feat: implement concurrent Smt construction (#341)

* merkle: add parent() helper function on NodeIndex
* smt: add pairs_to_leaf() to trait
* smt: add sorted_pairs_to_leaves() and test for it
* smt: implement single subtree-8 hashing, w/ benchmarks & tests

This will be composed into depth-8-subtree-based computation of entire
sparse Merkle trees.

* merkle: add a benchmark for constructing 256-balanced trees

This is intended for comparison with the benchmarks from the previous
commit. This benchmark represents the theoretical perfect-efficiency
performance we could possibly (but impractically) get for computing
depth-8 sparse Merkle subtrees.

* smt: test that SparseMerkleTree::build_subtree() is composable

* smt: test that subtree logic can correctly construct an entire tree

This commit ensures that `SparseMerkleTree::build_subtree()` can
correctly compose into building an entire sparse Merkle tree, without
yet getting into potential complications concurrency introduces.

* smt: implement test for basic parallelized subtree computation w/ rayon

Building on the previous commit, this commit implements a test proving
that `SparseMerkleTree::build_subtree()` can be composed into itself not
just concurrently, but in parallel, without issue.

* smt: add from_raw_parts() to trait interface

This commit adds a new required method to the SparseMerkleTree trait,
to allow generic construction from pre-computed parts.

This will be used to add a generic version of `with_entries()` in a
later commit.

* smt: add parallel constructors to Smt and SimpleSmt

What the previous few commits have been leading up to: SparseMerkleTree
now has a function to construct the tree from existing data in parallel.
This is significantly faster than the singlethreaded equivalent.
Benchmarks incoming!

---------

Co-authored-by: krushimir <krushimir@reilabs.co>
Co-authored-by: krushimir <kresimir.grofelnik@reilabs.io>

CHANGELOG.md

@@ -7,6 +7,7 @@
 ## 0.12.0 (2024-10-30)
 
 - [BREAKING] Updated Winterfell dependency to v0.10 (#338).
+- Added parallel implementation of `Smt::with_entries()` with significantly better performance when the `concurrent` feature is enabled (#341).
 
 ## 0.11.0 (2024-10-17)
 

Cargo.lock

@@ -541,6 +541,7 @@ dependencies = [
  "rand",
  "rand_chacha",
  "rand_core",
+ "rayon",
  "seq-macro",
  "serde",
  "sha3",

Cargo.toml

@@ -27,13 +27,28 @@ harness = false
 name = "smt"
 harness = false
 
+[[bench]]
+name = "smt-subtree"
+harness = false
+required-features = ["internal"]
+
+[[bench]]
+name = "merkle"
+harness = false
+
+[[bench]]
+name = "smt-with-entries"
+harness = false
+
 [[bench]]
 name = "store"
 harness = false
 
 [features]
-default = ["std"]
+concurrent = ["dep:rayon"]
+default = ["std", "concurrent"]
 executable = ["dep:clap", "dep:rand-utils", "std"]
+internal = []
 serde = ["dep:serde", "serde?/alloc", "winter-math/serde"]
 std = [
     "blake3/std",
@@ -53,6 +68,7 @@ num-complex = { version = "0.4", default-features = false }
 rand = { version = "0.8", default-features = false }
 rand_core = { version = "0.6", default-features = false }
 rand-utils = { version = "0.11", package = "winter-rand-utils", optional = true }
+rayon = { version = "1.10", optional = true }
 serde = { version = "1.0", default-features = false, optional = true, features = ["derive"] }
 sha3 = { version = "0.10", default-features = false }
 thiserror = { version = "2.0", default-features = false }

Makefile

@@ -83,4 +83,4 @@ build-sve: ## Build with sve support
 
 .PHONY: bench-tx
 bench-tx: ## Run crypto benchmarks
-	cargo bench
+	cargo bench --features="concurrent"

README.md

@@ -60,10 +60,11 @@ make
 
 This crate can be compiled with the following features:
 
+- `concurrent`- enabled by default; enables multi-threaded implementation of `Smt::with_entries()` which significantly improves performance on multi-core CPUs.
 - `std` - enabled by default and relies on the Rust standard library.
 - `no_std` does not rely on the Rust standard library and enables compilation to WebAssembly.
 
-Both of these features imply the use of [alloc](https://doc.rust-lang.org/alloc/) to support heap-allocated collections.
+All of these features imply the use of [alloc](https://doc.rust-lang.org/alloc/) to support heap-allocated collections.
 
 To compile with `no_std`, disable default features via `--no-default-features` flag or using the following command:
 

benches/merkle.rs

@@ -0,0 +1,66 @@
+//! Benchmark for building a [`miden_crypto::merkle::MerkleTree`]. This is intended to be compared
+//! with the results from `benches/smt-subtree.rs`, as building a fully balanced Merkle tree with
+//! 256 leaves should indicate the *absolute best* performance we could *possibly* get for building
+//! a depth-8 sparse Merkle subtree, though practically speaking building a fully balanced Merkle
+//! tree will perform better than the sparse version. At the time of this writing (2024/11/24), this
+//! benchmark is about four times more efficient than the equivalent benchmark in
+//! `benches/smt-subtree.rs`.
+use std::{hint, mem, time::Duration};
+
+use criterion::{criterion_group, criterion_main, BatchSize, Criterion};
+use miden_crypto::{merkle::MerkleTree, Felt, Word, ONE};
+use rand_utils::prng_array;
+
+fn balanced_merkle_even(c: &mut Criterion) {
+    c.bench_function("balanced-merkle-even", |b| {
+        b.iter_batched(
+            || {
+                let entries: Vec<Word> =
+                    (0..256).map(|i| [Felt::new(i), ONE, ONE, Felt::new(i)]).collect();
+                assert_eq!(entries.len(), 256);
+                entries
+            },
+            |leaves| {
+                let tree = MerkleTree::new(hint::black_box(leaves)).unwrap();
+                assert_eq!(tree.depth(), 8);
+            },
+            BatchSize::SmallInput,
+        );
+    });
+}
+
+fn balanced_merkle_rand(c: &mut Criterion) {
+    let mut seed = [0u8; 32];
+    c.bench_function("balanced-merkle-rand", |b| {
+        b.iter_batched(
+            || {
+                let entries: Vec<Word> = (0..256).map(|_| generate_word(&mut seed)).collect();
+                assert_eq!(entries.len(), 256);
+                entries
+            },
+            |leaves| {
+                let tree = MerkleTree::new(hint::black_box(leaves)).unwrap();
+                assert_eq!(tree.depth(), 8);
+            },
+            BatchSize::SmallInput,
+        );
+    });
+}
+
+criterion_group! {
+    name = smt_subtree_group;
+    config = Criterion::default()
+        .measurement_time(Duration::from_secs(20))
+        .configure_from_args();
+    targets = balanced_merkle_even, balanced_merkle_rand
+}
+criterion_main!(smt_subtree_group);
+
+// HELPER FUNCTIONS
+// --------------------------------------------------------------------------------------------
+
+fn generate_word(seed: &mut [u8; 32]) -> Word {
+    mem::swap(seed, &mut prng_array(*seed));
+    let nums: [u64; 4] = prng_array(*seed);
+    [Felt::new(nums[0]), Felt::new(nums[1]), Felt::new(nums[2]), Felt::new(nums[3])]
+}

benches/smt-subtree.rs

@@ -0,0 +1,142 @@
+use std::{fmt::Debug, hint, mem, time::Duration};
+
+use criterion::{criterion_group, criterion_main, BatchSize, BenchmarkId, Criterion};
+use miden_crypto::{
+    hash::rpo::RpoDigest,
+    merkle::{build_subtree_for_bench, NodeIndex, SmtLeaf, SubtreeLeaf, SMT_DEPTH},
+    Felt, Word, ONE,
+};
+use rand_utils::prng_array;
+use winter_utils::Randomizable;
+
+const PAIR_COUNTS: [u64; 5] = [1, 64, 128, 192, 256];
+
+fn smt_subtree_even(c: &mut Criterion) {
+    let mut seed = [0u8; 32];
+
+    let mut group = c.benchmark_group("subtree8-even");
+
+    for pair_count in PAIR_COUNTS {
+        let bench_id = BenchmarkId::from_parameter(pair_count);
+        group.bench_with_input(bench_id, &pair_count, |b, &pair_count| {
+            b.iter_batched(
+                || {
+                    // Setup.
+                    let entries: Vec<(RpoDigest, Word)> = (0..pair_count)
+                        .map(|n| {
+                            // A single depth-8 subtree can have a maximum of 255 leaves.
+                            let leaf_index = ((n as f64 / pair_count as f64) * 255.0) as u64;
+                            let key = RpoDigest::new([
+                                generate_value(&mut seed),
+                                ONE,
+                                Felt::new(n),
+                                Felt::new(leaf_index),
+                            ]);
+                            let value = generate_word(&mut seed);
+                            (key, value)
+                        })
+                        .collect();
+
+                    let mut leaves: Vec<_> = entries
+                        .iter()
+                        .map(|(key, value)| {
+                            let leaf = SmtLeaf::new_single(*key, *value);
+                            let col = NodeIndex::from(leaf.index()).value();
+                            let hash = leaf.hash();
+                            SubtreeLeaf { col, hash }
+                        })
+                        .collect();
+                    leaves.sort();
+                    leaves.dedup_by_key(|leaf| leaf.col);
+                    leaves
+                },
+                |leaves| {
+                    // Benchmarked function.
+                    let (subtree, _) = build_subtree_for_bench(
+                        hint::black_box(leaves),
+                        hint::black_box(SMT_DEPTH),
+                        hint::black_box(SMT_DEPTH),
+                    );
+                    assert!(!subtree.is_empty());
+                },
+                BatchSize::SmallInput,
+            );
+        });
+    }
+}
+
+fn smt_subtree_random(c: &mut Criterion) {
+    let mut seed = [0u8; 32];
+
+    let mut group = c.benchmark_group("subtree8-rand");
+
+    for pair_count in PAIR_COUNTS {
+        let bench_id = BenchmarkId::from_parameter(pair_count);
+        group.bench_with_input(bench_id, &pair_count, |b, &pair_count| {
+            b.iter_batched(
+                || {
+                    // Setup.
+                    let entries: Vec<(RpoDigest, Word)> = (0..pair_count)
+                        .map(|i| {
+                            let leaf_index: u8 = generate_value(&mut seed);
+                            let key = RpoDigest::new([
+                                ONE,
+                                ONE,
+                                Felt::new(i),
+                                Felt::new(leaf_index as u64),
+                            ]);
+                            let value = generate_word(&mut seed);
+                            (key, value)
+                        })
+                        .collect();
+
+                    let mut leaves: Vec<_> = entries
+                        .iter()
+                        .map(|(key, value)| {
+                            let leaf = SmtLeaf::new_single(*key, *value);
+                            let col = NodeIndex::from(leaf.index()).value();
+                            let hash = leaf.hash();
+                            SubtreeLeaf { col, hash }
+                        })
+                        .collect();
+                    leaves.sort();
+                    leaves
+                },
+                |leaves| {
+                    let (subtree, _) = build_subtree_for_bench(
+                        hint::black_box(leaves),
+                        hint::black_box(SMT_DEPTH),
+                        hint::black_box(SMT_DEPTH),
+                    );
+                    assert!(!subtree.is_empty());
+                },
+                BatchSize::SmallInput,
+            );
+        });
+    }
+}
+
+criterion_group! {
+    name = smt_subtree_group;
+    config = Criterion::default()
+        .measurement_time(Duration::from_secs(40))
+        .sample_size(60)
+        .configure_from_args();
+    targets = smt_subtree_even, smt_subtree_random
+}
+criterion_main!(smt_subtree_group);
+
+// HELPER FUNCTIONS
+// --------------------------------------------------------------------------------------------
+
+fn generate_value<T: Copy + Debug + Randomizable>(seed: &mut [u8; 32]) -> T {
+    mem::swap(seed, &mut prng_array(*seed));
+    let value: [T; 1] = rand_utils::prng_array(*seed);
+    value[0]
+}
+
+fn generate_word(seed: &mut [u8; 32]) -> Word {
+    mem::swap(seed, &mut prng_array(*seed));
+    let nums: [u64; 4] = prng_array(*seed);
+    [Felt::new(nums[0]), Felt::new(nums[1]), Felt::new(nums[2]), Felt::new(nums[3])]
+}

benches/smt-with-entries.rs

@@ -0,0 +1,71 @@
+use std::{fmt::Debug, hint, mem, time::Duration};
+
+use criterion::{criterion_group, criterion_main, BatchSize, BenchmarkId, Criterion};
+use miden_crypto::{hash::rpo::RpoDigest, merkle::Smt, Felt, Word, ONE};
+use rand_utils::prng_array;
+use winter_utils::Randomizable;
+
+// 2^0, 2^4, 2^8, 2^12, 2^16
+const PAIR_COUNTS: [u64; 6] = [1, 16, 256, 4096, 65536, 1_048_576];
+
+fn smt_with_entries(c: &mut Criterion) {
+    let mut seed = [0u8; 32];
+
+    let mut group = c.benchmark_group("smt-with-entries");
+
+    for pair_count in PAIR_COUNTS {
+        let bench_id = BenchmarkId::from_parameter(pair_count);
+        group.bench_with_input(bench_id, &pair_count, |b, &pair_count| {
+            b.iter_batched(
+                || {
+                    // Setup.
+                    prepare_entries(pair_count, &mut seed)
+                },
+                |entries| {
+                    // Benchmarked function.
+                    Smt::with_entries(hint::black_box(entries)).unwrap();
+                },
+                BatchSize::SmallInput,
+            );
+        });
+    }
+}
+
+criterion_group! {
+    name = smt_with_entries_group;
+    config = Criterion::default()
+        //.measurement_time(Duration::from_secs(960))
+        .measurement_time(Duration::from_secs(60))
+        .sample_size(10)
+        .configure_from_args();
+    targets = smt_with_entries
+}
+criterion_main!(smt_with_entries_group);
+
+// HELPER FUNCTIONS
+// --------------------------------------------------------------------------------------------
+
+fn prepare_entries(pair_count: u64, seed: &mut [u8; 32]) -> Vec<(RpoDigest, [Felt; 4])> {
+    let entries: Vec<(RpoDigest, Word)> = (0..pair_count)
+        .map(|i| {
+            let count = pair_count as f64;
+            let idx = ((i as f64 / count) * (count)) as u64;
+            let key = RpoDigest::new([generate_value(seed), ONE, Felt::new(i), Felt::new(idx)]);
+            let value = generate_word(seed);
+            (key, value)
+        })
+        .collect();
+    entries
+}
+
+fn generate_value<T: Copy + Debug + Randomizable>(seed: &mut [u8; 32]) -> T {
+    mem::swap(seed, &mut prng_array(*seed));
+    let value: [T; 1] = rand_utils::prng_array(*seed);
+    value[0]
+}
+
+fn generate_word(seed: &mut [u8; 32]) -> Word {
+    mem::swap(seed, &mut prng_array(*seed));
+    let nums: [u64; 4] = prng_array(*seed);
+    [Felt::new(nums[0]), Felt::new(nums[1]), Felt::new(nums[2]), Felt::new(nums[3])]
+}

src/merkle/index.rs

@@ -97,6 +97,14 @@ impl NodeIndex {
         self
     }
 
+    /// Returns the parent of the current node. This is the same as [`Self::move_up()`], but returns
+    /// a new value instead of mutating `self`.
+    pub const fn parent(mut self) -> Self {
+        self.depth = self.depth.saturating_sub(1);
+        self.value >>= 1;
+        self
+    }
+
     // PROVIDERS
     // --------------------------------------------------------------------------------------------
 

src/merkle/mod.rs

@@ -21,9 +21,11 @@ mod path;
 pub use path::{MerklePath, RootPath, ValuePath};
 
 mod smt;
+#[cfg(feature = "internal")]
+pub use smt::build_subtree_for_bench;
 pub use smt::{
     LeafIndex, MutationSet, SimpleSmt, Smt, SmtLeaf, SmtLeafError, SmtProof, SmtProofError,
-    SMT_DEPTH, SMT_MAX_DEPTH, SMT_MIN_DEPTH,
+    SubtreeLeaf, SMT_DEPTH, SMT_MAX_DEPTH, SMT_MIN_DEPTH,
 };
 
 mod mmr;

src/merkle/smt/full/mod.rs

@@ -71,12 +71,51 @@ impl Smt {
 
     /// Returns a new [Smt] instantiated with leaves set as specified by the provided entries.
     ///
+    /// If the `concurrent` feature is enabled, this function uses a parallel implementation to
+    /// process the entries efficiently, otherwise it defaults to the sequential implementation.
+    ///
     /// All leaves omitted from the entries list are set to [Self::EMPTY_VALUE].
     ///
     /// # Errors
     /// Returns an error if the provided entries contain multiple values for the same key.
     pub fn with_entries(
         entries: impl IntoIterator<Item = (RpoDigest, Word)>,
+    ) -> Result<Self, MerkleError> {
+        #[cfg(feature = "concurrent")]
+        {
+            let mut seen_keys = BTreeSet::new();
+            let entries: Vec<_> = entries
+                .into_iter()
+                .map(|(key, value)| {
+                    if seen_keys.insert(key) {
+                        Ok((key, value))
+                    } else {
+                        Err(MerkleError::DuplicateValuesForIndex(
+                            LeafIndex::<SMT_DEPTH>::from(key).value(),
+                        ))
+                    }
+                })
+                .collect::<Result<_, _>>()?;
+            if entries.is_empty() {
+                return Ok(Self::default());
+            }
+            <Self as SparseMerkleTree<SMT_DEPTH>>::with_entries_par(entries)
+        }
+        #[cfg(not(feature = "concurrent"))]
+        {
+            Self::with_entries_sequential(entries)
+        }
+    }
+
+    /// Returns a new [Smt] instantiated with leaves set as specified by the provided entries.
+    ///
+    /// This sequential implementation processes entries one at a time to build the tree.
+    /// All leaves omitted from the entries list are set to [Self::EMPTY_VALUE].
+    ///
+    /// # Errors
+    /// Returns an error if the provided entries contain multiple values for the same key.
+    pub fn with_entries_sequential(
+        entries: impl IntoIterator<Item = (RpoDigest, Word)>,
     ) -> Result<Self, MerkleError> {
         // create an empty tree
         let mut tree = Self::new();
@@ -101,6 +140,23 @@ impl Smt {
         Ok(tree)
     }
 
+    /// Returns a new [`Smt`] instantiated from already computed leaves and nodes.
+    ///
+    /// This function performs minimal consistency checking. It is the caller's responsibility to
+    /// ensure the passed arguments are correct and consistent with each other.
+    ///
+    /// # Panics
+    /// With debug assertions on, this function panics if `root` does not match the root node in
+    /// `inner_nodes`.
+    pub fn from_raw_parts(
+        inner_nodes: BTreeMap<NodeIndex, InnerNode>,
+        leaves: BTreeMap<u64, SmtLeaf>,
+        root: RpoDigest,
+    ) -> Self {
+        // Our particular implementation of `from_raw_parts()` never returns `Err`.
+        <Self as SparseMerkleTree<SMT_DEPTH>>::from_raw_parts(inner_nodes, leaves, root).unwrap()
+    }
+
     // PUBLIC ACCESSORS
     // --------------------------------------------------------------------------------------------
 
@@ -260,6 +316,19 @@ impl SparseMerkleTree for Smt {
     const EMPTY_VALUE: Self::Value = EMPTY_WORD;
     const EMPTY_ROOT: RpoDigest = *EmptySubtreeRoots::entry(SMT_DEPTH, 0);
 
+    fn from_raw_parts(
+        inner_nodes: BTreeMap<NodeIndex, InnerNode>,
+        leaves: BTreeMap<u64, SmtLeaf>,
+        root: RpoDigest,
+    ) -> Result<Self, MerkleError> {
+        if cfg!(debug_assertions) {
+            let root_node = inner_nodes.get(&NodeIndex::root()).unwrap();
+            assert_eq!(root_node.hash(), root);
+        }
+
+        Ok(Self { root, inner_nodes, leaves })
+    }
+
     fn root(&self) -> RpoDigest {
         self.root
     }
@@ -344,6 +413,23 @@ impl SparseMerkleTree for Smt {
     fn path_and_leaf_to_opening(path: MerklePath, leaf: SmtLeaf) -> SmtProof {
         SmtProof::new_unchecked(path, leaf)
     }
+
+    fn pairs_to_leaf(mut pairs: Vec<(RpoDigest, Word)>) -> SmtLeaf {
+        assert!(!pairs.is_empty());
+
+        if pairs.len() > 1 {
+            SmtLeaf::new_multiple(pairs).unwrap()
+        } else {
+            let (key, value) = pairs.pop().unwrap();
+            // TODO: should we ever be constructing empty leaves from pairs?
+            if value == Self::EMPTY_VALUE {
+                let index = Self::key_to_leaf_index(&key);
+                SmtLeaf::new_empty(index)
+            } else {
+                SmtLeaf::new_single(key, value)
+            }
+        }
+    }
 }
 
 impl Default for Smt {

src/merkle/smt/mod.rs

@@ -1,4 +1,7 @@
 use alloc::{collections::BTreeMap, vec::Vec};
+use core::mem;
+
+use num::Integer;
 
 use super::{EmptySubtreeRoots, InnerNodeInfo, MerkleError, MerklePath, NodeIndex};
 use crate::{
@@ -62,6 +65,17 @@ pub(crate) trait SparseMerkleTree {
     // PROVIDED METHODS
     // ---------------------------------------------------------------------------------------------
 
+    /// Creates a new sparse Merkle tree from an existing set of key-value pairs, in parallel.
+    #[cfg(feature = "concurrent")]
+    fn with_entries_par(entries: Vec<(Self::Key, Self::Value)>) -> Result<Self, MerkleError>
+    where
+        Self: Sized,
+    {
+        let (inner_nodes, leaves) = Self::build_subtrees(entries);
+        let root = inner_nodes.get(&NodeIndex::root()).unwrap().hash();
+        Self::from_raw_parts(inner_nodes, leaves, root)
+    }
+
     /// Returns an opening of the leaf associated with `key`. Conceptually, an opening is a Merkle
     /// path to the leaf, as well as the leaf itself.
     fn open(&self, key: &Self::Key) -> Self::Opening {
@@ -292,6 +306,16 @@ pub(crate) trait SparseMerkleTree {
     // REQUIRED METHODS
     // ---------------------------------------------------------------------------------------------
 
+    /// Construct this type from already computed leaves and nodes. The caller ensures passed
+    /// arguments are correct and consistent with each other.
+    fn from_raw_parts(
+        inner_nodes: BTreeMap<NodeIndex, InnerNode>,
+        leaves: BTreeMap<u64, Self::Leaf>,
+        root: RpoDigest,
+    ) -> Result<Self, MerkleError>
+    where
+        Self: Sized;
+
     /// The root of the tree
     fn root(&self) -> RpoDigest;
 
@@ -341,18 +365,137 @@ pub(crate) trait SparseMerkleTree {
     /// Maps a key to a leaf index
     fn key_to_leaf_index(key: &Self::Key) -> LeafIndex<DEPTH>;
 
+    /// Constructs a single leaf from an arbitrary amount of key-value pairs.
+    /// Those pairs must all have the same leaf index.
+    fn pairs_to_leaf(pairs: Vec<(Self::Key, Self::Value)>) -> Self::Leaf;
+
     /// Maps a (MerklePath, Self::Leaf) to an opening.
     ///
     /// The length `path` is guaranteed to be equal to `DEPTH`
     fn path_and_leaf_to_opening(path: MerklePath, leaf: Self::Leaf) -> Self::Opening;
+
+    /// Performs the initial transforms for constructing a [`SparseMerkleTree`] by composing
+    /// subtrees. In other words, this function takes the key-value inputs to the tree, and produces
+    /// the inputs to feed into [`build_subtree()`].
+    ///
+    /// `pairs` *must* already be sorted **by leaf index column**, not simply sorted by key. If
+    /// `pairs` is not correctly sorted, the returned computations will be incorrect.
+    ///
+    /// # Panics
+    /// With debug assertions on, this function panics if it detects that `pairs` is not correctly
+    /// sorted. Without debug assertions, the returned computations will be incorrect.
+    fn sorted_pairs_to_leaves(
+        pairs: Vec<(Self::Key, Self::Value)>,
+    ) -> PairComputations<u64, Self::Leaf> {
+        debug_assert!(pairs.is_sorted_by_key(|(key, _)| Self::key_to_leaf_index(key).value()));
+
+        let mut accumulator: PairComputations<u64, Self::Leaf> = Default::default();
+        let mut accumulated_leaves: Vec<SubtreeLeaf> = Vec::with_capacity(pairs.len() / 2);
+
+        // As we iterate, we'll keep track of the kv-pairs we've seen so far that correspond to a
+        // single leaf. When we see a pair that's in a different leaf, we'll swap these pairs
+        // out and store them in our accumulated leaves.
+        let mut current_leaf_buffer: Vec<(Self::Key, Self::Value)> = Default::default();
+
+        let mut iter = pairs.into_iter().peekable();
+        while let Some((key, value)) = iter.next() {
+            let col = Self::key_to_leaf_index(&key).index.value();
+            let peeked_col = iter.peek().map(|(key, _v)| {
+                let index = Self::key_to_leaf_index(key);
+                let next_col = index.index.value();
+                // We panic if `pairs` is not sorted by column.
+                debug_assert!(next_col >= col);
+                next_col
+            });
+            current_leaf_buffer.push((key, value));
+
+            // If the next pair is the same column as this one, then we're done after adding this
+            // pair to the buffer.
+            if peeked_col == Some(col) {
+                continue;
+            }
+
+            // Otherwise, the next pair is a different column, or there is no next pair. Either way
+            // it's time to swap out our buffer.
+            let leaf_pairs = mem::take(&mut current_leaf_buffer);
+            let leaf = Self::pairs_to_leaf(leaf_pairs);
+            let hash = Self::hash_leaf(&leaf);
+
+            accumulator.nodes.insert(col, leaf);
+            accumulated_leaves.push(SubtreeLeaf { col, hash });
+
+            debug_assert!(current_leaf_buffer.is_empty());
+        }
+
+        // TODO: determine is there is any notable performance difference between computing
+        // subtree boundaries after the fact as an iterator adapter (like this), versus computing
+        // subtree boundaries as we go. Either way this function is only used at the beginning of a
+        // parallel construction, so it should not be a critical path.
+        accumulator.leaves = SubtreeLeavesIter::from_leaves(&mut accumulated_leaves).collect();
+        accumulator
+    }
+
+    /// Computes the raw parts for a new sparse Merkle tree from a set of key-value pairs.
+    ///
+    /// `entries` need not be sorted. This function will sort them.
+    #[cfg(feature = "concurrent")]
+    fn build_subtrees(
+        mut entries: Vec<(Self::Key, Self::Value)>,
+    ) -> (BTreeMap<NodeIndex, InnerNode>, BTreeMap<u64, Self::Leaf>) {
+        entries.sort_by_key(|item| {
+            let index = Self::key_to_leaf_index(&item.0);
+            index.value()
+        });
+        Self::build_subtrees_from_sorted_entries(entries)
+    }
+
+    /// Computes the raw parts for a new sparse Merkle tree from a set of key-value pairs.
+    ///
+    /// This function is mostly an implementation detail of
+    /// [`SparseMerkleTree::with_entries_par()`].
+    #[cfg(feature = "concurrent")]
+    fn build_subtrees_from_sorted_entries(
+        entries: Vec<(Self::Key, Self::Value)>,
+    ) -> (BTreeMap<NodeIndex, InnerNode>, BTreeMap<u64, Self::Leaf>) {
+        use rayon::prelude::*;
+
+        let mut accumulated_nodes: BTreeMap<NodeIndex, InnerNode> = Default::default();
+
+        let PairComputations {
+            leaves: mut leaf_subtrees,
+            nodes: initial_leaves,
+        } = Self::sorted_pairs_to_leaves(entries);
+
+        for current_depth in (SUBTREE_DEPTH..=DEPTH).step_by(SUBTREE_DEPTH as usize).rev() {
+            let (nodes, mut subtree_roots): (Vec<BTreeMap<_, _>>, Vec<SubtreeLeaf>) = leaf_subtrees
+                .into_par_iter()
+                .map(|subtree| {
+                    debug_assert!(subtree.is_sorted());
+                    debug_assert!(!subtree.is_empty());
+
+                    let (nodes, subtree_root) = build_subtree(subtree, DEPTH, current_depth);
+                    (nodes, subtree_root)
+                })
+                .unzip();
+
+            leaf_subtrees = SubtreeLeavesIter::from_leaves(&mut subtree_roots).collect();
+            accumulated_nodes.extend(nodes.into_iter().flatten());
+
+            debug_assert!(!leaf_subtrees.is_empty());
+        }
+        (accumulated_nodes, initial_leaves)
+    }
 }
 
 // INNER NODE
 // ================================================================================================
 
+/// This struct is public so functions returning it can be used in `benches/`, but is otherwise not
+/// part of the public API.
+#[doc(hidden)]
 #[derive(Debug, Default, Clone, PartialEq, Eq)]
 #[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
-pub(crate) struct InnerNode {
+pub struct InnerNode {
     pub left: RpoDigest,
     pub right: RpoDigest,
 }
@@ -462,3 +605,197 @@ impl MutationSet {
         self.new_root
     }
 }
+
+// SUBTREES
+// ================================================================================================
+/// A subtree is of depth 8.
+const SUBTREE_DEPTH: u8 = 8;
+
+/// A depth-8 subtree contains 256 "columns" that can possibly be occupied.
+const COLS_PER_SUBTREE: u64 = u64::pow(2, SUBTREE_DEPTH as u32);
+
+/// Helper struct for organizing the data we care about when computing Merkle subtrees.
+///
+/// Note that these represet "conceptual" leaves of some subtree, not necessarily
+/// the leaf type for the sparse Merkle tree.
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Default)]
+pub struct SubtreeLeaf {
+    /// The 'value' field of [`NodeIndex`]. When computing a subtree, the depth is already known.
+    pub col: u64,
+    /// The hash of the node this `SubtreeLeaf` represents.
+    pub hash: RpoDigest,
+}
+
+/// Helper struct to organize the return value of [`SparseMerkleTree::sorted_pairs_to_leaves()`].
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub(crate) struct PairComputations<K, L> {
+    /// Literal leaves to be added to the sparse Merkle tree's internal mapping.
+    pub nodes: BTreeMap<K, L>,
+    /// "Conceptual" leaves that will be used for computations.
+    pub leaves: Vec<Vec<SubtreeLeaf>>,
+}
+
+// Derive requires `L` to impl Default, even though we don't actually need that.
+impl<K, L> Default for PairComputations<K, L> {
+    fn default() -> Self {
+        Self {
+            nodes: Default::default(),
+            leaves: Default::default(),
+        }
+    }
+}
+
+#[derive(Debug)]
+struct SubtreeLeavesIter<'s> {
+    leaves: core::iter::Peekable<alloc::vec::Drain<'s, SubtreeLeaf>>,
+}
+impl<'s> SubtreeLeavesIter<'s> {
+    fn from_leaves(leaves: &'s mut Vec<SubtreeLeaf>) -> Self {
+        // TODO: determine if there is any notable performance difference between taking a Vec,
+        // which many need flattening first, vs storing a `Box<dyn Iterator<Item = SubtreeLeaf>>`.
+        // The latter may have self-referential properties that are impossible to express in purely
+        // safe Rust Rust.
+        Self { leaves: leaves.drain(..).peekable() }
+    }
+}
+impl core::iter::Iterator for SubtreeLeavesIter<'_> {
+    type Item = Vec<SubtreeLeaf>;
+
+    /// Each `next()` collects an entire subtree.
+    fn next(&mut self) -> Option<Vec<SubtreeLeaf>> {
+        let mut subtree: Vec<SubtreeLeaf> = Default::default();
+
+        let mut last_subtree_col = 0;
+
+        while let Some(leaf) = self.leaves.peek() {
+            last_subtree_col = u64::max(1, last_subtree_col);
+            let is_exact_multiple = Integer::is_multiple_of(&last_subtree_col, &COLS_PER_SUBTREE);
+            let next_subtree_col = if is_exact_multiple {
+                u64::next_multiple_of(last_subtree_col + 1, COLS_PER_SUBTREE)
+            } else {
+                last_subtree_col.next_multiple_of(COLS_PER_SUBTREE)
+            };
+
+            last_subtree_col = leaf.col;
+            if leaf.col < next_subtree_col {
+                subtree.push(self.leaves.next().unwrap());
+            } else if subtree.is_empty() {
+                continue;
+            } else {
+                break;
+            }
+        }
+
+        if subtree.is_empty() {
+            debug_assert!(self.leaves.peek().is_none());
+            return None;
+        }
+
+        Some(subtree)
+    }
+}
+
+// HELPER FUNCTIONS
+// ================================================================================================
+
+/// Builds Merkle nodes from a bottom layer of "leaves" -- represented by a horizontal index and
+/// the hash of the leaf at that index. `leaves` *must* be sorted by horizontal index, and
+/// `leaves` must not contain more than one depth-8 subtree's worth of leaves.
+///
+/// This function will then calculate the inner nodes above each leaf for 8 layers, as well as
+/// the "leaves" for the next 8-deep subtree, so this function can effectively be chained into
+/// itself.
+///
+/// # Panics
+/// With debug assertions on, this function panics under invalid inputs: if `leaves` contains
+/// more entries than can fit in a depth-8 subtree, if `leaves` contains leaves belonging to
+/// different depth-8 subtrees, if `bottom_depth` is lower in the tree than the specified
+/// maximum depth (`DEPTH`), or if `leaves` is not sorted.
+fn build_subtree(
+    mut leaves: Vec<SubtreeLeaf>,
+    tree_depth: u8,
+    bottom_depth: u8,
+) -> (BTreeMap<NodeIndex, InnerNode>, SubtreeLeaf) {
+    debug_assert!(bottom_depth <= tree_depth);
+    debug_assert!(Integer::is_multiple_of(&bottom_depth, &SUBTREE_DEPTH));
+    debug_assert!(leaves.len() <= usize::pow(2, SUBTREE_DEPTH as u32));
+    let subtree_root = bottom_depth - SUBTREE_DEPTH;
+    let mut inner_nodes: BTreeMap<NodeIndex, InnerNode> = Default::default();
+    let mut next_leaves: Vec<SubtreeLeaf> = Vec::with_capacity(leaves.len() / 2);
+    for next_depth in (subtree_root..bottom_depth).rev() {
+        debug_assert!(next_depth <= bottom_depth);
+        // `next_depth` is the stuff we're making.
+        // `current_depth` is the stuff we have.
+        let current_depth = next_depth + 1;
+        let mut iter = leaves.drain(..).peekable();
+        while let Some(first) = iter.next() {
+            // On non-continuous iterations, including the first iteration, `first_column` may
+            // be a left or right node. On subsequent continuous iterations, we will always call
+            // `iter.next()` twice.
+            // On non-continuous iterations (including the very first iteration), this column
+            // could be either on the left or the right. If the next iteration is not
+            // discontinuous with our right node, then the next iteration's
+            let is_right = first.col.is_odd();
+            let (left, right) = if is_right {
+                // Discontinuous iteration: we have no left node, so it must be empty.
+                let left = SubtreeLeaf {
+                    col: first.col - 1,
+                    hash: *EmptySubtreeRoots::entry(tree_depth, current_depth),
+                };
+                let right = first;
+                (left, right)
+            } else {
+                let left = first;
+                let right_col = first.col + 1;
+                let right = match iter.peek().copied() {
+                    Some(SubtreeLeaf { col, .. }) if col == right_col => {
+                        // Our inputs must be sorted.
+                        debug_assert!(left.col <= col);
+                        // The next leaf in the iterator is our sibling. Use it and consume it!
+                        iter.next().unwrap()
+                    },
+                    // Otherwise, the leaves don't contain our sibling, so our sibling must be
+                    // empty.
+                    _ => SubtreeLeaf {
+                        col: right_col,
+                        hash: *EmptySubtreeRoots::entry(tree_depth, current_depth),
+                    },
+                };
+                (left, right)
+            };
+            let index = NodeIndex::new_unchecked(current_depth, left.col).parent();
+            let node = InnerNode { left: left.hash, right: right.hash };
+            let hash = node.hash();
+            let &equivalent_empty_hash = EmptySubtreeRoots::entry(tree_depth, next_depth);
+            // If this hash is empty, then it doesn't become a new inner node, nor does it count
+            // as a leaf for the next depth.
+            if hash != equivalent_empty_hash {
+                inner_nodes.insert(index, node);
+                next_leaves.push(SubtreeLeaf { col: index.value(), hash });
+            }
+        }
+        // Stop borrowing `leaves`, so we can swap it.
+        // The iterator is empty at this point anyway.
+        drop(iter);
+        // After each depth, consider the stuff we just made the new "leaves", and empty the
+        // other collection.
+        mem::swap(&mut leaves, &mut next_leaves);
+    }
+    debug_assert_eq!(leaves.len(), 1);
+    let root = leaves.pop().unwrap();
+    (inner_nodes, root)
+}
+
+#[cfg(feature = "internal")]
+pub fn build_subtree_for_bench(
+    leaves: Vec<SubtreeLeaf>,
+    tree_depth: u8,
+    bottom_depth: u8,
+) -> (BTreeMap<NodeIndex, InnerNode>, SubtreeLeaf) {
+    build_subtree(leaves, tree_depth, bottom_depth)
+}
+
+// TESTS
+// ================================================================================================
+#[cfg(test)]
+mod tests;

src/merkle/smt/simple/mod.rs

@@ -1,4 +1,7 @@
-use alloc::collections::{BTreeMap, BTreeSet};
+use alloc::{
+    collections::{BTreeMap, BTreeSet},
+    vec::Vec,
+};
 
 use super::{
     super::ValuePath, EmptySubtreeRoots, InnerNode, InnerNodeInfo, LeafIndex, MerkleError,
@@ -97,6 +100,23 @@ impl SimpleSmt {
         Ok(tree)
     }
 
+    /// Returns a new [`SimpleSmt`] instantiated from already computed leaves and nodes.
+    ///
+    /// This function performs minimal consistency checking. It is the caller's responsibility to
+    /// ensure the passed arguments are correct and consistent with each other.
+    ///
+    /// # Panics
+    /// With debug assertions on, this function panics if `root` does not match the root node in
+    /// `inner_nodes`.
+    pub fn from_raw_parts(
+        inner_nodes: BTreeMap<NodeIndex, InnerNode>,
+        leaves: BTreeMap<u64, Word>,
+        root: RpoDigest,
+    ) -> Self {
+        // Our particular implementation of `from_raw_parts()` never returns `Err`.
+        <Self as SparseMerkleTree<DEPTH>>::from_raw_parts(inner_nodes, leaves, root).unwrap()
+    }
+
     /// Wrapper around [`SimpleSmt::with_leaves`] which inserts leaves at contiguous indices
     /// starting at index 0.
     pub fn with_contiguous_leaves(
@@ -306,6 +326,19 @@ impl SparseMerkleTree for SimpleSmt {
     const EMPTY_VALUE: Self::Value = EMPTY_WORD;
     const EMPTY_ROOT: RpoDigest = *EmptySubtreeRoots::entry(DEPTH, 0);
 
+    fn from_raw_parts(
+        inner_nodes: BTreeMap<NodeIndex, InnerNode>,
+        leaves: BTreeMap<u64, Word>,
+        root: RpoDigest,
+    ) -> Result<Self, MerkleError> {
+        if cfg!(debug_assertions) {
+            let root_node = inner_nodes.get(&NodeIndex::root()).unwrap();
+            assert_eq!(root_node.hash(), root);
+        }
+
+        Ok(Self { root, inner_nodes, leaves })
+    }
+
     fn root(&self) -> RpoDigest {
         self.root
     }
@@ -370,4 +403,11 @@ impl SparseMerkleTree for SimpleSmt {
     fn path_and_leaf_to_opening(path: MerklePath, leaf: Word) -> ValuePath {
         (path, leaf).into()
     }
+
+    fn pairs_to_leaf(mut pairs: Vec<(LeafIndex<DEPTH>, Word)>) -> Word {
+        // SimpleSmt can't have more than one value per key.
+        assert_eq!(pairs.len(), 1);
+        let (_key, value) = pairs.pop().unwrap();
+        value
+    }
 }

src/merkle/smt/tests.rs

@@ -0,0 +1,417 @@
+use alloc::{collections::BTreeMap, vec::Vec};
+
+use super::{
+    build_subtree, InnerNode, LeafIndex, NodeIndex, PairComputations, SmtLeaf, SparseMerkleTree,
+    SubtreeLeaf, SubtreeLeavesIter, COLS_PER_SUBTREE, SUBTREE_DEPTH,
+};
+use crate::{
+    hash::rpo::RpoDigest,
+    merkle::{Smt, SMT_DEPTH},
+    Felt, Word, ONE,
+};
+
+fn smtleaf_to_subtree_leaf(leaf: &SmtLeaf) -> SubtreeLeaf {
+    SubtreeLeaf {
+        col: leaf.index().index.value(),
+        hash: leaf.hash(),
+    }
+}
+
+#[test]
+fn test_sorted_pairs_to_leaves() {
+    let entries: Vec<(RpoDigest, Word)> = vec![
+        // Subtree 0.
+        (RpoDigest::new([ONE, ONE, ONE, Felt::new(16)]), [ONE; 4]),
+        (RpoDigest::new([ONE, ONE, ONE, Felt::new(17)]), [ONE; 4]),
+        // Leaf index collision.
+        (RpoDigest::new([ONE, ONE, Felt::new(10), Felt::new(20)]), [ONE; 4]),
+        (RpoDigest::new([ONE, ONE, Felt::new(20), Felt::new(20)]), [ONE; 4]),
+        // Subtree 1. Normal single leaf again.
+        (RpoDigest::new([ONE, ONE, ONE, Felt::new(400)]), [ONE; 4]), // Subtree boundary.
+        (RpoDigest::new([ONE, ONE, ONE, Felt::new(401)]), [ONE; 4]),
+        // Subtree 2. Another normal leaf.
+        (RpoDigest::new([ONE, ONE, ONE, Felt::new(1024)]), [ONE; 4]),
+    ];
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    let control_leaves: Vec<SmtLeaf> = {
+        let mut entries_iter = entries.iter().cloned();
+        let mut next_entry = || entries_iter.next().unwrap();
+        let control_leaves = vec![
+            // Subtree 0.
+            SmtLeaf::Single(next_entry()),
+            SmtLeaf::Single(next_entry()),
+            SmtLeaf::new_multiple(vec![next_entry(), next_entry()]).unwrap(),
+            // Subtree 1.
+            SmtLeaf::Single(next_entry()),
+            SmtLeaf::Single(next_entry()),
+            // Subtree 2.
+            SmtLeaf::Single(next_entry()),
+        ];
+        assert_eq!(entries_iter.next(), None);
+        control_leaves
+    };
+
+    let control_subtree_leaves: Vec<Vec<SubtreeLeaf>> = {
+        let mut control_leaves_iter = control_leaves.iter();
+        let mut next_leaf = || control_leaves_iter.next().unwrap();
+
+        let control_subtree_leaves: Vec<Vec<SubtreeLeaf>> = [
+            // Subtree 0.
+            vec![next_leaf(), next_leaf(), next_leaf()],
+            // Subtree 1.
+            vec![next_leaf(), next_leaf()],
+            // Subtree 2.
+            vec![next_leaf()],
+        ]
+        .map(|subtree| subtree.into_iter().map(smtleaf_to_subtree_leaf).collect())
+        .to_vec();
+        assert_eq!(control_leaves_iter.next(), None);
+        control_subtree_leaves
+    };
+
+    let subtrees: PairComputations<u64, SmtLeaf> = Smt::sorted_pairs_to_leaves(entries);
+    // This will check that the hashes, columns, and subtree assignments all match.
+    assert_eq!(subtrees.leaves, control_subtree_leaves);
+
+    // Flattening and re-separating out the leaves into subtrees should have the same result.
+    let mut all_leaves: Vec<SubtreeLeaf> = subtrees.leaves.clone().into_iter().flatten().collect();
+    let re_grouped: Vec<Vec<_>> = SubtreeLeavesIter::from_leaves(&mut all_leaves).collect();
+    assert_eq!(subtrees.leaves, re_grouped);
+
+    // Then finally we might as well check the computed leaf nodes too.
+    let control_leaves: BTreeMap<u64, SmtLeaf> = control
+        .leaves()
+        .map(|(index, value)| (index.index.value(), value.clone()))
+        .collect();
+
+    for (column, test_leaf) in subtrees.nodes {
+        if test_leaf.is_empty() {
+            continue;
+        }
+        let control_leaf = control_leaves
+            .get(&column)
+            .unwrap_or_else(|| panic!("no leaf node found for column {column}"));
+        assert_eq!(control_leaf, &test_leaf);
+    }
+}
+
+// Helper for the below tests.
+fn generate_entries(pair_count: u64) -> Vec<(RpoDigest, Word)> {
+    (0..pair_count)
+        .map(|i| {
+            let leaf_index = ((i as f64 / pair_count as f64) * (pair_count as f64)) as u64;
+            let key = RpoDigest::new([ONE, ONE, Felt::new(i), Felt::new(leaf_index)]);
+            let value = [ONE, ONE, ONE, Felt::new(i)];
+            (key, value)
+        })
+        .collect()
+}
+
+#[test]
+fn test_single_subtree() {
+    // A single subtree's worth of leaves.
+    const PAIR_COUNT: u64 = COLS_PER_SUBTREE;
+
+    let entries = generate_entries(PAIR_COUNT);
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    // `entries` should already be sorted by nature of how we constructed it.
+    let leaves = Smt::sorted_pairs_to_leaves(entries).leaves;
+    let leaves = leaves.into_iter().next().unwrap();
+
+    let (first_subtree, subtree_root) = build_subtree(leaves, SMT_DEPTH, SMT_DEPTH);
+    assert!(!first_subtree.is_empty());
+
+    // The inner nodes computed from that subtree should match the nodes in our control tree.
+    for (index, node) in first_subtree.into_iter() {
+        let control = control.get_inner_node(index);
+        assert_eq!(
+            control, node,
+            "subtree-computed node at index {index:?} does not match control",
+        );
+    }
+
+    // The root returned should also match the equivalent node in the control tree.
+    let control_root_index =
+        NodeIndex::new(SMT_DEPTH - SUBTREE_DEPTH, subtree_root.col).expect("Valid root index");
+    let control_root_node = control.get_inner_node(control_root_index);
+    let control_hash = control_root_node.hash();
+    assert_eq!(
+        control_hash, subtree_root.hash,
+        "Subtree-computed root at index {control_root_index:?} does not match control"
+    );
+}
+
+// Test that not just can we compute a subtree correctly, but we can feed the results of one
+// subtree into computing another. In other words, test that `build_subtree()` is correctly
+// composable.
+#[test]
+fn test_two_subtrees() {
+    // Two subtrees' worth of leaves.
+    const PAIR_COUNT: u64 = COLS_PER_SUBTREE * 2;
+
+    let entries = generate_entries(PAIR_COUNT);
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    let PairComputations { leaves, .. } = Smt::sorted_pairs_to_leaves(entries);
+    // With two subtrees' worth of leaves, we should have exactly two subtrees.
+    let [first, second]: [Vec<_>; 2] = leaves.try_into().unwrap();
+    assert_eq!(first.len() as u64, PAIR_COUNT / 2);
+    assert_eq!(first.len(), second.len());
+
+    let mut current_depth = SMT_DEPTH;
+    let mut next_leaves: Vec<SubtreeLeaf> = Default::default();
+
+    let (first_nodes, first_root) = build_subtree(first, SMT_DEPTH, current_depth);
+    next_leaves.push(first_root);
+
+    let (second_nodes, second_root) = build_subtree(second, SMT_DEPTH, current_depth);
+    next_leaves.push(second_root);
+
+    // All new inner nodes + the new subtree-leaves should be 512, for one depth-cycle.
+    let total_computed = first_nodes.len() + second_nodes.len() + next_leaves.len();
+    assert_eq!(total_computed as u64, PAIR_COUNT);
+
+    // Verify the computed nodes of both subtrees.
+    let computed_nodes = first_nodes.clone().into_iter().chain(second_nodes);
+    for (index, test_node) in computed_nodes {
+        let control_node = control.get_inner_node(index);
+        assert_eq!(
+            control_node, test_node,
+            "subtree-computed node at index {index:?} does not match control",
+        );
+    }
+
+    current_depth -= SUBTREE_DEPTH;
+
+    let (nodes, root_leaf) = build_subtree(next_leaves, SMT_DEPTH, current_depth);
+    assert_eq!(nodes.len(), SUBTREE_DEPTH as usize);
+    assert_eq!(root_leaf.col, 0);
+
+    for (index, test_node) in nodes {
+        let control_node = control.get_inner_node(index);
+        assert_eq!(
+            control_node, test_node,
+            "subtree-computed node at index {index:?} does not match control",
+        );
+    }
+
+    let index = NodeIndex::new(current_depth - SUBTREE_DEPTH, root_leaf.col).unwrap();
+    let control_root = control.get_inner_node(index).hash();
+    assert_eq!(control_root, root_leaf.hash, "Root mismatch");
+}
+
+#[test]
+fn test_singlethreaded_subtrees() {
+    const PAIR_COUNT: u64 = COLS_PER_SUBTREE * 64;
+
+    let entries = generate_entries(PAIR_COUNT);
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    let mut accumulated_nodes: BTreeMap<NodeIndex, InnerNode> = Default::default();
+
+    let PairComputations {
+        leaves: mut leaf_subtrees,
+        nodes: test_leaves,
+    } = Smt::sorted_pairs_to_leaves(entries);
+
+    for current_depth in (SUBTREE_DEPTH..=SMT_DEPTH).step_by(SUBTREE_DEPTH as usize).rev() {
+        // There's no flat_map_unzip(), so this is the best we can do.
+        let (nodes, mut subtree_roots): (Vec<BTreeMap<_, _>>, Vec<SubtreeLeaf>) = leaf_subtrees
+            .into_iter()
+            .enumerate()
+            .map(|(i, subtree)| {
+                // Pre-assertions.
+                assert!(
+                    subtree.is_sorted(),
+                    "subtree {i} at bottom-depth {current_depth} is not sorted",
+                );
+                assert!(
+                    !subtree.is_empty(),
+                    "subtree {i} at bottom-depth {current_depth} is empty!",
+                );
+
+                // Do actual things.
+                let (nodes, subtree_root) = build_subtree(subtree, SMT_DEPTH, current_depth);
+
+                // Post-assertions.
+                for (&index, test_node) in nodes.iter() {
+                    let control_node = control.get_inner_node(index);
+                    assert_eq!(
+                        test_node, &control_node,
+                        "depth {} subtree {}: test node does not match control at index {:?}",
+                        current_depth, i, index,
+                    );
+                }
+
+                (nodes, subtree_root)
+            })
+            .unzip();
+
+        // Update state between each depth iteration.
+
+        leaf_subtrees = SubtreeLeavesIter::from_leaves(&mut subtree_roots).collect();
+        accumulated_nodes.extend(nodes.into_iter().flatten());
+
+        assert!(!leaf_subtrees.is_empty(), "on depth {current_depth}");
+    }
+
+    // Make sure the true leaves match, first checking length and then checking each individual
+    // leaf.
+    let control_leaves: BTreeMap<_, _> = control.leaves().collect();
+    let control_leaves_len = control_leaves.len();
+    let test_leaves_len = test_leaves.len();
+    assert_eq!(test_leaves_len, control_leaves_len);
+    for (col, ref test_leaf) in test_leaves {
+        let index = LeafIndex::new_max_depth(col);
+        let &control_leaf = control_leaves.get(&index).unwrap();
+        assert_eq!(test_leaf, control_leaf, "test leaf at column {col} does not match control");
+    }
+
+    // Make sure the inner nodes match, checking length first and then each individual leaf.
+    let control_nodes_len = control.inner_nodes().count();
+    let test_nodes_len = accumulated_nodes.len();
+    assert_eq!(test_nodes_len, control_nodes_len);
+    for (index, test_node) in accumulated_nodes.clone() {
+        let control_node = control.get_inner_node(index);
+        assert_eq!(test_node, control_node, "test node does not match control at {index:?}");
+    }
+
+    // After the last iteration of the above for loop, we should have the new root node actually
+    // in two places: one in `accumulated_nodes`, and the other as the "next leaves" return from
+    // `build_subtree()`. So let's check both!
+
+    let control_root = control.get_inner_node(NodeIndex::root());
+
+    // That for loop should have left us with only one leaf subtree...
+    let [leaf_subtree]: [Vec<_>; 1] = leaf_subtrees.try_into().unwrap();
+    // which itself contains only one 'leaf'...
+    let [root_leaf]: [SubtreeLeaf; 1] = leaf_subtree.try_into().unwrap();
+    // which matches the expected root.
+    assert_eq!(control.root(), root_leaf.hash);
+
+    // Likewise `accumulated_nodes` should contain a node at the root index...
+    assert!(accumulated_nodes.contains_key(&NodeIndex::root()));
+    // and it should match our actual root.
+    let test_root = accumulated_nodes.get(&NodeIndex::root()).unwrap();
+    assert_eq!(control_root, *test_root);
+    // And of course the root we got from each place should match.
+    assert_eq!(control.root(), root_leaf.hash);
+}
+
+/// The parallel version of `test_singlethreaded_subtree()`.
+#[test]
+#[cfg(feature = "concurrent")]
+fn test_multithreaded_subtrees() {
+    use rayon::prelude::*;
+
+    const PAIR_COUNT: u64 = COLS_PER_SUBTREE * 64;
+
+    let entries = generate_entries(PAIR_COUNT);
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    let mut accumulated_nodes: BTreeMap<NodeIndex, InnerNode> = Default::default();
+
+    let PairComputations {
+        leaves: mut leaf_subtrees,
+        nodes: test_leaves,
+    } = Smt::sorted_pairs_to_leaves(entries);
+
+    for current_depth in (SUBTREE_DEPTH..=SMT_DEPTH).step_by(SUBTREE_DEPTH as usize).rev() {
+        let (nodes, mut subtree_roots): (Vec<BTreeMap<_, _>>, Vec<SubtreeLeaf>) = leaf_subtrees
+            .into_par_iter()
+            .enumerate()
+            .map(|(i, subtree)| {
+                // Pre-assertions.
+                assert!(
+                    subtree.is_sorted(),
+                    "subtree {i} at bottom-depth {current_depth} is not sorted",
+                );
+                assert!(
+                    !subtree.is_empty(),
+                    "subtree {i} at bottom-depth {current_depth} is empty!",
+                );
+
+                let (nodes, subtree_root) = build_subtree(subtree, SMT_DEPTH, current_depth);
+
+                // Post-assertions.
+                for (&index, test_node) in nodes.iter() {
+                    let control_node = control.get_inner_node(index);
+                    assert_eq!(
+                        test_node, &control_node,
+                        "depth {} subtree {}: test node does not match control at index {:?}",
+                        current_depth, i, index,
+                    );
+                }
+
+                (nodes, subtree_root)
+            })
+            .unzip();
+
+        leaf_subtrees = SubtreeLeavesIter::from_leaves(&mut subtree_roots).collect();
+        accumulated_nodes.extend(nodes.into_iter().flatten());
+
+        assert!(!leaf_subtrees.is_empty(), "on depth {current_depth}");
+    }
+
+    // Make sure the true leaves match, checking length first and then each individual leaf.
+    let control_leaves: BTreeMap<_, _> = control.leaves().collect();
+    let control_leaves_len = control_leaves.len();
+    let test_leaves_len = test_leaves.len();
+    assert_eq!(test_leaves_len, control_leaves_len);
+    for (col, ref test_leaf) in test_leaves {
+        let index = LeafIndex::new_max_depth(col);
+        let &control_leaf = control_leaves.get(&index).unwrap();
+        assert_eq!(test_leaf, control_leaf);
+    }
+
+    // Make sure the inner nodes match, checking length first and then each individual leaf.
+    let control_nodes_len = control.inner_nodes().count();
+    let test_nodes_len = accumulated_nodes.len();
+    assert_eq!(test_nodes_len, control_nodes_len);
+    for (index, test_node) in accumulated_nodes.clone() {
+        let control_node = control.get_inner_node(index);
+        assert_eq!(test_node, control_node, "test node does not match control at {index:?}");
+    }
+
+    // After the last iteration of the above for loop, we should have the new root node actually
+    // in two places: one in `accumulated_nodes`, and the other as the "next leaves" return from
+    // `build_subtree()`. So let's check both!
+
+    let control_root = control.get_inner_node(NodeIndex::root());
+
+    // That for loop should have left us with only one leaf subtree...
+    let [leaf_subtree]: [_; 1] = leaf_subtrees.try_into().unwrap();
+    // which itself contains only one 'leaf'...
+    let [root_leaf]: [_; 1] = leaf_subtree.try_into().unwrap();
+    // which matches the expected root.
+    assert_eq!(control.root(), root_leaf.hash);
+
+    // Likewise `accumulated_nodes` should contain a node at the root index...
+    assert!(accumulated_nodes.contains_key(&NodeIndex::root()));
+    // and it should match our actual root.
+    let test_root = accumulated_nodes.get(&NodeIndex::root()).unwrap();
+    assert_eq!(control_root, *test_root);
+    // And of course the root we got from each place should match.
+    assert_eq!(control.root(), root_leaf.hash);
+}
+
+#[test]
+#[cfg(feature = "concurrent")]
+fn test_with_entries_parallel() {
+    const PAIR_COUNT: u64 = COLS_PER_SUBTREE * 64;
+
+    let entries = generate_entries(PAIR_COUNT);
+
+    let control = Smt::with_entries_sequential(entries.clone()).unwrap();
+
+    let smt = Smt::with_entries(entries.clone()).unwrap();
+    assert_eq!(smt.root(), control.root());
+    assert_eq!(smt, control);
+}