add prime field for stark101 tutorial (#875)

Co-authored-by: Diego K <[email protected]>

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

@@ -2,6 +2,8 @@
 pub mod babybear;
 /// Implemenation of the quadratic extension of the babybear field
 pub mod quadratic_babybear;
+/// Implementation of the prime field used in [Stark101](https://starkware.co/stark-101/) tutorial, p = 3 * 2^30 + 1
+pub mod stark_101_prime_field;
 /// Implementation of two-adic prime field over 256 bit unsigned integers.
 pub mod stark_252_prime_field;
 /// Implemenation of the Goldilocks Prime Field p = 2^64 - 2^32 + 1

math/src/field/fields/fft_friendly/stark_101_prime_field.rs

@@ -0,0 +1,113 @@
+use crate::{
+    field::{
+        element::FieldElement,
+        fields::montgomery_backed_prime_fields::{IsModulus, U64PrimeField},
+        traits::IsFFTField,
+    },
+    unsigned_integer::element::{UnsignedInteger, U64},
+};
+
+#[derive(Clone, Debug, Hash, Copy)]
+pub struct MontgomeryConfigStark101PrimeField;
+impl IsModulus<U64> for MontgomeryConfigStark101PrimeField {
+    /// 3 * 2^30 + 1
+    const MODULUS: U64 = U64::from_hex_unchecked("c0000001");
+}
+
+pub type Stark101PrimeField = U64PrimeField<MontgomeryConfigStark101PrimeField>;
+
+impl IsFFTField for Stark101PrimeField {
+    const TWO_ADICITY: u64 = 30;
+
+    const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: U64 = UnsignedInteger::from_hex_unchecked("bb6e79d");
+
+    fn field_name() -> &'static str {
+        "stark101"
+    }
+}
+
+impl FieldElement<Stark101PrimeField> {
+    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()
+    }
+}
+
+#[allow(clippy::non_canonical_partial_ord_impl)]
+impl PartialOrd for FieldElement<Stark101PrimeField> {
+    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
+        self.representative().partial_cmp(&other.representative())
+    }
+}
+
+impl Ord for FieldElement<Stark101PrimeField> {
+    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
+        self.representative().cmp(&other.representative())
+    }
+}
+
+#[cfg(test)]
+mod test_stark101_prime_field {
+    use super::Stark101PrimeField;
+    use crate::{
+        field::{element::FieldElement, traits::IsFFTField},
+        traits::ByteConversion,
+    };
+
+    #[test]
+    fn two_adic_order() {
+        let w = FieldElement::<Stark101PrimeField>::from(
+            Stark101PrimeField::TWO_ADIC_PRIMITVE_ROOT_OF_UNITY.limbs[0],
+        );
+
+        assert_eq!(
+            w.pow(1u64 << Stark101PrimeField::TWO_ADICITY),
+            FieldElement::one()
+        );
+        assert_ne!(
+            w.pow(1u64 << (Stark101PrimeField::TWO_ADICITY >> 1)),
+            FieldElement::one()
+        );
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn byte_serialization_for_a_number_matches_with_byte_conversion_implementation_le() {
+        let element = FieldElement::<Stark101PrimeField>::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 = "alloc")]
+    fn byte_serialization_for_a_number_matches_with_byte_conversion_implementation_be() {
+        let element = FieldElement::<Stark101PrimeField>::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::<Stark101PrimeField>::from_hex_unchecked("7654321076543210");
+        let bytes = element.to_bytes_le();
+        let from_bytes = FieldElement::<Stark101PrimeField>::from_bytes_le(&bytes).unwrap();
+        assert_eq!(element, from_bytes);
+    }
+
+    #[test]
+
+    fn byte_serialization_and_deserialization_works_be() {
+        let element = FieldElement::<Stark101PrimeField>::from_hex_unchecked("7654321076543210");
+        let bytes = element.to_bytes_be();
+        let from_bytes = FieldElement::<Stark101PrimeField>::from_bytes_be(&bytes).unwrap();
+        assert_eq!(element, from_bytes);
+    }
+}