commit c1211d2ca9a23ab005a43a26cc65454c20d2665c
Author: jjy <jjyruby@gmail.com>
Date:   Thu Sep 19 16:23:58 2019 +0800

    Init merkle-mountain-range
    
    The MMR code is copy from https://github.com/nervosnetwork/ckb/pull/1598

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..1e7caa9
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+Cargo.lock
+target/
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..706fe8d
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,27 @@
+[package]
+name = "ckb-merkle-mountain-range"
+version = "0.1.0"
+authors = ["Nervos Core Dev <dev@nervos.org>"]
+edition = "2018"
+license = "MIT"
+description = "A generalized merkle mountain range implementation"
+
+[dependencies]
+failure = "0.1.5"
+
+[dev-dependencies]
+faster-hex = "0.3"
+criterion = "0.3"
+rand = "0.6"
+proptest = "0.9.4"
+lazy_static = "1.3.0"
+bytes = "0.4"
+blake2b-rs = "0.1.4"
+
+[[bench]]
+name = "mmr_benchmark"
+harness = false
+
+[[bench]]
+name = "helper_benchmark"
+harness = false
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..19a3ffa
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,15 @@
+default: ci
+
+ci: fmt clippy test bench-test
+
+test:
+	cargo test --all --all-features
+
+bench-test:
+	cargo bench -- --test
+
+clippy:
+	cargo clippy  --all --all-features --all-targets
+
+fmt:
+	cargo fmt --all -- --check
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..8fd0ab2
--- /dev/null
+++ b/README.md
@@ -0,0 +1,8 @@
+# Merkle mountain range
+
+A generalized merkle mountain range implementation.
+
+## References
+
+* https://github.com/mimblewimble/grin/blob/master/doc/mmr.md#structure
+* https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/merkle-mountain-range.md
diff --git a/benches/helper_benchmark.rs b/benches/helper_benchmark.rs
new file mode 100644
index 0000000..b45b1c6
--- /dev/null
+++ b/benches/helper_benchmark.rs
@@ -0,0 +1,28 @@
+#[macro_use]
+extern crate criterion;
+use criterion::Criterion;
+
+use ckb_merkle_mountain_range::{leaf_index_to_mmr_size, leaf_index_to_pos};
+
+use rand::{thread_rng, Rng};
+
+fn bench(c: &mut Criterion) {
+    c.bench_function("left_index_to_pos", |b| {
+        let mut rng = thread_rng();
+        b.iter(|| {
+            let leaf_index = rng.gen_range(50_000_000_000, 70_000_000_000);
+            leaf_index_to_pos(leaf_index);
+        });
+    });
+
+    c.bench_function("left_index_to_mmr_size", |b| {
+        let mut rng = thread_rng();
+        b.iter(|| {
+            let leaf_index = rng.gen_range(50_000_000_000, 70_000_000_000);
+            leaf_index_to_mmr_size(leaf_index);
+        });
+    });
+}
+
+criterion_group!(benches, bench);
+criterion_main!(benches);
diff --git a/benches/mmr_benchmark.rs b/benches/mmr_benchmark.rs
new file mode 100644
index 0000000..ba4447e
--- /dev/null
+++ b/benches/mmr_benchmark.rs
@@ -0,0 +1,96 @@
+#[macro_use]
+extern crate criterion;
+
+use criterion::Criterion;
+
+use bytes::Bytes;
+use ckb_merkle_mountain_range::{util::MemStore, Error, MMRStore, Merge, Result, MMR};
+use rand::{seq::SliceRandom, thread_rng};
+use std::convert::TryFrom;
+
+use blake2b_rs::{Blake2b, Blake2bBuilder};
+
+fn new_blake2b() -> Blake2b {
+    Blake2bBuilder::new(32).build()
+}
+
+#[derive(Eq, PartialEq, Clone, Debug, Default)]
+struct NumberHash(pub Bytes);
+impl TryFrom<u32> for NumberHash {
+    type Error = Error;
+    fn try_from(num: u32) -> Result<Self> {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&num.to_le_bytes());
+        hasher.finalize(&mut hash);
+        Ok(NumberHash(hash.to_vec().into()))
+    }
+}
+
+struct MergeNumberHash;
+
+impl Merge for MergeNumberHash {
+    type Item = NumberHash;
+    fn merge(lhs: &Self::Item, rhs: &Self::Item) -> Self::Item {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&lhs.0);
+        hasher.update(&rhs.0);
+        hasher.finalize(&mut hash);
+        NumberHash(hash.to_vec().into())
+    }
+}
+
+fn prepare_mmr(count: u32) -> (u64, MemStore<NumberHash>, Vec<u64>) {
+    let store = MemStore::default();
+    let mut mmr = MMR::<_, MergeNumberHash, _>::new(0, &store);
+    let positions: Vec<u64> = (0u32..count)
+        .map(|i| mmr.push(NumberHash::try_from(i).unwrap()).unwrap())
+        .collect();
+    let mmr_size = mmr.mmr_size();
+    mmr.commit().expect("write to store");
+    (mmr_size, store, positions)
+}
+
+fn bench(c: &mut Criterion) {
+    c.bench_function_over_inputs(
+        "MMR insert",
+        |b, &&size| {
+            b.iter(|| prepare_mmr(size));
+        },
+        &[10_000, 100_000, 100_0000],
+    );
+
+    c.bench_function("MMR gen proof", |b| {
+        let (mmr_size, store, positions) = prepare_mmr(100_0000);
+        let mmr = MMR::<_, MergeNumberHash, _>::new(mmr_size, &store);
+        let mut rng = thread_rng();
+        b.iter(|| mmr.gen_proof(*positions.choose(&mut rng).unwrap()));
+    });
+
+    c.bench_function("MMR verify", |b| {
+        let (mmr_size, store, positions) = prepare_mmr(100_0000);
+        let mmr = MMR::<_, MergeNumberHash, _>::new(mmr_size, &store);
+        let mut rng = thread_rng();
+        let root: NumberHash = mmr.get_root().unwrap();
+        let proofs: Vec<_> = (0..10_000)
+            .map(|_| {
+                let pos = positions.choose(&mut rng).unwrap();
+                let elem = (&store).get_elem(*pos).unwrap().unwrap();
+                let proof = mmr.gen_proof(*pos).unwrap();
+                (pos, elem, proof)
+            })
+            .collect();
+        b.iter(|| {
+            let (pos, elem, proof) = proofs.choose(&mut rng).unwrap();
+            proof.verify(root.clone(), **pos, elem.clone()).unwrap();
+        });
+    });
+}
+
+criterion_group!(
+    name = benches;
+    config = Criterion::default().sample_size(20);
+    targets = bench
+);
+criterion_main!(benches);
diff --git a/src/error.rs b/src/error.rs
new file mode 100644
index 0000000..a2c0d1f
--- /dev/null
+++ b/src/error.rs
@@ -0,0 +1,12 @@
+pub use failure::Fail;
+pub type Result<T> = ::std::result::Result<T, Error>;
+
+#[derive(Fail, Debug, PartialEq, Eq, Clone)]
+pub enum Error {
+    #[fail(display = "Get root on an empty MMR")]
+    GetRootOnEmpty,
+    #[fail(display = "Inconsistent store")]
+    InconsistentStore,
+    #[fail(display = "Store error {}", _0)]
+    StoreError(String),
+}
diff --git a/src/helper.rs b/src/helper.rs
new file mode 100644
index 0000000..c8dfff5
--- /dev/null
+++ b/src/helper.rs
@@ -0,0 +1,111 @@
+pub fn leaf_index_to_pos(index: u64) -> u64 {
+    if index == 0 {
+        return 0;
+    }
+    // leaf_count
+    let mut leaves = index + 1;
+    let mut tree_node_count = 0;
+    let mut height = 0u32;
+    while leaves > 1 {
+        // get heighest peak height
+        height = (leaves as f64).log2() as u32;
+        // calculate leaves in peak
+        let peak_leaves = 1 << height;
+        // heighest positon
+        let sub_tree_node_count = get_peak_pos_by_height(height) + 1;
+        tree_node_count += sub_tree_node_count;
+        leaves -= peak_leaves;
+    }
+    // two leaves can construct a new peak, the only valid number of leaves is 0 or 1.
+    debug_assert!(leaves == 0 || leaves == 1, "remain leaves incorrect");
+    if leaves == 1 {
+        // add one pos for remain leaf
+        // equals to `tree_node_count - 1 + 1`
+        tree_node_count
+    } else {
+        let pos = tree_node_count - 1;
+        pos - u64::from(height)
+    }
+}
+
+// TODO optimize
+pub fn leaf_index_to_mmr_size(index: u64) -> u64 {
+    let mut pos = leaf_index_to_pos(index);
+    while pos_height_in_tree(pos + 1) > pos_height_in_tree(pos) {
+        pos += 1
+    }
+    pos + 1
+}
+
+pub fn pos_height_in_tree(mut pos: u64) -> u32 {
+    pos += 1;
+    fn all_ones(num: u64) -> bool {
+        num != 0 && num.count_zeros() == num.leading_zeros()
+    }
+    fn jump_left(pos: u64) -> u64 {
+        let bit_length = 64 - pos.leading_zeros();
+        let most_significant_bits = 1 << (bit_length - 1);
+        pos - (most_significant_bits - 1)
+    }
+
+    while !all_ones(pos) {
+        pos = jump_left(pos)
+    }
+
+    64 - pos.leading_zeros() - 1
+}
+
+pub fn parent_offset(height: u32) -> u64 {
+    2 << height
+}
+
+pub fn sibling_offset(height: u32) -> u64 {
+    (2 << height) - 1
+}
+
+pub fn get_peaks(mmr_size: u64) -> Vec<u64> {
+    let mut pos_s = Vec::new();
+    let (mut height, mut pos) = left_peak_height_pos(mmr_size);
+    pos_s.push(pos);
+    while height > 0 {
+        let peak = match get_right_peak(height, pos, mmr_size) {
+            Some(peak) => peak,
+            None => break,
+        };
+        height = peak.0;
+        pos = peak.1;
+        pos_s.push(pos);
+    }
+    pos_s
+}
+
+fn get_right_peak(mut height: u32, mut pos: u64, mmr_size: u64) -> Option<(u32, u64)> {
+    // move to right sibling pos
+    pos += sibling_offset(height);
+    // loop until we find a pos in mmr
+    while pos > mmr_size - 1 {
+        if height == 0 {
+            return None;
+        }
+        // move to left child
+        pos -= parent_offset(height - 1);
+        height -= 1;
+    }
+    Some((height, pos))
+}
+
+fn get_peak_pos_by_height(height: u32) -> u64 {
+    (1 << (height + 1)) - 2
+}
+
+fn left_peak_height_pos(mmr_size: u64) -> (u32, u64) {
+    let mut height = 1;
+    let mut prev_pos = 0;
+    let mut pos = get_peak_pos_by_height(height);
+    while pos < mmr_size {
+        height += 1;
+        prev_pos = pos;
+        pos = get_peak_pos_by_height(height);
+    }
+    (height - 1, prev_pos)
+}
diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..a36e787
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,14 @@
+mod error;
+mod helper;
+mod merge;
+mod mmr;
+mod mmr_store;
+#[cfg(test)]
+mod tests;
+pub mod util;
+
+pub use error::{Error, Result};
+pub use helper::{leaf_index_to_mmr_size, leaf_index_to_pos};
+pub use merge::Merge;
+pub use mmr::{MerkleProof, MMR};
+pub use mmr_store::MMRStore;
diff --git a/src/merge.rs b/src/merge.rs
new file mode 100644
index 0000000..8cbbfd3
--- /dev/null
+++ b/src/merge.rs
@@ -0,0 +1,4 @@
+pub trait Merge {
+    type Item;
+    fn merge(left: &Self::Item, right: &Self::Item) -> Self::Item;
+}
diff --git a/src/mmr.rs b/src/mmr.rs
new file mode 100644
index 0000000..3fa80fb
--- /dev/null
+++ b/src/mmr.rs
@@ -0,0 +1,207 @@
+//! Merkle Mountain Range
+//!
+//! references:
+//! https://github.com/mimblewimble/grin/blob/master/doc/mmr.md#structure
+//! https://github.com/mimblewimble/grin/blob/0ff6763ee64e5a14e70ddd4642b99789a1648a32/core/src/core/pmmr.rs#L606
+
+use crate::helper::{get_peaks, parent_offset, pos_height_in_tree, sibling_offset};
+use crate::mmr_store::{MMRBatch, MMRStore};
+use crate::{Error, Merge, Result};
+use std::borrow::Cow;
+use std::fmt::Debug;
+use std::marker::PhantomData;
+
+pub struct MMR<T, M, S: MMRStore<T>> {
+    mmr_size: u64,
+    batch: MMRBatch<T, S>,
+    merge: PhantomData<M>,
+}
+
+impl<'a, T: Clone + PartialEq + Debug, M: Merge<Item = T>, S: MMRStore<T>> MMR<T, M, S> {
+    pub fn new(mmr_size: u64, store: S) -> Self {
+        MMR {
+            mmr_size,
+            batch: MMRBatch::new(store),
+            merge: PhantomData,
+        }
+    }
+
+    // find internal MMR elem, the pos must exists, otherwise a error will return
+    fn find_elem<'b>(&self, pos: u64, hashes: &'b [T]) -> Result<Cow<'b, T>> {
+        let pos_offset = pos.checked_sub(self.mmr_size);
+        if let Some(elem) = pos_offset.and_then(|i| hashes.get(i as usize)) {
+            return Ok(Cow::Borrowed(elem));
+        }
+        let elem = self.batch.get_elem(pos)?.ok_or(Error::InconsistentStore)?;
+        Ok(Cow::Owned(elem))
+    }
+
+    pub fn mmr_size(&self) -> u64 {
+        self.mmr_size
+    }
+
+    pub fn is_empty(&self) -> bool {
+        self.mmr_size == 0
+    }
+
+    // push a element and return position
+    pub fn push(&mut self, elem: T) -> Result<u64> {
+        let mut elems: Vec<T> = Vec::new();
+        // position of new elem
+        let elem_pos = self.mmr_size;
+        elems.push(elem);
+        let mut height = 0u32;
+        let mut pos = elem_pos;
+        // continue to merge tree node if next pos heigher than current
+        while pos_height_in_tree(pos + 1) > height {
+            pos += 1;
+            let left_pos = pos - parent_offset(height);
+            let right_pos = left_pos + sibling_offset(height);
+            let left_elem = self.find_elem(left_pos, &elems)?;
+            let right_elem = self.find_elem(right_pos, &elems)?;
+            let parent_elem = M::merge(&left_elem, &right_elem);
+            elems.push(parent_elem);
+            height += 1
+        }
+        // store hashes
+        self.batch.append(elem_pos, elems);
+        // update mmr_size
+        self.mmr_size = pos + 1;
+        Ok(elem_pos)
+    }
+
+    /// get_root
+    pub fn get_root(&self) -> Result<T> {
+        if self.mmr_size == 0 {
+            return Err(Error::GetRootOnEmpty);
+        } else if self.mmr_size == 1 {
+            return self.batch.get_elem(0)?.ok_or(Error::InconsistentStore);
+        }
+        let peaks = get_peaks(self.mmr_size);
+        self.bag_rhs_peaks(0, &peaks)?
+            .ok_or(Error::InconsistentStore)
+    }
+
+    fn bag_rhs_peaks(&self, skip_peak_pos: u64, peaks: &[u64]) -> Result<Option<T>> {
+        let mut rhs_peak_elems: Vec<T> = peaks
+            .iter()
+            .filter(|&&p| p > skip_peak_pos)
+            .map(|&p| self.batch.get_elem(p))
+            .collect::<Result<Option<_>>>()?
+            .ok_or(Error::InconsistentStore)?;
+        while rhs_peak_elems.len() > 1 {
+            let right_peak = rhs_peak_elems.pop().expect("pop");
+            let left_peak = rhs_peak_elems.pop().expect("pop");
+            rhs_peak_elems.push(M::merge(&right_peak, &left_peak));
+        }
+        Ok(rhs_peak_elems.pop())
+    }
+
+    pub fn gen_proof(&self, mut pos: u64) -> Result<MerkleProof<T, M>> {
+        let mut proof: Vec<T> = Vec::new();
+        let mut height = 0;
+        while pos < self.mmr_size {
+            let pos_height = pos_height_in_tree(pos);
+            let next_height = pos_height_in_tree(pos + 1);
+            let (sib_pos, next_pos) = if next_height > pos_height {
+                // implies pos is right sibling
+                let sib_pos = pos - sibling_offset(height);
+                (sib_pos, pos + 1)
+            } else {
+                // pos is left sibling
+                let sib_pos = pos + sibling_offset(height);
+                (sib_pos, pos + parent_offset(height))
+            };
+            if sib_pos > self.mmr_size - 1 {
+                break;
+            }
+            proof.push(
+                self.batch
+                    .get_elem(sib_pos)?
+                    .ok_or(Error::InconsistentStore)?,
+            );
+            pos = next_pos;
+            height += 1;
+        }
+        // now we get peak merkle proof
+        let peak_pos = pos;
+        // calculate bagging proof
+        let peaks = get_peaks(self.mmr_size);
+        if let Some(rhs_peak_hash) = self.bag_rhs_peaks(peak_pos, &peaks[..])? {
+            proof.push(rhs_peak_hash);
+        }
+        let lhs_peaks: Vec<_> = peaks
+            .iter()
+            .filter(|&&p| p < peak_pos)
+            .map(|&p| self.batch.get_elem(p))
+            .rev()
+            .collect::<Result<Option<_>>>()?
+            .ok_or(Error::InconsistentStore)?;
+        proof.extend(lhs_peaks);
+        Ok(MerkleProof::new(self.mmr_size, proof))
+    }
+
+    pub fn commit(self) -> Result<()> {
+        self.batch.commit()
+    }
+}
+
+#[derive(Debug)]
+pub struct MerkleProof<T, M> {
+    mmr_size: u64,
+    proof: Vec<T>,
+    merge: PhantomData<M>,
+}
+
+impl<T: PartialEq + Debug, M: Merge<Item = T>> MerkleProof<T, M> {
+    pub fn new(mmr_size: u64, proof: Vec<T>) -> Self {
+        MerkleProof {
+            mmr_size,
+            proof,
+            merge: PhantomData,
+        }
+    }
+
+    pub fn verify(&self, root: T, mut pos: u64, elem: T) -> Result<bool> {
+        let peaks = get_peaks(self.mmr_size);
+        let mut sum_elem = elem;
+        let mut height = 0;
+        let mut proof_iter = self.proof.iter();
+        // calculate peak's merkle root
+        // start bagging peaks if pos reach a peak pos
+        while !peaks.contains(&pos) {
+            let proof = match proof_iter.next() {
+                Some(proof) => proof,
+                None => break,
+            };
+            // verify merkle path
+            let pos_height = pos_height_in_tree(pos);
+            let next_height = pos_height_in_tree(pos + 1);
+            sum_elem = if next_height > pos_height {
+                // to next pos
+                pos += 1;
+                M::merge(proof, &sum_elem)
+            } else {
+                pos += parent_offset(height);
+                M::merge(&sum_elem, proof)
+            };
+            height += 1
+        }
+
+        // bagging peaks
+        // bagging with left peaks if pos is last peak
+        let mut bagging_left = Some(&pos) == peaks.last();
+        for proof in &mut proof_iter {
+            sum_elem = if bagging_left {
+                M::merge(&sum_elem, &proof)
+            } else {
+                // we are not in the last peak, so bag with right peaks first
+                // notice the right peaks is already bagging into one hash in proof,
+                // so after this merge, the remain proofs are always left peaks.
+                bagging_left = true;
+                M::merge(&proof, &sum_elem)
+            };
+        }
+        Ok(root == sum_elem)
+    }
+}
diff --git a/src/mmr_store.rs b/src/mmr_store.rs
new file mode 100644
index 0000000..2114ad6
--- /dev/null
+++ b/src/mmr_store.rs
@@ -0,0 +1,58 @@
+use crate::Result;
+
+#[derive(Default)]
+pub struct MMRBatch<Elem, Store: MMRStore<Elem>> {
+    memory_batch: Vec<(u64, Vec<Elem>)>,
+    store: Store,
+}
+
+impl<Elem: Clone, Store: MMRStore<Elem>> MMRBatch<Elem, Store> {
+    pub fn new(store: Store) -> Self {
+        MMRBatch {
+            memory_batch: Vec::new(),
+            store,
+        }
+    }
+
+    pub fn append(&mut self, pos: u64, elems: Vec<Elem>) {
+        self.memory_batch.push((pos, elems));
+    }
+
+    pub fn get_elem(&self, pos: u64) -> Result<Option<Elem>> {
+        for (start_pos, elems) in self.memory_batch.iter().rev() {
+            if pos < *start_pos {
+                continue;
+            } else if pos < start_pos + elems.len() as u64 {
+                return Ok(elems.get((pos - start_pos) as usize).cloned());
+            } else {
+                break;
+            }
+        }
+        self.store.get_elem(pos)
+    }
+
+    pub fn commit(self) -> Result<()> {
+        let Self {
+            mut store,
+            memory_batch,
+        } = self;
+        for (pos, elems) in memory_batch {
+            store.append(pos, elems)?;
+        }
+        Ok(())
+    }
+}
+
+impl<Elem, Store: MMRStore<Elem>> IntoIterator for MMRBatch<Elem, Store> {
+    type Item = (u64, Vec<Elem>);
+    type IntoIter = ::std::vec::IntoIter<Self::Item>;
+
+    fn into_iter(self) -> Self::IntoIter {
+        self.memory_batch.into_iter()
+    }
+}
+
+pub trait MMRStore<Elem> {
+    fn get_elem(&self, pos: u64) -> Result<Option<Elem>>;
+    fn append(&mut self, pos: u64, elems: Vec<Elem>) -> Result<()>;
+}
diff --git a/src/tests/mod.rs b/src/tests/mod.rs
new file mode 100644
index 0000000..221e645
--- /dev/null
+++ b/src/tests/mod.rs
@@ -0,0 +1,37 @@
+mod test_accumulate_headers;
+mod test_helper;
+mod test_mmr;
+
+use crate::Merge;
+use blake2b_rs::{Blake2b, Blake2bBuilder};
+use bytes::Bytes;
+
+fn new_blake2b() -> Blake2b {
+    Blake2bBuilder::new(32).build()
+}
+
+#[derive(Eq, PartialEq, Clone, Debug, Default)]
+struct NumberHash(pub Bytes);
+impl From<u32> for NumberHash {
+    fn from(num: u32) -> Self {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&num.to_le_bytes());
+        hasher.finalize(&mut hash);
+        NumberHash(hash.to_vec().into())
+    }
+}
+
+struct MergeNumberHash;
+
+impl Merge for MergeNumberHash {
+    type Item = NumberHash;
+    fn merge(lhs: &Self::Item, rhs: &Self::Item) -> Self::Item {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&lhs.0);
+        hasher.update(&rhs.0);
+        hasher.finalize(&mut hash);
+        NumberHash(hash.to_vec().into())
+    }
+}
diff --git a/src/tests/test_accumulate_headers.rs b/src/tests/test_accumulate_headers.rs
new file mode 100644
index 0000000..ddbc007
--- /dev/null
+++ b/src/tests/test_accumulate_headers.rs
@@ -0,0 +1,193 @@
+use super::new_blake2b;
+use crate::{leaf_index_to_pos, util::MemStore, MMRStore, Merge, MerkleProof, Result, MMR};
+use bytes::Bytes;
+use std::fmt::{self, Debug};
+
+#[derive(Clone)]
+struct Header {
+    number: u64,
+    parent_hash: Bytes,
+    difficulty: u64,
+    // MMR root
+    chain_root: Bytes,
+}
+
+impl Header {
+    fn default() -> Self {
+        Header {
+            number: 0,
+            parent_hash: vec![0; 32].into(),
+            difficulty: 0,
+            chain_root: vec![0; 32].into(),
+        }
+    }
+
+    fn hash(&self) -> Bytes {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&self.number.to_le_bytes());
+        hasher.update(&self.parent_hash);
+        hasher.update(&self.difficulty.to_le_bytes());
+        hasher.update(&self.chain_root);
+        hasher.finalize(&mut hash);
+        hash.to_vec().into()
+    }
+}
+
+#[derive(Eq, PartialEq, Clone, Default)]
+struct HashWithTD {
+    hash: Bytes,
+    td: u64,
+}
+
+impl HashWithTD {
+    fn serialize(&self) -> Bytes {
+        let mut data = self.hash.clone();
+        data.extend(&self.td.to_le_bytes());
+        data
+    }
+
+    fn deserialize(mut data: Bytes) -> Self {
+        assert_eq!(data.len(), 40);
+        let mut td_bytes = [0u8; 8];
+        td_bytes.copy_from_slice(&data[32..]);
+        let td = u64::from_le_bytes(td_bytes);
+        data.truncate(32);
+        HashWithTD { hash: data, td }
+    }
+}
+
+impl Debug for HashWithTD {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(
+            f,
+            "HashWithTD {{ hash: {}, td: {} }}",
+            faster_hex::hex_string(&self.hash).unwrap(),
+            self.td
+        )
+    }
+}
+
+struct MergeHashWithTD;
+
+impl Merge for MergeHashWithTD {
+    type Item = HashWithTD;
+    fn merge(lhs: &Self::Item, rhs: &Self::Item) -> Self::Item {
+        let mut hasher = new_blake2b();
+        let mut hash = [0u8; 32];
+        hasher.update(&lhs.serialize());
+        hasher.update(&rhs.serialize());
+        hasher.finalize(&mut hash);
+        let td = lhs.td + rhs.td;
+        HashWithTD {
+            hash: hash.to_vec().into(),
+            td,
+        }
+    }
+}
+
+struct Prover {
+    headers: Vec<(Header, u64)>,
+    positions: Vec<u64>,
+    store: MemStore<HashWithTD>,
+}
+
+impl Prover {
+    fn new() -> Prover {
+        let store = MemStore::default();
+        Prover {
+            headers: Vec::new(),
+            positions: Vec::new(),
+            store,
+        }
+    }
+
+    fn gen_blocks(&mut self, count: u64) -> Result<()> {
+        let mut mmr = MMR::<_, MergeHashWithTD, _>::new(self.positions.len() as u64, &self.store);
+        // get previous element
+        let mut previous = if let Some(pos) = self.positions.last() {
+            MMRStore::<_>::get_elem(&&self.store, *pos)?.expect("exists")
+        } else {
+            let genesis = Header::default();
+
+            let previous = HashWithTD {
+                hash: genesis.hash(),
+                td: genesis.difficulty,
+            };
+            self.headers.push((genesis, previous.td));
+            let pos = mmr.push(previous.clone())?;
+            self.positions.push(pos);
+            previous
+        };
+        let last_number = self.headers.last().unwrap().0.number;
+        for i in (last_number + 1)..=(last_number + count) {
+            let block = Header {
+                number: i,
+                parent_hash: previous.hash.clone(),
+                difficulty: i,
+                chain_root: mmr.get_root()?.serialize(),
+            };
+            previous = HashWithTD {
+                hash: block.hash(),
+                td: block.difficulty,
+            };
+            let pos = mmr.push(previous.clone())?;
+            self.positions.push(pos);
+            self.headers.push((block, previous.td));
+        }
+        mmr.commit()
+    }
+
+    fn get_header(&self, number: u64) -> (Header, u64) {
+        self.headers[number as usize].clone()
+    }
+
+    // generate proof that headers are in same chain
+    fn gen_proof(
+        &mut self,
+        number: u64,
+        later_number: u64,
+    ) -> Result<MerkleProof<HashWithTD, MergeHashWithTD>> {
+        assert!(number < later_number);
+        let pos = self.positions[number as usize];
+        let later_pos = self.positions[later_number as usize];
+        let mmr = MMR::new(later_pos, &self.store);
+        assert_eq!(
+            mmr.get_root()?.serialize(),
+            self.headers[later_number as usize].0.chain_root
+        );
+        mmr.gen_proof(pos)
+    }
+
+    fn get_pos(&self, number: u64) -> u64 {
+        self.positions[number as usize]
+    }
+}
+
+#[test]
+fn test_insert_header() {
+    let mut prover = Prover::new();
+    prover.gen_blocks(30).expect("gen blocks");
+    let h1 = 11;
+    let h2 = 19;
+
+    // get headers from prover
+    let prove_elem = {
+        let (header, td) = prover.get_header(h1);
+        HashWithTD {
+            hash: header.hash(),
+            td,
+        }
+    };
+    let root = {
+        let (later_header, _later_td) = prover.get_header(h2);
+        HashWithTD::deserialize(later_header.chain_root)
+    };
+    // gen proof,  blocks are in the same chain
+    let proof = prover.gen_proof(h1, h2).expect("gen proof");
+    let pos = leaf_index_to_pos(h1);
+    assert_eq!(pos, prover.get_pos(h1));
+    assert_eq!(prove_elem, (&prover.store).get_elem(pos).unwrap().unwrap());
+    let result = proof.verify(root, pos, prove_elem).expect("verify");
+    assert!(result);
+}
diff --git a/src/tests/test_helper.rs b/src/tests/test_helper.rs
new file mode 100644
index 0000000..dbc08f0
--- /dev/null
+++ b/src/tests/test_helper.rs
@@ -0,0 +1,82 @@
+use super::{MergeNumberHash, NumberHash};
+use crate::{
+    helper::{get_peaks, pos_height_in_tree},
+    leaf_index_to_mmr_size, leaf_index_to_pos,
+    util::MemStore,
+    MMR,
+};
+use lazy_static::lazy_static;
+use proptest::prelude::*;
+
+lazy_static! {
+    /// Positions of 0..100_000 elem
+    static ref INDEX_TO_POS: Vec<u64> = {
+        let store = MemStore::default();
+        let mut mmr = MMR::<_,MergeNumberHash,_>::new(0, &store);
+        (0u32..100_000)
+            .map(|i| mmr.push(NumberHash::from(i)).unwrap())
+            .collect()
+    };
+    /// mmr size when 0..100_000 elem
+    static ref INDEX_TO_MMR_SIZE: Vec<u64> = {
+        let store = MemStore::default();
+        let mut mmr = MMR::<_,MergeNumberHash,_>::new(0, &store);
+        (0u32..100_000)
+            .map(|i| {
+                mmr.push(NumberHash::from(i)).unwrap();
+                mmr.mmr_size()
+            })
+            .collect()
+    };
+}
+
+#[test]
+fn test_leaf_index_to_pos() {
+    assert_eq!(leaf_index_to_pos(0), 0);
+    assert_eq!(leaf_index_to_pos(1), 1);
+    assert_eq!(leaf_index_to_pos(2), 3);
+}
+
+#[test]
+fn test_leaf_index_to_mmr_size() {
+    assert_eq!(leaf_index_to_mmr_size(0), 1);
+    assert_eq!(leaf_index_to_mmr_size(1), 3);
+    assert_eq!(leaf_index_to_mmr_size(2), 4);
+}
+
+#[test]
+fn test_pos_height_in_tree() {
+    assert_eq!(pos_height_in_tree(0), 0);
+    assert_eq!(pos_height_in_tree(1), 0);
+    assert_eq!(pos_height_in_tree(2), 1);
+    assert_eq!(pos_height_in_tree(3), 0);
+    assert_eq!(pos_height_in_tree(4), 0);
+    assert_eq!(pos_height_in_tree(6), 2);
+    assert_eq!(pos_height_in_tree(7), 0);
+}
+
+#[test]
+fn test_get_peaks() {
+    assert_eq!(get_peaks(0), vec![0]);
+    assert_eq!(get_peaks(1), vec![0]);
+    assert_eq!(get_peaks(2), vec![0]);
+    assert_eq!(get_peaks(3), vec![2]);
+    assert_eq!(get_peaks(4), vec![2, 3]);
+    assert_eq!(get_peaks(5), vec![2, 3]);
+    assert_eq!(get_peaks(6), vec![2, 5]);
+    assert_eq!(get_peaks(7), vec![6]);
+    assert_eq!(get_peaks(19), vec![14, 17, 18]);
+}
+
+proptest! {
+    #[test]
+    fn test_leaf_index_to_pos_randomly(index in 0..INDEX_TO_POS.len()) {
+        let pos = leaf_index_to_pos(index as u64);
+        assert_eq!(pos, INDEX_TO_POS[index]);
+    }
+
+    #[test]
+    fn test_leaf_index_to_mmr_size_randomly(index in 0..INDEX_TO_MMR_SIZE.len()) {
+        assert_eq!(leaf_index_to_mmr_size(index as u64), INDEX_TO_MMR_SIZE[index]);
+    }
+}
diff --git a/src/tests/test_mmr.rs b/src/tests/test_mmr.rs
new file mode 100644
index 0000000..d9242b2
--- /dev/null
+++ b/src/tests/test_mmr.rs
@@ -0,0 +1,98 @@
+use super::{MergeNumberHash, NumberHash};
+use crate::{util::MemStore, Error, MMR};
+use faster_hex::hex_string;
+use proptest::prelude::*;
+
+fn test_mmr(count: u32, proof_elem: u32) {
+    let store = MemStore::default();
+    let mut mmr = MMR::<_, MergeNumberHash, _>::new(0, &store);
+    let positions: Vec<u64> = (0u32..count)
+        .map(|i| mmr.push(NumberHash::from(i)).unwrap())
+        .collect();
+    let root = mmr.get_root().expect("get root");
+    let proof = mmr
+        .gen_proof(positions[proof_elem as usize])
+        .expect("gen proof");
+    mmr.commit().expect("commit changes");
+    let result = proof
+        .verify(
+            root,
+            positions[proof_elem as usize],
+            NumberHash::from(proof_elem),
+        )
+        .unwrap();
+    assert!(result);
+}
+
+#[test]
+fn test_mmr_root() {
+    let store = MemStore::default();
+    let mut mmr = MMR::<_, MergeNumberHash, _>::new(0, &store);
+    (0u32..11).for_each(|i| {
+        mmr.push(NumberHash::from(i)).unwrap();
+    });
+    let root = mmr.get_root().expect("get root");
+    let hex_root = hex_string(&root.0).unwrap();
+    assert_eq!(
+        "f6794677f37a57df6a5ec36ce61036e43a36c1a009d05c81c9aa685dde1fd6e3",
+        hex_root
+    );
+}
+
+#[test]
+fn test_empty_mmr_root() {
+    let store = MemStore::<NumberHash>::default();
+    let mmr = MMR::<_, MergeNumberHash, _>::new(0, &store);
+    assert_eq!(Err(Error::GetRootOnEmpty), mmr.get_root());
+}
+
+#[test]
+fn test_mmr_3_peaks() {
+    test_mmr(11, 5);
+}
+
+#[test]
+fn test_mmr_2_peaks() {
+    test_mmr(10, 5);
+}
+
+#[test]
+fn test_mmr_1_peak() {
+    test_mmr(8, 5);
+}
+
+#[test]
+fn test_mmr_first_elem_proof() {
+    test_mmr(11, 0);
+}
+
+#[test]
+fn test_mmr_last_elem_proof() {
+    test_mmr(11, 10);
+}
+
+#[test]
+fn test_mmr_1_elem() {
+    test_mmr(1, 0);
+}
+
+#[test]
+fn test_mmr_2_elems() {
+    test_mmr(2, 0);
+    test_mmr(2, 1);
+}
+
+prop_compose! {
+    fn count_elem(count: u32)
+                (elem in 0..count)
+                -> (u32, u32) {
+                    (count, elem)
+    }
+}
+
+proptest! {
+    #[test]
+    fn test_random_mmr((count , elem) in count_elem(500)) {
+        test_mmr(count, elem);
+    }
+}
diff --git a/src/util.rs b/src/util.rs
new file mode 100644
index 0000000..1c68af0
--- /dev/null
+++ b/src/util.rs
@@ -0,0 +1,73 @@
+use crate::{MMRStore, Merge, Result, MMR};
+use std::cell::RefCell;
+use std::collections::HashMap;
+use std::fmt::Debug;
+use std::marker::PhantomData;
+
+#[derive(Clone)]
+pub struct MemStore<T>(RefCell<HashMap<u64, T>>);
+
+impl<T> Default for MemStore<T> {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl<T> MemStore<T> {
+    fn new() -> Self {
+        MemStore(RefCell::new(HashMap::new()))
+    }
+}
+
+impl<T: Clone> MMRStore<T> for &MemStore<T> {
+    fn get_elem(&self, pos: u64) -> Result<Option<T>> {
+        Ok(self.0.borrow().get(&pos).cloned())
+    }
+
+    fn append(&mut self, pos: u64, elems: Vec<T>) -> Result<()> {
+        let mut store = self.0.borrow_mut();
+        for (i, elem) in elems.into_iter().enumerate() {
+            store.insert(pos + i as u64, elem);
+        }
+        Ok(())
+    }
+}
+
+pub struct MemMMR<T, M> {
+    store: MemStore<T>,
+    mmr_size: u64,
+    merge: PhantomData<M>,
+}
+
+impl<T: Clone + Debug + PartialEq, M: Merge<Item = T>> Default for MemMMR<T, M> {
+    fn default() -> Self {
+        Self::new(0, Default::default())
+    }
+}
+
+impl<T: Clone + Debug + PartialEq, M: Merge<Item = T>> MemMMR<T, M> {
+    pub fn new(mmr_size: u64, store: MemStore<T>) -> Self {
+        MemMMR {
+            mmr_size,
+            store,
+            merge: PhantomData,
+        }
+    }
+
+    pub fn store(&self) -> &MemStore<T> {
+        &self.store
+    }
+
+    pub fn get_root(&self) -> Result<T> {
+        let mmr = MMR::<T, M, &MemStore<T>>::new(self.mmr_size, &self.store);
+        mmr.get_root()
+    }
+
+    pub fn push(&mut self, elem: T) -> Result<u64> {
+        let mut mmr = MMR::<T, M, &MemStore<T>>::new(self.mmr_size, &self.store);
+        let pos = mmr.push(elem)?;
+        self.mmr_size = mmr.mmr_size();
+        mmr.commit()?;
+        Ok(pos)
+    }
+}