// Copyright (C) 2019-2021 Aleo Systems Inc.
// This file is part of the snarkVM library.
// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.
use snarkvm_utilities::biginteger::*;
/// A trait that defines parameters for a prime field.
pub trait FpParameters: 'static + Send + Sync + Sized {
type BigInteger: BigInteger;
/// The modulus of the field.
const MODULUS: Self::BigInteger;
/// The number of bits needed to represent the `Self::MODULUS`.
const MODULUS_BITS: u32;
/// The number of bits that must be shaved from the beginning of
/// the representation when randomly sampling.
const REPR_SHAVE_BITS: u32;
/// R = 2^256 % Self::MODULUS
const R: Self::BigInteger;
/// R2 = R^2 % Self::MODULUS
const R2: Self::BigInteger;
/// INV = -(MODULUS^{-1} mod MODULUS) mod MODULUS
const INV: u64;
/// A multiplicative generator that is also a quadratic nonresidue.
/// `Self::GENERATOR` is an element having multiplicative order
/// `Self::MODULUS - 1`.
/// There also does not exist `x` such that `Self::GENERATOR = x^2 %
/// Self::MODULUS`
const GENERATOR: Self::BigInteger;
/// The number of bits that can be reliably stored.
/// (Should equal `SELF::MODULUS_BITS - 1`)
const CAPACITY: u32;
/// 2^s * t = MODULUS - 1 with t odd. This is the two-adicity of the prime.
const TWO_ADICITY: u32;
/// 2^s root of unity computed by GENERATOR^t
const ROOT_OF_UNITY: Self::BigInteger;
/// t for 2^s * t = MODULUS - 1
const T: Self::BigInteger;
/// (t - 1) / 2
const T_MINUS_ONE_DIV_TWO: Self::BigInteger;
/// (Self::MODULUS - 1) / 2
const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInteger;
}