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use crate::{get_zero_hash, Hash256, HASHSIZE};
use ethereum_hashing::{Context, Sha256Context, HASH_LEN};
use smallvec::{smallvec, SmallVec};
use std::mem;
type SmallVec8<T> = SmallVec<[T; 8]>;
#[derive(Clone, Debug, PartialEq)]
pub enum Error {
/// The maximum number of leaves defined by the initialization `depth` has been exceed.
MaximumLeavesExceeded { max_leaves: usize },
}
/// Helper struct to store either a hash digest or a slice.
///
/// Should be used as a left or right value for some node.
enum Preimage<'a> {
Digest([u8; HASH_LEN]),
Slice(&'a [u8]),
}
impl<'a> Preimage<'a> {
/// Returns a 32-byte slice.
fn as_bytes(&self) -> &[u8] {
match self {
Preimage::Digest(digest) => digest.as_ref(),
Preimage::Slice(slice) => slice,
}
}
}
/// A node that has had a left child supplied, but not a right child.
struct HalfNode {
/// The hasher context.
context: Context,
/// The tree id of the node. The root node has in id of `1` and ids increase moving down the
/// tree from left to right.
id: usize,
}
impl HalfNode {
/// Create a new half-node from the given `left` value.
fn new(id: usize, left: Preimage) -> Self {
let mut context = Context::new();
context.update(left.as_bytes());
Self { context, id }
}
/// Complete the half-node by providing a `right` value. Returns a digest of the left and right
/// nodes.
fn finish(mut self, right: Preimage) -> [u8; HASH_LEN] {
self.context.update(right.as_bytes());
self.context.finalize()
}
}
/// Provides a Merkle-root hasher that allows for streaming bytes (i.e., providing any-length byte
/// slices without need to separate into leaves). Efficiently handles cases where not all leaves
/// have been provided by assuming all non-provided leaves are `[0; 32]` and pre-computing the
/// zero-value hashes at all depths of the tree.
///
/// This algorithm aims to allocate as little memory as possible and it does this by "folding" up
/// the tree as each leaf is provided. Consider this step-by-step functional diagram of hashing a
/// tree with depth three:
///
/// ## Functional Diagram
///
/// Nodes that are `-` have not been defined and do not occupy memory. Nodes that are `L` are
/// leaves that are provided but are not stored. Nodes that have integers (`1`, `2`) are stored in
/// our struct. Finally, nodes that are `X` were stored, but are now removed.
///
/// ### Start
///
/// ```ignore
/// -
/// / \
/// - -
/// / \ / \
/// - - - -
/// ```
///
/// ### Provide first leaf
///
/// ```ignore
/// -
/// / \
/// 2 -
/// / \ / \
/// L - - -
/// ```
///
/// ### Provide second leaf
///
/// ```ignore
/// 1
/// / \
/// X -
/// / \ / \
/// L L - -
/// ```
///
/// ### Provide third leaf
///
/// ```ignore
/// 1
/// / \
/// X 3
/// / \ / \
/// L L L -
/// ```
///
/// ### Provide fourth and final leaf
///
/// ```ignore
/// 1
/// / \
/// X X
/// / \ / \
/// L L L L
/// ```
///
pub struct MerkleHasher {
/// Stores the nodes that are half-complete and awaiting a right node.
///
/// A smallvec of size 8 means we can hash a tree with 256 leaves without allocating on the
/// heap. Each half-node is 232 bytes, so this smallvec may store 1856 bytes on the stack.
half_nodes: SmallVec8<HalfNode>,
/// The depth of the tree that will be produced.
///
/// Depth is counted top-down (i.e., the root node is at depth 0). A tree with 1 leaf has a
/// depth of 1, a tree with 4 leaves has a depth of 3.
depth: usize,
/// The next leaf that we are expecting to process.
next_leaf: usize,
/// A buffer of bytes that are waiting to be written to a leaf.
buffer: SmallVec<[u8; 32]>,
/// Set to Some(root) when the root of the tree is known.
root: Option<Hash256>,
}
/// Returns the parent of node with id `i`.
fn get_parent(i: usize) -> usize {
i / 2
}
/// Gets the depth of a node with an id of `i`.
///
/// It is a logic error to provide `i == 0`.
///
/// E.g., if `i` is 1, depth is 0. If `i` is is 1, depth is 1.
fn get_depth(i: usize) -> usize {
let total_bits = mem::size_of::<usize>() * 8;
total_bits - i.leading_zeros() as usize - 1
}
impl MerkleHasher {
/// Instantiate a hasher for a tree with a given number of leaves.
///
/// `num_leaves` will be rounded to the next power of two. E.g., if `num_leaves == 6`, then the
/// tree will _actually_ be able to accomodate 8 leaves and the resulting hasher is exactly the
/// same as one that was instantiated with `Self::with_leaves(8)`.
///
/// ## Notes
///
/// If `num_leaves == 0`, a tree of depth 1 will be created. If no leaves are provided it will
/// return a root of `[0; 32]`.
pub fn with_leaves(num_leaves: usize) -> Self {
let depth = get_depth(num_leaves.next_power_of_two()) + 1;
Self::with_depth(depth)
}
/// Instantiates a new, empty hasher for a tree with `depth` layers which will have capacity
/// for `1 << (depth - 1)` leaf nodes.
///
/// It is not possible to grow the depth of the tree after instantiation.
///
/// ## Panics
///
/// Panics if `depth == 0`.
fn with_depth(depth: usize) -> Self {
assert!(depth > 0, "merkle tree cannot have a depth of zero");
Self {
half_nodes: SmallVec::with_capacity(depth - 1),
depth,
next_leaf: 1 << (depth - 1),
buffer: SmallVec::with_capacity(32),
root: None,
}
}
/// Write some bytes to the hasher.
///
/// ## Errors
///
/// Returns an error if the given bytes would create a leaf that would exceed the maximum
/// permissible number of leaves defined by the initialization `depth`. E.g., a tree of `depth
/// == 2` can only accept 2 leaves. A tree of `depth == 14` can only accept 8,192 leaves.
pub fn write(&mut self, bytes: &[u8]) -> Result<(), Error> {
let mut ptr = 0;
while ptr <= bytes.len() {
let slice = &bytes[ptr..std::cmp::min(bytes.len(), ptr + HASHSIZE)];
if self.buffer.is_empty() && slice.len() == HASHSIZE {
self.process_leaf(slice)?;
ptr += HASHSIZE
} else if self.buffer.len() + slice.len() < HASHSIZE {
self.buffer.extend_from_slice(slice);
ptr += HASHSIZE
} else {
let buf_len = self.buffer.len();
let required = HASHSIZE - buf_len;
let mut leaf = [0; HASHSIZE];
leaf[..buf_len].copy_from_slice(&self.buffer);
leaf[buf_len..].copy_from_slice(&slice[0..required]);
self.process_leaf(&leaf)?;
self.buffer = smallvec![];
ptr += required
}
}
Ok(())
}
/// Process the next leaf in the tree.
///
/// ## Errors
///
/// Returns an error if the given leaf would exceed the maximum permissible number of leaves
/// defined by the initialization `depth`. E.g., a tree of `depth == 2` can only accept 2
/// leaves. A tree of `depth == 14` can only accept 8,192 leaves.
fn process_leaf(&mut self, leaf: &[u8]) -> Result<(), Error> {
assert_eq!(leaf.len(), HASHSIZE, "a leaf must be 32 bytes");
let max_leaves = 1 << (self.depth + 1);
if self.next_leaf > max_leaves {
return Err(Error::MaximumLeavesExceeded { max_leaves });
} else if self.next_leaf == 1 {
// A tree of depth one has a root that is equal to the first given leaf.
self.root = Some(Hash256::from_slice(leaf))
} else if self.next_leaf % 2 == 0 {
self.process_left_node(self.next_leaf, Preimage::Slice(leaf))
} else {
self.process_right_node(self.next_leaf, Preimage::Slice(leaf))
}
self.next_leaf += 1;
Ok(())
}
/// Returns the root of the Merkle tree.
///
/// If not all leaves have been provided, the tree will be efficiently completed under the
/// assumption that all not-yet-provided leaves are equal to `[0; 32]`.
///
/// ## Errors
///
/// Returns an error if the bytes remaining in the buffer would create a leaf that would exceed
/// the maximum permissible number of leaves defined by the initialization `depth`.
pub fn finish(mut self) -> Result<Hash256, Error> {
if !self.buffer.is_empty() {
let mut leaf = [0; HASHSIZE];
leaf[..self.buffer.len()].copy_from_slice(&self.buffer);
self.process_leaf(&leaf)?
}
// If the tree is incomplete, we must complete it by providing zero-hashes.
loop {
if let Some(root) = self.root {
break Ok(root);
} else if let Some(node) = self.half_nodes.last() {
let right_child = node.id * 2 + 1;
self.process_right_node(right_child, self.zero_hash(right_child));
} else if self.next_leaf == 1 {
// The next_leaf can only be 1 if the tree has a depth of one. If have been no
// leaves supplied, assume a root of zero.
break Ok(Hash256::zero());
} else {
// The only scenario where there are (a) no half nodes and (b) a tree of depth
// two or more is where no leaves have been supplied at all.
//
// Once we supply this first zero-hash leaf then all future operations will be
// triggered via the `process_right_node` branch.
self.process_left_node(self.next_leaf, self.zero_hash(self.next_leaf))
}
}
}
/// Process a node that will become the left-hand node of some parent. The supplied `id` is
/// that of the node (not the parent). The `preimage` is the value of the node (i.e., if this
/// is a leaf node it will be the value of that leaf).
///
/// In this scenario, the only option is to push a new half-node.
fn process_left_node(&mut self, id: usize, preimage: Preimage) {
self.half_nodes
.push(HalfNode::new(get_parent(id), preimage))
}
/// Process a node that will become the right-hand node of some parent. The supplied `id` is
/// that of the node (not the parent). The `preimage` is the value of the node (i.e., if this
/// is a leaf node it will be the value of that leaf).
///
/// This operation will always complete one node, then it will attempt to crawl up the tree and
/// collapse all other completed nodes. For example, consider a tree of depth 3 (see diagram
/// below). When providing the node with id `7`, the node with id `3` will be completed which
/// will also provide the right-node for the `1` node. This function will complete both of
/// those nodes and ultimately find the root of the tree.
///
/// ```ignore
/// 1 <-- completed
/// / \
/// 2 3 <-- completed
/// / \ / \
/// 4 5 6 7 <-- supplied right node
/// ```
fn process_right_node(&mut self, id: usize, mut preimage: Preimage) {
let mut parent = get_parent(id);
loop {
match self.half_nodes.last() {
Some(node) if node.id == parent => {
preimage = Preimage::Digest(
self.half_nodes
.pop()
.expect("if .last() is Some then .pop() must succeed")
.finish(preimage),
);
if parent == 1 {
self.root = Some(Hash256::from_slice(preimage.as_bytes()));
break;
} else {
parent = get_parent(parent);
}
}
_ => {
self.half_nodes.push(HalfNode::new(parent, preimage));
break;
}
}
}
}
/// Returns a "zero hash" from a pre-computed set for the given node.
///
/// Note: this node is not always zero, instead it is the result of hashing up a tree where the
/// leaves are all zeros. E.g., in a tree of depth 2, the `zero_hash` of a node at depth 1
/// will be `[0; 32]`. However, the `zero_hash` for a node at depth 0 will be
/// `hash(concat([0; 32], [0; 32])))`.
fn zero_hash(&self, id: usize) -> Preimage<'static> {
Preimage::Slice(get_zero_hash(self.depth - (get_depth(id) + 1)))
}
}
#[cfg(test)]
mod test {
use super::*;
use crate::merkleize_padded;
/// This test is just to ensure that the stack size of the `Context` remains the same. We choose
/// our smallvec size based upon this, so it's good to know if it suddenly changes in size.
#[test]
fn context_size() {
assert_eq!(
mem::size_of::<HalfNode>(),
224,
"Halfnode size should be as expected"
);
}
fn compare_with_reference(leaves: &[Hash256], depth: usize) {
let reference_bytes = leaves
.iter()
.flat_map(|hash| hash.as_bytes())
.copied()
.collect::<Vec<_>>();
let reference_root = merkleize_padded(&reference_bytes, 1 << (depth - 1));
let merklizer_root_32_bytes = {
let mut m = MerkleHasher::with_depth(depth);
for leaf in leaves.iter() {
m.write(leaf.as_bytes()).expect("should process leaf");
}
m.finish().expect("should finish")
};
assert_eq!(
reference_root, merklizer_root_32_bytes,
"32 bytes should match reference root"
);
let merklizer_root_individual_3_bytes = {
let mut m = MerkleHasher::with_depth(depth);
for bytes in reference_bytes.chunks(3) {
m.write(bytes).expect("should process byte");
}
m.finish().expect("should finish")
};
assert_eq!(
reference_root, merklizer_root_individual_3_bytes,
"3 bytes should match reference root"
);
let merklizer_root_individual_single_bytes = {
let mut m = MerkleHasher::with_depth(depth);
for byte in reference_bytes.iter() {
m.write(&[*byte]).expect("should process byte");
}
m.finish().expect("should finish")
};
assert_eq!(
reference_root, merklizer_root_individual_single_bytes,
"single bytes should match reference root"
);
}
/// A simple wrapper to compare MerkleHasher to the reference function by just giving a number
/// of leaves and a depth.
fn compare_reference_with_len(leaves: u64, depth: usize) {
let leaves = (0..leaves)
.map(Hash256::from_low_u64_be)
.collect::<Vec<_>>();
compare_with_reference(&leaves, depth)
}
/// Compares the `MerkleHasher::with_depth` and `MerkleHasher::with_leaves` generate consistent
/// results.
fn compare_new_with_leaf_count(num_leaves: u64, depth: usize) {
let leaves = (0..num_leaves)
.map(Hash256::from_low_u64_be)
.collect::<Vec<_>>();
let from_depth = {
let mut m = MerkleHasher::with_depth(depth);
for leaf in leaves.iter() {
m.write(leaf.as_bytes()).expect("should process leaf");
}
m.finish()
};
let from_num_leaves = {
let mut m = MerkleHasher::with_leaves(num_leaves as usize);
for leaf in leaves.iter() {
m.process_leaf(leaf.as_bytes())
.expect("should process leaf");
}
m.finish()
};
assert_eq!(
from_depth, from_num_leaves,
"hash generated by depth should match that from num leaves"
);
}
#[test]
fn with_leaves() {
compare_new_with_leaf_count(1, 1);
compare_new_with_leaf_count(2, 2);
compare_new_with_leaf_count(3, 3);
compare_new_with_leaf_count(4, 3);
compare_new_with_leaf_count(5, 4);
compare_new_with_leaf_count(6, 4);
compare_new_with_leaf_count(7, 4);
compare_new_with_leaf_count(8, 4);
compare_new_with_leaf_count(9, 5);
compare_new_with_leaf_count(10, 5);
compare_new_with_leaf_count(11, 5);
compare_new_with_leaf_count(12, 5);
compare_new_with_leaf_count(13, 5);
compare_new_with_leaf_count(14, 5);
compare_new_with_leaf_count(15, 5);
}
#[test]
fn depth() {
assert_eq!(get_depth(1), 0);
assert_eq!(get_depth(2), 1);
assert_eq!(get_depth(3), 1);
assert_eq!(get_depth(4), 2);
assert_eq!(get_depth(5), 2);
assert_eq!(get_depth(6), 2);
assert_eq!(get_depth(7), 2);
assert_eq!(get_depth(8), 3);
}
#[test]
fn with_0_leaves() {
let hasher = MerkleHasher::with_leaves(0);
assert_eq!(hasher.finish().unwrap(), Hash256::zero());
}
#[test]
#[should_panic]
fn too_many_leaves() {
compare_reference_with_len(2, 1);
}
#[test]
fn full_trees() {
compare_reference_with_len(1, 1);
compare_reference_with_len(2, 2);
compare_reference_with_len(4, 3);
compare_reference_with_len(8, 4);
compare_reference_with_len(16, 5);
compare_reference_with_len(32, 6);
compare_reference_with_len(64, 7);
compare_reference_with_len(128, 8);
compare_reference_with_len(256, 9);
compare_reference_with_len(256, 9);
compare_reference_with_len(8192, 14);
}
#[test]
fn incomplete_trees() {
compare_reference_with_len(0, 1);
compare_reference_with_len(0, 2);
compare_reference_with_len(1, 2);
for i in 0..=4 {
compare_reference_with_len(i, 3);
}
for i in 0..=7 {
compare_reference_with_len(i, 4);
}
for i in 0..=15 {
compare_reference_with_len(i, 5);
}
for i in 0..=32 {
compare_reference_with_len(i, 6);
}
for i in 0..=64 {
compare_reference_with_len(i, 7);
}
compare_reference_with_len(0, 14);
compare_reference_with_len(13, 14);
compare_reference_with_len(8191, 14);
}
#[test]
fn remaining_buffer() {
let a = {
let mut m = MerkleHasher::with_leaves(2);
m.write(&[1]).expect("should write");
m.finish().expect("should finish")
};
let b = {
let mut m = MerkleHasher::with_leaves(2);
let mut leaf = vec![1];
leaf.extend_from_slice(&[0; 31]);
m.write(&leaf).expect("should write");
m.write(&[0; 32]).expect("should write");
m.finish().expect("should finish")
};
assert_eq!(a, b, "should complete buffer");
}
}