#ifndef STARKWARE_ALGEBRA_FRACTION_FIELD_ELEMENT_H_
#define STARKWARE_ALGEBRA_FRACTION_FIELD_ELEMENT_H_

#include "error_handling.h"
#include "prng.h"

namespace starkware {

/*
  Represents a field element as an element of the fraction field of the original field. The elements
  of the fraction field are a/b for a,b in the original field, and b != 0. The representation of
  a FieldElementT b is b/1. Addition and multiplication for the fraction field are defined naturally
  (see operator+ and operator*). The resulting field is isomorphic to the original field. This
  fractional representation of the original field enables to perform an inverse cheaply: the inverse
  of a/b is simply b/a.
*/
template <typename FieldElementT>
class FractionFieldElement {
 public:
  explicit constexpr FractionFieldElement(const FieldElementT& num_val)
      : numerator_(num_val), denominator_(FieldElementT::One()) {}

  /*
    Creates a FractionFieldElement with the value num_val/denom_val.
    denom_val can't be zero.
  */
  constexpr FractionFieldElement(const FieldElementT& num_val, const FieldElementT& denom_val)
      : numerator_(num_val), denominator_(denom_val) {
    ASSERT(denominator_ != FieldElementT::Zero(), "Denominator can't be zero.");
  }

  FractionFieldElement operator+(const FractionFieldElement& rhs) const;

  FractionFieldElement operator-(const FractionFieldElement& rhs) const;

  FractionFieldElement operator-() const { return FractionFieldElement(-numerator_, denominator_); }

  FractionFieldElement operator*(const FractionFieldElement& rhs) const;
  FractionFieldElement operator/(const FractionFieldElement& rhs) const {
    return *this * rhs.Inverse();
  }

  bool operator==(const FractionFieldElement& rhs) const;
  bool operator!=(const FractionFieldElement& rhs) const { return !(*this == rhs); }

  FractionFieldElement Inverse() const;

  static constexpr FractionFieldElement Zero() {
    return FractionFieldElement(FieldElementT::Zero());
  }

  static constexpr FractionFieldElement One() { return FractionFieldElement(FieldElementT::One()); }

  /*
    Returns a fraction field element: its numerator is a random FieldElementT generated by
    FieldElementT::RandomElement of and its denominator is FieldElementT::One().
  */
  static FractionFieldElement RandomElement(Prng* prng) {
    return FractionFieldElement(FieldElementT::RandomElement(prng));
  }

  FieldElementT ToBaseFieldElement() const { return this->numerator_ * denominator_.Inverse(); }

  explicit operator FieldElementT() const { return ToBaseFieldElement(); }

 private:
  FieldElementT numerator_;
  FieldElementT denominator_;
};

}  // namespace starkware

#include "fraction_field_element.inl"

#endif  // STARKWARE_ALGEBRA_FRACTION_FIELD_ELEMENT_H_