6.S096 | January IAP 2014 | Undergraduate
Effective Programming in C and C++
Assignments

Sample Solution to Assignment 2, Problem 3

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Here are the contents of rational.h:


#ifndef _6S096_RATIONAL_H
#define _6S096_RATIONAL_H
 
#include <cstdint>
#include <iosfwd>
#include <stdexcept>
 
class Rational {
  intmax_t _num, _den;
public:
  enum sign_type { POSITIVE, NEGATIVE };
 
  Rational() : _num{0}, _den{1} {}
  Rational( intmax_t numer ) : _num{numer}, _den{1} {}
  Rational( intmax_t numer, intmax_t denom ) : _num{numer}, _den{denom} { normalize(); }
 
  inline intmax_t num() const { return _num; }
  inline intmax_t den() const { return _den; }
 
  void normalize();
  float to_float()const;
  double to_double()const;
  sign_type sign() const;
  Rational inverse() const;
};
 
std::ostream& operator<<( std::ostream& os, const Rational &ratio );
 
inline bool operator==( const Rational &lhs, const Rational &rhs ) {
  return lhs.num() * rhs.den() == rhs.num() * lhs.den();
}
 
inline bool operator<( const Rational &lhs, const Rational &rhs ) {
  if( lhs.sign() == Rational::POSITIVE && rhs.sign() == Rational::POSITIVE ) {
      return lhs.num() * rhs.den() < rhs.num() * lhs.den();
  } else if( lhs.sign() == Rational::NEGATIVE && rhs.sign() == Rational::NEGATIVE ) {
    return lhs.num() * rhs.den() > rhs.num() * lhs.den();
  } else {
    return lhs.sign() == Rational::NEGATIVE;
  }
}
 
inline Rational operator*( const Rational &a, const Rational &b ) {
  return Rational{ a.num() * b.num(), a.den() * b.den() };
}
 
inline Rational operator+( const Rational &a, const Rational &b ) {
  return Rational{ a.num() * b.den() + b.num() * a.den(), a.den() * b.den() };
}
 
inline Rational operator-( const Rational &a, const Rational &b ) {
  return Rational{ a.num() * b.den() - b.num() * a.den(), a.den() * b.den() };
}
 
inline Rational operator/( const Rational &a, const Rational &b ) {
  return a * b.inverse();
}
 
class bad_rational : public std::domain_error {
public:
  explicit bad_rational() : std::domain_error("Bad rational: zero denominator" ) {}
};
 
#endif // _6S096_RATIONAL_H

Here is the source code file rational.cpp:


#include "rational.h"
#include "gcd.h"
 
#include <stdexcept>
#include <ostream>
#include <iostream>
#include <cmath>
 
Rational Rational::inverse() const {
  return Rational{ _den, _num };
}
 
Rational::sign_type Rational::sign()const {
  return _num >= 0 ? POSITIVE : NEGATIVE;
}
 
std::ostream& operator<<( std::ostream& os, const Rational &ratio ) {
  if( ratio == 0 ) {
    os << "0";
  } else {
    if( ratio.sign() == Rational::NEGATIVE ) {
      os << "-";
    }
    os << std::abs( ratio.num() ) << "/" << std::abs( ratio.den() );
  }
  return os;
}
 
void Rational::normalize() {
  if( _den == 0 ) {
    throw bad_rational();
  }
 
  if( _num == 0 ) {
    _den = 1; return;
  }
 
  auto g = gcd( std::abs( _num ), std::abs( _den ) );
  _num /= g; _den /= g;
 
  if( _den < 0 ) {
    _num = -_num;
    _den = -_den;
  }
}
 
float Rational::to_float() const {
  return static_cast<float>( _num ) / static_cast<float>( _den );
}
 
double Rational::to_double()const {
  return static_cast<double>( _num ) / static_cast<double>( _den );
}

Below is the output using the test data:


rational:
 1: OK [0.007 seconds] OK! add
 2: OK [0.006 seconds] OK! mult
 3: OK [0.009 seconds] OK! add1024
 4: OK [0.014 seconds] OK! add1024
 5: OK [0.158 seconds] OK! add32768
 6: OK [0.007 seconds] OK! op<<
 7: OK [0.289 seconds] OK! div65536 in 0.280000 s
 8: OK [0.006 seconds] OK! phi, 0.000000e+00
 9: OK [0.006 seconds] OK! (Bad rational: zero denominator)
10: OK [0.006 seconds] OK! xyz
11: OK [0.007 seconds] OK! pow2
12: OK [0.006 seconds] OK! x1z

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January IAP 2014
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