use crate::*;
use ark_ec::{
    bls12,
    bls12::Bls12Parameters,
    models::{ModelParameters, SWModelParameters},
    short_weierstrass_jacobian::GroupAffine,
    AffineCurve, ProjectiveCurve,
};
use ark_ff::{biginteger::BigInteger256, field_new, Zero};
use ark_std::ops::Neg;

pub type G1Affine = bls12::G1Affine<crate::Parameters>;
pub type G1Projective = bls12::G1Projective<crate::Parameters>;

#[derive(Clone, Default, PartialEq, Eq)]
pub struct Parameters;

impl ModelParameters for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
}

impl SWModelParameters for Parameters {
    /// COEFF_A = 0
    const COEFF_A: Fq = field_new!(Fq, "0");

    /// COEFF_B = 4
    #[rustfmt::skip]
    const COEFF_B: Fq = field_new!(Fq, "4");

    /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
    const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
    #[rustfmt::skip]
    const COFACTOR_INV: Fr = field_new!(Fr, "52435875175126190458656871551744051925719901746859129887267498875565241663483");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
        (G1_GENERATOR_X, G1_GENERATOR_Y);

    #[inline(always)]
    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }

    fn is_in_correct_subgroup_assuming_on_curve(p: &GroupAffine<Parameters>) -> bool {
        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
        //
        // Check that endomorphism_p(P) == -[X^2]P

        let x = BigInteger256::new([crate::Parameters::X[0], 0, 0, 0]);

        // An early-out optimization described in Section 6.
        // If uP == P but P != point of infinity, then the point is not in the right subgroup.
        let x_times_p = p.mul(x);
        if x_times_p.eq(p) && !p.infinity {
            return false;
        }

        let minus_x_squared_times_p = x_times_p.mul(x).neg();
        let endomorphism_p = endomorphism(p);
        minus_x_squared_times_p.eq(&endomorphism_p)
    }
}

/// G1_GENERATOR_X =
/// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
#[rustfmt::skip]
pub const G1_GENERATOR_X: Fq = field_new!(Fq, "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");

/// G1_GENERATOR_Y =
/// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
#[rustfmt::skip]
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");

/// BETA is a non-trivial cubic root of unity in Fq.
pub const BETA: Fq = field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");

pub fn endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
    // Endomorphism of the points on the curve.
    // endomorphism_p(x,y) = (BETA * x, y) where BETA is a non-trivial cubic root of unity in Fq.
    let mut res = (*p).clone();
    res.x *= BETA;
    res
}