chore(Internal): Remove the superseded cmp_keys (#902)

This function was superseded by the change in #847 to have `Word`
compare lexicographically. This commit removes the last few uses and
replaces them with calls to the `Ord` implementation for `Word` instead,
simplifying the codebase.

Author: iamrecursion

miden-crypto/src/merkle/smt/full/concurrent/mod.rs

@@ -6,7 +6,7 @@ use p3_maybe_rayon::prelude::*;
 
 use super::{
     EmptySubtreeRoots, InnerNode, InnerNodes, Leaves, MerkleError, MutationSet, NodeIndex,
-    SMT_DEPTH, Smt, SmtLeaf, SparseMerkleTree, Word, leaf,
+    SMT_DEPTH, Smt, SmtLeaf, SparseMerkleTree, Word,
 };
 use crate::merkle::smt::{Map, NodeMutation, NodeMutations, SmtLeafError};
 
@@ -279,7 +279,7 @@ impl Smt {
         assert!(!pairs.is_empty());
 
         if pairs.len() > 1 {
-            pairs.sort_by(|(key_1, _), (key_2, _)| leaf::cmp_keys(*key_1, *key_2));
+            pairs.sort_by(|(key_1, _), (key_2, _)| key_1.cmp(key_2));
             // Check for duplicates in a sorted list by comparing adjacent pairs
             Self::check_for_duplicate_keys(&pairs)?;
             Ok(Some(SmtLeaf::new_multiple(pairs).unwrap()))

miden-crypto/src/merkle/smt/full/leaf.rs

@@ -1,5 +1,4 @@
 use alloc::{string::ToString, vec::Vec};
-use core::cmp::Ordering;
 
 use super::EMPTY_WORD;
 use crate::{
@@ -314,13 +313,13 @@ impl SmtLeaf {
                     // This stays within MAX_LEAF_ENTRIES limit. We're only adding one entry to a
                     // single leaf
                     let mut pairs = vec![*kv_pair, (key, value)];
-                    pairs.sort_by(|(key_1, _), (key_2, _)| cmp_keys(*key_1, *key_2));
+                    pairs.sort_by(|(key_1, _), (key_2, _)| key_1.cmp(key_2));
                     *self = SmtLeaf::Multiple(pairs);
                     Ok(None)
                 }
             },
             SmtLeaf::Multiple(kv_pairs) => {
-                match kv_pairs.binary_search_by(|kv_pair| cmp_keys(kv_pair.0, key)) {
+                match kv_pairs.binary_search_by(|kv_pair| kv_pair.0.cmp(&key)) {
                     Ok(pos) => {
                         let old_value = kv_pairs[pos].1;
                         kv_pairs[pos].1 = value;
@@ -363,7 +362,7 @@ impl SmtLeaf {
                 }
             },
             SmtLeaf::Multiple(kv_pairs) => {
-                match kv_pairs.binary_search_by(|kv_pair| cmp_keys(kv_pair.0, key)) {
+                match kv_pairs.binary_search_by(|kv_pair| kv_pair.0.cmp(&key)) {
                     Ok(pos) => {
                         let old_value = kv_pairs[pos].1;
 
@@ -439,17 +438,3 @@ pub(crate) fn kv_to_elements((key, value): (Word, Word)) -> impl Iterator<Item =
 
     key_elements.chain(value_elements)
 }
-
-/// Compares two keys, compared element-by-element using their integer representations starting with
-/// the most significant element.
-pub(crate) fn cmp_keys(key_1: Word, key_2: Word) -> Ordering {
-    for (v1, v2) in key_1.iter().zip(key_2.iter()).rev() {
-        let v1 = (*v1).as_canonical_u64();
-        let v2 = (*v2).as_canonical_u64();
-        if v1 != v2 {
-            return v1.cmp(&v2);
-        }
-    }
-
-    Ordering::Equal
-}