626 lines
24 KiB
Rust
626 lines
24 KiB
Rust
use alloc::{collections::BTreeMap, vec::Vec};
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use core::mem;
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use num::Integer;
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use super::{EmptySubtreeRoots, InnerNodeInfo, MerkleError, MerklePath, NodeIndex};
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use crate::{
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hash::rpo::{Rpo256, RpoDigest},
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Felt, Word, EMPTY_WORD,
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};
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mod full;
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pub use full::{Smt, SmtLeaf, SmtLeafError, SmtProof, SmtProofError, SMT_DEPTH};
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mod simple;
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pub use simple::SimpleSmt;
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// CONSTANTS
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// ================================================================================================
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/// Minimum supported depth.
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pub const SMT_MIN_DEPTH: u8 = 1;
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/// Maximum supported depth.
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pub const SMT_MAX_DEPTH: u8 = 64;
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// SPARSE MERKLE TREE
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// ================================================================================================
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/// An abstract description of a sparse Merkle tree.
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///
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/// A sparse Merkle tree is a key-value map which also supports proving that a given value is indeed
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/// stored at a given key in the tree. It is viewed as always being fully populated. If a leaf's
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/// value was not explicitly set, then its value is the default value. Typically, the vast majority
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/// of leaves will store the default value (hence it is "sparse"), and therefore the internal
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/// representation of the tree will only keep track of the leaves that have a different value from
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/// the default.
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///
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/// All leaves sit at the same depth. The deeper the tree, the more leaves it has; but also the
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/// longer its proofs are - of exactly `log(depth)` size. A tree cannot have depth 0, since such a
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/// tree is just a single value, and is probably a programming mistake.
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///
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/// Every key maps to one leaf. If there are as many keys as there are leaves, then
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/// [Self::Leaf] should be the same type as [Self::Value], as is the case with
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/// [crate::merkle::SimpleSmt]. However, if there are more keys than leaves, then [`Self::Leaf`]
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/// must accomodate all keys that map to the same leaf.
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///
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/// [SparseMerkleTree] currently doesn't support optimizations that compress Merkle proofs.
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pub(crate) trait SparseMerkleTree<const DEPTH: u8> {
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/// The type for a key
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type Key: Clone + Ord;
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/// The type for a value
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type Value: Clone + PartialEq;
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/// The type for a leaf
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type Leaf: Clone;
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/// The type for an opening (i.e. a "proof") of a leaf
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type Opening;
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/// The default value used to compute the hash of empty leaves
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const EMPTY_VALUE: Self::Value;
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/// The root of the empty tree with provided DEPTH
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const EMPTY_ROOT: RpoDigest;
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// PROVIDED METHODS
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// ---------------------------------------------------------------------------------------------
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/// Returns an opening of the leaf associated with `key`. Conceptually, an opening is a Merkle
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/// path to the leaf, as well as the leaf itself.
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fn open(&self, key: &Self::Key) -> Self::Opening {
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let leaf = self.get_leaf(key);
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let mut index: NodeIndex = {
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let leaf_index: LeafIndex<DEPTH> = Self::key_to_leaf_index(key);
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leaf_index.into()
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};
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let merkle_path = {
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let mut path = Vec::with_capacity(index.depth() as usize);
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for _ in 0..index.depth() {
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let is_right = index.is_value_odd();
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index.move_up();
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let InnerNode { left, right } = self.get_inner_node(index);
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let value = if is_right { left } else { right };
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path.push(value);
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}
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MerklePath::new(path)
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};
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Self::path_and_leaf_to_opening(merkle_path, leaf)
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}
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/// Inserts a value at the specified key, returning the previous value associated with that key.
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/// Recall that by definition, any key that hasn't been updated is associated with
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/// [`Self::EMPTY_VALUE`].
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///
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/// This also recomputes all hashes between the leaf (associated with the key) and the root,
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/// updating the root itself.
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fn insert(&mut self, key: Self::Key, value: Self::Value) -> Self::Value {
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let old_value = self.insert_value(key.clone(), value.clone()).unwrap_or(Self::EMPTY_VALUE);
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// if the old value and new value are the same, there is nothing to update
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if value == old_value {
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return value;
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}
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let leaf = self.get_leaf(&key);
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let node_index = {
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let leaf_index: LeafIndex<DEPTH> = Self::key_to_leaf_index(&key);
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leaf_index.into()
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};
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self.recompute_nodes_from_index_to_root(node_index, Self::hash_leaf(&leaf));
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old_value
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}
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/// Recomputes the branch nodes (including the root) from `index` all the way to the root.
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/// `node_hash_at_index` is the hash of the node stored at index.
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fn recompute_nodes_from_index_to_root(
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&mut self,
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mut index: NodeIndex,
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node_hash_at_index: RpoDigest,
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) {
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let mut node_hash = node_hash_at_index;
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for node_depth in (0..index.depth()).rev() {
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let is_right = index.is_value_odd();
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index.move_up();
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let InnerNode { left, right } = self.get_inner_node(index);
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let (left, right) = if is_right {
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(left, node_hash)
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} else {
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(node_hash, right)
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};
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node_hash = Rpo256::merge(&[left, right]);
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if node_hash == *EmptySubtreeRoots::entry(DEPTH, node_depth) {
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// If a subtree is empty, when can remove the inner node, since it's equal to the
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// default value
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self.remove_inner_node(index)
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} else {
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self.insert_inner_node(index, InnerNode { left, right });
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}
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}
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self.set_root(node_hash);
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}
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/// Computes what changes are necessary to insert the specified key-value pairs into this Merkle
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/// tree, allowing for validation before applying those changes.
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///
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/// This method returns a [`MutationSet`], which contains all the information for inserting
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/// `kv_pairs` into this Merkle tree already calculated, including the new root hash, which can
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/// be queried with [`MutationSet::root()`]. Once a mutation set is returned,
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/// [`SparseMerkleTree::apply_mutations()`] can be called in order to commit these changes to
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/// the Merkle tree, or [`drop()`] to discard them.
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fn compute_mutations(
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&self,
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kv_pairs: impl IntoIterator<Item = (Self::Key, Self::Value)>,
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) -> MutationSet<DEPTH, Self::Key, Self::Value> {
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use NodeMutation::*;
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let mut new_root = self.root();
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let mut new_pairs: BTreeMap<Self::Key, Self::Value> = Default::default();
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let mut node_mutations: BTreeMap<NodeIndex, NodeMutation> = Default::default();
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for (key, value) in kv_pairs {
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// If the old value and the new value are the same, there is nothing to update.
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// For the unusual case that kv_pairs has multiple values at the same key, we'll have
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// to check the key-value pairs we've already seen to get the "effective" old value.
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let old_value = new_pairs.get(&key).cloned().unwrap_or_else(|| self.get_value(&key));
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if value == old_value {
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continue;
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}
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let leaf_index = Self::key_to_leaf_index(&key);
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let mut node_index = NodeIndex::from(leaf_index);
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// We need the current leaf's hash to calculate the new leaf, but in the rare case that
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// `kv_pairs` has multiple pairs that go into the same leaf, then those pairs are also
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// part of the "current leaf".
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let old_leaf = {
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let pairs_at_index = new_pairs
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.iter()
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.filter(|&(new_key, _)| Self::key_to_leaf_index(new_key) == leaf_index);
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pairs_at_index.fold(self.get_leaf(&key), |acc, (k, v)| {
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// Most of the time `pairs_at_index` should only contain a single entry (or
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// none at all), as multi-leaves should be really rare.
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let existing_leaf = acc.clone();
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self.construct_prospective_leaf(existing_leaf, k, v)
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})
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};
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let new_leaf = self.construct_prospective_leaf(old_leaf, &key, &value);
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let mut new_child_hash = Self::hash_leaf(&new_leaf);
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for node_depth in (0..node_index.depth()).rev() {
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// Whether the node we're replacing is the right child or the left child.
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let is_right = node_index.is_value_odd();
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node_index.move_up();
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let old_node = node_mutations
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.get(&node_index)
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.map(|mutation| match mutation {
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Addition(node) => node.clone(),
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Removal => EmptySubtreeRoots::get_inner_node(DEPTH, node_depth),
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})
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.unwrap_or_else(|| self.get_inner_node(node_index));
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let new_node = if is_right {
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InnerNode {
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left: old_node.left,
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right: new_child_hash,
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}
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} else {
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InnerNode {
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left: new_child_hash,
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right: old_node.right,
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}
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};
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// The next iteration will operate on this new node's hash.
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new_child_hash = new_node.hash();
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let &equivalent_empty_hash = EmptySubtreeRoots::entry(DEPTH, node_depth);
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let is_removal = new_child_hash == equivalent_empty_hash;
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let new_entry = if is_removal { Removal } else { Addition(new_node) };
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node_mutations.insert(node_index, new_entry);
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}
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// Once we're at depth 0, the last node we made is the new root.
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new_root = new_child_hash;
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// And then we're done with this pair; on to the next one.
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new_pairs.insert(key, value);
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}
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MutationSet {
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old_root: self.root(),
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new_root,
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node_mutations,
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new_pairs,
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}
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}
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/// Apply the prospective mutations computed with [`SparseMerkleTree::compute_mutations()`] to
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/// this tree.
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///
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/// # Errors
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/// If `mutations` was computed on a tree with a different root than this one, returns
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/// [`MerkleError::ConflictingRoots`] with a two-item [`Vec`]. The first item is the root hash
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/// the `mutations` were computed against, and the second item is the actual current root of
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/// this tree.
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fn apply_mutations(
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&mut self,
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mutations: MutationSet<DEPTH, Self::Key, Self::Value>,
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) -> Result<(), MerkleError>
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where
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Self: Sized,
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{
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use NodeMutation::*;
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let MutationSet {
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old_root,
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node_mutations,
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new_pairs,
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new_root,
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} = mutations;
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// Guard against accidentally trying to apply mutations that were computed against a
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// different tree, including a stale version of this tree.
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if old_root != self.root() {
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return Err(MerkleError::ConflictingRoots(vec![old_root, self.root()]));
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}
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for (index, mutation) in node_mutations {
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match mutation {
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Removal => self.remove_inner_node(index),
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Addition(node) => self.insert_inner_node(index, node),
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}
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}
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for (key, value) in new_pairs {
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self.insert_value(key, value);
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}
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self.set_root(new_root);
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Ok(())
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}
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// REQUIRED METHODS
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// ---------------------------------------------------------------------------------------------
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/// The root of the tree
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fn root(&self) -> RpoDigest;
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/// Sets the root of the tree
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fn set_root(&mut self, root: RpoDigest);
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/// Retrieves an inner node at the given index
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fn get_inner_node(&self, index: NodeIndex) -> InnerNode;
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/// Inserts an inner node at the given index
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fn insert_inner_node(&mut self, index: NodeIndex, inner_node: InnerNode);
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/// Removes an inner node at the given index
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fn remove_inner_node(&mut self, index: NodeIndex);
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/// Inserts a leaf node, and returns the value at the key if already exists
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fn insert_value(&mut self, key: Self::Key, value: Self::Value) -> Option<Self::Value>;
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/// Returns the value at the specified key. Recall that by definition, any key that hasn't been
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/// updated is associated with [`Self::EMPTY_VALUE`].
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fn get_value(&self, key: &Self::Key) -> Self::Value;
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/// Returns the leaf at the specified index.
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fn get_leaf(&self, key: &Self::Key) -> Self::Leaf;
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/// Returns the hash of a leaf
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fn hash_leaf(leaf: &Self::Leaf) -> RpoDigest;
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/// Returns what a leaf would look like if a key-value pair were inserted into the tree, without
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/// mutating the tree itself. The existing leaf can be empty.
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///
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/// To get a prospective leaf based on the current state of the tree, use `self.get_leaf(key)`
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/// as the argument for `existing_leaf`. The return value from this function can be chained back
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/// into this function as the first argument to continue making prospective changes.
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///
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/// # Invariants
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/// Because this method is for a prospective key-value insertion into a specific leaf,
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/// `existing_leaf` must have the same leaf index as `key` (as determined by
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/// [`SparseMerkleTree::key_to_leaf_index()`]), or the result will be meaningless.
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fn construct_prospective_leaf(
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&self,
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existing_leaf: Self::Leaf,
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key: &Self::Key,
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value: &Self::Value,
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) -> Self::Leaf;
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/// Maps a key to a leaf index
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fn key_to_leaf_index(key: &Self::Key) -> LeafIndex<DEPTH>;
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/// Maps a (MerklePath, Self::Leaf) to an opening.
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///
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/// The length `path` is guaranteed to be equal to `DEPTH`
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fn path_and_leaf_to_opening(path: MerklePath, leaf: Self::Leaf) -> Self::Opening;
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/// Builds Merkle nodes from a bottom layer of tuples of horizontal indices and their hashes,
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/// sorted by their position.
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///
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/// The leaves are 'conceptual' leaves, simply being entities at the bottom of some subtree, not
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/// [`Self::Leaf`].
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///
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/// # Panics
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/// With debug assertions on, this function panics under invalid inputs: if `leaves` contains
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/// more entries than can fit in a depth-8 subtree (more than 256), if `bottom_depth` is
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/// lower in the tree than the specified maximum depth (`DEPTH`), or if `leaves` is not sorted.
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// FIXME: more complete docstring.
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fn build_subtree(
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mut leaves: Vec<SubtreeLeaf>,
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bottom_depth: u8,
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) -> (BTreeMap<NodeIndex, InnerNode>, Vec<SubtreeLeaf>) {
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debug_assert!(bottom_depth <= DEPTH);
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debug_assert!(bottom_depth.is_multiple_of(&8));
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debug_assert!(leaves.len() <= usize::pow(2, 8));
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let subtree_root = bottom_depth - 8;
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let mut inner_nodes: BTreeMap<NodeIndex, InnerNode> = Default::default();
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let mut next_leaves: Vec<SubtreeLeaf> = Vec::with_capacity(leaves.len() / 2);
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for next_depth in (subtree_root..bottom_depth).rev() {
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debug_assert!(next_depth <= bottom_depth);
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// `next_depth` is the stuff we're making.
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// `current_depth` is the stuff we have.
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let current_depth = next_depth + 1;
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let mut iter = leaves.drain(..).peekable();
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while let Some(first) = iter.next() {
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// On non-continuous iterations, including the first iteration, `first_column` may
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// be a left or right node. On subsequent continuous iterations, we will always call
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// `iter.next()` twice.
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// On non-continuous iterations (including the very first iteration), this column
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// could be either on the left or the right. If the next iteration is not
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// discontinuous with our right node, then the next iteration's
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let is_right = first.col.is_odd();
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let (left, right) = if is_right {
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// Discontinuous iteration: we have no left node, so it must be empty.
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let left = SubtreeLeaf {
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col: first.col - 1,
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hash: *EmptySubtreeRoots::entry(DEPTH, current_depth),
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};
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let right = first;
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(left, right)
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} else {
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let left = first;
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let right_col = first.col + 1;
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let right = match iter.peek().copied() {
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Some(SubtreeLeaf { col, .. }) if col == right_col => {
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// Our inputs must be sorted.
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debug_assert!(left.col <= col);
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// The next leaf in the iterator is our sibling. Use it and consume it!
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iter.next().unwrap()
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},
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// Otherwise, the leaves don't contain our sibling, so our sibling must be
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// empty.
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_ => SubtreeLeaf {
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col: right_col,
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hash: *EmptySubtreeRoots::entry(DEPTH, current_depth),
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},
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};
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(left, right)
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};
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let index = NodeIndex::new_unchecked(current_depth, left.col).parent();
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let node = InnerNode { left: left.hash, right: right.hash };
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let hash = node.hash();
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let &equivalent_empty_hash = EmptySubtreeRoots::entry(DEPTH, next_depth);
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// If this hash is empty, then it doesn't become a new inner node, nor does it count
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// as a leaf for the next depth.
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if hash != equivalent_empty_hash {
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inner_nodes.insert(index, node);
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// FIXME: is it possible for this to end up not being sorted? I don't think so.
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next_leaves.push(SubtreeLeaf { col: index.value(), hash });
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}
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}
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// Stop borrowing `leaves`, so we can swap it.
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// The iterator is empty at this point anyway.
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drop(iter);
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// After each depth, consider the stuff we just made the new "leaves", and empty the
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// other collection.
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mem::swap(&mut leaves, &mut next_leaves);
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}
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(inner_nodes, leaves)
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}
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}
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// INNER NODE
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// ================================================================================================
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#[derive(Debug, Default, Clone, PartialEq, Eq)]
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#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
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pub struct InnerNode {
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pub left: RpoDigest,
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pub right: RpoDigest,
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}
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impl InnerNode {
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pub fn hash(&self) -> RpoDigest {
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Rpo256::merge(&[self.left, self.right])
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}
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}
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// LEAF INDEX
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// ================================================================================================
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/// The index of a leaf, at a depth known at compile-time.
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#[derive(Debug, Default, Copy, Clone, Eq, PartialEq, PartialOrd, Ord, Hash)]
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#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
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pub struct LeafIndex<const DEPTH: u8> {
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index: NodeIndex,
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}
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impl<const DEPTH: u8> LeafIndex<DEPTH> {
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pub fn new(value: u64) -> Result<Self, MerkleError> {
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if DEPTH < SMT_MIN_DEPTH {
|
|
return Err(MerkleError::DepthTooSmall(DEPTH));
|
|
}
|
|
|
|
Ok(LeafIndex { index: NodeIndex::new(DEPTH, value)? })
|
|
}
|
|
|
|
pub fn value(&self) -> u64 {
|
|
self.index.value()
|
|
}
|
|
}
|
|
|
|
impl LeafIndex<SMT_MAX_DEPTH> {
|
|
pub const fn new_max_depth(value: u64) -> Self {
|
|
LeafIndex {
|
|
index: NodeIndex::new_unchecked(SMT_MAX_DEPTH, value),
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<const DEPTH: u8> From<LeafIndex<DEPTH>> for NodeIndex {
|
|
fn from(value: LeafIndex<DEPTH>) -> Self {
|
|
value.index
|
|
}
|
|
}
|
|
|
|
impl<const DEPTH: u8> TryFrom<NodeIndex> for LeafIndex<DEPTH> {
|
|
type Error = MerkleError;
|
|
|
|
fn try_from(node_index: NodeIndex) -> Result<Self, Self::Error> {
|
|
if node_index.depth() != DEPTH {
|
|
return Err(MerkleError::InvalidDepth {
|
|
expected: DEPTH,
|
|
provided: node_index.depth(),
|
|
});
|
|
}
|
|
|
|
Self::new(node_index.value())
|
|
}
|
|
}
|
|
|
|
// MUTATIONS
|
|
// ================================================================================================
|
|
|
|
/// A change to an inner node of a [`SparseMerkleTree`] that hasn't yet been applied.
|
|
/// [`MutationSet`] stores this type in relation to a [`NodeIndex`] to keep track of what changes
|
|
/// need to occur at which node indices.
|
|
#[derive(Debug, Clone, PartialEq, Eq)]
|
|
pub(crate) enum NodeMutation {
|
|
/// Corresponds to [`SparseMerkleTree::remove_inner_node()`].
|
|
Removal,
|
|
/// Corresponds to [`SparseMerkleTree::insert_inner_node()`].
|
|
Addition(InnerNode),
|
|
}
|
|
|
|
/// Represents a group of prospective mutations to a `SparseMerkleTree`, created by
|
|
/// `SparseMerkleTree::compute_mutations()`, and that can be applied with
|
|
/// `SparseMerkleTree::apply_mutations()`.
|
|
#[derive(Debug, Clone, PartialEq, Eq, Default)]
|
|
pub struct MutationSet<const DEPTH: u8, K, V> {
|
|
/// The root of the Merkle tree this MutationSet is for, recorded at the time
|
|
/// [`SparseMerkleTree::compute_mutations()`] was called. Exists to guard against applying
|
|
/// mutations to the wrong tree or applying stale mutations to a tree that has since changed.
|
|
old_root: RpoDigest,
|
|
/// The set of nodes that need to be removed or added. The "effective" node at an index is the
|
|
/// Merkle tree's existing node at that index, with the [`NodeMutation`] in this map at that
|
|
/// index overlayed, if any. Each [`NodeMutation::Addition`] corresponds to a
|
|
/// [`SparseMerkleTree::insert_inner_node()`] call, and each [`NodeMutation::Removal`]
|
|
/// corresponds to a [`SparseMerkleTree::remove_inner_node()`] call.
|
|
node_mutations: BTreeMap<NodeIndex, NodeMutation>,
|
|
/// The set of top-level key-value pairs we're prospectively adding to the tree, including
|
|
/// adding empty values. The "effective" value for a key is the value in this BTreeMap, falling
|
|
/// back to the existing value in the Merkle tree. Each entry corresponds to a
|
|
/// [`SparseMerkleTree::insert_value()`] call.
|
|
new_pairs: BTreeMap<K, V>,
|
|
/// The calculated root for the Merkle tree, given these mutations. Publicly retrievable with
|
|
/// [`MutationSet::root()`]. Corresponds to a [`SparseMerkleTree::set_root()`]. call.
|
|
new_root: RpoDigest,
|
|
}
|
|
|
|
impl<const DEPTH: u8, K, V> MutationSet<DEPTH, K, V> {
|
|
/// Queries the root that was calculated during `SparseMerkleTree::compute_mutations()`. See
|
|
/// that method for more information.
|
|
pub fn root(&self) -> RpoDigest {
|
|
self.new_root
|
|
}
|
|
}
|
|
|
|
// HELPERS
|
|
// ================================================================================================
|
|
#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Default)]
|
|
pub struct SubtreeLeaf {
|
|
pub col: u64,
|
|
pub hash: RpoDigest,
|
|
}
|
|
|
|
// TESTS
|
|
// ================================================================================================
|
|
#[cfg(test)]
|
|
mod test {
|
|
use alloc::vec::Vec;
|
|
|
|
use super::SparseMerkleTree;
|
|
use crate::{
|
|
hash::rpo::RpoDigest,
|
|
merkle::{smt::SubtreeLeaf, Smt, SmtLeaf, SMT_DEPTH},
|
|
Felt, Word, ONE,
|
|
};
|
|
|
|
#[test]
|
|
fn test_build_subtree_from_leaves() {
|
|
const PAIR_COUNT: u64 = u64::pow(2, 8);
|
|
|
|
let entries: Vec<(RpoDigest, Word)> = (0..PAIR_COUNT)
|
|
.map(|i| {
|
|
let leaf_index = ((i as f64 / PAIR_COUNT as f64) * 255.0) as u64;
|
|
let key = RpoDigest::new([ONE, ONE, Felt::new(i), Felt::new(leaf_index)]);
|
|
let value = [ONE, ONE, ONE, Felt::new(i)];
|
|
(key, value)
|
|
})
|
|
.collect();
|
|
|
|
let control = Smt::with_entries(entries.clone()).unwrap();
|
|
|
|
let mut leaves: Vec<SubtreeLeaf> = entries
|
|
.iter()
|
|
.map(|(key, value)| {
|
|
let leaf = SmtLeaf::new_single(*key, *value);
|
|
let col = leaf.index().index.value();
|
|
let hash = leaf.hash();
|
|
SubtreeLeaf { col, hash }
|
|
})
|
|
.collect();
|
|
leaves.sort();
|
|
leaves.dedup_by_key(|leaf| leaf.col);
|
|
|
|
let (first_subtree, _) = Smt::build_subtree(leaves, SMT_DEPTH);
|
|
assert!(!first_subtree.is_empty());
|
|
|
|
for (index, node) in first_subtree.into_iter() {
|
|
let control = control.get_inner_node(index);
|
|
assert_eq!(
|
|
control, node,
|
|
"subtree-computed node at index {index:?} does not match control",
|
|
);
|
|
}
|
|
}
|
|
}
|