1 // Boost.Units - A C++ library for zero-overhead dimensional analysis and
2 // unit/quantity manipulation and conversion
4 // Copyright (C) 2003-2008 Matthias Christian Schabel
5 // Copyright (C) 2008 Steven Watanabe
7 // Distributed under the Boost Software License, Version 1.0. (See
8 // accompanying file LICENSE_1_0.txt or copy at
9 // http://www.boost.org/LICENSE_1_0.txt)
11 #ifndef BOOST_UNITS_STATIC_RATIONAL_HPP
12 #define BOOST_UNITS_STATIC_RATIONAL_HPP
14 #include <boost/integer/common_factor_ct.hpp>
15 #include <boost/mpl/less.hpp>
16 #include <boost/mpl/arithmetic.hpp>
19 #include <boost/mpl/eval_if.hpp>
20 #include <boost/mpl/integral_c.hpp>
21 #include <boost/mpl/identity.hpp>
24 #include <boost/units/config.hpp>
25 #include <boost/units/operators.hpp>
28 /// \brief Compile-time rational numbers and operators.
36 struct static_rational_tag {};
40 typedef long integer_type;
42 /// Compile time absolute value.
43 template<integer_type Value>
46 BOOST_STATIC_CONSTANT(integer_type,value = Value < 0 ? -Value : Value);
49 // Compile time rational number.
51 This is an implementation of a compile time rational number, where @c static_rational<N,D> represents
52 a rational number with numerator @c N and denominator @c D. Because of the potential for ambiguity arising
53 from multiple equivalent values of @c static_rational (e.g. @c static_rational<6,2>==static_rational<3>),
54 static rationals should always be accessed through @c static_rational<N,D>::type. Template specialization
55 prevents instantiation of zero denominators (i.e. @c static_rational<N,0>). The following compile-time
56 arithmetic operators are provided for static_rational variables only (no operators are defined between
57 long and static_rational):
64 Neither @c static_power nor @c static_root are defined for @c static_rational. This is because template types
65 may not be floating point values, while powers and roots of rational numbers can produce floating point
70 template<integer_type X>
71 struct make_integral_c {
72 typedef boost::mpl::integral_c<integer_type, X> type;
75 template<integer_type N,integer_type D = 1>
80 typedef static_rational this_type;
82 typedef boost::mpl::integral_c<integer_type, N> N_type;
83 typedef boost::mpl::integral_c<integer_type, D> D_type;
85 typedef typename make_integral_c<
86 (::boost::integer::static_gcd<
87 ::boost::units::static_abs<N>::value,
88 ::boost::units::static_abs<D>::value
89 >::value)>::type gcd_type;
90 typedef typename boost::mpl::eval_if<
93 boost::mpl::integral_c<integer_type, 0>
95 boost::mpl::negate<gcd_type>,
100 // for mpl arithmetic support
101 typedef detail::static_rational_tag tag;
103 BOOST_STATIC_CONSTANT(integer_type, Numerator =
104 (::boost::mpl::divides<N_type, den_type>::value));
105 BOOST_STATIC_CONSTANT(integer_type, Denominator =
106 (::boost::mpl::divides<D_type, den_type>::value));
109 typedef static_rational<N,D> this_type;
111 /// static_rational<N,D> reduced by GCD
112 typedef static_rational<
113 (::boost::mpl::divides<N_type, den_type>::value),
114 (::boost::mpl::divides<D_type, den_type>::value)
117 static BOOST_CONSTEXPR integer_type numerator() { return Numerator; }
118 static BOOST_CONSTEXPR integer_type denominator() { return Denominator; }
121 BOOST_CONSTEXPR static_rational() { }
122 //~static_rational() { }
125 template<integer_type N,integer_type D = 1>
126 class static_rational
130 BOOST_STATIC_CONSTEXPR integer_type nabs = static_abs<N>::value,
131 dabs = static_abs<D>::value;
133 /// greatest common divisor of N and D
134 // need cast to signed because static_gcd returns unsigned long
135 BOOST_STATIC_CONSTEXPR integer_type den =
136 static_cast<integer_type>(boost::integer::static_gcd<nabs,dabs>::value) * ((D < 0) ? -1 : 1);
139 // for mpl arithmetic support
140 typedef detail::static_rational_tag tag;
142 BOOST_STATIC_CONSTEXPR integer_type Numerator = N/den,
146 typedef static_rational<N,D> this_type;
148 /// static_rational<N,D> reduced by GCD
149 typedef static_rational<Numerator,Denominator> type;
151 static BOOST_CONSTEXPR integer_type numerator() { return Numerator; }
152 static BOOST_CONSTEXPR integer_type denominator() { return Denominator; }
155 BOOST_CONSTEXPR static_rational() { }
156 //~static_rational() { }
164 #if BOOST_UNITS_HAS_BOOST_TYPEOF
166 #include BOOST_TYPEOF_INCREMENT_REGISTRATION_GROUP()
168 BOOST_TYPEOF_REGISTER_TEMPLATE(boost::units::static_rational, (long)(long))
176 // prohibit zero denominator
177 template<integer_type N> class static_rational<N,0>;
179 /// get decimal value of @c static_rational
180 template<class T,integer_type N,integer_type D>
181 inline BOOST_CONSTEXPR typename divide_typeof_helper<T,T>::type
182 value(const static_rational<N,D>&)
189 #ifndef BOOST_UNITS_DOXYGEN
193 #ifdef BOOST_BORLANDC
196 struct plus_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
198 template<class T0, class T1>
200 typedef typename boost::units::static_rational<
202 boost::mpl::times<typename T0::N_type, typename T1::D_type>,
203 boost::mpl::times<typename T1::N_type, typename T0::D_type>
205 ::boost::mpl::times<typename T0::D_type, typename T1::D_type>::value
211 struct minus_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
213 template<class T0, class T1>
215 typedef typename boost::units::static_rational<
217 boost::mpl::times<typename T0::N_type, typename T1::D_type>,
218 boost::mpl::times<typename T1::N_type, typename T0::D_type>
220 ::boost::mpl::times<typename T0::D_type, typename T1::D_type>::value
226 struct times_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
228 template<class T0, class T1>
230 typedef typename boost::units::static_rational<
231 ::boost::mpl::times<typename T0::N_type, typename T1::N_type>::value,
232 ::boost::mpl::times<typename T0::D_type, typename T1::D_type>::value
238 struct divides_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
240 template<class T0, class T1>
242 typedef typename boost::units::static_rational<
243 ::boost::mpl::times<typename T0::N_type, typename T1::D_type>::value,
244 ::boost::mpl::times<typename T0::D_type, typename T1::N_type>::value
250 struct negate_impl<boost::units::detail::static_rational_tag>
254 typedef typename boost::units::static_rational<
255 ::boost::mpl::negate<typename T0::N_type>::value,
256 ::boost::mpl::identity<T0>::type::Denominator
262 struct less_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
264 template<class T0, class T1>
267 typedef mpl::bool_<((mpl::minus<T0, T1>::type::Numerator) < 0)> type;
274 struct plus_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
276 template<class T0, class T1>
278 typedef typename boost::units::static_rational<
279 T0::Numerator*T1::Denominator+T1::Numerator*T0::Denominator,
280 T0::Denominator*T1::Denominator
286 struct minus_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
288 template<class T0, class T1>
290 typedef typename boost::units::static_rational<
291 T0::Numerator*T1::Denominator-T1::Numerator*T0::Denominator,
292 T0::Denominator*T1::Denominator
298 struct times_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
300 template<class T0, class T1>
302 typedef typename boost::units::static_rational<
303 T0::Numerator*T1::Numerator,
304 T0::Denominator*T1::Denominator
310 struct divides_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
312 template<class T0, class T1>
314 typedef typename boost::units::static_rational<
315 T0::Numerator*T1::Denominator,
316 T0::Denominator*T1::Numerator
322 struct negate_impl<boost::units::detail::static_rational_tag>
326 typedef typename boost::units::static_rational<-T0::Numerator,T0::Denominator>::type type;
331 struct less_impl<boost::units::detail::static_rational_tag, boost::units::detail::static_rational_tag>
333 template<class T0, class T1>
336 typedef mpl::bool_<((mpl::minus<T0, T1>::type::Numerator) < 0)> type;
349 #endif // BOOST_UNITS_STATIC_RATIONAL_HPP