add some documentation

Author: FrancoGiachetta

src/utils/montgomery.rs

@@ -1,18 +1,18 @@
 //! # Montgomery implementation for Felt252.
-//! 
+//!
 //! This module holds utility functions for performing arithmetic operations
 //! inside the Montgomery space.
-//! 
-//! Representing felts in the Montgomery space allows for optimizations when 
-//! performing multiplication and division operations. This is because it 
-//! avoids having to perform modulo operations and even divisions. Montgomery 
-//! reduces these operations to shifts and simple arithmetic operation such as 
+//!
+//! Representing felts in the Montgomery space allows for optimizations when
+//! performing multiplication and division operations. This is because it
+//! avoids having to perform modulo operations and even divisions. Montgomery
+//! reduces these operations to shifts and simple arithmetic operation such as
 //! additions and subtractions.
-//! 
-//! The way this works is by representing a values as x' = x * r mod n. This 
+//!
+//! The way this works is by representing a values as x' = x * r mod n. This
 //! introduces a new constant `r` which, for performance reasons, it is defined
 //! as r = 2^{k} where k should be big enough to satisfy r > n.
-//! 
+//!
 //! For more information on check: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication.
 
 use std::sync::LazyLock;
@@ -31,14 +31,15 @@ use starknet_types_core::felt::Felt;
 
 // R parameter for felts. R = 2^{256} which is the smallets power of 2 greater than prime.
 pub static MONTY_R: LazyLock<BigUint> = LazyLock::new(|| BigUint::from(1u64) << 256);
-// R2 parameter for felts. R2 = 2^{256 * 2} mod prime. 
+// R2 parameter for felts. R2 = 2^{256 * 2} mod prime. This value is a U256 instead of a 
+// BigUint to integrate with lambdaworks with ease.
 pub static MONTY_R2: LazyLock<U256> = LazyLock::new(|| {
     UnsignedInteger::from_hex_unchecked(
         "7FFD4AB5E008810FFFFFFFFFF6F800000000001330FFFFFFFFFFD737E000401",
     )
 });
 // MU parameter for felts. MU = -prime^{-1} mod 2^{64}. The variant is used to
-// allow a better integration with lambdaworks. 
+// allow a better integration with lambdaworks.
 // Check: https://github.com/lambdaclass/lambdaworks/blob/main/crates/math/src/field/fields/montgomery_backed_prime_fields.rs#L60
 pub const MONTY_MU_U64: u64 = 18446744073709551615;
 // MU parameter for felts. MU = prime^{-1} mod R.