394 lines
11 KiB
Rust
394 lines
11 KiB
Rust
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//! Types that describe positions within a Merkle tree
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use serde::{Deserialize, Serialize};
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use std::convert::{TryFrom, TryInto};
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use std::num::TryFromIntError;
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use std::ops::{Add, AddAssign, Range};
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/// A type-safe wrapper for indexing into "levels" of a binary tree, such that
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/// nodes at level `0` are leaves, nodes at level `1` are parents of nodes at
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/// level `0`, and so forth. This type is capable of representing levels in
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/// trees containing up to 2^255 leaves.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash, Serialize, Deserialize)]
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#[repr(transparent)]
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pub struct Level(u8);
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impl Level {
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// TODO: replace with an instance for `Step<Level>` once `step_trait`
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// is stabilized
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pub fn iter_to(self, other: Level) -> impl Iterator<Item = Self> {
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(self.0..other.0).into_iter().map(Level)
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}
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}
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impl Add<u8> for Level {
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type Output = Self;
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fn add(self, value: u8) -> Self {
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Self(self.0 + value)
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}
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}
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impl From<u8> for Level {
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fn from(value: u8) -> Self {
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Self(value)
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}
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}
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impl From<Level> for u8 {
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fn from(level: Level) -> u8 {
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level.0
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}
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}
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impl From<Level> for usize {
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fn from(level: Level) -> usize {
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level.0 as usize
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}
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}
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/// A type representing the position of a leaf in a Merkle tree.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash, Serialize, Deserialize)]
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#[repr(transparent)]
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pub struct Position(usize);
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impl Position {
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/// Return whether the position is odd-valued.
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pub fn is_odd(&self) -> bool {
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self.0 & 0x1 == 1
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}
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/// Returns the minimum possible level of the root of a binary tree containing at least
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/// `self + 1` nodes.
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pub fn root_level(&self) -> Level {
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Level(64 - self.0.leading_zeros() as u8)
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}
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/// Returns the number of cousins and/or ommers required to construct an authentication
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/// path to the root of a merkle tree that has `self + 1` nodes.
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pub fn past_ommer_count(&self) -> usize {
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(0..self.root_level().0)
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.filter(|i| (self.0 >> i) & 0x1 == 1)
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.count()
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}
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/// Returns whether the binary tree having `self` as the position of the rightmost leaf
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/// contains a perfect balanced tree with a root at level `root_level` that contains the
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/// aforesaid leaf.
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pub fn is_complete_subtree(&self, root_level: Level) -> bool {
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!(0..(root_level.0)).any(|l| self.0 & (1 << l) == 0)
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}
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/// Returns an iterator over the addresses of nodes required to create a witness for this
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/// position, beginning with the sibling of the leaf at this position and ending with the
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/// sibling of the ancestor of the leaf at this position that is required to compute a root at
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/// the specified level.
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pub(crate) fn witness_addrs(
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&self,
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root_level: Level,
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) -> impl Iterator<Item = (Address, Source)> {
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WitnessAddrsIter {
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root_level,
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current: Address::from(self),
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ommer_count: 0,
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}
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}
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}
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impl From<Position> for usize {
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fn from(p: Position) -> usize {
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p.0
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}
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}
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impl From<Position> for u64 {
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fn from(p: Position) -> Self {
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p.0 as u64
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}
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}
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impl Add<usize> for Position {
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type Output = Position;
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fn add(self, other: usize) -> Self {
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Position(self.0 + other)
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}
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}
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impl AddAssign<usize> for Position {
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fn add_assign(&mut self, other: usize) {
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self.0 += other
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}
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}
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impl From<usize> for Position {
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fn from(sz: usize) -> Self {
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Self(sz)
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}
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}
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impl TryFrom<u64> for Position {
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type Error = TryFromIntError;
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fn try_from(sz: u64) -> Result<Self, Self::Error> {
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<usize>::try_from(sz).map(Self)
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}
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}
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/// The address of an internal node of the Merkle tree.
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/// When `level == 0`, the index has the same value as the
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/// position.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash, Serialize, Deserialize)]
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pub struct Address {
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level: Level,
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index: usize,
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}
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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pub(crate) enum Source {
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/// The sibling to the address can be derived from the incremental frontier
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/// at the contained ommer index
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Past(usize),
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/// The sibling to the address must be obtained from values discovered by
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/// the addition of more nodes to the tree
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Future,
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}
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impl Address {
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pub fn from_parts(level: Level, index: usize) -> Self {
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Address { level, index }
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}
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pub fn position_range(&self) -> Range<Position> {
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Range {
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start: (self.index << self.level.0).try_into().unwrap(),
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end: ((self.index + 1) << self.level.0).try_into().unwrap(),
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}
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}
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pub fn level(&self) -> Level {
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self.level
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}
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pub fn index(&self) -> usize {
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self.index
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}
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pub fn parent(&self) -> Address {
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Address {
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level: self.level + 1,
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index: self.index >> 1,
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}
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}
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pub fn sibling(&self) -> Address {
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Address {
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level: self.level,
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index: if self.index & 0x1 == 0 {
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self.index + 1
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} else {
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self.index - 1
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},
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}
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}
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pub fn is_complete_node(&self) -> bool {
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self.index & 0x1 == 1
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}
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pub fn current_incomplete(&self) -> Address {
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// find the first zero bit in the index, searching from the least significant bit
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let mut index = self.index;
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for level in self.level.0.. {
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if index & 0x1 == 1 {
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index >>= 1;
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} else {
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return Address {
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level: Level(level),
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index,
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};
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}
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}
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unreachable!("The loop will always terminate via return in at most 64 iterations.")
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}
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pub fn next_incomplete_parent(&self) -> Address {
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if self.is_complete_node() {
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self.current_incomplete()
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} else {
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let complete = Address {
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level: self.level,
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index: self.index + 1,
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};
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complete.current_incomplete()
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}
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}
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}
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impl From<Position> for Address {
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fn from(p: Position) -> Self {
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Address {
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level: 0.into(),
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index: p.into(),
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}
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}
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}
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impl<'a> From<&'a Position> for Address {
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fn from(p: &'a Position) -> Self {
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Address {
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level: 0.into(),
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index: (*p).into(),
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}
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}
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}
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impl From<Address> for Option<Position> {
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fn from(addr: Address) -> Self {
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if addr.level == 0.into() {
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Some(addr.index.into())
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} else {
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None
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}
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}
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}
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impl<'a> From<&'a Address> for Option<Position> {
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fn from(addr: &'a Address) -> Self {
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if addr.level == 0.into() {
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Some(addr.index.into())
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} else {
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None
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}
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}
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}
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#[must_use = "iterators are lazy and do nothing unless consumed"]
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pub(crate) struct WitnessAddrsIter {
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root_level: Level,
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current: Address,
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ommer_count: usize,
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}
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impl Iterator for WitnessAddrsIter {
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type Item = (Address, Source);
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fn next(&mut self) -> Option<(Address, Source)> {
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if self.current.level() < self.root_level {
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let current = self.current;
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let source = if current.is_complete_node() {
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Source::Past(self.ommer_count)
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} else {
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Source::Future
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};
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self.current = current.parent();
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if matches!(source, Source::Past(_)) {
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self.ommer_count += 1;
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}
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Some((current.sibling(), source))
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} else {
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None
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}
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}
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}
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#[cfg(test)]
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pub(crate) mod tests {
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use super::{Address, Level, Position, Source};
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#[test]
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fn position_is_complete_subtree() {
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assert!(Position(0).is_complete_subtree(Level(0)));
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assert!(Position(1).is_complete_subtree(Level(1)));
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assert!(!Position(2).is_complete_subtree(Level(1)));
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assert!(!Position(2).is_complete_subtree(Level(2)));
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assert!(Position(3).is_complete_subtree(Level(2)));
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assert!(!Position(4).is_complete_subtree(Level(2)));
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assert!(Position(7).is_complete_subtree(Level(3)));
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assert!(Position(u32::MAX as usize).is_complete_subtree(Level(32)));
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}
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#[test]
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fn position_past_ommer_count() {
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assert_eq!(0, Position(0).past_ommer_count());
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assert_eq!(1, Position(1).past_ommer_count());
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assert_eq!(1, Position(2).past_ommer_count());
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assert_eq!(2, Position(3).past_ommer_count());
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assert_eq!(1, Position(4).past_ommer_count());
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assert_eq!(3, Position(7).past_ommer_count());
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assert_eq!(1, Position(8).past_ommer_count());
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}
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#[test]
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fn position_root_level() {
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assert_eq!(Level(0), Position(0).root_level());
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assert_eq!(Level(1), Position(1).root_level());
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assert_eq!(Level(2), Position(2).root_level());
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assert_eq!(Level(2), Position(3).root_level());
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assert_eq!(Level(3), Position(4).root_level());
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assert_eq!(Level(3), Position(7).root_level());
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assert_eq!(Level(4), Position(8).root_level());
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}
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#[test]
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fn current_incomplete() {
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let addr = |l, i| Address::from_parts(Level(l), i);
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assert_eq!(addr(0, 0), addr(0, 0).current_incomplete());
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assert_eq!(addr(1, 0), addr(0, 1).current_incomplete());
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assert_eq!(addr(0, 2), addr(0, 2).current_incomplete());
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assert_eq!(addr(2, 0), addr(0, 3).current_incomplete());
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}
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#[test]
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fn next_incomplete_parent() {
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let addr = |l, i| Address::from_parts(Level(l), i);
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assert_eq!(addr(1, 0), addr(0, 0).next_incomplete_parent());
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assert_eq!(addr(1, 0), addr(0, 1).next_incomplete_parent());
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assert_eq!(addr(2, 0), addr(0, 2).next_incomplete_parent());
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assert_eq!(addr(2, 0), addr(0, 3).next_incomplete_parent());
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assert_eq!(addr(3, 0), addr(2, 0).next_incomplete_parent());
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assert_eq!(addr(1, 2), addr(0, 4).next_incomplete_parent());
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assert_eq!(addr(3, 0), addr(1, 2).next_incomplete_parent());
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}
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#[test]
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fn position_witness_addrs() {
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use Source::*;
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let path_elem = |l, i, s| (Address::from_parts(Level(l), i), s);
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assert_eq!(
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vec![path_elem(0, 1, Future), path_elem(1, 1, Future)],
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Position(0).witness_addrs(Level(2)).collect::<Vec<_>>()
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);
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assert_eq!(
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vec![path_elem(0, 3, Future), path_elem(1, 0, Past(0))],
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Position(2).witness_addrs(Level(2)).collect::<Vec<_>>()
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);
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assert_eq!(
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vec![
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path_elem(0, 2, Past(0)),
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path_elem(1, 0, Past(1)),
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path_elem(2, 1, Future)
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],
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Position(3).witness_addrs(Level(3)).collect::<Vec<_>>()
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);
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assert_eq!(
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vec![
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path_elem(0, 5, Future),
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path_elem(1, 3, Future),
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path_elem(2, 0, Past(0)),
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path_elem(3, 1, Future)
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],
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Position(4).witness_addrs(Level(4)).collect::<Vec<_>>()
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);
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assert_eq!(
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vec![
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path_elem(0, 7, Future),
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path_elem(1, 2, Past(0)),
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path_elem(2, 0, Past(1)),
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path_elem(3, 1, Future)
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],
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Position(6).witness_addrs(Level(4)).collect::<Vec<_>>()
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);
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}
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}
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