use ark_ff::{
    biginteger::BigInteger768 as BigInteger,
    field_new,
    fields::fp3::{Fp3, Fp3Parameters},
};

use crate::Fq;

pub type Fq3 = Fp3<Fq3Parameters>;

pub struct Fq3Parameters;

impl Fp3Parameters for Fq3Parameters {
    type Fp = Fq;

    /// NONRESIDUE = -4
    // Fq3 = Fq[u]/u^3+4
    #[rustfmt::skip]
    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
        0xe12e00000001e9c2,
        0x63c1e3faa001cd69,
        0xb1b4384fcbe29cf6,
        0xc79630bc713d5a1d,
        0x30127ac071851e2d,
        0x0979f350dcd36af1,
        0x6a66defed8b361f2,
        0x53abac78b24d4e23,
        0xb7ab89dede485a92,
        0x5c3a0745675e8452,
        0x446f17918c5f5700,
        0xfdf24e3267fa1e,
    ]));

    // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
    const TWO_ADICITY: u32 = 1;

    // (T-1)/2 with T = (MODULUS^3-1) / 2^TWO_ADICITY
    #[rustfmt::skip]
    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
        0xb5e7c000000a3eac,
        0xf79b99dbf41cf4ab,
        0xe9372b1919e55ee5,
        0xbb7bbc4936c1980b,
        0x7c0cb9d4399b36e1,
        0x73304a5507bb1ae0,
        0x92f639be8963936f,
        0x4f574ac2439ba816,
        0x670d9bd389dd29ef,
        0x606ddf900d2124f1,
        0x928fb14985ec3270,
        0x6b2f2428c5f420f3,
        0xac9ade29d5ab5fbe,
        0xec0d0434c4005822,
        0x973f10d7f3c5c108,
        0x6d5e83fc81095979,
        0xdac3e6e4e1647752,
        0x227febf93994603e,
        0x4ab8755d894167d1,
        0x4fd2d3f67d8b537a,
        0x33e196a4d5f4030a,
        0x88b51fb72092df1a,
        0xa67e5b1e8fc48316,
        0xb0855eb2a00d7dab,
        0xe875dd2da6751442,
        0x777594a243e25676,
        0x294e0f70376a85a8,
        0x83f431c7988e4f18,
        0x8e8fb6af3ca2f5f1,
        0x7297896b4b9e90f1,
        0xff38f54664d66123,
        0xb5ecf80bfff41e13,
        0x1662a3666bb8392a,
        0x07a0968e8742d3e1,
        0xf12927e564bcdfdc,
        0x5de9825a0e,
    ];

    // NONRESIDUE^T % q
    #[rustfmt::skip]
    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
        field_new!(Fq, BigInteger([
            0xf29a000000007ab6,
            0x8c391832e000739b,
            0x77738a6b6870f959,
            0xbe36179047832b03,
            0x84f3089e56574722,
            0xc5a3614ac0b1d984,
            0x5c81153f4906e9fe,
            0x4d28be3a9f55c815,
            0xd72c1d6f77d5f5c5,
            0x73a18e069ac04458,
            0xf9dfaa846595555f,
            0xd0f0a60a5be58c,
        ])),
        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
    );

    // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
        field_new!(Fq, BigInteger([
            0x0202ffffffff85d5,
            0x5a5826358fff8ce7,
            0x9e996e43827faade,
            0xda6aff320ee47df4,
            0xece9cb3e1d94b80b,
            0xc0e667a25248240b,
            0xa74da5bfdcad3905,
            0x2352e7fe462f2103,
            0x7b56588008b1c87c,
            0x45848a63e711022f,
            0xd7a81ebb9f65a9df,
            0x51f77ef127e87d,
        ])),
        field_new!(Fq, BigInteger([
            0x7f96b51bd840c549,
            0xd59782096496171f,
            0x49b046fd9ce14bbc,
            0x4b6163bba7527a56,
            0xef6c92fb771d59f1,
            0x0425bedbac1dfdc7,
            0xd3ac39de759c0ffd,
            0x9f43ed0e063a81d0,
            0x5bd7d20b4f9a3ce2,
            0x0411f03c36cf5c3c,
            0x2d658fd49661c472,
            0x1100249ae760b93,
        ])),
        field_new!(Fq, BigInteger([
            0x67a04ae427bfb5f8,
            0x9d32d491eb6a5cff,
            0x43d03c1cb68051d4,
            0x0b75ca96f69859a5,
            0x0763497f5325ec60,
            0x48076b5c278dd94d,
            0x8ca3965ff91efd06,
            0x1e6077657ea02f5d,
            0xcdd6c153a8c37724,
            0x28b5b634e5c22ea4,
            0x9e01e3efd42e902c,
            0xe3d6815769a804,

        ])),
    ];

    // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
        field_new!(Fq, BigInteger([
            0x0202ffffffff85d5,
            0x5a5826358fff8ce7,
            0x9e996e43827faade,
            0xda6aff320ee47df4,
            0xece9cb3e1d94b80b,
            0xc0e667a25248240b,
            0xa74da5bfdcad3905,
            0x2352e7fe462f2103,
            0x7b56588008b1c87c,
            0x45848a63e711022f,
            0xd7a81ebb9f65a9df,
            0x51f77ef127e87d,
        ])),
        field_new!(Fq, BigInteger([
            0x67a04ae427bfb5f8,
            0x9d32d491eb6a5cff,
            0x43d03c1cb68051d4,
            0x0b75ca96f69859a5,
            0x0763497f5325ec60,
            0x48076b5c278dd94d,
            0x8ca3965ff91efd06,
            0x1e6077657ea02f5d,
            0xcdd6c153a8c37724,
            0x28b5b634e5c22ea4,
            0x9e01e3efd42e902c,
            0xe3d6815769a804,
        ])),
        field_new!(Fq, BigInteger([
            0x7f96b51bd840c549,
            0xd59782096496171f,
            0x49b046fd9ce14bbc,
            0x4b6163bba7527a56,
            0xef6c92fb771d59f1,
            0x0425bedbac1dfdc7,
            0xd3ac39de759c0ffd,
            0x9f43ed0e063a81d0,
            0x5bd7d20b4f9a3ce2,
            0x0411f03c36cf5c3c,
            0x2d658fd49661c472,
            0x1100249ae760b93,
        ])),
    ];

    #[inline(always)]
    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
        let original = -(*fe);
        let double = original + &original;
        double + &double
    }
}