feat: add simple sparse merkle tree

This commit moves the previous implementation of `SparseMerkleTree` from
miden-core to this crate.

It also include a couple of new tests, a bench suite, and a couple of
minor fixes. The original API was preserved to maintain compatibility
with `AdviceTape`.

closes #21

src/merkle/mod.rs

@@ -1,8 +1,9 @@
 use super::{
-    hash::rpo::{Rpo256, RpoDigest as Digest},
+    hash::rpo::{Rpo256, RpoDigest},
     utils::collections::{BTreeMap, Vec},
     Felt, Word, ZERO,
 };
+use core::fmt;
 
 mod merkle_tree;
 pub use merkle_tree::MerkleTree;
@@ -10,20 +11,51 @@ pub use merkle_tree::MerkleTree;
 mod merkle_path_set;
 pub use merkle_path_set::MerklePathSet;
 
+mod simple_smt;
+pub use simple_smt::SimpleSmt;
+
 // ERRORS
 // ================================================================================================
 
 #[derive(Clone, Debug)]
 pub enum MerkleError {
-    DepthTooSmall,
+    DepthTooSmall(u32),
     DepthTooBig(u32),
     NumLeavesNotPowerOfTwo(usize),
     InvalidIndex(u32, u64),
     InvalidDepth(u32, u32),
     InvalidPath(Vec<Word>),
+    InvalidEntriesCount(usize, usize),
     NodeNotInSet(u64),
 }
 
+impl fmt::Display for MerkleError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        use MerkleError::*;
+        match self {
+            DepthTooSmall(depth) => write!(f, "the provided depth {depth} is too small"),
+            DepthTooBig(depth) => write!(f, "the provided depth {depth} is too big"),
+            NumLeavesNotPowerOfTwo(leaves) => {
+                write!(f, "the leaves count {leaves} is not a power of 2")
+            }
+            InvalidIndex(depth, index) => write!(
+                f,
+                "the leaf index {index} is not valid for the depth {depth}"
+            ),
+            InvalidDepth(expected, provided) => write!(
+                f,
+                "the provided depth {provided} is not valid for {expected}"
+            ),
+            InvalidPath(_path) => write!(f, "the provided path is not valid"),
+            InvalidEntriesCount(max, provided) => write!(f, "the provided number of entries is {provided}, but the maximum for the given depth is {max}"),
+            NodeNotInSet(index) => write!(f, "the node indexed by {index} is not in the set"),
+        }
+    }
+}
+
+#[cfg(feature = "std")]
+impl std::error::Error for MerkleError {}
+
 // HELPER FUNCTIONS
 // ================================================================================================