complex.cpp
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// Boost.Units - A C++ library for zero-overhead dimensional analysis and
// unit/quantity manipulation and conversion
//
// Copyright (C) 2003-2008 Matthias Christian Schabel
// Copyright (C) 2008 Steven Watanabe
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
/**
\file
\brief complex.cpp
\details
Demonstrate a complex number class that functions correctly with quantities.
Output:
@verbatim
//[complex_output_1
+L = 2 + 1 i m
-L = -2 + -1 i m
L+L = 4 + 2 i m
L-L = 0 + 0 i m
L*L = 3 + 4 i m^2
L/L = 1 + 0 i dimensionless
L^3 = 2 + 11 i m^3
L^(3/2) = 2.56713 + 2.14247 i m^(3/2)
3vL = 1.29207 + 0.201294 i m^(1/3)
(3/2)vL = 1.62894 + 0.520175 i m^(2/3)
//]
//[complex_output_2
+L = 2 m + 1 m i
-L = -2 m + -1 m i
L+L = 4 m + 2 m i
L-L = 0 m + 0 m i
L*L = 3 m^2 + 4 m^2 i
L/L = 1 dimensionless + 0 dimensionless i
L^3 = 2 m^3 + 11 m^3 i
L^(3/2) = 2.56713 m^(3/2) + 2.14247 m^(3/2) i
3vL = 1.29207 m^(1/3) + 0.201294 m^(1/3) i
(3/2)vL = 1.62894 m^(2/3) + 0.520175 m^(2/3) i
//]
@endverbatim
**/
#include <cmath>
#include <complex>
#include <iostream>
#include <boost/mpl/list.hpp>
#include <boost/units/io.hpp>
#include <boost/units/pow.hpp>
#include <boost/units/quantity.hpp>
#include "test_system.hpp"
//[complex_class_snippet_1
namespace boost {
namespace units {
/// replacement complex class
template<class T>
class complex
{
public:
typedef complex<T> this_type;
constexpr complex(const T& r = 0,const T& i = 0) : r_(r),i_(i) { }
constexpr complex(const this_type& source) : r_(source.r_),i_(source.i_) { }
constexpr this_type& operator=(const this_type& source)
{
if (this == &source) return *this;
r_ = source.r_;
i_ = source.i_;
return *this;
}
constexpr T& real() { return r_; }
constexpr T& imag() { return i_; }
constexpr const T& real() const { return r_; }
constexpr const T& imag() const { return i_; }
constexpr this_type& operator+=(const T& val)
{
r_ += val;
return *this;
}
constexpr this_type& operator-=(const T& val)
{
r_ -= val;
return *this;
}
constexpr this_type& operator*=(const T& val)
{
r_ *= val;
i_ *= val;
return *this;
}
constexpr this_type& operator/=(const T& val)
{
r_ /= val;
i_ /= val;
return *this;
}
constexpr this_type& operator+=(const this_type& source)
{
r_ += source.r_;
i_ += source.i_;
return *this;
}
constexpr this_type& operator-=(const this_type& source)
{
r_ -= source.r_;
i_ -= source.i_;
return *this;
}
constexpr this_type& operator*=(const this_type& source)
{
*this = *this * source;
return *this;
}
constexpr this_type& operator/=(const this_type& source)
{
*this = *this / source;
return *this;
}
private:
T r_,i_;
};
}
}
#if BOOST_UNITS_HAS_BOOST_TYPEOF
#include BOOST_TYPEOF_INCREMENT_REGISTRATION_GROUP()
BOOST_TYPEOF_REGISTER_TEMPLATE(boost::units::complex, 1)
#endif
namespace boost {
namespace units {
template<class X>
constexpr
complex<typename unary_plus_typeof_helper<X>::type>
operator+(const complex<X>& x)
{
typedef typename unary_plus_typeof_helper<X>::type type;
return complex<type>(x.real(),x.imag());
}
template<class X>
constexpr
complex<typename unary_minus_typeof_helper<X>::type>
operator-(const complex<X>& x)
{
typedef typename unary_minus_typeof_helper<X>::type type;
return complex<type>(-x.real(),-x.imag());
}
template<class X,class Y>
constexpr
complex<typename add_typeof_helper<X,Y>::type>
operator+(const complex<X>& x,const complex<Y>& y)
{
typedef typename boost::units::add_typeof_helper<X,Y>::type type;
return complex<type>(x.real()+y.real(),x.imag()+y.imag());
}
template<class X,class Y>
constexpr
complex<typename boost::units::subtract_typeof_helper<X,Y>::type>
operator-(const complex<X>& x,const complex<Y>& y)
{
typedef typename boost::units::subtract_typeof_helper<X,Y>::type type;
return complex<type>(x.real()-y.real(),x.imag()-y.imag());
}
template<class X,class Y>
constexpr
complex<typename boost::units::multiply_typeof_helper<X,Y>::type>
operator*(const complex<X>& x,const complex<Y>& y)
{
typedef typename boost::units::multiply_typeof_helper<X,Y>::type type;
return complex<type>(x.real()*y.real() - x.imag()*y.imag(),
x.real()*y.imag() + x.imag()*y.real());
// fully correct implementation has more complex return type
//
// typedef typename boost::units::multiply_typeof_helper<X,Y>::type xy_type;
//
// typedef typename boost::units::add_typeof_helper<
// xy_type,xy_type>::type xy_plus_xy_type;
// typedef typename
// boost::units::subtract_typeof_helper<xy_type,xy_type>::type
// xy_minus_xy_type;
//
// BOOST_STATIC_ASSERT((boost::is_same<xy_plus_xy_type,
// xy_minus_xy_type>::value == true));
//
// return complex<xy_plus_xy_type>(x.real()*y.real()-x.imag()*y.imag(),
// x.real()*y.imag()+x.imag()*y.real());
}
template<class X,class Y>
constexpr
complex<typename boost::units::divide_typeof_helper<X,Y>::type>
operator/(const complex<X>& x,const complex<Y>& y)
{
// naive implementation of complex division
typedef typename boost::units::divide_typeof_helper<X,Y>::type type;
return complex<type>((x.real()*y.real()+x.imag()*y.imag())/
(y.real()*y.real()+y.imag()*y.imag()),
(x.imag()*y.real()-x.real()*y.imag())/
(y.real()*y.real()+y.imag()*y.imag()));
// fully correct implementation has more complex return type
//
// typedef typename boost::units::multiply_typeof_helper<X,Y>::type xy_type;
// typedef typename boost::units::multiply_typeof_helper<Y,Y>::type yy_type;
//
// typedef typename boost::units::add_typeof_helper<xy_type, xy_type>::type
// xy_plus_xy_type;
// typedef typename boost::units::subtract_typeof_helper<
// xy_type,xy_type>::type xy_minus_xy_type;
//
// typedef typename boost::units::divide_typeof_helper<
// xy_plus_xy_type,yy_type>::type xy_plus_xy_over_yy_type;
// typedef typename boost::units::divide_typeof_helper<
// xy_minus_xy_type,yy_type>::type xy_minus_xy_over_yy_type;
//
// BOOST_STATIC_ASSERT((boost::is_same<xy_plus_xy_over_yy_type,
// xy_minus_xy_over_yy_type>::value == true));
//
// return complex<xy_plus_xy_over_yy_type>(
// (x.real()*y.real()+x.imag()*y.imag())/
// (y.real()*y.real()+y.imag()*y.imag()),
// (x.imag()*y.real()-x.real()*y.imag())/
// (y.real()*y.real()+y.imag()*y.imag()));
}
template<class Y>
complex<Y>
pow(const complex<Y>& x,const Y& y)
{
std::complex<Y> tmp(x.real(),x.imag());
tmp = std::pow(tmp,y);
return complex<Y>(tmp.real(),tmp.imag());
}
template<class Y>
std::ostream& operator<<(std::ostream& os,const complex<Y>& val)
{
os << val.real() << " + " << val.imag() << " i";
return os;
}
/// specialize power typeof helper for complex<Y>
template<class Y,long N,long D>
struct power_typeof_helper<complex<Y>,static_rational<N,D> >
{
typedef complex<
typename power_typeof_helper<Y,static_rational<N,D> >::type
> type;
static type value(const complex<Y>& x)
{
const static_rational<N,D> rat;
const Y m = Y(rat.numerator())/Y(rat.denominator());
return boost::units::pow(x,m);
}
};
/// specialize root typeof helper for complex<Y>
template<class Y,long N,long D>
struct root_typeof_helper<complex<Y>,static_rational<N,D> >
{
typedef complex<
typename root_typeof_helper<Y,static_rational<N,D> >::type
> type;
static type value(const complex<Y>& x)
{
const static_rational<N,D> rat;
const Y m = Y(rat.denominator())/Y(rat.numerator());
return boost::units::pow(x,m);
}
};
/// specialize power typeof helper for complex<quantity<Unit,Y> >
template<class Y,class Unit,long N,long D>
struct power_typeof_helper<complex<quantity<Unit,Y> >,static_rational<N,D> >
{
typedef typename
power_typeof_helper<Y,static_rational<N,D> >::type value_type;
typedef typename
power_typeof_helper<Unit,static_rational<N,D> >::type unit_type;
typedef quantity<unit_type,value_type> quantity_type;
typedef complex<quantity_type> type;
static type value(const complex<quantity<Unit,Y> >& x)
{
const complex<value_type> tmp =
pow<static_rational<N,D> >(complex<Y>(x.real().value(),
x.imag().value()));
return type(quantity_type::from_value(tmp.real()),
quantity_type::from_value(tmp.imag()));
}
};
/// specialize root typeof helper for complex<quantity<Unit,Y> >
template<class Y,class Unit,long N,long D>
struct root_typeof_helper<complex<quantity<Unit,Y> >,static_rational<N,D> >
{
typedef typename
root_typeof_helper<Y,static_rational<N,D> >::type value_type;
typedef typename
root_typeof_helper<Unit,static_rational<N,D> >::type unit_type;
typedef quantity<unit_type,value_type> quantity_type;
typedef complex<quantity_type> type;
static type value(const complex<quantity<Unit,Y> >& x)
{
const complex<value_type> tmp =
root<static_rational<N,D> >(complex<Y>(x.real().value(),
x.imag().value()));
return type(quantity_type::from_value(tmp.real()),
quantity_type::from_value(tmp.imag()));
}
};
} // namespace units
} // namespace boost
//]
int main(void)
{
using namespace boost::units;
using namespace boost::units::test;
{
//[complex_snippet_1
typedef quantity<length,complex<double> > length_dimension;
const length_dimension L(complex<double>(2.0,1.0)*meters);
//]
std::cout << "+L = " << +L << std::endl
<< "-L = " << -L << std::endl
<< "L+L = " << L+L << std::endl
<< "L-L = " << L-L << std::endl
<< "L*L = " << L*L << std::endl
<< "L/L = " << L/L << std::endl
<< "L^3 = " << pow<3>(L) << std::endl
<< "L^(3/2) = " << pow< static_rational<3,2> >(L) << std::endl
<< "3vL = " << root<3>(L) << std::endl
<< "(3/2)vL = " << root< static_rational<3,2> >(L) << std::endl
<< std::endl;
}
{
//[complex_snippet_2
typedef complex<quantity<length> > length_dimension;
const length_dimension L(2.0*meters,1.0*meters);
//]
std::cout << "+L = " << +L << std::endl
<< "-L = " << -L << std::endl
<< "L+L = " << L+L << std::endl
<< "L-L = " << L-L << std::endl
<< "L*L = " << L*L << std::endl
<< "L/L = " << L/L << std::endl
<< "L^3 = " << pow<3>(L) << std::endl
<< "L^(3/2) = " << pow< static_rational<3,2> >(L) << std::endl
<< "3vL = " << root<3>(L) << std::endl
<< "(3/2)vL = " << root< static_rational<3,2> >(L) << std::endl
<< std::endl;
}
return 0;
}