of +//! capacity), the more compactions are frequent, and the more lifetime is used. +//! +//! 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 store may behave in unexpected ways if the following assumptions don't hold: +//! - 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 +//! weaker probabilities as the usage diverges from them. +//! +//! # 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: +//! +//! ``` +//! 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. +//! +//! ``` +//! forall j, t_{j + 1} = t_j + |h_{j + 1}| - |h_j| + 1 +//! ``` +//! +//! By induction, we have: +//! +//! ``` +//! t_{I + i} <= t_I + |h_{I + i}| - |h_I| + i +//! ``` +//! +//! We have the following properties: +//! +//! ``` +//! 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: +//! +//! ``` +//! 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. +//! +//! ``` +//! 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: +//! +//! ``` +//! 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: +//! +//! ``` +//! 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: +//! +//! ``` +//! 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 bit 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. +//! +//! 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 format; mod storage; mod store; From f9f428dcbf8498db59f27fd77c7345a06514035a Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 30 Sep 2020 18:37:33 +0200 Subject: [PATCH 02/15] Fix documentation --- libraries/persistent_store/src/lib.rs | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index 242a218..0ab47a4 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -214,7 +214,7 @@ //! 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 //! ``` //! @@ -224,19 +224,19 @@ //! 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 @@ -244,7 +244,7 @@ //! //! 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 @@ -256,7 +256,7 @@ //! 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. @@ -264,14 +264,14 @@ //! //! 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 @@ -279,7 +279,7 @@ //! //! 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| From c09a5ed71982efcc739d4e33a2356dfdcad7dbb1 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 7 Oct 2020 14:40:46 +0200 Subject: [PATCH 03/15] Address comments --- libraries/persistent_store/src/format.rs | 146 ++++++++++------------- 1 file changed, 60 insertions(+), 86 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 21f4abc..5814a2d 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -19,7 +19,6 @@ use crate::bitfield::*; use crate::{Storage, StorageIndex, StoreError, StoreResult}; use alloc::vec::Vec; use core::cmp::min; -use core::convert::TryFrom; type WORD = u32; @@ -30,15 +29,15 @@ const WORD_SIZE: usize = core::mem::size_of::(); const MAX_PAGE_SIZE: usize = 4096; /// Maximum number of erase cycles. -const MAX_CYCLE: usize = 65535; +const MAX_ERASE_CYCLE: usize = 65535; /// Maximum page index. /// /// Thus the maximum number of pages in one more than this number. -const MAX_PAGE: usize = 63; +const MAX_PAGE_INDEX: usize = 63; /// Maximum number of keys. -const MAX_KEY: usize = 4095; +const MAX_KEY_INDEX: usize = 4095; /// Maximum length in bytes of a user payload. const MAX_VALUE_LEN: usize = 1023; @@ -91,13 +90,13 @@ impl Format { /// - A page contains at least 8 words. /// - A page contains at most [`MAX_PAGE_SIZE`] bytes. /// - There is at least 3 pages. - /// - There is at most [`MAX_PAGE`]` + 1` pages. + /// - There is at most [`MAX_PAGE_INDEX`]` + 1` pages. /// - A word can be written at least twice between erase cycles. - /// - A page can be erased at most [`MAX_CYCLE`] times. + /// - A page can be erased at most [`MAX_ERASE_CYCLE`] times. /// /// [`MAX_PAGE_SIZE`]: constant.MAX_PAGE_SIZE.html - /// [`MAX_PAGE`]: constant.MAX_PAGE.html - /// [`MAX_CYCLE`]: constant.MAX_CYCLE.html + /// [`MAX_PAGE_INDEX`]: constant.MAX_PAGE_INDEX.html + /// [`MAX_ERASE_CYCLE`]: constant.MAX_ERASE_CYCLE.html fn is_storage_supported(storage: &S) -> bool { let word_size = storage.word_size(); let page_size = storage.page_size(); @@ -107,9 +106,9 @@ impl Format { word_size == 4 && page_size % word_size == 0 && (8 * word_size <= page_size && page_size <= MAX_PAGE_SIZE) - && (3 <= num_pages && num_pages <= MAX_PAGE + 1) + && (3 <= num_pages && num_pages <= MAX_PAGE_INDEX + 1) && max_word_writes >= 2 - && max_page_erases <= MAX_CYCLE + && max_page_erases <= MAX_ERASE_CYCLE } /// The size of a word in bytes. @@ -126,28 +125,28 @@ impl Format { /// The number of pages in the storage. /// - /// Notation: `N`. We have `3 <= N <= MAX_PAGE + 1`. + /// Notation: `N`. We have `3 <= N <= MAX_PAGE_INDEX + 1`. pub fn num_pages(&self) -> usize { self.num_pages } /// The maximum page index. /// - /// We have `2 <= self.max_page() <= MAX_PAGE`. + /// We have `2 <= self.max_page() <= MAX_PAGE_INDEX`. pub fn max_page(&self) -> usize { self.num_pages - 1 } /// The maximum number of times a page can be erased. /// - /// Notation: `E`. We have `E <= MAX_CYCLE`. + /// Notation: `E`. We have `E <= MAX_ERASE_CYCLE`. pub fn max_page_erases(&self) -> usize { self.max_page_erases } /// The maximum key. pub fn max_key(&self) -> usize { - MAX_KEY + MAX_KEY_INDEX } /// The maximum number of updates per transaction. @@ -222,8 +221,7 @@ impl Format { } /// Parses the init info of a page from its storage representation. - pub fn parse_init(&self, word: &[u8]) -> StoreResult> { - let word = slice_to_word(word); + pub fn parse_init(&self, word: WORD) -> StoreResult> { Ok(if word == ERASED_WORD { WordState::Erased } else if WORD_CHECKSUM.get(word)? != 0 { @@ -254,8 +252,7 @@ impl Format { } /// Parses the compact info of a page from its storage representation. - pub fn parse_compact(&self, word: &[u8]) -> StoreResult> { - let word = slice_to_word(word); + pub fn parse_compact(&self, word: WORD) -> StoreResult> { Ok(if word == ERASED_WORD { WordState::Erased } else if WORD_CHECKSUM.get(word)? != 0 { @@ -278,22 +275,22 @@ impl Format { } /// Builds the storage representation of an internal entry. - pub fn build_internal(&self, internal: Internal) -> [u8; WORD_SIZE] { + pub fn build_internal(&self, internal: InternalEntry) -> [u8; WORD_SIZE] { let mut word = ERASED_WORD; match internal { - Internal::Erase { page } => { + InternalEntry::Erase { page } => { ID_ERASE.set(&mut word); ERASE_PAGE.set(&mut word, page); } - Internal::Clear { min_key } => { + InternalEntry::Clear { min_key } => { ID_CLEAR.set(&mut word); CLEAR_MIN_KEY.set(&mut word, min_key); } - Internal::Marker { count } => { + InternalEntry::Marker { count } => { ID_MARKER.set(&mut word); MARKER_COUNT.set(&mut word, count); } - Internal::Remove { key } => { + InternalEntry::Remove { key } => { ID_REMOVE.set(&mut word); REMOVE_KEY.set(&mut word, key); } @@ -303,8 +300,7 @@ impl Format { } /// Parses the first word of an entry from its storage representation. - pub fn parse_word(&self, word: &[u8]) -> StoreResult> { - let word = slice_to_word(word); + pub fn parse_word(&self, word: WORD) -> StoreResult> { let valid = if ID_PADDING.check(word) { ParsedWord::Padding(Padding { length: 0 }) } else if ID_HEADER.check(word) { @@ -329,16 +325,16 @@ impl Format { } } else if ID_ERASE.check(word) { let page = ERASE_PAGE.get(word); - ParsedWord::Internal(Internal::Erase { page }) + ParsedWord::Internal(InternalEntry::Erase { page }) } else if ID_CLEAR.check(word) { let min_key = CLEAR_MIN_KEY.get(word); - ParsedWord::Internal(Internal::Clear { min_key }) + ParsedWord::Internal(InternalEntry::Clear { min_key }) } else if ID_MARKER.check(word) { let count = MARKER_COUNT.get(word); - ParsedWord::Internal(Internal::Marker { count }) + ParsedWord::Internal(InternalEntry::Marker { count }) } else if ID_REMOVE.check(word) { let key = REMOVE_KEY.get(word); - ParsedWord::Internal(Internal::Remove { key }) + ParsedWord::Internal(InternalEntry::Remove { key }) } else if word == ERASED_WORD { return Ok(WordState::Erased); } else { @@ -349,10 +345,10 @@ impl Format { return Ok(WordState::Partial); } let invalid = match internal { - Internal::Erase { page } => *page > self.max_page(), - Internal::Clear { min_key } => *min_key > self.max_key(), - Internal::Marker { count } => *count > MAX_UPDATES, - Internal::Remove { key } => *key > self.max_key(), + InternalEntry::Erase { page } => *page > self.max_page(), + InternalEntry::Clear { min_key } => *min_key > self.max_key(), + InternalEntry::Marker { count } => *count > MAX_UPDATES, + InternalEntry::Remove { key } => *key > self.max_key(), }; if invalid { return Err(StoreError::InvalidStorage); @@ -382,32 +378,18 @@ impl Format { } /// Sets the padding bit in the first word of a user entry. - /// - /// The word is taken as a slice for convenience. - /// - /// # Panics - /// - /// Panics if `slice.len() != WORD_SIZE`. - pub fn set_padding(&self, slice: &mut [u8]) { - let mut word = slice_to_word(slice); - ID_PADDING.set(&mut word); - slice.copy_from_slice(&word.to_ne_bytes()); + pub fn set_padding(&self, word: &mut WORD) { + ID_PADDING.set(word); } /// Sets the deleted bit in the first word of a user entry. - /// - /// The word is taken as a slice for convenience. - /// - /// # Panics - /// - /// Panics if `slice.len() != WORD_SIZE`. - pub fn set_deleted(&self, slice: &mut [u8]) { - let mut word = slice_to_word(slice); - HEADER_DELETED.set(&mut word); - slice.copy_from_slice(&word.to_ne_bytes()); + pub fn set_deleted(&self, word: &mut WORD) { + HEADER_DELETED.set(word); } /// Returns the minimum number of words to represent a given number of bytes. + /// + /// Assumes `bytes + 4` does not overflow. pub fn bytes_to_words(&self, bytes: usize) -> usize { div_ceil(bytes, self.word_size()) } @@ -424,7 +406,8 @@ const CONTENT_WORD: usize = 2; /// The checksum for a single word. /// -/// It needs 5 bits to store numbers between 0 and 27. +/// Since checksums are the number of bits set to zero and a word is 32 bits, we need 5 bits to +/// store numbers between 0 and 27 (which is 32 - 5). const WORD_CHECKSUM: Checksum = Checksum { field: Field { pos: 27, len: 5 }, }; @@ -432,7 +415,7 @@ const WORD_CHECKSUM: Checksum = Checksum { // The fields of the init info of a page. bitfield! { /// The number of times the page has been erased. - INIT_CYCLE: Field <= MAX_CYCLE, + INIT_CYCLE: Field <= MAX_ERASE_CYCLE, /// The word index of the first entry in this virtual page. INIT_PREFIX: Field <= div_ceil(MAX_VALUE_LEN, WORD_SIZE), @@ -447,7 +430,7 @@ bitfield! { /// /// In particular, compaction copies non-deleted user entries from the head to the tail as long /// as entries span the page to be compacted. - COMPACT_TAIL: Field <= MAX_VIRT_PAGE_SIZE * MAX_PAGE, + COMPACT_TAIL: Field <= MAX_VIRT_PAGE_SIZE * MAX_PAGE_INDEX, #[cfg(test)] LEN_COMPACT: Length, @@ -488,7 +471,7 @@ bitfield! { HEADER_LENGTH: Field <= MAX_VALUE_LEN, /// The key of the user entry. - HEADER_KEY: Field <= MAX_KEY, + HEADER_KEY: Field <= MAX_KEY_INDEX, /// The checksum of the user entry. /// @@ -509,7 +492,7 @@ bitfield! { ID_ERASE: ConstField = [1 1 0 0 0], /// The page to be erased. - ERASE_PAGE: Field <= MAX_PAGE, + ERASE_PAGE: Field <= MAX_PAGE_INDEX, #[cfg(test)] LEN_ERASE: Length, @@ -523,7 +506,7 @@ bitfield! { /// The minimum key to be cleared. /// /// All entries with a key below this limit are not cleared. All other entries are deleted. - CLEAR_MIN_KEY: Field <= MAX_KEY, + CLEAR_MIN_KEY: Field <= MAX_KEY_INDEX, #[cfg(test)] LEN_CLEAR: Length, @@ -549,7 +532,7 @@ bitfield! { ID_REMOVE: ConstField = [1 1 0 1 1], /// The key of the user entry to be removed. - REMOVE_KEY: Field <= MAX_KEY, + REMOVE_KEY: Field <= MAX_KEY_INDEX, #[cfg(test)] LEN_REMOVE: Length, @@ -678,7 +661,7 @@ pub enum ParsedWord { Header(Header), /// Internal entry. - Internal(Internal), + Internal(InternalEntry), } /// Padding entry. @@ -710,13 +693,13 @@ impl Header { /// If the user entry has no payload, the `footer` must be set to `None`. Otherwise it should be /// the last word of the entry. pub fn check(&self, footer: Option<&[u8]>) -> bool { - footer.map_or(0, |x| count_zeros(x)) == self.checksum + footer.map_or(0, count_zeros) == self.checksum } } /// Internal entry. #[derive(Debug)] -pub enum Internal { +pub enum InternalEntry { /// Indicates that a page should be erased. Erase { /// The page to be erased. @@ -753,18 +736,9 @@ pub fn is_erased(slice: &[u8]) -> bool { slice.iter().all(|&x| x == 0xff) } -/// Converts a word slice into a word. -/// -/// # Panics -/// -/// Panics if `word.len() != WORD_SIZE`. -fn slice_to_word(word: &[u8]) -> WORD { - u32::from_ne_bytes(<[u8; WORD_SIZE]>::try_from(word).unwrap()) -} - /// Divides then takes ceiling. /// -/// Returns `ceil(x / m)` with mathematical notations. +/// Returns `ceil(x / m)` with mathematical notations. Assumes `x + m` does not overflow. pub const fn div_ceil(x: usize, m: usize) -> usize { (x + m - 1) / m } @@ -881,19 +855,6 @@ mod tests { assert!(!is_erased(&[0x7f, 0xff])); } - #[test] - fn slice_to_word_ok() { - // We write test with little-endian in mind, but use this helper function to test regardless - // of endianness. - fn test(slice: &[u8], word: u32) { - #[cfg(target_endian = "little")] - let word = word.swap_bytes(); - assert_eq!(slice_to_word(slice), word); - } - test(&[0x01, 0x02, 0x03, 0x04], 0x01020304); - test(&[0xf0, 0x78, 0x3c, 0x1e], 0xf0783c1e); - } - #[test] fn div_ceil_ok() { assert_eq!(div_ceil(0, 1), 0); @@ -904,4 +865,17 @@ mod tests { assert_eq!(div_ceil(2, 2), 1); assert_eq!(div_ceil(3, 2), 2); } + + #[test] + fn positions_fit_in_a_word() { + // All reachable positions are smaller than this value, which is one past the last position. + // It is simply the total number of virtual words, i.e. the number of words per virtual page + // times the number of virtual pages times the number of times a virtual page can be used + // (one more than the number of times it can be erased since we can write before the first + // erase cycle and after the last erase cycle). + assert_eq!( + (MAX_ERASE_CYCLE + 1) * (MAX_PAGE_INDEX + 1) * MAX_VIRT_PAGE_SIZE, + 0xff800000 + ); + } } From 7b21eba5df2110cbd7c192c4704b571151f56d29 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Fri, 9 Oct 2020 11:55:51 +0200 Subject: [PATCH 04/15] Expand documentation --- libraries/persistent_store/src/format.rs | 55 ++++++++++++++++-------- 1 file changed, 37 insertions(+), 18 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 5814a2d..b55e575 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -36,7 +36,9 @@ const MAX_ERASE_CYCLE: usize = 65535; /// Thus the maximum number of pages in one more than this number. const MAX_PAGE_INDEX: usize = 63; -/// Maximum number of keys. +/// Maximum key index. +/// +/// Thus the number of keys in one more than this number. const MAX_KEY_INDEX: usize = 4095; /// Maximum length in bytes of a user payload. @@ -55,12 +57,27 @@ const ERASED_WORD: u32 = 0xffffffff; #[derive(Clone, Debug)] pub struct Format { /// The size in bytes of a page in the storage. + /// + /// # Invariant + /// + /// - Words divide a page evenly. + /// - There are at least 8 words in a page. + /// - There are at most `MAX_PAGE_SIZE` bytes in a page. page_size: usize, /// The number of pages in the storage. + /// + /// # Invariant + /// + /// - There are at least 3 pages. + /// - There are at most `MAX_PAGE_INDEX + 1` pages. num_pages: usize, /// The maximum number of times a page can be erased. + /// + /// # Invariant + /// + /// - A page can be erased at most `MAX_ERASE_CYCLE` times. max_page_erases: usize, } @@ -118,14 +135,14 @@ impl Format { /// The size of a page in bytes. /// - /// We have `32 <= self.page_size() <= MAX_PAGE_SIZE`. + /// We have `32 <= self.page_size() <= MAX_PAGE_SIZE` assuming a word is 4 bytes. pub fn page_size(&self) -> usize { self.page_size } - /// The number of pages in the storage. + /// The number of pages in the storage, denoted by `N`. /// - /// Notation: `N`. We have `3 <= N <= MAX_PAGE_INDEX + 1`. + /// We have `3 <= N <= MAX_PAGE_INDEX + 1`. pub fn num_pages(&self) -> usize { self.num_pages } @@ -137,9 +154,9 @@ impl Format { self.num_pages - 1 } - /// The maximum number of times a page can be erased. + /// The maximum number of times a page can be erased, denoted by `E`. /// - /// Notation: `E`. We have `E <= MAX_ERASE_CYCLE`. + /// We have `E <= MAX_ERASE_CYCLE`. pub fn max_page_erases(&self) -> usize { self.max_page_erases } @@ -154,18 +171,18 @@ impl Format { MAX_UPDATES } - /// The size of a virtual page in words. + /// The size of a virtual page in words, denoted by `Q`. /// /// A virtual page is stored in a physical page after the page header. /// - /// Notation: `Q`. We have `6 <= Q <= MAX_VIRT_PAGE_SIZE`. + /// We have `6 <= Q <= MAX_VIRT_PAGE_SIZE`. pub fn virt_page_size(&self) -> usize { self.page_size() / self.word_size() - CONTENT_WORD } /// The maximum length in bytes of a user payload. /// - /// We have `20 <= self.max_value_len() <= MAX_VALUE_LEN`. + /// We have `20 <= self.max_value_len() <= MAX_VALUE_LEN` assuming words are 4 bytes. pub fn max_value_len(&self) -> usize { min( (self.virt_page_size() - 1) * self.word_size(), @@ -173,35 +190,35 @@ impl Format { ) } - /// The maximum prefix length in words. + /// The maximum prefix length in words, denoted by `M`. /// /// A prefix is the first words of a virtual page that belong to the last entry of the previous /// virtual page. This happens because entries may overlap up to 2 virtual pages. /// - /// Notation: `M`. We have `5 <= M < Q`. + /// We have `5 <= M < Q`. pub fn max_prefix_len(&self) -> usize { self.bytes_to_words(self.max_value_len()) } - /// The total virtual capacity in words. + /// The total virtual capacity in words, denoted by `V`. /// - /// Notation: `V`. We have `V = (N - 1) * (Q - 1) - M`. + /// We have `V = (N - 1) * (Q - 1) - M`. pub fn virt_size(&self) -> usize { (self.num_pages() - 1) * (self.virt_page_size() - 1) - self.max_prefix_len() } - /// The total user capacity in words. + /// The total user capacity in words, denoted by `C`. /// - /// Notation: `C`. We have `C = V - N = (N - 1) * (Q - 2) - M - 1`. + /// We have `C = V - N = (N - 1) * (Q - 2) - M - 1`. pub fn total_capacity(&self) -> usize { // From the virtual capacity, we reserve N - 1 words for `Erase` entries and 1 word for a // `Clear` entry. self.virt_size() - self.num_pages() } - /// The total virtual lifetime in words. + /// The total virtual lifetime in words, denoted by `L`. /// - /// Notation: `L`. We have `L = (E * N + N - 1) * Q`. + /// We have `L = (E * N + N - 1) * Q`. pub fn total_lifetime(&self) -> Position { Position::new(self, self.max_page_erases(), self.num_pages() - 1, 0) } @@ -389,7 +406,7 @@ impl Format { /// Returns the minimum number of words to represent a given number of bytes. /// - /// Assumes `bytes + 4` does not overflow. + /// Assumes `bytes + self.word_size()` does not overflow. pub fn bytes_to_words(&self, bytes: usize) -> usize { div_ceil(bytes, self.word_size()) } @@ -402,6 +419,8 @@ const INIT_WORD: usize = 0; const COMPACT_WORD: usize = 1; /// The word index of the content of a page. +/// +/// Since a page is at least 8 words, there is always at least 6 words of content. const CONTENT_WORD: usize = 2; /// The checksum for a single word. From d721949806609ddcb3f64a8c05bb6c7aa91d6b4e Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Mon, 12 Oct 2020 14:40:30 +0200 Subject: [PATCH 05/15] Improve documentation --- libraries/persistent_store/src/format.rs | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index b55e575..f0c910f 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -33,12 +33,12 @@ const MAX_ERASE_CYCLE: usize = 65535; /// Maximum page index. /// -/// Thus the maximum number of pages in one more than this number. +/// Thus the maximum number of pages is one more than this number. const MAX_PAGE_INDEX: usize = 63; /// Maximum key index. /// -/// Thus the number of keys in one more than this number. +/// Thus the number of keys is one more than this number. const MAX_KEY_INDEX: usize = 4095; /// Maximum length in bytes of a user payload. @@ -106,8 +106,8 @@ impl Format { /// - The size of a word evenly divides the size of a page. /// - A page contains at least 8 words. /// - A page contains at most [`MAX_PAGE_SIZE`] bytes. - /// - There is at least 3 pages. - /// - There is at most [`MAX_PAGE_INDEX`]` + 1` pages. + /// - There are at least 3 pages. + /// - There are at most [`MAX_PAGE_INDEX`]` + 1` pages. /// - A word can be written at least twice between erase cycles. /// - A page can be erased at most [`MAX_ERASE_CYCLE`] times. /// From 0242873a232abcaf60d2fdc149bd77041bb87df4 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Mon, 12 Oct 2020 16:25:25 +0200 Subject: [PATCH 06/15] Improve comments --- libraries/persistent_store/src/format.rs | 3 ++- libraries/persistent_store/src/lib.rs | 4 ++-- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index f0c910f..147f318 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -109,7 +109,8 @@ impl Format { /// - There are at least 3 pages. /// - There are at most [`MAX_PAGE_INDEX`]` + 1` pages. /// - A word can be written at least twice between erase cycles. - /// - A page can be erased at most [`MAX_ERASE_CYCLE`] times. + /// - The maximum number of erase cycles (i.e. the maximum number of times a page can be erased) + /// is at most [`MAX_ERASE_CYCLE`]. /// /// [`MAX_PAGE_SIZE`]: constant.MAX_PAGE_SIZE.html /// [`MAX_PAGE_INDEX`]: constant.MAX_PAGE_INDEX.html diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index 0ab47a4..f168e89 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -39,9 +39,9 @@ //! //! 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 value for other keys are left unchanged. +//! 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 for -//! the key. The value for other keys are left unchanged. Additionally, if there +//! 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). //! From eede767fe33b2cb0ebb134e7ce76b7f9e8031e18 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Mon, 12 Oct 2020 18:07:29 +0200 Subject: [PATCH 07/15] Improve documentation --- libraries/persistent_store/src/lib.rs | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index f168e89..20f5088 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -40,7 +40,7 @@ //! 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 for +//! - 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). @@ -95,8 +95,8 @@ //! 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. The more the store is loaded (few remaining words of -//! capacity), the more compactions are frequent, and the more lifetime is used. +//! compaction occurs. Compaction frequency and litetime 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 @@ -104,7 +104,7 @@ //! //! ## Preconditions //! -//! The store may behave in unexpected ways if the following assumptions don't hold: +//! 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 From f51264583747624d7e7c1fb6d2fe34492d44e745 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Tue, 13 Oct 2020 12:46:25 +0200 Subject: [PATCH 08/15] Improve documentation --- libraries/persistent_store/src/format.rs | 12 ++++++++++-- libraries/persistent_store/src/lib.rs | 19 ++++++++++++++----- 2 files changed, 24 insertions(+), 7 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 147f318..4969e6d 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -456,8 +456,15 @@ bitfield! { LEN_COMPACT: Length, } -// Overview of the first word of the different kind of entries: +// Overview of the first word of the different kind of entries. // +// Each column represents a bit of the word. The first 2 lines give the position in hexadecimal of +// the bit in the word (the exponent of 2 when the word is written in binary). Each entry starts +// with the sequence of bits of its identifier. The dots following the identifier are the number of +// bits necessary to hold the information of the entry (including the checksum). The remaining free +// bits after the dots are not used by the entry. +// +// 0 1 // 0123456789abcdef0123456789abcdef // padding 0 // header 10.............................. @@ -466,7 +473,8 @@ bitfield! { // marker 11010.......... // remove 11011................. // -// NOTE: We could pad the internal entries to the right. +// NOTE: We could pad the internal entries to the right by extending their identifier. This permits +// to free some space for shorter identifier for future kind of entries. // The fields of a padding entry. bitfield! { diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index 20f5088..6e358a9 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -95,7 +95,7 @@ //! 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 litetime consumption are positively +//! 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: @@ -125,8 +125,8 @@ //! 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 -//! weaker probabilities as the usage diverges from them. +//! The store properties may still hold outside some of those assumptions, but with +//! an increasing chance of failure. //! //! # Implementation //! @@ -301,9 +301,18 @@ //! 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 bit equal +//! 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. +//! 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: From 223908febdcfb61e0bfd1e29686629a549fd666f Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 14 Oct 2020 11:41:46 +0200 Subject: [PATCH 09/15] Remove confusing clarification --- libraries/persistent_store/src/format.rs | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 4969e6d..bcd3c66 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -109,8 +109,7 @@ impl Format { /// - There are at least 3 pages. /// - There are at most [`MAX_PAGE_INDEX`]` + 1` pages. /// - A word can be written at least twice between erase cycles. - /// - The maximum number of erase cycles (i.e. the maximum number of times a page can be erased) - /// is at most [`MAX_ERASE_CYCLE`]. + /// - The maximum number of erase cycles is at most [`MAX_ERASE_CYCLE`]. /// /// [`MAX_PAGE_SIZE`]: constant.MAX_PAGE_SIZE.html /// [`MAX_PAGE_INDEX`]: constant.MAX_PAGE_INDEX.html From c098f2695ba1395d741c15ede740faea0aa866ad Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 14 Oct 2020 12:20:48 +0200 Subject: [PATCH 10/15] Clarify current supported values --- libraries/persistent_store/src/format.rs | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index bcd3c66..808dd03 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -23,28 +23,43 @@ use core::cmp::min; type WORD = u32; /// Size of a word in bytes. +/// +/// Currently, the store only supports storages where a word is 4 bytes. const WORD_SIZE: usize = core::mem::size_of::(); /// Maximum size of a page in bytes. +/// +/// Currently, the store only supports storages where pages are between 8 and 1024 [words]. +/// +/// [words]: constant.WORD_SIZE.html const MAX_PAGE_SIZE: usize = 4096; /// Maximum number of erase cycles. +/// +/// Currently, the store only supports storages where the maximum number of erase cycles fits on 16 +/// bits. const MAX_ERASE_CYCLE: usize = 65535; /// Maximum page index. /// -/// Thus the maximum number of pages is one more than this number. +/// Thus the maximum number of pages is one more than this number. Currently, the store only +/// supports storages where the number of pages is between 3 and 64. const MAX_PAGE_INDEX: usize = 63; /// Maximum key index. /// -/// Thus the number of keys is one more than this number. +/// Thus the number of keys is one more than this number. Currently, the store only supports 4096 +/// keys. const MAX_KEY_INDEX: usize = 4095; /// Maximum length in bytes of a user payload. +/// +/// Currently, the store only supports values smaller than 1024 bytes. const MAX_VALUE_LEN: usize = 1023; /// Maximum number of updates per transaction. +/// +/// Currently, the store only supports transactions with at most 31 updates. const MAX_UPDATES: usize = 31; /// Maximum number of words per virtual page. From f8fe1a94933bff355bcfa68a01c2e8d145461d48 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Wed, 14 Oct 2020 17:36:52 +0200 Subject: [PATCH 11/15] Add small proofs --- libraries/persistent_store/src/format.rs | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 808dd03..c36d19e 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -218,6 +218,13 @@ impl Format { /// The total virtual capacity in words, denoted by `V`. /// /// We have `V = (N - 1) * (Q - 1) - M`. + /// + /// We can show `V >= (N - 2) * (Q - 1)` with the following steps: + /// - `M <= Q - 1` from `M < Q` from [`M`] definition + /// - `-M >= -(Q - 1)` from above + /// - `V >= (N - 1) * (Q - 1) - (Q - 1)` from `V` definition + /// + /// [`M`]: struct.Format.html#method.max_prefix_len pub fn virt_size(&self) -> usize { (self.num_pages() - 1) * (self.virt_page_size() - 1) - self.max_prefix_len() } @@ -225,6 +232,13 @@ impl Format { /// The total user capacity in words, denoted by `C`. /// /// We have `C = V - N = (N - 1) * (Q - 2) - M - 1`. + /// + /// We can show `C >= (N - 2) * (Q - 2) - 2` with the following steps: + /// - `V >= (N - 2) * (Q - 1)` from [`V`] definition + /// - `C >= (N - 2) * (Q - 1) - N` from `C` definition + /// - `(N - 2) * (Q - 1) - N = (N - 2) * (Q - 2) - 2` by calculus + /// + /// [`V`]: struct.Format.html#method.virt_size pub fn total_capacity(&self) -> usize { // From the virtual capacity, we reserve N - 1 words for `Erase` entries and 1 word for a // `Clear` entry. From cb3369213f9326eec58f0f39fd96d9e073047e7e Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Fri, 23 Oct 2020 17:26:25 +0200 Subject: [PATCH 12/15] Fix merge missing conflict --- libraries/persistent_store/src/lib.rs | 2 -- 1 file changed, 2 deletions(-) diff --git a/libraries/persistent_store/src/lib.rs b/libraries/persistent_store/src/lib.rs index a051716..f2753db 100644 --- a/libraries/persistent_store/src/lib.rs +++ b/libraries/persistent_store/src/lib.rs @@ -345,8 +345,6 @@ #![cfg_attr(not(feature = "std"), no_std)] -extern crate alloc; - #[macro_use] extern crate alloc; From 552bab6ba9652f11e904d53795575f67206c9543 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Mon, 26 Oct 2020 17:51:40 +0100 Subject: [PATCH 13/15] Remove public visibility for internal function --- libraries/persistent_store/src/format.rs | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index c36d19e..47419c1 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -795,7 +795,7 @@ pub fn is_erased(slice: &[u8]) -> bool { /// Divides then takes ceiling. /// /// Returns `ceil(x / m)` with mathematical notations. Assumes `x + m` does not overflow. -pub const fn div_ceil(x: usize, m: usize) -> usize { +const fn div_ceil(x: usize, m: usize) -> usize { (x + m - 1) / m } From edd1bcf5d2126770815a9d170df6aba0ceca2628 Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Tue, 27 Oct 2020 11:25:08 +0100 Subject: [PATCH 14/15] Do not inline constants in documentation --- libraries/persistent_store/src/format.rs | 36 ++++++++++++++++-------- 1 file changed, 25 insertions(+), 11 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 47419c1..4c3c317 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -27,6 +27,11 @@ type WORD = u32; /// Currently, the store only supports storages where a word is 4 bytes. const WORD_SIZE: usize = core::mem::size_of::(); +/// Minimum number of words per page. +/// +/// Currently, the store only supports storages where pages have at least 8 words. +const MIN_NUM_WORDS_PER_PAGE: usize = 8; + /// Maximum size of a page in bytes. /// /// Currently, the store only supports storages where pages are between 8 and 1024 [words]. @@ -40,6 +45,11 @@ const MAX_PAGE_SIZE: usize = 4096; /// bits. const MAX_ERASE_CYCLE: usize = 65535; +/// Minimum number of pages. +/// +/// Currently, the store only supports storages with at least 3 pages. +const MIN_NUM_PAGES: usize = 3; + /// Maximum page index. /// /// Thus the maximum number of pages is one more than this number. Currently, the store only @@ -117,16 +127,19 @@ impl Format { /// Returns whether a storage is supported. /// /// A storage is supported if the following conditions hold: - /// - The size of a word is 4 bytes. + /// - The size of a word is [`WORD_SIZE`] bytes. /// - The size of a word evenly divides the size of a page. - /// - A page contains at least 8 words. + /// - A page contains at least [`MIN_NUM_WORDS_PER_PAGE`] words. /// - A page contains at most [`MAX_PAGE_SIZE`] bytes. - /// - There are at least 3 pages. + /// - There are at least [`MIN_NUM_PAGES`] pages. /// - There are at most [`MAX_PAGE_INDEX`]` + 1` pages. /// - A word can be written at least twice between erase cycles. /// - The maximum number of erase cycles is at most [`MAX_ERASE_CYCLE`]. /// + /// [`WORD_SIZE`]: constant.WORD_SIZE.html + /// [`MIN_NUM_WORDS_PER_PAGE`]: constant.MIN_NUM_WORDS_PER_PAGE.html /// [`MAX_PAGE_SIZE`]: constant.MAX_PAGE_SIZE.html + /// [`MIN_NUM_PAGES`]: constant.MIN_NUM_PAGES.html /// [`MAX_PAGE_INDEX`]: constant.MAX_PAGE_INDEX.html /// [`MAX_ERASE_CYCLE`]: constant.MAX_ERASE_CYCLE.html fn is_storage_supported(storage: &S) -> bool { @@ -135,10 +148,10 @@ impl Format { let num_pages = storage.num_pages(); let max_word_writes = storage.max_word_writes(); let max_page_erases = storage.max_page_erases(); - word_size == 4 + word_size == WORD_SIZE && page_size % word_size == 0 - && (8 * word_size <= page_size && page_size <= MAX_PAGE_SIZE) - && (3 <= num_pages && num_pages <= MAX_PAGE_INDEX + 1) + && (MIN_NUM_WORDS_PER_PAGE * word_size <= page_size && page_size <= MAX_PAGE_SIZE) + && (MIN_NUM_PAGES <= num_pages && num_pages <= MAX_PAGE_INDEX + 1) && max_word_writes >= 2 && max_page_erases <= MAX_ERASE_CYCLE } @@ -150,14 +163,14 @@ impl Format { /// The size of a page in bytes. /// - /// We have `32 <= self.page_size() <= MAX_PAGE_SIZE` assuming a word is 4 bytes. + /// We have `MIN_NUM_WORDS_PER_PAGE * self.word_size() <= self.page_size() <= MAX_PAGE_SIZE`. pub fn page_size(&self) -> usize { self.page_size } /// The number of pages in the storage, denoted by `N`. /// - /// We have `3 <= N <= MAX_PAGE_INDEX + 1`. + /// We have `MIN_NUM_PAGES <= N <= MAX_PAGE_INDEX + 1`. pub fn num_pages(&self) -> usize { self.num_pages } @@ -190,14 +203,15 @@ impl Format { /// /// A virtual page is stored in a physical page after the page header. /// - /// We have `6 <= Q <= MAX_VIRT_PAGE_SIZE`. + /// We have `MIN_NUM_WORDS_PER_PAGE - 2 <= Q <= MAX_VIRT_PAGE_SIZE`. pub fn virt_page_size(&self) -> usize { self.page_size() / self.word_size() - CONTENT_WORD } /// The maximum length in bytes of a user payload. /// - /// We have `20 <= self.max_value_len() <= MAX_VALUE_LEN` assuming words are 4 bytes. + /// We have `(MIN_NUM_WORDS_PER_PAGE - 3) * self.word_size() <= self.max_value_len() <= + /// MAX_VALUE_LEN`. pub fn max_value_len(&self) -> usize { min( (self.virt_page_size() - 1) * self.word_size(), @@ -210,7 +224,7 @@ impl Format { /// A prefix is the first words of a virtual page that belong to the last entry of the previous /// virtual page. This happens because entries may overlap up to 2 virtual pages. /// - /// We have `5 <= M < Q`. + /// We have `MIN_NUM_WORDS_PER_PAGE - 3 <= M < Q`. pub fn max_prefix_len(&self) -> usize { self.bytes_to_words(self.max_value_len()) } From 71815cad092e3d0c53808b521b673a51036e53fa Mon Sep 17 00:00:00 2001 From: Julien Cretin Date: Tue, 27 Oct 2020 13:45:18 +0100 Subject: [PATCH 15/15] Update ERASED_WORD definition to use WORD --- libraries/persistent_store/src/format.rs | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/libraries/persistent_store/src/format.rs b/libraries/persistent_store/src/format.rs index 4c3c317..1fa6521 100644 --- a/libraries/persistent_store/src/format.rs +++ b/libraries/persistent_store/src/format.rs @@ -76,7 +76,7 @@ const MAX_UPDATES: usize = 31; const MAX_VIRT_PAGE_SIZE: usize = div_ceil(MAX_PAGE_SIZE, WORD_SIZE) - CONTENT_WORD; /// Word with all bits set to one. -const ERASED_WORD: u32 = 0xffffffff; +const ERASED_WORD: WORD = !(0 as WORD); /// Helpers for a given storage configuration. #[derive(Clone, Debug)] @@ -449,7 +449,9 @@ impl Format { /// Returns the minimum number of words to represent a given number of bytes. /// - /// Assumes `bytes + self.word_size()` does not overflow. + /// # Preconditions + /// + /// - `bytes + self.word_size()` does not overflow. pub fn bytes_to_words(&self, bytes: usize) -> usize { div_ceil(bytes, self.word_size()) } @@ -808,7 +810,11 @@ pub fn is_erased(slice: &[u8]) -> bool { /// Divides then takes ceiling. /// -/// Returns `ceil(x / m)` with mathematical notations. Assumes `x + m` does not overflow. +/// Returns `ceil(x / m)` in mathematical notations (not Rust code). +/// +/// # Preconditions +/// +/// - `x + m` does not overflow. const fn div_ceil(x: usize, m: usize) -> usize { (x + m - 1) / m }