1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
// Copyright (c) The Diem Core Contributors
// SPDX-License-Identifier: Apache-2.0

#![forbid(unsafe_code)]

//! This module implements [`JellyfishMerkleTree`] backed by storage module. The tree itself doesn't
//! persist anything, but realizes the logic of R/W only. The write path will produce all the
//! intermediate results in a batch for storage layer to commit and the read path will return
//! results directly. The public APIs are only [`new`], [`put_value_sets`], [`put_value_set`] and
//! [`get_with_proof`]. After each put with a `value_set` based on a known version, the tree will
//! return a new root hash with a [`TreeUpdateBatch`] containing all the new nodes and indices of
//! stale nodes.
//!
//! A Jellyfish Merkle Tree itself logically is a 256-bit sparse Merkle tree with an optimization
//! that any subtree containing 0 or 1 leaf node will be replaced by that leaf node or a placeholder
//! node with default hash value. With this optimization we can save CPU by avoiding hashing on
//! many sparse levels in the tree. Physically, the tree is structurally similar to the modified
//! Patricia Merkle tree of Ethereum but with some modifications. A standard Jellyfish Merkle tree
//! will look like the following figure:
//!
//! ```text
//!                                    .──────────────────────.
//!                            _.─────'                        `──────.
//!                       _.──'                                        `───.
//!                   _.─'                                                  `──.
//!               _.─'                                                          `──.
//!             ,'                                                                  `.
//!          ,─'                                                                      '─.
//!        ,'                                                                            `.
//!      ,'                                                                                `.
//!     ╱                                                                                    ╲
//!    ╱                                                                                      ╲
//!   ╱                                                                                        ╲
//!  ╱                                                                                          ╲
//! ;                                                                                            :
//! ;                                                                                            :
//!;                                                                                              :
//!│                                                                                              │
//!+──────────────────────────────────────────────────────────────────────────────────────────────+
//! .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.  .''.
//!/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \/    \
//!+----++----++----++----++----++----++----++----++----++----++----++----++----++----++----++----+
//! (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (
//!  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )
//! (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (
//!  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )
//! (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (
//!  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )
//! (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (
//!  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )  )
//! (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (  (
//! ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■  ■
//! ■: the [`Value`] type this tree stores.
//! ```
//!
//! A Jellyfish Merkle Tree consists of [`InternalNode`] and [`LeafNode`]. [`InternalNode`] is like
//! branch node in ethereum patricia merkle with 16 children to represent a 4-level binary tree and
//! [`LeafNode`] is similar to that in patricia merkle too. In the above figure, each `bell` in the
//! jellyfish is an [`InternalNode`] while each tentacle is a [`LeafNode`]. It is noted that
//! Jellyfish merkle doesn't have a counterpart for `extension` node of ethereum patricia merkle.
//!
//! [`JellyfishMerkleTree`]: struct.JellyfishMerkleTree.html
//! [`new`]: struct.JellyfishMerkleTree.html#method.new
//! [`put_value_sets`]: struct.JellyfishMerkleTree.html#method.put_value_sets
//! [`put_value_set`]: struct.JellyfishMerkleTree.html#method.put_value_set
//! [`get_with_proof`]: struct.JellyfishMerkleTree.html#method.get_with_proof
//! [`TreeUpdateBatch`]: struct.TreeUpdateBatch.html
//! [`InternalNode`]: node_type/struct.InternalNode.html
//! [`LeafNode`]: node_type/struct.LeafNode.html

pub mod iterator;
#[cfg(test)]
mod jellyfish_merkle_test;
pub mod metrics;
#[cfg(any(test, feature = "fuzzing"))]
mod mock_tree_store;
pub mod node_type;
pub mod restore;
#[cfg(any(test, feature = "fuzzing"))]
pub mod test_helper;
mod tree_cache;

use anyhow::{bail, ensure, format_err, Result};
use diem_crypto::{hash::CryptoHash, HashValue};
use diem_types::{
    nibble::{
        nibble_path::{skip_common_prefix, NibbleIterator, NibblePath},
        Nibble, ROOT_NIBBLE_HEIGHT,
    },
    proof::{SparseMerkleProof, SparseMerkleRangeProof},
    transaction::Version,
};
use node_type::{Child, Children, InternalNode, LeafNode, Node, NodeKey};
#[cfg(any(test, feature = "fuzzing"))]
use proptest::arbitrary::Arbitrary;
#[cfg(any(test, feature = "fuzzing"))]
use proptest_derive::Arbitrary;
use serde::{de::DeserializeOwned, Serialize};
use std::{
    collections::{BTreeMap, BTreeSet, HashMap},
    marker::PhantomData,
};
use thiserror::Error;
use tree_cache::TreeCache;

#[derive(Error, Debug)]
#[error("Missing state root node at version {version}, probably pruned.")]
pub struct MissingRootError {
    pub version: Version,
}

/// `TreeReader` defines the interface between
/// [`JellyfishMerkleTree`](struct.JellyfishMerkleTree.html)
/// and underlying storage holding nodes.
pub trait TreeReader<V> {
    /// Gets node given a node key. Returns error if the node does not exist.
    fn get_node(&self, node_key: &NodeKey) -> Result<Node<V>> {
        self.get_node_option(node_key)?
            .ok_or_else(|| format_err!("Missing node at {:?}.", node_key))
    }

    /// Gets node given a node key. Returns `None` if the node does not exist.
    fn get_node_option(&self, node_key: &NodeKey) -> Result<Option<Node<V>>>;

    /// Gets the rightmost leaf. Note that this assumes we are in the process of restoring the tree
    /// and all nodes are at the same version.
    fn get_rightmost_leaf(&self) -> Result<Option<(NodeKey, LeafNode<V>)>>;
}

pub trait TreeWriter<V> {
    /// Writes a node batch into storage.
    fn write_node_batch(&self, node_batch: &NodeBatch<V>) -> Result<()>;
}

/// `Value` defines the types of data that can be stored in a Jellyfish Merkle tree.
pub trait Value: Clone + CryptoHash + Serialize + DeserializeOwned {}

/// `TestValue` defines the types of data that can be stored in a Jellyfish Merkle tree and used in
/// tests.
#[cfg(any(test, feature = "fuzzing"))]
pub trait TestValue: Value + Arbitrary + std::fmt::Debug + Eq + PartialEq + 'static {}

// This crate still depends on types for a few things, therefore we implement `Value` and
// `TestValue` for `AccountStateBlob` here. Ideally the module that defines the specific value like
// `AccountStateBlob` should import the `Value` trait and implement it there.
impl Value for diem_types::account_state_blob::AccountStateBlob {}
#[cfg(any(test, feature = "fuzzing"))]
impl TestValue for diem_types::account_state_blob::AccountStateBlob {}

/// Node batch that will be written into db atomically with other batches.
pub type NodeBatch<V> = BTreeMap<NodeKey, Node<V>>;
/// [`StaleNodeIndex`](struct.StaleNodeIndex.html) batch that will be written into db atomically
/// with other batches.
pub type StaleNodeIndexBatch = BTreeSet<StaleNodeIndex>;

#[derive(Clone, Debug, Default, Eq, PartialEq)]
pub struct NodeStats {
    pub new_nodes: usize,
    pub new_leaves: usize,
    pub stale_nodes: usize,
    pub stale_leaves: usize,
}

/// Indicates a node becomes stale since `stale_since_version`.
#[derive(Clone, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)]
#[cfg_attr(any(test, feature = "fuzzing"), derive(Arbitrary))]
pub struct StaleNodeIndex {
    /// The version since when the node is overwritten and becomes stale.
    pub stale_since_version: Version,
    /// The [`NodeKey`](node_type/struct.NodeKey.html) identifying the node associated with this
    /// record.
    pub node_key: NodeKey,
}

/// This is a wrapper of [`NodeBatch`](type.NodeBatch.html),
/// [`StaleNodeIndexBatch`](type.StaleNodeIndexBatch.html) and some stats of nodes that represents
/// the incremental updates of a tree and pruning indices after applying a write set,
/// which is a vector of `hashed_account_address` and `new_value` pairs.
#[derive(Clone, Debug, Default, Eq, PartialEq)]
pub struct TreeUpdateBatch<V> {
    pub node_batch: NodeBatch<V>,
    pub stale_node_index_batch: StaleNodeIndexBatch,
    pub node_stats: Vec<NodeStats>,
}

/// An iterator that iterates the index range (inclusive) of each different nibble at given
/// `nibble_idx` of all the keys in a sorted key-value pairs.
struct NibbleRangeIterator<'a, V> {
    sorted_kvs: &'a [(HashValue, V)],
    nibble_idx: usize,
    pos: usize,
}

impl<'a, V> NibbleRangeIterator<'a, V> {
    fn new(sorted_kvs: &'a [(HashValue, V)], nibble_idx: usize) -> Self {
        assert!(nibble_idx < ROOT_NIBBLE_HEIGHT);
        NibbleRangeIterator {
            sorted_kvs,
            nibble_idx,
            pos: 0,
        }
    }
}

impl<'a, V> std::iter::Iterator for NibbleRangeIterator<'a, V> {
    type Item = (usize, usize);

    fn next(&mut self) -> Option<Self::Item> {
        let left = self.pos;
        if self.pos < self.sorted_kvs.len() {
            let cur_nibble: u8 = self.sorted_kvs[left].0.nibble(self.nibble_idx);
            let (mut i, mut j) = (left, self.sorted_kvs.len() - 1);
            // Find the last index of the cur_nibble.
            while i < j {
                let mid = j - (j - i) / 2;
                if self.sorted_kvs[mid].0.nibble(self.nibble_idx) > cur_nibble {
                    j = mid - 1;
                } else {
                    i = mid;
                }
            }
            self.pos = i + 1;
            Some((left, i))
        } else {
            None
        }
    }
}

/// The Jellyfish Merkle tree data structure. See [`crate`] for description.
pub struct JellyfishMerkleTree<'a, R, V> {
    reader: &'a R,
    phantom_value: PhantomData<V>,
}

impl<'a, R, V> JellyfishMerkleTree<'a, R, V>
where
    R: 'a + TreeReader<V>,
    V: Value,
{
    /// Creates a `JellyfishMerkleTree` backed by the given [`TreeReader`](trait.TreeReader.html).
    pub fn new(reader: &'a R) -> Self {
        Self {
            reader,
            phantom_value: PhantomData,
        }
    }

    /// Get the node hash from the cache if exists, otherwise compute it.
    fn get_hash(
        node_key: &NodeKey,
        node: &Node<V>,
        hash_cache: &Option<&HashMap<NibblePath, HashValue>>,
    ) -> HashValue {
        if let Some(cache) = hash_cache {
            match cache.get(node_key.nibble_path()) {
                Some(hash) => *hash,
                None => unreachable!("{:?} can not be found in hash cache", node_key),
            }
        } else {
            node.hash()
        }
    }

    /// The batch version of `put_value_sets`.
    pub fn batch_put_value_sets(
        &self,
        value_sets: Vec<Vec<(HashValue, V)>>,
        node_hashes: Option<Vec<&HashMap<NibblePath, HashValue>>>,
        first_version: Version,
    ) -> Result<(Vec<HashValue>, TreeUpdateBatch<V>)> {
        let mut tree_cache = TreeCache::new(self.reader, first_version)?;
        let hash_sets: Vec<_> = match node_hashes {
            Some(hashes) => hashes.into_iter().map(Some).collect(),
            None => (0..value_sets.len()).map(|_| None).collect(),
        };

        for (idx, (value_set, hash_set)) in
            itertools::zip_eq(value_sets.into_iter(), hash_sets.into_iter()).enumerate()
        {
            assert!(
                !value_set.is_empty(),
                "Transactions that output empty write set should not be included.",
            );
            let version = first_version + idx as u64;
            let deduped_and_sorted_kvs = value_set
                .into_iter()
                .collect::<BTreeMap<_, _>>()
                .into_iter()
                .collect::<Vec<_>>();
            let root_node_key = tree_cache.get_root_node_key().clone();
            let (new_root_node_key, _) = Self::batch_insert_at(
                root_node_key,
                version,
                deduped_and_sorted_kvs.as_slice(),
                0,
                &hash_set,
                &mut tree_cache,
            )?;
            tree_cache.set_root_node_key(new_root_node_key);

            // Freezes the current cache to make all contents in the current cache immutable.
            tree_cache.freeze();
        }

        Ok(tree_cache.into())
    }

    fn batch_insert_at(
        mut node_key: NodeKey,
        version: Version,
        kvs: &[(HashValue, V)],
        depth: usize,
        hash_cache: &Option<&HashMap<NibblePath, HashValue>>,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        assert!(!kvs.is_empty());

        let node = tree_cache.get_node(&node_key)?;
        Ok(match node {
            Node::Internal(internal_node) => {
                // We always delete the existing internal node here because it will not be referenced anyway
                // since this version.
                tree_cache.delete_node(&node_key, false /* is_leaf */);

                // Reuse the current `InternalNode` in memory to create a new internal node.
                let mut children: Children = internal_node.clone().into();

                // Traverse all the path touched by `kvs` from this internal node.
                for (left, right) in NibbleRangeIterator::new(kvs, depth) {
                    // Traverse downwards from this internal node recursively by splitting the updates into
                    // each child index
                    let child_index = kvs[left].0.get_nibble(depth);

                    let (new_child_node_key, new_child_node) =
                        match internal_node.child(child_index) {
                            Some(child) => {
                                let child_node_key =
                                    node_key.gen_child_node_key(child.version, child_index);
                                Self::batch_insert_at(
                                    child_node_key,
                                    version,
                                    &kvs[left..=right],
                                    depth + 1,
                                    hash_cache,
                                    tree_cache,
                                )?
                            }
                            None => {
                                let new_child_node_key =
                                    node_key.gen_child_node_key(version, child_index);
                                Self::batch_create_subtree(
                                    new_child_node_key,
                                    version,
                                    &kvs[left..=right],
                                    depth + 1,
                                    hash_cache,
                                    tree_cache,
                                )?
                            }
                        };

                    children.insert(
                        child_index,
                        Child::new(
                            Self::get_hash(&new_child_node_key, &new_child_node, hash_cache),
                            version,
                            new_child_node.is_leaf(),
                        ),
                    );
                }
                let new_internal_node = InternalNode::new(children);

                node_key.set_version(version);

                // Cache this new internal node.
                tree_cache.put_node(node_key.clone(), new_internal_node.clone().into())?;
                (node_key, new_internal_node.into())
            }
            Node::Leaf(leaf_node) => {
                // We are on a leaf node but trying to insert another node, so we may diverge.
                // We always delete the existing leaf node here because it will not be referenced anyway
                // since this version.
                tree_cache.delete_node(&node_key, true /* is_leaf */);
                node_key.set_version(version);
                Self::batch_create_subtree_with_existing_leaf(
                    node_key, version, leaf_node, kvs, depth, hash_cache, tree_cache,
                )?
            }
            Node::Null => {
                if !node_key.nibble_path().is_empty() {
                    bail!(
                        "Null node exists for non-root node with node_key {:?}",
                        node_key
                    );
                }

                if node_key.version() == version {
                    tree_cache.delete_node(&node_key, false /* is_leaf */);
                }
                Self::batch_create_subtree(
                    NodeKey::new_empty_path(version),
                    version,
                    kvs,
                    depth,
                    hash_cache,
                    tree_cache,
                )?
            }
        })
    }

    fn batch_create_subtree_with_existing_leaf(
        node_key: NodeKey,
        version: Version,
        existing_leaf_node: LeafNode<V>,
        kvs: &[(HashValue, V)],
        depth: usize,
        hash_cache: &Option<&HashMap<NibblePath, HashValue>>,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        let existing_leaf_key = existing_leaf_node.account_key();

        if kvs.len() == 1 && kvs[0].0 == existing_leaf_key {
            let new_leaf_node = Node::new_leaf(existing_leaf_key, kvs[0].1.clone());
            tree_cache.put_node(node_key.clone(), new_leaf_node.clone())?;
            Ok((node_key, new_leaf_node))
        } else {
            let existing_leaf_bucket = existing_leaf_key.get_nibble(depth);
            let mut isolated_existing_leaf = true;
            let mut children = Children::new();
            for (left, right) in NibbleRangeIterator::new(kvs, depth) {
                let child_index = kvs[left].0.get_nibble(depth);
                let child_node_key = node_key.gen_child_node_key(version, child_index);
                let (new_child_node_key, new_child_node) = if existing_leaf_bucket == child_index {
                    isolated_existing_leaf = false;
                    Self::batch_create_subtree_with_existing_leaf(
                        child_node_key,
                        version,
                        existing_leaf_node.clone(),
                        &kvs[left..=right],
                        depth + 1,
                        hash_cache,
                        tree_cache,
                    )?
                } else {
                    Self::batch_create_subtree(
                        child_node_key,
                        version,
                        &kvs[left..=right],
                        depth + 1,
                        hash_cache,
                        tree_cache,
                    )?
                };
                children.insert(
                    child_index,
                    Child::new(
                        Self::get_hash(&new_child_node_key, &new_child_node, hash_cache),
                        version,
                        new_child_node.is_leaf(),
                    ),
                );
            }
            if isolated_existing_leaf {
                let existing_leaf_node_key =
                    node_key.gen_child_node_key(version, existing_leaf_bucket);
                children.insert(
                    existing_leaf_bucket,
                    Child::new(existing_leaf_node.hash(), version, true /* is_leaf */),
                );

                tree_cache.put_node(existing_leaf_node_key, existing_leaf_node.into())?;
            }

            let new_internal_node = InternalNode::new(children);

            tree_cache.put_node(node_key.clone(), new_internal_node.clone().into())?;
            Ok((node_key, new_internal_node.into()))
        }
    }

    fn batch_create_subtree(
        node_key: NodeKey,
        version: Version,
        kvs: &[(HashValue, V)],
        depth: usize,
        hash_cache: &Option<&HashMap<NibblePath, HashValue>>,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        if kvs.len() == 1 {
            let new_leaf_node = Node::new_leaf(kvs[0].0, kvs[0].1.clone());
            tree_cache.put_node(node_key.clone(), new_leaf_node.clone())?;
            Ok((node_key, new_leaf_node))
        } else {
            let mut children = Children::new();
            for (left, right) in NibbleRangeIterator::new(kvs, depth) {
                let child_index = kvs[left].0.get_nibble(depth);
                let child_node_key = node_key.gen_child_node_key(version, child_index);
                let (new_child_node_key, new_child_node) = Self::batch_create_subtree(
                    child_node_key,
                    version,
                    &kvs[left..=right],
                    depth + 1,
                    hash_cache,
                    tree_cache,
                )?;
                children.insert(
                    child_index,
                    Child::new(
                        Self::get_hash(&new_child_node_key, &new_child_node, hash_cache),
                        version,
                        new_child_node.is_leaf(),
                    ),
                );
            }
            let new_internal_node = InternalNode::new(children);

            tree_cache.put_node(node_key.clone(), new_internal_node.clone().into())?;
            Ok((node_key, new_internal_node.into()))
        }
    }

    /// This is a convenient function that calls
    /// [`put_value_sets`](struct.JellyfishMerkleTree.html#method.put_value_sets) with a single
    /// `keyed_value_set`.
    #[cfg(any(test, feature = "fuzzing"))]
    pub fn put_value_set(
        &self,
        value_set: Vec<(HashValue, V)>,
        version: Version,
    ) -> Result<(HashValue, TreeUpdateBatch<V>)> {
        let (root_hashes, tree_update_batch) =
            self.batch_put_value_sets(vec![value_set], None, version)?;
        assert_eq!(
            root_hashes.len(),
            1,
            "root_hashes must consist of a single value.",
        );
        Ok((root_hashes[0], tree_update_batch))
    }

    /// Returns the new nodes and values in a batch after applying `value_set`. For
    /// example, if after transaction `T_i` the committed state of tree in the persistent storage
    /// looks like the following structure:
    ///
    /// ```text
    ///              S_i
    ///             /   \
    ///            .     .
    ///           .       .
    ///          /         \
    ///         o           x
    ///        / \
    ///       A   B
    ///        storage (disk)
    /// ```
    ///
    /// where `A` and `B` denote the states of two adjacent accounts, and `x` is a sibling subtree
    /// of the path from root to A and B in the tree. Then a `value_set` produced by the next
    /// transaction `T_{i+1}` modifies other accounts `C` and `D` exist in the subtree under `x`, a
    /// new partial tree will be constructed in memory and the structure will be:
    ///
    /// ```text
    ///                 S_i      |      S_{i+1}
    ///                /   \     |     /       \
    ///               .     .    |    .         .
    ///              .       .   |   .           .
    ///             /         \  |  /             \
    ///            /           x | /               x'
    ///           o<-------------+-               / \
    ///          / \             |               C   D
    ///         A   B            |
    ///           storage (disk) |    cache (memory)
    /// ```
    ///
    /// With this design, we are able to query the global state in persistent storage and
    /// generate the proposed tree delta based on a specific root hash and `value_set`. For
    /// example, if we want to execute another transaction `T_{i+1}'`, we can use the tree `S_i` in
    /// storage and apply the `value_set` of transaction `T_{i+1}`. Then if the storage commits
    /// the returned batch, the state `S_{i+1}` is ready to be read from the tree by calling
    /// [`get_with_proof`](struct.JellyfishMerkleTree.html#method.get_with_proof). Anything inside
    /// the batch is not reachable from public interfaces before being committed.
    pub fn put_value_sets(
        &self,
        value_sets: Vec<Vec<(HashValue, V)>>,
        first_version: Version,
    ) -> Result<(Vec<HashValue>, TreeUpdateBatch<V>)> {
        let mut tree_cache = TreeCache::new(self.reader, first_version)?;
        for (idx, value_set) in value_sets.into_iter().enumerate() {
            assert!(
                !value_set.is_empty(),
                "Transactions that output empty write set should not be included.",
            );
            let version = first_version + idx as u64;
            value_set
                .into_iter()
                .try_for_each(|(key, value)| Self::put(key, value, version, &mut tree_cache))?;
            // Freezes the current cache to make all contents in the current cache immutable.
            tree_cache.freeze();
        }

        Ok(tree_cache.into())
    }

    fn put(
        key: HashValue,
        value: V,
        version: Version,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<()> {
        let nibble_path = NibblePath::new(key.to_vec());

        // Get the root node. If this is the first operation, it would get the root node from the
        // underlying db. Otherwise it most likely would come from `cache`.
        let root_node_key = tree_cache.get_root_node_key();
        let mut nibble_iter = nibble_path.nibbles();

        // Start insertion from the root node.
        let (new_root_node_key, _) = Self::insert_at(
            root_node_key.clone(),
            version,
            &mut nibble_iter,
            value,
            tree_cache,
        )?;

        tree_cache.set_root_node_key(new_root_node_key);
        Ok(())
    }

    /// Helper function for recursive insertion into the subtree that starts from the current
    /// [`NodeKey`](node_type/struct.NodeKey.html). Returns the newly inserted node.
    /// It is safe to use recursion here because the max depth is limited by the key length which
    /// for this tree is the length of the hash of account addresses.
    fn insert_at(
        node_key: NodeKey,
        version: Version,
        nibble_iter: &mut NibbleIterator,
        value: V,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        let node = tree_cache.get_node(&node_key)?;
        match node {
            Node::Internal(internal_node) => Self::insert_at_internal_node(
                node_key,
                internal_node,
                version,
                nibble_iter,
                value,
                tree_cache,
            ),
            Node::Leaf(leaf_node) => Self::insert_at_leaf_node(
                node_key,
                leaf_node,
                version,
                nibble_iter,
                value,
                tree_cache,
            ),
            Node::Null => {
                if !node_key.nibble_path().is_empty() {
                    bail!(
                        "Null node exists for non-root node with node_key {:?}",
                        node_key
                    );
                }
                // delete the old null node if the at the same version.
                if node_key.version() == version {
                    tree_cache.delete_node(&node_key, false /* is_leaf */);
                }
                Self::create_leaf_node(
                    NodeKey::new_empty_path(version),
                    nibble_iter,
                    value,
                    tree_cache,
                )
            }
        }
    }

    /// Helper function for recursive insertion into the subtree that starts from the current
    /// `internal_node`. Returns the newly inserted node with its
    /// [`NodeKey`](node_type/struct.NodeKey.html).
    fn insert_at_internal_node(
        mut node_key: NodeKey,
        internal_node: InternalNode,
        version: Version,
        nibble_iter: &mut NibbleIterator,
        value: V,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        // We always delete the existing internal node here because it will not be referenced anyway
        // since this version.
        tree_cache.delete_node(&node_key, false /* is_leaf */);

        // Find the next node to visit following the next nibble as index.
        let child_index = nibble_iter.next().expect("Ran out of nibbles");

        // Traverse downwards from this internal node recursively to get the `node_key` of the child
        // node at `child_index`.
        let (_, new_child_node) = match internal_node.child(child_index) {
            Some(child) => {
                let child_node_key = node_key.gen_child_node_key(child.version, child_index);
                Self::insert_at(child_node_key, version, nibble_iter, value, tree_cache)?
            }
            None => {
                let new_child_node_key = node_key.gen_child_node_key(version, child_index);
                Self::create_leaf_node(new_child_node_key, nibble_iter, value, tree_cache)?
            }
        };

        // Reuse the current `InternalNode` in memory to create a new internal node.
        let mut children: Children = internal_node.into();
        children.insert(
            child_index,
            Child::new(new_child_node.hash(), version, new_child_node.is_leaf()),
        );
        let new_internal_node = InternalNode::new(children);

        node_key.set_version(version);

        // Cache this new internal node.
        tree_cache.put_node(node_key.clone(), new_internal_node.clone().into())?;
        Ok((node_key, new_internal_node.into()))
    }

    /// Helper function for recursive insertion into the subtree that starts from the
    /// `existing_leaf_node`. Returns the newly inserted node with its
    /// [`NodeKey`](node_type/struct.NodeKey.html).
    fn insert_at_leaf_node(
        mut node_key: NodeKey,
        existing_leaf_node: LeafNode<V>,
        version: Version,
        nibble_iter: &mut NibbleIterator,
        value: V,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        // We are on a leaf node but trying to insert another node, so we may diverge.
        // We always delete the existing leaf node here because it will not be referenced anyway
        // since this version.
        tree_cache.delete_node(&node_key, true /* is_leaf */);

        // 1. Make sure that the existing leaf nibble_path has the same prefix as the already
        // visited part of the nibble iter of the incoming key and advances the existing leaf
        // nibble iterator by the length of that prefix.
        let mut visited_nibble_iter = nibble_iter.visited_nibbles();
        let existing_leaf_nibble_path = NibblePath::new(existing_leaf_node.account_key().to_vec());
        let mut existing_leaf_nibble_iter = existing_leaf_nibble_path.nibbles();
        skip_common_prefix(&mut visited_nibble_iter, &mut existing_leaf_nibble_iter);

        // TODO(lightmark): Change this to corrupted error.
        assert!(
            visited_nibble_iter.is_finished(),
            "Leaf nodes failed to share the same visited nibbles before index {}",
            existing_leaf_nibble_iter.visited_nibbles().num_nibbles()
        );

        // 2. Determine the extra part of the common prefix that extends from the position where
        // step 1 ends between this leaf node and the incoming key.
        let mut existing_leaf_nibble_iter_below_internal =
            existing_leaf_nibble_iter.remaining_nibbles();
        let num_common_nibbles_below_internal =
            skip_common_prefix(nibble_iter, &mut existing_leaf_nibble_iter_below_internal);
        let mut common_nibble_path = nibble_iter.visited_nibbles().collect::<NibblePath>();

        // 2.1. Both are finished. That means the incoming key already exists in the tree and we
        // just need to update its value.
        if nibble_iter.is_finished() {
            assert!(existing_leaf_nibble_iter_below_internal.is_finished());
            // The new leaf node will have the same nibble_path with a new version as node_key.
            node_key.set_version(version);
            // Create the new leaf node with the same address but the new value.
            return Self::create_leaf_node(node_key, nibble_iter, value, tree_cache);
        }

        // 2.2. both are unfinished(They have keys with same length so it's impossible to have one
        // finished and the other not). This means the incoming key forks at some point between the
        // position where step 1 ends and the last nibble, inclusive. Then create a seris of
        // internal nodes the number of which equals to the length of the extra part of the
        // common prefix in step 2, a new leaf node for the incoming key, and update the
        // [`NodeKey`] of existing leaf node. We create new internal nodes in a bottom-up
        // order.
        let existing_leaf_index = existing_leaf_nibble_iter_below_internal
            .next()
            .expect("Ran out of nibbles");
        let new_leaf_index = nibble_iter.next().expect("Ran out of nibbles");
        assert_ne!(existing_leaf_index, new_leaf_index);

        let mut children = Children::new();
        children.insert(
            existing_leaf_index,
            Child::new(existing_leaf_node.hash(), version, true /* is_leaf */),
        );
        node_key = NodeKey::new(version, common_nibble_path.clone());
        tree_cache.put_node(
            node_key.gen_child_node_key(version, existing_leaf_index),
            existing_leaf_node.into(),
        )?;

        let (_, new_leaf_node) = Self::create_leaf_node(
            node_key.gen_child_node_key(version, new_leaf_index),
            nibble_iter,
            value,
            tree_cache,
        )?;
        children.insert(
            new_leaf_index,
            Child::new(new_leaf_node.hash(), version, true /* is_leaf */),
        );

        let internal_node = InternalNode::new(children);
        let mut next_internal_node: Node<V> = internal_node.clone().into();
        tree_cache.put_node(node_key.clone(), internal_node.into())?;

        for _i in 0..num_common_nibbles_below_internal {
            let nibble = common_nibble_path
                .pop()
                .expect("Common nibble_path below internal node ran out of nibble");
            node_key = NodeKey::new(version, common_nibble_path.clone());
            let mut children = Children::new();
            children.insert(
                nibble,
                Child::new(next_internal_node.hash(), version, false /* is_leaf */),
            );
            let internal_node = InternalNode::new(children);
            next_internal_node = internal_node.clone().into();
            tree_cache.put_node(node_key.clone(), internal_node.into())?;
        }

        Ok((node_key, next_internal_node))
    }

    /// Helper function for creating leaf nodes. Returns the newly created leaf node.
    fn create_leaf_node(
        node_key: NodeKey,
        nibble_iter: &NibbleIterator,
        value: V,
        tree_cache: &mut TreeCache<R, V>,
    ) -> Result<(NodeKey, Node<V>)> {
        // Get the underlying bytes of nibble_iter which must be a key, i.e., hashed account address
        // with `HashValue::LENGTH` bytes.
        let new_leaf_node = Node::new_leaf(
            HashValue::from_slice(nibble_iter.get_nibble_path().bytes())
                .expect("LeafNode must have full nibble path."),
            value,
        );

        tree_cache.put_node(node_key.clone(), new_leaf_node.clone())?;
        Ok((node_key, new_leaf_node))
    }

    /// Returns the value (if applicable) and the corresponding merkle proof.
    pub fn get_with_proof(
        &self,
        key: HashValue,
        version: Version,
    ) -> Result<(Option<V>, SparseMerkleProof<V>)> {
        // Empty tree just returns proof with no sibling hash.
        let mut next_node_key = NodeKey::new_empty_path(version);
        let mut siblings = vec![];
        let nibble_path = NibblePath::new(key.to_vec());
        let mut nibble_iter = nibble_path.nibbles();

        // We limit the number of loops here deliberately to avoid potential cyclic graph bugs
        // in the tree structure.
        for nibble_depth in 0..=ROOT_NIBBLE_HEIGHT {
            let next_node = self.reader.get_node(&next_node_key).map_err(|err| {
                if nibble_depth == 0 {
                    MissingRootError { version }.into()
                } else {
                    err
                }
            })?;
            match next_node {
                Node::Internal(internal_node) => {
                    let queried_child_index = nibble_iter
                        .next()
                        .ok_or_else(|| format_err!("ran out of nibbles"))?;
                    let (child_node_key, mut siblings_in_internal) =
                        internal_node.get_child_with_siblings(&next_node_key, queried_child_index);
                    siblings.append(&mut siblings_in_internal);
                    next_node_key = match child_node_key {
                        Some(node_key) => node_key,
                        None => {
                            return Ok((
                                None,
                                SparseMerkleProof::new(None, {
                                    siblings.reverse();
                                    siblings
                                }),
                            ))
                        }
                    };
                }
                Node::Leaf(leaf_node) => {
                    return Ok((
                        if leaf_node.account_key() == key {
                            Some(leaf_node.value().clone())
                        } else {
                            None
                        },
                        SparseMerkleProof::new(Some(leaf_node.into()), {
                            siblings.reverse();
                            siblings
                        }),
                    ));
                }
                Node::Null => {
                    if nibble_depth == 0 {
                        return Ok((None, SparseMerkleProof::new(None, vec![])));
                    } else {
                        bail!(
                            "Non-root null node exists with node key {:?}",
                            next_node_key
                        );
                    }
                }
            }
        }
        bail!("Jellyfish Merkle tree has cyclic graph inside.");
    }

    /// Gets the proof that shows a list of keys up to `rightmost_key_to_prove` exist at `version`.
    pub fn get_range_proof(
        &self,
        rightmost_key_to_prove: HashValue,
        version: Version,
    ) -> Result<SparseMerkleRangeProof> {
        let (account, proof) = self.get_with_proof(rightmost_key_to_prove, version)?;
        ensure!(account.is_some(), "rightmost_key_to_prove must exist.");

        let siblings = proof
            .siblings()
            .iter()
            .rev()
            .zip(rightmost_key_to_prove.iter_bits())
            .filter_map(|(sibling, bit)| {
                // We only need to keep the siblings on the right.
                if !bit {
                    Some(*sibling)
                } else {
                    None
                }
            })
            .rev()
            .collect();
        Ok(SparseMerkleRangeProof::new(siblings))
    }

    #[cfg(test)]
    pub fn get(&self, key: HashValue, version: Version) -> Result<Option<V>> {
        Ok(self.get_with_proof(key, version)?.0)
    }

    pub fn get_root_hash(&self, version: Version) -> Result<HashValue> {
        self.get_root_hash_option(version)?
            .ok_or_else(|| format_err!("Root node not found for version {}.", version))
    }

    pub fn get_root_hash_option(&self, version: Version) -> Result<Option<HashValue>> {
        let root_node_key = NodeKey::new_empty_path(version);
        Ok(self
            .reader
            .get_node_option(&root_node_key)?
            .map(|root_node| root_node.hash()))
    }
}

trait NibbleExt {
    fn get_nibble(&self, index: usize) -> Nibble;
    fn common_prefix_nibbles_len(&self, other: HashValue) -> usize;
}

impl NibbleExt for HashValue {
    /// Returns the `index`-th nibble.
    fn get_nibble(&self, index: usize) -> Nibble {
        mirai_annotations::precondition!(index < HashValue::LENGTH);
        Nibble::from(if index % 2 == 0 {
            self[index / 2] >> 4
        } else {
            self[index / 2] & 0x0F
        })
    }

    /// Returns the length of common prefix of `self` and `other` in nibbles.
    fn common_prefix_nibbles_len(&self, other: HashValue) -> usize {
        self.common_prefix_bits_len(other) / 4
    }
}

#[cfg(test)]
mod test {
    use super::NibbleExt;
    use diem_crypto::hash::{HashValue, TestOnlyHash};
    use diem_types::nibble::Nibble;

    #[test]
    fn test_common_prefix_nibbles_len() {
        {
            let hash1 = b"hello".test_only_hash();
            let hash2 = b"HELLO".test_only_hash();
            assert_eq!(hash1[0], 0b0011_0011);
            assert_eq!(hash2[0], 0b1011_1000);
            assert_eq!(hash1.common_prefix_nibbles_len(hash2), 0);
        }
        {
            let hash1 = b"hello".test_only_hash();
            let hash2 = b"world".test_only_hash();
            assert_eq!(hash1[0], 0b0011_0011);
            assert_eq!(hash2[0], 0b0100_0010);
            assert_eq!(hash1.common_prefix_nibbles_len(hash2), 0);
        }
        {
            let hash1 = b"hello".test_only_hash();
            let hash2 = b"100011001000".test_only_hash();
            assert_eq!(hash1[0], 0b0011_0011);
            assert_eq!(hash2[0], 0b0011_0011);
            assert_eq!(hash1[1], 0b0011_1000);
            assert_eq!(hash2[1], 0b0010_0010);
            assert_eq!(hash1.common_prefix_nibbles_len(hash2), 2);
        }
        {
            let hash1 = b"hello".test_only_hash();
            let hash2 = b"hello".test_only_hash();
            assert_eq!(
                hash1.common_prefix_nibbles_len(hash2),
                HashValue::LENGTH * 2
            );
        }
    }

    #[test]
    fn test_get_nibble() {
        let hash = b"hello".test_only_hash();
        assert_eq!(hash.get_nibble(0), Nibble::from(3));
        assert_eq!(hash.get_nibble(1), Nibble::from(3));
        assert_eq!(hash.get_nibble(2), Nibble::from(3));
        assert_eq!(hash.get_nibble(3), Nibble::from(8));
        assert_eq!(hash.get_nibble(62), Nibble::from(9));
        assert_eq!(hash.get_nibble(63), Nibble::from(2));
    }
}