/** @file
 *****************************************************************************
 Declaration of arithmetic in the finite  field F[p^3].
 *****************************************************************************
 * @author     This file is part of libsnark, developed by SCIPR Lab
 *             and contributors (see AUTHORS).
 * @copyright  MIT license (see LICENSE file)
 *****************************************************************************/

#ifndef FP3_HPP_
#define FP3_HPP_
#include "algebra/fields/fp.hpp"
#include <vector>

namespace libsnark {

template<mp_size_t n, const bigint<n>& modulus>
class Fp3_model;

template<mp_size_t n, const bigint<n>& modulus>
std::ostream& operator<<(std::ostream &, const Fp3_model<n, modulus> &);

template<mp_size_t n, const bigint<n>& modulus>
std::istream& operator>>(std::istream &, Fp3_model<n, modulus> &);

/**
 * Arithmetic in the field F[p^3].
 *
 * Let p := modulus. This interface provides arithmetic for the extension field
 * Fp3 = Fp[U]/(U^3-non_residue), where non_residue is in Fp.
 *
 * ASSUMPTION: p = 1 (mod 6)
 */
template<mp_size_t n, const bigint<n>& modulus>
class Fp3_model {
public:
    typedef Fp_model<n, modulus> my_Fp;

    static bigint<3*n> euler; // (modulus^3-1)/2
    static size_t s;       // modulus^3 = 2^s * t + 1
    static bigint<3*n> t;  // with t odd
    static bigint<3*n> t_minus_1_over_2; // (t-1)/2
    static my_Fp non_residue; // X^6-non_residue irreducible over Fp; used for constructing Fp3 = Fp[X] / (X^3 - non_residue)
    static Fp3_model<n, modulus> nqr; // a quadratic nonresidue in Fp3
    static Fp3_model<n, modulus> nqr_to_t; // nqr^t
    static my_Fp Frobenius_coeffs_c1[3]; // non_residue^((modulus^i-1)/3)   for i=0,1,2
    static my_Fp Frobenius_coeffs_c2[3]; // non_residue^((2*modulus^i-2)/3) for i=0,1,2

    my_Fp c0, c1, c2;
    Fp3_model() {};
    Fp3_model(const my_Fp& c0, const my_Fp& c1, const my_Fp& c2) : c0(c0), c1(c1), c2(c2) {};

    void clear() { c0.clear(); c1.clear(); c2.clear(); }
    void print() const { printf("c0/c1/c2:\n"); c0.print(); c1.print(); c2.print(); }

    static Fp3_model<n, modulus> zero();
    static Fp3_model<n, modulus> one();
    static Fp3_model<n, modulus> random_element();

    bool is_zero() const { return c0.is_zero() && c1.is_zero() && c2.is_zero(); }
    bool operator==(const Fp3_model &other) const;
    bool operator!=(const Fp3_model &other) const;

    Fp3_model operator+(const Fp3_model &other) const;
    Fp3_model operator-(const Fp3_model &other) const;
    Fp3_model operator*(const Fp3_model &other) const;
    Fp3_model operator-() const;
    Fp3_model squared() const;
    Fp3_model inverse() const;
    Fp3_model Frobenius_map(unsigned long power) const;
    Fp3_model sqrt() const; // HAS TO BE A SQUARE (else does not terminate)

    template<mp_size_t m>
    Fp3_model operator^(const bigint<m> &other) const;

    static size_t size_in_bits() { return 3*my_Fp::size_in_bits(); }
    static bigint<n> base_field_char() { return modulus; }

    friend std::ostream& operator<< <n, modulus>(std::ostream &out, const Fp3_model<n, modulus> &el);
    friend std::istream& operator>> <n, modulus>(std::istream &in, Fp3_model<n, modulus> &el);
};

template<mp_size_t n, const bigint<n>& modulus>
std::ostream& operator<<(std::ostream& out, const std::vector<Fp3_model<n, modulus> > &v);

template<mp_size_t n, const bigint<n>& modulus>
std::istream& operator>>(std::istream& in, std::vector<Fp3_model<n, modulus> > &v);

template<mp_size_t n, const bigint<n>& modulus>
Fp3_model<n, modulus> operator*(const Fp_model<n, modulus> &lhs, const Fp3_model<n, modulus> &rhs);

template<mp_size_t n, const bigint<n>& modulus>
bigint<3*n> Fp3_model<n, modulus>::euler;

template<mp_size_t n, const bigint<n>& modulus>
size_t Fp3_model<n, modulus>::s;

template<mp_size_t n, const bigint<n>& modulus>
bigint<3*n> Fp3_model<n, modulus>::t;

template<mp_size_t n, const bigint<n>& modulus>
bigint<3*n> Fp3_model<n, modulus>::t_minus_1_over_2;

template<mp_size_t n, const bigint<n>& modulus>
Fp_model<n, modulus> Fp3_model<n, modulus>::non_residue;

template<mp_size_t n, const bigint<n>& modulus>
Fp3_model<n, modulus> Fp3_model<n, modulus>::nqr;

template<mp_size_t n, const bigint<n>& modulus>
Fp3_model<n, modulus> Fp3_model<n, modulus>::nqr_to_t;

template<mp_size_t n, const bigint<n>& modulus>
Fp_model<n, modulus> Fp3_model<n, modulus>::Frobenius_coeffs_c1[3];

template<mp_size_t n, const bigint<n>& modulus>
Fp_model<n, modulus> Fp3_model<n, modulus>::Frobenius_coeffs_c2[3];

} // libsnark
#include "algebra/fields/fp3.tcc"

#endif // FP3_HPP_