//! Bls12-377 scalar field.
///
/// Roots of unity computed from modulus and R using this sage code:
///
/// ```ignore
/// q = 8444461749428370424248824938781546531375899335154063827935233455917409239041
/// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403 # Montgomery R
/// s = 47
/// o = q - 1
/// F = GF(q)
/// g = F.multiplicative_generator()
/// g = F.multiplicative_generator()
/// assert g.multiplicative_order() == o
/// g2 = g ** (o/2**s)
/// assert g2.multiplicative_order() == 2**s
/// def into_chunks(val, width, n):
///     return [int(int(val) // (2 ** (width * i)) % 2 ** width) for i in range(n)]
/// print("Gen: ", g * R % q)
/// print("Gen: ", into_chunks(g * R % q, 64, 4))
/// print("2-adic gen: ", into_chunks(g2 * R % q, 64, 4))
/// ```
use ark_ff::{biginteger::BigInteger256 as BigInteger, fields::*};

pub type Fr = Fp256<FrParameters>;

pub struct FrParameters;

impl Fp256Parameters for FrParameters {}
impl FftParameters for FrParameters {
    type BigInt = BigInteger;

    const TWO_ADICITY: u32 = 47;

    #[rustfmt::skip]
    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
        12646347781564978760u64,
        6783048705277173164u64,
        268534165941069093u64,
        1121515446318641358u64,
    ]);
}
impl FpParameters for FrParameters {
    /// MODULUS = 8444461749428370424248824938781546531375899335154063827935233455917409239041
    #[rustfmt::skip]
    const MODULUS: BigInteger = BigInteger([
        725501752471715841u64,
        6461107452199829505u64,
        6968279316240510977u64,
        1345280370688173398u64,
    ]);

    const MODULUS_BITS: u32 = 253;

    const CAPACITY: u32 = Self::MODULUS_BITS - 1;

    const REPR_SHAVE_BITS: u32 = 3;

    /// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403
    #[rustfmt::skip]
    const R: BigInteger = BigInteger([
        9015221291577245683u64,
        8239323489949974514u64,
        1646089257421115374u64,
        958099254763297437u64,
    ]);

    #[rustfmt::skip]
    const R2: BigInteger = BigInteger([
        2726216793283724667u64,
        14712177743343147295u64,
        12091039717619697043u64,
        81024008013859129u64,
    ]);

    const INV: u64 = 725501752471715839u64;

    /// GENERATOR = 22
    /// Encoded in Montgomery form, so the value is
    /// (22 * R) % q =
    /// 5642976643016801619665363617888466827793962762719196659561577942948671127251
    #[rustfmt::skip]
    const GENERATOR: BigInteger = BigInteger([
        2984901390528151251u64,
        10561528701063790279u64,
        5476750214495080041u64,
        898978044469942640u64,
    ]);

    /// (r - 1)/2 =
    /// 4222230874714185212124412469390773265687949667577031913967616727958704619520
    #[rustfmt::skip]
    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
        0x8508c00000000000,
        0xacd53b7f68000000,
        0x305a268f2e1bd800,
        0x955b2af4d1652ab,
    ]);

    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
    // For T coprime to 2

    /// t = (r - 1) / 2^s =
    /// 60001509534603559531609739528203892656505753216962260608619555
    #[rustfmt::skip]
    const T: BigInteger = BigInteger([
        0xedfda00000021423,
        0x9a3cb86f6002b354,
        0xcabd34594aacc168,
        0x2556,
    ]);

    /// (t - 1) / 2 =
    /// 30000754767301779765804869764101946328252876608481130304309777
    #[rustfmt::skip]
    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
        0x76fed00000010a11,
        0x4d1e5c37b00159aa,
        0x655e9a2ca55660b4,
        0x12ab,
    ]);
}