ironfish_primitives/

merkle_tree.rs

//! Implementation of a Merkle tree of commitments used to prove the existence of notes.

use byteorder::{LittleEndian, ReadBytesExt};
use incrementalmerkletree::{
    self,
    bridgetree::{self, Leaf},
    Altitude,
};
use std::collections::VecDeque;
use std::convert::TryFrom;
use std::io::{self, Read, Write};
use std::iter::repeat;
use zcash_encoding::{Optional, Vector};

use crate::sapling::SAPLING_COMMITMENT_TREE_DEPTH;

pub mod incremental;

/// A hashable node within a Merkle tree.
pub trait Hashable: Clone + Copy {
    /// Parses a node from the given byte source.
    fn read<R: Read>(reader: R) -> io::Result<Self>;

    /// Serializes this node.
    fn write<W: Write>(&self, writer: W) -> io::Result<()>;

    /// Returns the parent node within the tree of the two given nodes.
    fn combine(_: usize, _: &Self, _: &Self) -> Self;

    /// Returns a blank leaf node.
    fn blank() -> Self;

    /// Returns the empty root for the given depth.
    fn empty_root(_: usize) -> Self;
}

/// A hashable node within a Merkle tree.
pub trait HashSer {
    /// Parses a node from the given byte source.
    fn read<R: Read>(reader: R) -> io::Result<Self>
    where
        Self: Sized;

    /// Serializes this node.
    fn write<W: Write>(&self, writer: W) -> io::Result<()>;
}

impl<T> Hashable for T
where
    T: incrementalmerkletree::Hashable + HashSer + Copy,
{
    /// Parses a node from the given byte source.
    fn read<R: Read>(reader: R) -> io::Result<Self> {
        <Self as HashSer>::read(reader)
    }

    /// Serializes this node.
    fn write<W: Write>(&self, writer: W) -> io::Result<()> {
        <Self as HashSer>::write(self, writer)
    }

    /// Returns the parent node within the tree of the two given nodes.
    fn combine(alt: usize, lhs: &Self, rhs: &Self) -> Self {
        <Self as incrementalmerkletree::Hashable>::combine(
            Altitude::from(
                u8::try_from(alt).expect("Tree heights greater than 255 are unsupported."),
            ),
            lhs,
            rhs,
        )
    }

    /// Returns a blank leaf node.
    fn blank() -> Self {
        <Self as incrementalmerkletree::Hashable>::empty_leaf()
    }

    /// Returns the empty root for the given depth.
    fn empty_root(alt: usize) -> Self {
        <Self as incrementalmerkletree::Hashable>::empty_root(Altitude::from(
            u8::try_from(alt).expect("Tree heights greater than 255 are unsupported."),
        ))
    }
}

struct PathFiller<Node: Hashable> {
    queue: VecDeque<Node>,
}

impl<Node: Hashable> PathFiller<Node> {
    fn empty() -> Self {
        PathFiller {
            queue: VecDeque::new(),
        }
    }

    fn next(&mut self, depth: usize) -> Node {
        self.queue
            .pop_front()
            .unwrap_or_else(|| Node::empty_root(depth))
    }
}

/// A Merkle tree of note commitments.
///
/// The depth of the Merkle tree is fixed at 32, equal to the depth of the Sapling
/// commitment tree.
#[derive(Clone, Debug, PartialEq, Eq)]
pub struct CommitmentTree<Node> {
    pub(crate) left: Option<Node>,
    pub(crate) right: Option<Node>,
    pub(crate) parents: Vec<Option<Node>>,
}

impl<Node> CommitmentTree<Node> {
    /// Creates an empty tree.
    pub fn empty() -> Self {
        CommitmentTree {
            left: None,
            right: None,
            parents: vec![],
        }
    }

    pub fn from_frontier<const DEPTH: u8>(frontier: &bridgetree::Frontier<Node, DEPTH>) -> Self
    where
        Node: Clone,
    {
        frontier.value().map_or_else(Self::empty, |f| {
            let (left, right) = match f.leaf() {
                Leaf::Left(v) => (Some(v.clone()), None),
                Leaf::Right(l, r) => (Some(l.clone()), Some(r.clone())),
            };
            let mut ommers_iter = f.ommers().iter().cloned();
            let upos: usize = f.position().into();
            Self {
                left,
                right,
                parents: (1..DEPTH)
                    .into_iter()
                    .map(|i| {
                        if upos & (1 << i) == 0 {
                            None
                        } else {
                            ommers_iter.next()
                        }
                    })
                    .collect(),
            }
        })
    }

    pub fn to_frontier<const DEPTH: u8>(&self) -> bridgetree::Frontier<Node, DEPTH>
    where
        Node: incrementalmerkletree::Hashable + Clone,
    {
        if self.size() == 0 {
            bridgetree::Frontier::empty()
        } else {
            let leaf = match (self.left.as_ref(), self.right.as_ref()) {
                (Some(a), None) => bridgetree::Leaf::Left(a.clone()),
                (Some(a), Some(b)) => bridgetree::Leaf::Right(a.clone(), b.clone()),
                _ => unreachable!(),
            };

            let ommers = self
                .parents
                .iter()
                .filter_map(|v| v.as_ref())
                .cloned()
                .collect();

            // If a frontier cannot be successfully constructed from the
            // parts of a commitment tree, it is a programming error.
            bridgetree::Frontier::from_parts((self.size() - 1).into(), leaf, ommers)
                .expect("Frontier should be constructable from CommitmentTree.")
        }
    }

    /// Returns the number of leaf nodes in the tree.
    pub fn size(&self) -> usize {
        self.parents.iter().enumerate().fold(
            match (self.left.as_ref(), self.right.as_ref()) {
                (None, None) => 0,
                (Some(_), None) => 1,
                (Some(_), Some(_)) => 2,
                (None, Some(_)) => unreachable!(),
            },
            |acc, (i, p)| {
                // Treat occupation of parents array as a binary number
                // (right-shifted by 1)
                acc + if p.is_some() { 1 << (i + 1) } else { 0 }
            },
        )
    }

    fn is_complete(&self, depth: usize) -> bool {
        if depth == 0 {
            self.left.is_some() && self.right.is_none() && self.parents.is_empty()
        } else {
            self.left.is_some()
                && self.right.is_some()
                && self
                    .parents
                    .iter()
                    .chain(repeat(&None))
                    .take(depth - 1)
                    .all(|p| p.is_some())
        }
    }
}

impl<Node: Hashable> CommitmentTree<Node> {
    /// Reads a `CommitmentTree` from its serialized form.
    pub fn read<R: Read>(mut reader: R) -> io::Result<Self> {
        let left = Optional::read(&mut reader, Node::read)?;
        let right = Optional::read(&mut reader, Node::read)?;
        let parents = Vector::read(&mut reader, |r| Optional::read(r, Node::read))?;

        Ok(CommitmentTree {
            left,
            right,
            parents,
        })
    }

    /// Serializes this tree as an array of bytes.
    pub fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
        Optional::write(&mut writer, self.left, |w, n| n.write(w))?;
        Optional::write(&mut writer, self.right, |w, n| n.write(w))?;
        Vector::write(&mut writer, &self.parents, |w, e| {
            Optional::write(w, *e, |w, n| n.write(w))
        })
    }

    /// Adds a leaf node to the tree.
    ///
    /// Returns an error if the tree is full.
    pub fn append(&mut self, node: Node) -> Result<(), ()> {
        self.append_inner(node, SAPLING_COMMITMENT_TREE_DEPTH)
    }

    fn append_inner(&mut self, node: Node, depth: usize) -> Result<(), ()> {
        if self.is_complete(depth) {
            // Tree is full
            return Err(());
        }

        match (self.left, self.right) {
            (None, _) => self.left = Some(node),
            (_, None) => self.right = Some(node),
            (Some(l), Some(r)) => {
                let mut combined = Node::combine(0, &l, &r);
                self.left = Some(node);
                self.right = None;

                for i in 0..depth {
                    if i < self.parents.len() {
                        if let Some(p) = self.parents[i] {
                            combined = Node::combine(i + 1, &p, &combined);
                            self.parents[i] = None;
                        } else {
                            self.parents[i] = Some(combined);
                            break;
                        }
                    } else {
                        self.parents.push(Some(combined));
                        break;
                    }
                }
            }
        }

        Ok(())
    }

    /// Returns the current root of the tree.
    pub fn root(&self) -> Node {
        self.root_inner(SAPLING_COMMITMENT_TREE_DEPTH, PathFiller::empty())
    }

    fn root_inner(&self, depth: usize, mut filler: PathFiller<Node>) -> Node {
        assert!(depth > 0);

        // 1) Hash left and right leaves together.
        //    - Empty leaves are used as needed.
        let leaf_root = Node::combine(
            0,
            &self.left.unwrap_or_else(|| filler.next(0)),
            &self.right.unwrap_or_else(|| filler.next(0)),
        );

        // 2) Extend the parents to the desired depth with None values, then hash from leaf to
        //    root. Roots of the empty subtrees are used as needed.
        self.parents
            .iter()
            .chain(repeat(&None))
            .take(depth - 1)
            .enumerate()
            .fold(leaf_root, |root, (i, p)| match p {
                Some(node) => Node::combine(i + 1, node, &root),
                None => Node::combine(i + 1, &root, &filler.next(i + 1)),
            })
    }
}

/// An updatable witness to a path from a position in a particular [`CommitmentTree`].
///
/// Appending the same commitments in the same order to both the original
/// [`CommitmentTree`] and this `IncrementalWitness` will result in a witness to the path
/// from the target position to the root of the updated tree.
///
/// # Examples
///
/// ```
/// use ff::{Field, PrimeField};
/// use rand_core::OsRng;
/// use ironfish_primitives::{
///     merkle_tree::{CommitmentTree, IncrementalWitness},
///     sapling::Node,
/// };
///
/// let mut rng = OsRng;
///
/// let mut tree = CommitmentTree::<Node>::empty();
///
/// tree.append(Node::new(blstrs::Scalar::random(&mut rng).to_repr()));
/// tree.append(Node::new(blstrs::Scalar::random(&mut rng).to_repr()));
/// let mut witness = IncrementalWitness::from_tree(&tree);
/// assert_eq!(witness.position(), 1);
/// assert_eq!(tree.root(), witness.root());
///
/// let cmu = Node::new(blstrs::Scalar::random(&mut rng).to_repr());
/// tree.append(cmu);
/// witness.append(cmu);
/// assert_eq!(tree.root(), witness.root());
/// ```
#[derive(Clone)]
pub struct IncrementalWitness<Node: Hashable> {
    tree: CommitmentTree<Node>,
    filled: Vec<Node>,
    cursor_depth: usize,
    cursor: Option<CommitmentTree<Node>>,
}

impl<Node: Hashable> IncrementalWitness<Node> {
    /// Creates an `IncrementalWitness` for the most recent commitment added to the given
    /// [`CommitmentTree`].
    pub fn from_tree(tree: &CommitmentTree<Node>) -> IncrementalWitness<Node> {
        IncrementalWitness {
            tree: tree.clone(),
            filled: vec![],
            cursor_depth: 0,
            cursor: None,
        }
    }

    /// Reads an `IncrementalWitness` from its serialized form.
    #[allow(clippy::redundant_closure)]
    pub fn read<R: Read>(mut reader: R) -> io::Result<Self> {
        let tree = CommitmentTree::read(&mut reader)?;
        let filled = Vector::read(&mut reader, |r| Node::read(r))?;
        let cursor = Optional::read(&mut reader, CommitmentTree::read)?;

        let mut witness = IncrementalWitness {
            tree,
            filled,
            cursor_depth: 0,
            cursor,
        };

        witness.cursor_depth = witness.next_depth();

        Ok(witness)
    }

    /// Serializes this `IncrementalWitness` as an array of bytes.
    pub fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
        self.tree.write(&mut writer)?;
        Vector::write(&mut writer, &self.filled, |w, n| n.write(w))?;
        Optional::write(&mut writer, self.cursor.as_ref(), |w, t| t.write(w))
    }

    /// Returns the position of the witnessed leaf node in the commitment tree.
    pub fn position(&self) -> usize {
        self.tree.size() - 1
    }

    fn filler(&self) -> PathFiller<Node> {
        let cursor_root = self
            .cursor
            .as_ref()
            .map(|c| c.root_inner(self.cursor_depth, PathFiller::empty()));

        PathFiller {
            queue: self.filled.iter().cloned().chain(cursor_root).collect(),
        }
    }

    /// Finds the next "depth" of an unfilled subtree.
    fn next_depth(&self) -> usize {
        let mut skip = self.filled.len();

        if self.tree.left.is_none() {
            if skip > 0 {
                skip -= 1;
            } else {
                return 0;
            }
        }

        if self.tree.right.is_none() {
            if skip > 0 {
                skip -= 1;
            } else {
                return 0;
            }
        }

        let mut d = 1;
        for p in &self.tree.parents {
            if p.is_none() {
                if skip > 0 {
                    skip -= 1;
                } else {
                    return d;
                }
            }
            d += 1;
        }

        d + skip
    }

    /// Tracks a leaf node that has been added to the underlying tree.
    ///
    /// Returns an error if the tree is full.
    pub fn append(&mut self, node: Node) -> Result<(), ()> {
        self.append_inner(node, SAPLING_COMMITMENT_TREE_DEPTH)
    }

    fn append_inner(&mut self, node: Node, depth: usize) -> Result<(), ()> {
        if let Some(mut cursor) = self.cursor.take() {
            cursor
                .append_inner(node, depth)
                .expect("cursor should not be full");
            if cursor.is_complete(self.cursor_depth) {
                self.filled
                    .push(cursor.root_inner(self.cursor_depth, PathFiller::empty()));
            } else {
                self.cursor = Some(cursor);
            }
        } else {
            self.cursor_depth = self.next_depth();
            if self.cursor_depth >= depth {
                // Tree is full
                return Err(());
            }

            if self.cursor_depth == 0 {
                self.filled.push(node);
            } else {
                let mut cursor = CommitmentTree::empty();
                cursor
                    .append_inner(node, depth)
                    .expect("cursor should not be full");
                self.cursor = Some(cursor);
            }
        }

        Ok(())
    }

    /// Returns the current root of the tree corresponding to the witness.
    pub fn root(&self) -> Node {
        self.root_inner(SAPLING_COMMITMENT_TREE_DEPTH)
    }

    fn root_inner(&self, depth: usize) -> Node {
        self.tree.root_inner(depth, self.filler())
    }

    /// Returns the current witness, or None if the tree is empty.
    pub fn path(&self) -> Option<MerklePath<Node>> {
        self.path_inner(SAPLING_COMMITMENT_TREE_DEPTH)
    }

    fn path_inner(&self, depth: usize) -> Option<MerklePath<Node>> {
        let mut filler = self.filler();
        let mut auth_path = Vec::new();

        if let Some(node) = self.tree.left {
            if self.tree.right.is_some() {
                auth_path.push((node, true));
            } else {
                auth_path.push((filler.next(0), false));
            }
        } else {
            // Can't create an authentication path for the beginning of the tree
            return None;
        }

        for (i, p) in self
            .tree
            .parents
            .iter()
            .chain(repeat(&None))
            .take(depth - 1)
            .enumerate()
        {
            auth_path.push(match p {
                Some(node) => (*node, true),
                None => (filler.next(i + 1), false),
            });
        }

        assert_eq!(auth_path.len(), depth);

        Some(MerklePath::from_path(auth_path, self.position() as u64))
    }
}

/// A path from a position in a particular commitment tree to the root of that tree.
#[derive(Clone, Debug, PartialEq)]
pub struct MerklePath<Node: Hashable> {
    pub auth_path: Vec<(Node, bool)>,
    pub position: u64,
}

impl<Node: Hashable> MerklePath<Node> {
    /// Constructs a Merkle path directly from a path and position.
    pub fn from_path(auth_path: Vec<(Node, bool)>, position: u64) -> Self {
        MerklePath {
            auth_path,
            position,
        }
    }

    /// Reads a Merkle path from its serialized form.
    pub fn from_slice(witness: &[u8]) -> Result<Self, ()> {
        Self::from_slice_with_depth(witness, SAPLING_COMMITMENT_TREE_DEPTH)
    }

    fn from_slice_with_depth(mut witness: &[u8], depth: usize) -> Result<Self, ()> {
        // Skip the first byte, which should be "depth" to signify the length of
        // the following vector of Pedersen hashes.
        if witness[0] != depth as u8 {
            return Err(());
        }
        witness = &witness[1..];

        // Begin to construct the authentication path
        let iter = witness.chunks_exact(33);
        witness = iter.remainder();

        // The vector works in reverse
        let mut auth_path = iter
            .rev()
            .map(|bytes| {
                // Length of inner vector should be the length of a Pedersen hash
                if bytes[0] == 32 {
                    // Sibling node should be an element of Fr
                    Node::read(&bytes[1..])
                        .map(|sibling| {
                            // Set the value in the auth path; we put false here
                            // for now (signifying the position bit) which we'll
                            // fill in later.
                            (sibling, false)
                        })
                        .map_err(|_| ())
                } else {
                    Err(())
                }
            })
            .collect::<Result<Vec<_>, _>>()?;
        if auth_path.len() != depth {
            return Err(());
        }

        // Read the position from the witness
        let position = witness.read_u64::<LittleEndian>().map_err(|_| ())?;

        // Given the position, let's finish constructing the authentication
        // path
        let mut tmp = position;
        for entry in auth_path.iter_mut() {
            entry.1 = (tmp & 1) == 1;
            tmp >>= 1;
        }

        // The witness should be empty now; if it wasn't, the caller would
        // have provided more information than they should have, indicating
        // a bug downstream
        if witness.is_empty() {
            Ok(MerklePath {
                auth_path,
                position,
            })
        } else {
            Err(())
        }
    }

    /// Returns the root of the tree corresponding to this path applied to `leaf`.
    pub fn root(&self, leaf: Node) -> Node {
        self.auth_path
            .iter()
            .enumerate()
            .fold(
                leaf,
                |root, (i, (p, leaf_is_on_right))| match leaf_is_on_right {
                    false => Node::combine(i, &root, p),
                    true => Node::combine(i, p, &root),
                },
            )
    }
}

#[cfg(test)]
mod tests {
    use incrementalmerkletree::bridgetree::Frontier;
    use proptest::prelude::*;
    use std::convert::TryInto;
    use std::io::{self, Read, Write};

    use crate::sapling::{testing::arb_node, Node};

    use super::{
        testing::{arb_commitment_tree, TestNode},
        CommitmentTree, Hashable, IncrementalWitness, MerklePath, PathFiller,
    };

    const HEX_EMPTY_ROOTS: [&str; 33] = [
        "0100000000000000000000000000000000000000000000000000000000000000",
        "817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca155",
        "ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e34",
        "d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c",
        "e110de65c907b9dea4ae0bd83a4b0a51bea175646a64c12b4c9f931b2cb31b49",
        "912d82b2c2bca231f71efcf61737fbf0a08befa0416215aeef53e8bb6d23390a",
        "8ac9cf9c391e3fd42891d27238a81a8a5c1d3a72b1bcbea8cf44a58ce7389613",
        "d6c639ac24b46bd19341c91b13fdcab31581ddaf7f1411336a271f3d0aa52813",
        "7b99abdc3730991cc9274727d7d82d28cb794edbc7034b4f0053ff7c4b680444",
        "43ff5457f13b926b61df552d4e402ee6dc1463f99a535f9a713439264d5b616b",
        "ba49b659fbd0b7334211ea6a9d9df185c757e70aa81da562fb912b84f49bce72",
        "4777c8776a3b1e69b73a62fa701fa4f7a6282d9aee2c7a6b82e7937d7081c23c",
        "ec677114c27206f5debc1c1ed66f95e2b1885da5b7be3d736b1de98579473048",
        "1b77dac4d24fb7258c3c528704c59430b630718bec486421837021cf75dab651",
        "bd74b25aacb92378a871bf27d225cfc26baca344a1ea35fdd94510f3d157082c",
        "d6acdedf95f608e09fa53fb43dcd0990475726c5131210c9e5caeab97f0e642f",
        "1ea6675f9551eeb9dfaaa9247bc9858270d3d3a4c5afa7177a984d5ed1be2451",
        "6edb16d01907b759977d7650dad7e3ec049af1a3d875380b697c862c9ec5d51c",
        "cd1c8dbf6e3acc7a80439bc4962cf25b9dce7c896f3a5bd70803fc5a0e33cf00",
        "6aca8448d8263e547d5ff2950e2ed3839e998d31cbc6ac9fd57bc6002b159216",
        "8d5fa43e5a10d11605ac7430ba1f5d81fb1b68d29a640405767749e841527673",
        "08eeab0c13abd6069e6310197bf80f9c1ea6de78fd19cbae24d4a520e6cf3023",
        "0769557bc682b1bf308646fd0b22e648e8b9e98f57e29f5af40f6edb833e2c49",
        "4c6937d78f42685f84b43ad3b7b00f81285662f85c6a68ef11d62ad1a3ee0850",
        "fee0e52802cb0c46b1eb4d376c62697f4759f6c8917fa352571202fd778fd712",
        "16d6252968971a83da8521d65382e61f0176646d771c91528e3276ee45383e4a",
        "d2e1642c9a462229289e5b0e3b7f9008e0301cbb93385ee0e21da2545073cb58",
        "a5122c08ff9c161d9ca6fc462073396c7d7d38e8ee48cdb3bea7e2230134ed6a",
        "28e7b841dcbc47cceb69d7cb8d94245fb7cb2ba3a7a6bc18f13f945f7dbd6e2a",
        "e1f34b034d4a3cd28557e2907ebf990c918f64ecb50a94f01d6fda5ca5c7ef72",
        "12935f14b676509b81eb49ef25f39269ed72309238b4c145803544b646dca62d",
        "b2eed031d4d6a4f02a097f80b54cc1541d4163c6b6f5971f88b6e41d35c53814",
        "fbc2f4300c01f0b7820d00e3347c8da4ee614674376cbc45359daa54f9b5493e",
    ];

    const TESTING_DEPTH: usize = 4;

    struct TestCommitmentTree(CommitmentTree<Node>);

    impl TestCommitmentTree {
        fn new() -> Self {
            TestCommitmentTree(CommitmentTree::empty())
        }

        pub fn read<R: Read>(reader: R) -> io::Result<Self> {
            let tree = CommitmentTree::read(reader)?;
            Ok(TestCommitmentTree(tree))
        }

        pub fn write<W: Write>(&self, writer: W) -> io::Result<()> {
            self.0.write(writer)
        }

        fn size(&self) -> usize {
            self.0.size()
        }

        fn append(&mut self, node: Node) -> Result<(), ()> {
            self.0.append_inner(node, TESTING_DEPTH)
        }

        fn root(&self) -> Node {
            self.0.root_inner(TESTING_DEPTH, PathFiller::empty())
        }
    }

    struct TestIncrementalWitness(IncrementalWitness<Node>);

    impl TestIncrementalWitness {
        fn from_tree(tree: &TestCommitmentTree) -> Self {
            TestIncrementalWitness(IncrementalWitness::from_tree(&tree.0))
        }

        pub fn read<R: Read>(reader: R) -> io::Result<Self> {
            let witness = IncrementalWitness::read(reader)?;
            Ok(TestIncrementalWitness(witness))
        }

        pub fn write<W: Write>(&self, writer: W) -> io::Result<()> {
            self.0.write(writer)
        }

        fn append(&mut self, node: Node) -> Result<(), ()> {
            self.0.append_inner(node, TESTING_DEPTH)
        }

        fn root(&self) -> Node {
            self.0.root_inner(TESTING_DEPTH)
        }

        fn path(&self) -> Option<MerklePath<Node>> {
            self.0.path_inner(TESTING_DEPTH)
        }
    }

    #[test]
    fn empty_root_test_vectors() {
        let mut tmp = [0u8; 32];
        for (i, &expected) in HEX_EMPTY_ROOTS.iter().enumerate() {
            Node::empty_root(i)
                .write(&mut tmp[..])
                .expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }
    }

    #[test]
    fn sapling_empty_root() {
        let mut tmp = [0u8; 32];
        CommitmentTree::<Node>::empty()
            .root()
            .write(&mut tmp[..])
            .expect("length is 32 bytes");
        assert_eq!(
            hex::encode(tmp),
            "fbc2f4300c01f0b7820d00e3347c8da4ee614674376cbc45359daa54f9b5493e"
        );
    }

    #[test]
    fn empty_commitment_tree_roots() {
        let tree = CommitmentTree::<Node>::empty();
        let mut tmp = [0u8; 32];
        for (i, &expected) in HEX_EMPTY_ROOTS.iter().enumerate().skip(1) {
            tree.root_inner(i, PathFiller::empty())
                .write(&mut tmp[..])
                .expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }
    }

    #[test]
    fn test_sapling_tree() {
        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_commitments_sapling.json
        // Byte-reversed because the original test vectors are loaded using uint256S()
        let commitments = [
            "b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55",
            "225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458",
            "7c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c",
            "50421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030",
            "aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12",
            "f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a02",
            "bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e",
            "da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a511",
            "3a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f77446",
            "c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f163008",
            "f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c3702",
            "e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c608",
            "8cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e826",
            "22fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c03",
            "f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c",
            "3a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac15",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_roots_sapling.json
        let roots = [
            "8c3daa300c9710bf24d2595536e7c80ff8d147faca726636d28e8683a0c27703",
            "8611f17378eb55e8c3c3f0a5f002e2b0a7ca39442fc928322b8072d1079c213d",
            "3db73b998d536be0e1c2ec124df8e0f383ae7b602968ff6a5276ca0695023c46",
            "7ac2e6442fec5970e116dfa4f2ee606f395366cafb1fa7dfd6c3de3ce18c4363",
            "6a8f11ab2a11c262e39ed4ea3825ae6c94739ccf94479cb69402c5722b034532",
            "149595eed0b54a7e694cc8a68372525b9ae2c7b102514f527460db91eb690565",
            "8c0432f1994a2381a7a4b5fda770336011f9e0b30784f9a5597901619c797045",
            "e780c48d70420601f3313ff8488d7766b70c059c53aa3cda2ff1ef57ff62383c",
            "f919f03caaed8a2c60f58c0d43838f83e670dc7e8ccd25daa04a13f3e8f45541",
            "74f32b36629724038e71cbd6823b5a666440205a7d1a9242e95870b53d81f34a",
            "a4af205a4e1ee02102866b23a68930ac33efda9235832f49b17fcc4939be4525",
            "a946a42f1636045a16e65b2308e036d9da70089686c87c692e45912bd1cab772",
            "a1db2dbac055364c1cb43cbeb49c7e2815bff855122602a2ad0fb981a91e0e39",
            "16329b3ba4f0640f4d306532d9ea6ba0fbf0e70e44ed57d27b4277ed9cda6849",
            "7b6523b2d9b23f72fec6234aa6a1f8fae3dba1c6a266023ea8b1826feba7a25c",
            "5c0bea7e17bde5bee4eb795c2eec3d389a68da587b36dd687b134826ecc09308",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_serialization_sapling.json
        let tree_ser = [
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000201eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e01da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110201eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f7744600030000010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f7744601c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f163008030000010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c3702000301cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173200010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c370201e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c6080301cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173200010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "018cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e82600030001002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "018cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e8260122fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c03030001002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c0003015991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c34901002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c013a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac1503015991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c34901002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_path_sapling.json
        let paths = [
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca15520225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342037b3a0921a4047e617bde62b8958f86c010e6af6cc650959b9f50af8c7e8392620225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342037b3a0921a4047e617bde62b8958f86c010e6af6cc650959b9f50af8c7e8392620b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f1740220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f1740220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f174022062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f174022062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c157320f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c157320f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c15732062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c15732062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca15520f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d32220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d32220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d3222062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d3222062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564206ab2e08286c36f6fe4374baebdc28b97e2f1f4ea3544fafd8a6489f42824bf0e20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564206ab2e08286c36f6fe4374baebdc28b97e2f1f4ea3544fafd8a6489f42824bf0e20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
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            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c20afa80a9a1bb8b6aad144cfb53e0bab004dd541c8b72025ae694bb60d6050a532208cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e8260d00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c205991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c349203a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac150e00000000000000",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_witness_serialization_sapling.json
        let witness_ser = [
            "00000001b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5500",
            "00000002b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000001225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "00000002b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145801017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000001225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145801017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458000001017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000002225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580001f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a03000",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000002225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580001f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666000101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000002225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580001f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666000101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656401f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a0200",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000101eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000002225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000101eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580001f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000101eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000101eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666000101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000101eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656401f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e0000",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564000101bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e0000",
            "00000004b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000003225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580002f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2400",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660250421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2400",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e66601130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2400",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656402f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a02d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c00",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656401d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c00",
            "01bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000201eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656401da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a51100",
            "00000004b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2401013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000003225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2401013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580002f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a8264130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2401013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660250421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2401013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e66601130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2401013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656402f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a02d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c01013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460000",
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        ];

        fn assert_root_eq(root: Node, expected: &str) {
            let mut tmp = [0u8; 32];
            root.write(&mut tmp[..]).expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }

        fn assert_tree_ser_eq(tree: &TestCommitmentTree, expected: &str) {
            // Check that the tree matches its encoding
            let mut tmp = Vec::new();
            tree.write(&mut tmp).unwrap();
            assert_eq!(hex::encode(&tmp[..]), expected);

            // Check round-trip encoding
            let decoded = TestCommitmentTree::read(&hex::decode(expected).unwrap()[..]).unwrap();
            tmp.clear();
            decoded.write(&mut tmp).unwrap();
            assert_eq!(hex::encode(tmp), expected);
        }

        fn assert_witness_ser_eq(witness: &TestIncrementalWitness, expected: &str) {
            // Check that the witness matches its encoding
            let mut tmp = Vec::new();
            witness.write(&mut tmp).unwrap();
            assert_eq!(hex::encode(&tmp[..]), expected);

            // Check round-trip encoding
            let decoded =
                TestIncrementalWitness::read(&hex::decode(expected).unwrap()[..]).unwrap();
            tmp.clear();
            decoded.write(&mut tmp).unwrap();
            assert_eq!(hex::encode(tmp), expected);
        }

        let mut tree = TestCommitmentTree::new();
        assert_eq!(tree.size(), 0);

        let mut witnesses = vec![];
        let mut last_cmu = None;
        let mut paths_i = 0;
        let mut witness_ser_i = 0;
        for i in 0..16 {
            let cmu = hex::decode(commitments[i]).unwrap();

            let cmu = Node::new(cmu[..].try_into().unwrap());

            // Witness here
            witnesses.push((TestIncrementalWitness::from_tree(&tree), last_cmu));

            // Now append a commitment to the tree
            assert!(tree.append(cmu).is_ok());

            // Size incremented by one.
            assert_eq!(tree.size(), i + 1);

            // Check tree root consistency
            assert_root_eq(tree.root(), roots[i]);

            // Check serialization of tree
            assert_tree_ser_eq(&tree, tree_ser[i]);

            for (witness, leaf) in witnesses.as_mut_slice() {
                // Append the same commitment to all the witnesses
                assert!(witness.append(cmu).is_ok());

                if let Some(leaf) = leaf {
                    let path = witness.path().expect("should be able to create a path");
                    let expected = MerklePath::from_slice_with_depth(
                        &hex::decode(paths[paths_i]).unwrap(),
                        TESTING_DEPTH,
                    )
                    .unwrap();
                    assert_eq!(path, expected);
                    assert_eq!(path.root(*leaf), witness.root());
                    paths_i += 1;
                } else {
                    // The first witness can never form a path
                    assert!(witness.path().is_none());
                }

                // Check witness serialization
                assert_witness_ser_eq(witness, witness_ser[witness_ser_i]);
                witness_ser_i += 1;

                assert_eq!(witness.root(), tree.root());
            }

            last_cmu = Some(cmu);
        }

        // Tree should be full now
        let node = Node::blank();
        assert!(tree.append(node).is_err());
        for (witness, _) in witnesses.as_mut_slice() {
            assert!(witness.append(node).is_err());
        }
    }

    proptest! {
        #[test]
        fn prop_commitment_tree_roundtrip(ct in arb_commitment_tree(32, arb_node(), 8)) {
            let frontier: Frontier<Node, 8> = ct.to_frontier();
            let ct0 = CommitmentTree::from_frontier(&frontier);
            assert_eq!(ct, ct0);
            let frontier0: Frontier<Node, 8> = ct0.to_frontier();
            assert_eq!(frontier, frontier0);
        }
    }

    #[test]
    fn test_commitment_tree_complete() {
        let mut t: CommitmentTree<TestNode> = CommitmentTree::empty();
        for n in 1u64..=32 {
            t.append(TestNode(n)).unwrap();
            // every tree of a power-of-two height is complete
            let is_complete = n.count_ones() == 1;
            let level = 63 - n.leading_zeros(); //log2
            assert_eq!(
                is_complete,
                t.is_complete(level.try_into().unwrap()),
                "Tree {:?} {} complete at height {}",
                t,
                if is_complete {
                    "should be"
                } else {
                    "should not be"
                },
                n
            );
        }
    }
}

#[cfg(any(test, feature = "test-dependencies"))]
pub mod testing {
    use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
    use core::fmt::Debug;
    use proptest::collection::vec;
    use proptest::prelude::*;
    use std::collections::hash_map::DefaultHasher;
    use std::hash::Hasher;
    use std::io::{self, Read, Write};

    use super::{CommitmentTree, Hashable};

    pub fn arb_commitment_tree<Node: Hashable + Debug, T: Strategy<Value = Node>>(
        min_size: usize,
        arb_node: T,
        depth: u8,
    ) -> impl Strategy<Value = CommitmentTree<Node>> {
        assert!((1 << depth) >= min_size + 100);
        vec(arb_node, min_size..(min_size + 100)).prop_map(move |v| {
            let mut tree = CommitmentTree::empty();
            for node in v.into_iter() {
                tree.append(node).unwrap();
            }
            tree.parents.resize_with((depth - 1).into(), || None);
            tree
        })
    }

    #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
    pub(crate) struct TestNode(pub(crate) u64);

    impl Hashable for TestNode {
        fn read<R: Read>(mut reader: R) -> io::Result<TestNode> {
            reader.read_u64::<LittleEndian>().map(TestNode)
        }

        fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
            writer.write_u64::<LittleEndian>(self.0)
        }

        fn combine(_: usize, a: &TestNode, b: &TestNode) -> TestNode {
            let mut hasher = DefaultHasher::new();
            hasher.write_u64(a.0);
            hasher.write_u64(b.0);
            TestNode(hasher.finish())
        }

        fn blank() -> TestNode {
            TestNode(0)
        }

        fn empty_root(alt: usize) -> TestNode {
            (0..alt).fold(Self::blank(), |v, lvl| Self::combine(lvl, &v, &v))
        }
    }
}