Add Babybear field (#549)

* starting with babybear field and add function

* implemented all traits for babybear

* added test for the babybear field

* Babybear field from MontgomeryBackendPrimeField

* added tests to babybear.rs

* added requested changes and isFFTField trait

* ran `cargo fmt` to pass the lint check.

* deleted the isFFTField trait implementation

* deleted .vscode directory

math/src/field/fields/fft_friendly/babybear.rs

@@ -0,0 +1,101 @@
+use crate::{
+    field::{
+        element::FieldElement,
+        fields::montgomery_backed_prime_fields::{IsModulus, MontgomeryBackendPrimeField},
+    },
+    unsigned_integer::element::U64,
+};
+
+pub type U64MontgomeryBackendPrimeField<T> = MontgomeryBackendPrimeField<T, 1>;
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct MontgomeryConfigBabybear31PrimeField;
+impl IsModulus<U64> for MontgomeryConfigBabybear31PrimeField {
+    //Babybear Prime p = 2^31 - 2^27 + 1 = 0x78000001
+    const MODULUS: U64 = U64::from_u64(2013265921);
+}
+
+pub type Babybear31PrimeField =
+    U64MontgomeryBackendPrimeField<MontgomeryConfigBabybear31PrimeField>;
+
+impl FieldElement<Babybear31PrimeField> {
+    pub fn to_bytes_le(&self) -> [u8; 8] {
+        let limbs = self.representative().limbs;
+        limbs[0].to_le_bytes()
+    }
+
+    pub fn to_bytes_be(&self) -> [u8; 8] {
+        let limbs = self.representative().limbs;
+        limbs[0].to_be_bytes()
+    }
+}
+
+impl PartialOrd for FieldElement<Babybear31PrimeField> {
+    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
+        self.representative().partial_cmp(&other.representative())
+    }
+}
+
+impl Ord for FieldElement<Babybear31PrimeField> {
+    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
+        self.representative().cmp(&other.representative())
+    }
+}
+
+#[cfg(test)]
+mod test_babybear_31_bytes_ops {
+    use super::Babybear31PrimeField;
+    use crate::{field::element::FieldElement, traits::ByteConversion};
+
+    #[test]
+    #[cfg(feature = "std")]
+    fn byte_serialization_for_a_number_matches_with_byte_conversion_implementation_le() {
+        let element = FieldElement::<Babybear31PrimeField>::from_hex_unchecked(
+            "\
+            0123456701234567\
+        ",
+        );
+        let bytes = element.to_bytes_le();
+        let expected_bytes: [u8; 8] = ByteConversion::to_bytes_le(&element).try_into().unwrap();
+        assert_eq!(bytes, expected_bytes);
+    }
+
+    #[test]
+    #[cfg(feature = "std")]
+    fn byte_serialization_for_a_number_matches_with_byte_conversion_implementation_be() {
+        let element = FieldElement::<Babybear31PrimeField>::from_hex_unchecked(
+            "\
+            0123456701234567\
+        ",
+        );
+        let bytes = element.to_bytes_be();
+        let expected_bytes: [u8; 8] = ByteConversion::to_bytes_be(&element).try_into().unwrap();
+        assert_eq!(bytes, expected_bytes);
+    }
+
+    #[test]
+
+    fn byte_serialization_and_deserialization_works_le() {
+        let element = FieldElement::<Babybear31PrimeField>::from_hex_unchecked(
+            "\
+            7654321076543210\
+        ",
+        );
+        let bytes = element.to_bytes_le();
+        let from_bytes = FieldElement::<Babybear31PrimeField>::from_bytes_le(&bytes).unwrap();
+        assert_eq!(element, from_bytes);
+    }
+
+    #[test]
+
+    fn byte_serialization_and_deserialization_works_be() {
+        let element = FieldElement::<Babybear31PrimeField>::from_hex_unchecked(
+            "\
+            7654321076543210\
+        ",
+        );
+        let bytes = element.to_bytes_be();
+        let from_bytes = FieldElement::<Babybear31PrimeField>::from_bytes_be(&bytes).unwrap();
+        assert_eq!(element, from_bytes);
+    }
+}

math/src/field/fields/fft_friendly/mod.rs

@@ -1,2 +1,4 @@
+/// Implemenation of the Babybear Prime field p = 2^31 - 2^27 + 1
+pub mod babybear;
 /// Implementation of two-adic prime field over 256 bit unsigned integers.
 pub mod stark_252_prime_field;

math/src/unsigned_integer/element.rs

@@ -22,6 +22,7 @@ use core::fmt::{self, Debug, Display};
 pub type U384 = UnsignedInteger<6>;
 pub type U256 = UnsignedInteger<4>;
 pub type U128 = UnsignedInteger<2>;
+pub type U64 = UnsignedInteger<1>;
 
 /// A big unsigned integer in base 2^{64} represented
 /// as fixed-size array `limbs` of `u64` components.