fp.hpp

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#ifndef FP_HPP_
#define FP_HPP_
 
#include <libff/algebra/exponentiation/exponentiation.hpp>
#include <libff/algebra/fields/bigint.hpp>
 
namespace libff
{
 
template<mp_size_t n, const bigint<n> &modulus> class Fp_model;
 
template<mp_size_t n, const bigint<n> &modulus>
std::ostream &operator<<(std::ostream &, const Fp_model<n, modulus> &);
 
template<mp_size_t n, const bigint<n> &modulus>
std::istream &operator>>(std::istream &, Fp_model<n, modulus> &);
 
template<mp_size_t n, const bigint<n> &modulus> class Fp_model
{
public:
    typedef Fp_model<n, modulus> my_Fp;
 
    bigint<n> mont_repr;
 
    static void static_init();
 
    static const mp_size_t num_limbs = n;
    static const constexpr bigint<n> &mod = modulus;
#ifdef PROFILE_OP_COUNTS
    static long long add_cnt;
    static long long sub_cnt;
    static long long mul_cnt;
    static long long sqr_cnt;
    static long long inv_cnt;
#endif
 
    static const size_t tower_extension_degree = 1;
 
    static size_t num_bits;
    static bigint<n> euler;
    static size_t s;
    static bigint<n> t;
    static bigint<n> t_minus_1_over_2;
    static Fp_model<n, modulus> nqr;
    static Fp_model<n, modulus> nqr_to_t;
    static Fp_model<n, modulus> multiplicative_generator;
    static Fp_model<n, modulus> root_of_unity;
    static mp_limb_t inv;
    static bigint<n> Rsquared;
    static bigint<n> Rcubed;
 
    static bool modulus_is_valid()
    {
        return modulus.data[n - 1] != 0;
    } // mpn inverse assumes that highest limb is non-zero
 
    Fp_model(){};
    Fp_model(const bigint<n> &b);
    Fp_model(const long x, const bool is_unsigned = false);
 
    void set_ulong(const unsigned long x);
 
    void mul_reduce(const bigint<n> &other);
 
    void clear();
 
    bigint<n> as_bigint() const;
    unsigned long as_ulong() const;
 
    bool operator==(const Fp_model &other) const;
    bool operator!=(const Fp_model &other) const;
    bool is_zero() const;
 
    void print() const;
 
    Fp_model &operator+=(const Fp_model &other);
    Fp_model &operator-=(const Fp_model &other);
    Fp_model &operator*=(const Fp_model &other);
    Fp_model &operator^=(const unsigned long pow);
 
    template<mp_size_t m> Fp_model &operator^=(const bigint<m> &pow);
 
    Fp_model operator+(const Fp_model &other) const;
    Fp_model operator-(const Fp_model &other) const;
    Fp_model operator*(const Fp_model &other) const;
    Fp_model operator-() const;
    Fp_model squared() const;
    Fp_model &invert();
    Fp_model inverse() const;
    Fp_model sqrt() const;
 
    Fp_model operator^(const unsigned long pow) const;
    template<mp_size_t m> Fp_model operator^(const bigint<m> &pow) const;
 
    static size_t size_in_bits() { return num_bits; }
    static size_t capacity() { return num_bits - 1; }
    static const bigint<n> &field_char() { return modulus; }
    static constexpr size_t extension_degree() { return 1; }
 
    static const Fp_model<n, modulus> &zero();
    static const Fp_model<n, modulus> &one();
 
    static Fp_model<n, modulus> random_element();
 
    static Fp_model<n, modulus> geometric_generator();
 
    static Fp_model<n, modulus> arithmetic_generator();
 
protected:
    static bool s_initialized;
    static Fp_model<n, modulus> s_zero;
    static Fp_model<n, modulus> s_one;
 
    friend std::ostream &operator<<<n, modulus>(
        std::ostream &out, const Fp_model<n, modulus> &p);
    friend std::istream &operator>>
        <n, modulus>(std::istream &in, Fp_model<n, modulus> &p);
};
 
#ifdef PROFILE_OP_COUNTS
template<mp_size_t n, const bigint<n> &modulus>
long long Fp_model<n, modulus>::add_cnt = 0;
 
template<mp_size_t n, const bigint<n> &modulus>
long long Fp_model<n, modulus>::sub_cnt = 0;
 
template<mp_size_t n, const bigint<n> &modulus>
long long Fp_model<n, modulus>::mul_cnt = 0;
 
template<mp_size_t n, const bigint<n> &modulus>
long long Fp_model<n, modulus>::sqr_cnt = 0;
 
template<mp_size_t n, const bigint<n> &modulus>
long long Fp_model<n, modulus>::inv_cnt = 0;
#endif
 
template<mp_size_t n, const bigint<n> &modulus>
size_t Fp_model<n, modulus>::num_bits;
 
template<mp_size_t n, const bigint<n> &modulus>
bigint<n> Fp_model<n, modulus>::euler;
 
template<mp_size_t n, const bigint<n> &modulus> size_t Fp_model<n, modulus>::s;
 
template<mp_size_t n, const bigint<n> &modulus>
bigint<n> Fp_model<n, modulus>::t;
 
template<mp_size_t n, const bigint<n> &modulus>
bigint<n> Fp_model<n, modulus>::t_minus_1_over_2;
 
template<mp_size_t n, const bigint<n> &modulus>
Fp_model<n, modulus> Fp_model<n, modulus>::nqr;
 
template<mp_size_t n, const bigint<n> &modulus>
Fp_model<n, modulus> Fp_model<n, modulus>::nqr_to_t;
 
template<mp_size_t n, const bigint<n> &modulus>
Fp_model<n, modulus> Fp_model<n, modulus>::multiplicative_generator;
 
template<mp_size_t n, const bigint<n> &modulus>
Fp_model<n, modulus> Fp_model<n, modulus>::root_of_unity;
 
template<mp_size_t n, const bigint<n> &modulus>
mp_limb_t Fp_model<n, modulus>::inv;
 
template<mp_size_t n, const bigint<n> &modulus>
bigint<n> Fp_model<n, modulus>::Rsquared;
 
template<mp_size_t n, const bigint<n> &modulus>
bigint<n> Fp_model<n, modulus>::Rcubed;
 
} // namespace libff
 
#include <libff/algebra/fields/fp.tcc>
 
#endif // FP_HPP_