stwo 1.0.0

use core::fmt::{Debug, Display};
use core::ops::{
    Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign,
};

use serde::{Deserialize, Serialize};

use super::{ComplexConjugate, FieldExpOps};
use crate::core::fields::cm31::CM31;
use crate::core::fields::m31::M31;
use crate::{impl_extension_field, impl_field};

pub const P4: u128 = 21267647892944572736998860269687930881; // (2 ** 31 - 1) ** 4
pub const R: CM31 = CM31::from_u32_unchecked(2, 1);

/// Extension field of CM31.
/// Equivalent to CM31\[x\] over (x^2 - 2 - i) as the irreducible polynomial.
/// Represented as ((a, b), (c, d)) of (a + bi) + (c + di)u.
#[derive(Copy, Clone, Default, PartialEq, Eq, PartialOrd, Ord, Hash, Deserialize, Serialize)]
pub struct QM31(pub CM31, pub CM31);
pub type SecureField = QM31;

pub const SECURE_EXTENSION_DEGREE: usize =
    <SecureField as ExtensionOf<super::m31::BaseField>>::EXTENSION_DEGREE;

impl_field!(QM31, P4);
impl_extension_field!(QM31, CM31);

impl QM31 {
    pub const fn from_u32_unchecked(a: u32, b: u32, c: u32, d: u32) -> Self {
        Self(
            CM31::from_u32_unchecked(a, b),
            CM31::from_u32_unchecked(c, d),
        )
    }

    pub const fn from_m31(a: M31, b: M31, c: M31, d: M31) -> Self {
        Self(CM31::from_m31(a, b), CM31::from_m31(c, d))
    }

    pub const fn from_m31_array(array: [M31; SECURE_EXTENSION_DEGREE]) -> Self {
        Self::from_m31(array[0], array[1], array[2], array[3])
    }

    pub const fn to_m31_array(self) -> [M31; SECURE_EXTENSION_DEGREE] {
        [self.0 .0, self.0 .1, self.1 .0, self.1 .1]
    }

    /// Returns the combined value, given the values of its composing base field polynomials at that
    /// point.
    pub fn from_partial_evals(evals: [Self; SECURE_EXTENSION_DEGREE]) -> Self {
        let mut res = evals[0];
        res += evals[1] * Self::from_u32_unchecked(0, 1, 0, 0);
        res += evals[2] * Self::from_u32_unchecked(0, 0, 1, 0);
        res += evals[3] * Self::from_u32_unchecked(0, 0, 0, 1);
        res
    }

    // Note: Adding this as a Mul impl drives rust insane, and it tries to infer Qm31*Qm31 as
    // QM31*CM31.
    pub fn mul_cm31(self, rhs: CM31) -> Self {
        Self(self.0 * rhs, self.1 * rhs)
    }
}

impl Display for QM31 {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        write!(f, "({}) + ({})u", self.0, self.1)
    }
}

impl Debug for QM31 {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        write!(f, "({}) + ({})u", self.0, self.1)
    }
}

impl Mul for QM31 {
    type Output = Self;

    fn mul(self, rhs: Self) -> Self::Output {
        // (a + bu) * (c + du) = (ac + rbd) + (ad + bc)u.
        Self(
            self.0 * rhs.0 + R * self.1 * rhs.1,
            self.0 * rhs.1 + self.1 * rhs.0,
        )
    }
}

impl From<usize> for QM31 {
    fn from(value: usize) -> Self {
        M31::from(value).into()
    }
}

impl From<u32> for QM31 {
    fn from(value: u32) -> Self {
        M31::from(value).into()
    }
}

impl From<i32> for QM31 {
    fn from(value: i32) -> Self {
        M31::from(value).into()
    }
}

impl TryInto<M31> for QM31 {
    type Error = ();

    fn try_into(self) -> Result<M31, Self::Error> {
        if self.1 != CM31::zero() {
            return Err(());
        }
        self.0.try_into()
    }
}

impl FieldExpOps for QM31 {
    fn inverse(&self) -> Self {
        assert!(!self.is_zero(), "0 has no inverse");
        // (a + bu)^-1 = (a - bu) / (a^2 - (2+i)b^2).
        let b2 = self.1.square();
        let ib2 = CM31(-b2.1, b2.0);
        let denom = self.0.square() - (b2 + b2 + ib2);
        let denom_inverse = denom.inverse();
        Self(self.0 * denom_inverse, -self.1 * denom_inverse)
    }
}

#[cfg(test)]
#[macro_export]
macro_rules! qm31 {
    ($m0:expr, $m1:expr, $m2:expr, $m3:expr) => {{
        use $crate::core::fields::qm31::QM31;
        QM31::from_u32_unchecked($m0, $m1, $m2, $m3)
    }};
}

#[cfg(test)]
mod tests {
    use num_traits::One;

    use super::QM31;
    use crate::core::fields::m31::P;
    use crate::core::fields::FieldExpOps;
    use crate::m31;

    #[test]
    fn test_inverse() {
        let qm = qm31!(1, 2, 3, 4);
        let qm_inv = qm.inverse();
        assert_eq!(qm * qm_inv, QM31::one());
    }

    #[test]
    fn test_ops() {
        let qm0 = qm31!(1, 2, 3, 4);
        let qm1 = qm31!(4, 5, 6, 7);
        let m = m31!(8);
        let qm = QM31::from(m);
        let qm0_x_qm1 = qm31!(P - 71, 93, P - 16, 50);

        assert_eq!(qm0 + qm1, qm31!(5, 7, 9, 11));
        assert_eq!(qm1 + m, qm1 + qm);
        assert_eq!(qm0 * qm1, qm0_x_qm1);
        assert_eq!(qm1 * m, qm1 * qm);
        assert_eq!(-qm0, qm31!(P - 1, P - 2, P - 3, P - 4));
        assert_eq!(qm0 - qm1, qm31!(P - 3, P - 3, P - 3, P - 3));
        assert_eq!(qm1 - m, qm1 - qm);
        assert_eq!(qm0_x_qm1 / qm1, qm31!(1, 2, 3, 4));
        assert_eq!(qm1 / m, qm1 / qm);
    }
}