RationalApproximations.h

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//
// Created by Nikhil Chandra Admal on 4/20/23.
//
 
#ifndef OILAB_RATIONALAPPROXIMATIONS_H
#define OILAB_RATIONALAPPROXIMATIONS_H
 
#include "IntegerMath.h"
#include "Rational.h"
#include "Farey.h"
 
namespace oILAB {
template <typename IntScalarType> class RationalApproximations {
public:
  double number;
  double tolerance;
  IntScalarType max_denominator;
  std::vector<Rational<IntScalarType>> approximations;
 
  RationalApproximations(double number, int max_denominator, double tolerance)
      : /* init */ number(number),
        /* init */ max_denominator(max_denominator),
        /* init */ tolerance(tolerance) {
    double n = floor(number);
    auto seq = farey(max_denominator, false);
    for (auto p : seq) {
      double approx =
          static_cast<double>(p.first) / static_cast<double>(p.second);
      if (std::abs(number - n - approx) <= tolerance) {
        p.first = p.first + n * p.second;
        approximations.push_back(Rational<IntScalarType>(p.first, p.second));
      }
    }
  }
 
 
 
 
    };
 
    } // namespace oILAB
#endif //OILAB_RATIONALAPPROXIMATIONS_H