Chris@16: //  ratio.hpp  ---------------------------------------------------------------//
Chris@16: 
Chris@16: //  Copyright 2008 Howard Hinnant
Chris@16: //  Copyright 2008 Beman Dawes
Chris@16: //  Copyright 2009 Vicente J. Botet Escriba
Chris@16: 
Chris@16: //  Distributed under the Boost Software License, Version 1.0.
Chris@16: //  See http://www.boost.org/LICENSE_1_0.txt
Chris@16: 
Chris@16: /*
Chris@16: 
Chris@16: This code was derived by Beman Dawes from Howard Hinnant's time2_demo prototype.
Chris@16: Many thanks to Howard for making his code available under the Boost license.
Chris@16: The original code was modified to conform to Boost conventions and to section
Chris@16: 20.4 Compile-time rational arithmetic [ratio], of the C++ committee working
Chris@16: paper N2798.
Chris@16: See http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2798.pdf.
Chris@16: 
Chris@16: time2_demo contained this comment:
Chris@16: 
Chris@16:     Much thanks to Andrei Alexandrescu,
Chris@16:                    Walter Brown,
Chris@16:                    Peter Dimov,
Chris@16:                    Jeff Garland,
Chris@16:                    Terry Golubiewski,
Chris@16:                    Daniel Krugler,
Chris@16:                    Anthony Williams.
Chris@16: */
Chris@16: 
Chris@16: // The way overflow is managed for ratio_less is taken from llvm/libcxx/include/ratio
Chris@16: 
Chris@16: #ifndef BOOST_RATIO_DETAIL_RATIO_OPERATIONS_HPP
Chris@16: #define BOOST_RATIO_DETAIL_RATIO_OPERATIONS_HPP
Chris@16: 
Chris@16: #include <boost/ratio/config.hpp>
Chris@16: #include <boost/ratio/detail/mpl/abs.hpp>
Chris@16: #include <boost/ratio/detail/mpl/sign.hpp>
Chris@16: #include <cstdlib>
Chris@16: #include <climits>
Chris@16: #include <limits>
Chris@16: #include <boost/cstdint.hpp>
Chris@16: #include <boost/type_traits/integral_constant.hpp>
Chris@101: #include <boost/core/enable_if.hpp>
Chris@16: #include <boost/integer_traits.hpp>
Chris@16: 
Chris@16: //
Chris@16: // We simply cannot include this header on gcc without getting copious warnings of the kind:
Chris@16: //
Chris@16: // boost/integer.hpp:77:30: warning: use of C99 long long integer constant
Chris@16: //
Chris@16: // And yet there is no other reasonable implementation, so we declare this a system header
Chris@16: // to suppress these warnings.
Chris@16: //
Chris@16: #if defined(__GNUC__) && (__GNUC__ >= 4)
Chris@16: #pragma GCC system_header
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16: 
Chris@16: //----------------------------------------------------------------------------//
Chris@16: //                                 helpers                                    //
Chris@16: //----------------------------------------------------------------------------//
Chris@16: 
Chris@16: namespace ratio_detail
Chris@16: {
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y, boost::intmax_t = mpl::sign_c<boost::intmax_t, Y>::value>
Chris@16:   class br_add;
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_add<X, Y, 1>
Chris@16:   {
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(X <= max - Y , BOOST_RATIO_OVERFLOW_IN_ADD, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X + Y;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_add<X, Y, 0>
Chris@16:   {
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_add<X, Y, -1>
Chris@16:   {
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(min - Y <= X, BOOST_RATIO_OVERFLOW_IN_ADD, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X + Y;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y, boost::intmax_t = mpl::sign_c<boost::intmax_t, Y>::value>
Chris@16:   class br_sub;
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_sub<X, Y, 1>
Chris@16:   {
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(min + Y <= X, BOOST_RATIO_OVERFLOW_IN_SUB, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X - Y;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_sub<X, Y, 0>
Chris@16:   {
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_sub<X, Y, -1>
Chris@16:   {
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(X <= max + Y, BOOST_RATIO_OVERFLOW_IN_SUB, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X - Y;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_mul
Chris@16:   {
Chris@16:       static const boost::intmax_t nan =
Chris@16:           boost::intmax_t(BOOST_RATIO_UINTMAX_C(1) << (sizeof(boost::intmax_t) * CHAR_BIT - 1));
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       static const boost::intmax_t a_x = mpl::abs_c<boost::intmax_t, X>::value;
Chris@16:       static const boost::intmax_t a_y = mpl::abs_c<boost::intmax_t, Y>::value;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(X != nan, BOOST_RATIO_OVERFLOW_IN_MUL, ());
Chris@16:       BOOST_RATIO_STATIC_ASSERT(Y != nan, BOOST_RATIO_OVERFLOW_IN_MUL, ());
Chris@16:       BOOST_RATIO_STATIC_ASSERT(a_x <= max / a_y, BOOST_RATIO_OVERFLOW_IN_MUL, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X * Y;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t Y>
Chris@16:   class br_mul<0, Y>
Chris@16:   {
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = 0;
Chris@16:   };
Chris@16: 
Chris@16:   template <boost::intmax_t X>
Chris@16:   class br_mul<X, 0>
Chris@16:   {
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = 0;
Chris@16:   };
Chris@16: 
Chris@16:   template <>
Chris@16:   class br_mul<0, 0>
Chris@16:   {
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = 0;
Chris@16:   };
Chris@16: 
Chris@16:   // Not actually used but left here in case needed in future maintenance
Chris@16:   template <boost::intmax_t X, boost::intmax_t Y>
Chris@16:   class br_div
Chris@16:   {
Chris@16:       static const boost::intmax_t nan = boost::intmax_t(BOOST_RATIO_UINTMAX_C(1) << (sizeof(boost::intmax_t) * CHAR_BIT - 1));
Chris@16:       static const boost::intmax_t min = boost::integer_traits<boost::intmax_t>::const_min;
Chris@16:       static const boost::intmax_t max = boost::integer_traits<boost::intmax_t>::const_max;
Chris@16: 
Chris@16:       BOOST_RATIO_STATIC_ASSERT(X != nan, BOOST_RATIO_OVERFLOW_IN_DIV, ());
Chris@16:       BOOST_RATIO_STATIC_ASSERT(Y != nan, BOOST_RATIO_OVERFLOW_IN_DIV, ());
Chris@16:       BOOST_RATIO_STATIC_ASSERT(Y != 0, BOOST_RATIO_DIVIDE_BY_0, ());
Chris@16:   public:
Chris@16:       static const boost::intmax_t value = X / Y;
Chris@16:   };
Chris@16: 
Chris@16:   // ratio arithmetic
Chris@16:   template <class R1, class R2> struct ratio_add;
Chris@16:   template <class R1, class R2> struct ratio_subtract;
Chris@16:   template <class R1, class R2> struct ratio_multiply;
Chris@16:   template <class R1, class R2> struct ratio_divide;
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_add
Chris@16:   {
Chris@16:       //The nested typedef type shall be a synonym for ratio<T1, T2>::type where T1 has the value R1::num *
Chris@16:       //R2::den + R2::num * R1::den and T2 has the value R1::den * R2::den.
Chris@16:       // As the preceding doesn't works because of overflow on boost::intmax_t we need something more elaborated.
Chris@16:   private:
Chris@16:       static const boost::intmax_t gcd_n1_n2 = mpl::gcd_c<boost::intmax_t, R1::num, R2::num>::value;
Chris@16:       static const boost::intmax_t gcd_d1_d2 = mpl::gcd_c<boost::intmax_t, R1::den, R2::den>::value;
Chris@16:   public:
Chris@16:       // No need to normalize as ratio_multiply is already normalized
Chris@16:       typedef typename ratio_multiply
Chris@16:          <
Chris@16:              ratio<gcd_n1_n2, R1::den / gcd_d1_d2>,
Chris@16:              ratio
Chris@16:              <
Chris@16:                  boost::ratio_detail::br_add
Chris@16:                  <
Chris@16:                      boost::ratio_detail::br_mul<R1::num / gcd_n1_n2, R2::den / gcd_d1_d2>::value,
Chris@16:                      boost::ratio_detail::br_mul<R2::num / gcd_n1_n2, R1::den / gcd_d1_d2>::value
Chris@16:                  >::value,
Chris@16:                  R2::den
Chris@16:              >
Chris@16:          >::type type;
Chris@16:   };
Chris@16:   template <class R, boost::intmax_t D>
Chris@16:   struct ratio_add<R, ratio<0,D> >
Chris@16:   {
Chris@16:     typedef R type;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_subtract
Chris@16:   {
Chris@16:       //The nested typedef type shall be a synonym for ratio<T1, T2>::type where T1 has the value
Chris@16:       // R1::num *R2::den - R2::num * R1::den and T2 has the value R1::den * R2::den.
Chris@16:       // As the preceding doesn't works because of overflow on boost::intmax_t we need something more elaborated.
Chris@16:   private:
Chris@16:       static const boost::intmax_t gcd_n1_n2 = mpl::gcd_c<boost::intmax_t, R1::num, R2::num>::value;
Chris@16:       static const boost::intmax_t gcd_d1_d2 = mpl::gcd_c<boost::intmax_t, R1::den, R2::den>::value;
Chris@16:   public:
Chris@16:       // No need to normalize as ratio_multiply is already normalized
Chris@16:       typedef typename ratio_multiply
Chris@16:          <
Chris@16:              ratio<gcd_n1_n2, R1::den / gcd_d1_d2>,
Chris@16:              ratio
Chris@16:              <
Chris@16:                  boost::ratio_detail::br_sub
Chris@16:                  <
Chris@16:                      boost::ratio_detail::br_mul<R1::num / gcd_n1_n2, R2::den / gcd_d1_d2>::value,
Chris@16:                      boost::ratio_detail::br_mul<R2::num / gcd_n1_n2, R1::den / gcd_d1_d2>::value
Chris@16:                  >::value,
Chris@16:                  R2::den
Chris@16:              >
Chris@16:          >::type type;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R, boost::intmax_t D>
Chris@16:   struct ratio_subtract<R, ratio<0,D> >
Chris@16:   {
Chris@16:     typedef R type;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_multiply
Chris@16:   {
Chris@16:       // The nested typedef type  shall be a synonym for ratio<R1::num * R2::den - R2::num * R1::den, R1::den * R2::den>::type.
Chris@16:       // As the preceding doesn't works because of overflow on boost::intmax_t we need something more elaborated.
Chris@16:   private:
Chris@16:      static const boost::intmax_t gcd_n1_d2 = mpl::gcd_c<boost::intmax_t, R1::num, R2::den>::value;
Chris@16:      static const boost::intmax_t gcd_d1_n2 = mpl::gcd_c<boost::intmax_t, R1::den, R2::num>::value;
Chris@16:   public:
Chris@16:       typedef typename ratio
Chris@16:          <
Chris@16:              boost::ratio_detail::br_mul<R1::num / gcd_n1_d2, R2::num / gcd_d1_n2>::value,
Chris@16:              boost::ratio_detail::br_mul<R2::den / gcd_n1_d2, R1::den / gcd_d1_n2>::value
Chris@16:          >::type type;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_divide
Chris@16:   {
Chris@16:       // The nested typedef type  shall be a synonym for ratio<R1::num * R2::den, R2::num * R1::den>::type.
Chris@16:       // As the preceding doesn't works because of overflow on boost::intmax_t we need something more elaborated.
Chris@16:   private:
Chris@16:       static const boost::intmax_t gcd_n1_n2 = mpl::gcd_c<boost::intmax_t, R1::num, R2::num>::value;
Chris@16:       static const boost::intmax_t gcd_d1_d2 = mpl::gcd_c<boost::intmax_t, R1::den, R2::den>::value;
Chris@16:   public:
Chris@16:       typedef typename ratio
Chris@16:          <
Chris@16:              boost::ratio_detail::br_mul<R1::num / gcd_n1_n2, R2::den / gcd_d1_d2>::value,
Chris@16:              boost::ratio_detail::br_mul<R2::num / gcd_n1_n2, R1::den / gcd_d1_d2>::value
Chris@16:          >::type type;
Chris@16:   };
Chris@16:   template <class R1, class R2>
Chris@16:   struct is_evenly_divisible_by
Chris@16:   {
Chris@16:   private:
Chris@16:       static const boost::intmax_t gcd_n1_n2 = mpl::gcd_c<boost::intmax_t, R1::num, R2::num>::value;
Chris@16:       static const boost::intmax_t gcd_d1_d2 = mpl::gcd_c<boost::intmax_t, R1::den, R2::den>::value;
Chris@16:   public:
Chris@16:       typedef integral_constant<bool,
Chris@16:              ((R2::num / gcd_n1_n2 ==1) && (R1::den / gcd_d1_d2)==1)
Chris@16:       > type;
Chris@16:   };
Chris@16: 
Chris@16:   template <class T>
Chris@16:   struct is_ratio : public boost::false_type
Chris@16:   {};
Chris@16:   template <boost::intmax_t N, boost::intmax_t D>
Chris@16:   struct is_ratio<ratio<N, D> > : public boost::true_type
Chris@16:   {};
Chris@16: 
Chris@16:   template <class R1, class R2,
Chris@16:             boost::intmax_t Q1 = R1::num / R1::den, boost::intmax_t M1 = R1::num % R1::den,
Chris@16:             boost::intmax_t Q2 = R2::num / R2::den, boost::intmax_t M2 = R2::num % R2::den>
Chris@16:   struct ratio_less1
Chris@16:   {
Chris@16:     static const bool value = Q1 < Q2;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2, boost::intmax_t Q>
Chris@16:   struct ratio_less1<R1, R2, Q, 0, Q, 0>
Chris@16:   {
Chris@16:     static const bool value = false;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2, boost::intmax_t Q, boost::intmax_t M2>
Chris@16:   struct ratio_less1<R1, R2, Q, 0, Q, M2>
Chris@16:   {
Chris@16:     static const bool value = true;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2, boost::intmax_t Q, boost::intmax_t M1>
Chris@16:   struct ratio_less1<R1, R2, Q, M1, Q, 0>
Chris@16:   {
Chris@16:     static const bool value = false;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2, boost::intmax_t Q, boost::intmax_t M1, boost::intmax_t M2>
Chris@16:   struct ratio_less1<R1, R2, Q, M1, Q, M2>
Chris@16:   {
Chris@16:     static const bool value = ratio_less1<ratio<R2::den, M2>, ratio<R1::den, M1>
Chris@16:                                             >::value;
Chris@16:   };
Chris@16: 
Chris@16:   template <
Chris@16:       class R1,
Chris@16:       class R2,
Chris@16:       boost::intmax_t S1 = mpl::sign_c<boost::intmax_t, R1::num>::value,
Chris@16:     boost::intmax_t S2 = mpl::sign_c<boost::intmax_t, R2::num>::value
Chris@16: >
Chris@16:   struct ratio_less
Chris@16:   {
Chris@16:       static const bool value = S1 < S2;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_less<R1, R2, 1LL, 1LL>
Chris@16:   {
Chris@16:       static const bool value = ratio_less1<R1, R2>::value;
Chris@16:   };
Chris@16: 
Chris@16:   template <class R1, class R2>
Chris@16:   struct ratio_less<R1, R2, -1LL, -1LL>
Chris@16:   {
Chris@16:       static const bool value = ratio_less1<ratio<-R2::num, R2::den>,
Chris@16:                                             ratio<-R1::num, R1::den> >::value;
Chris@16:   };
Chris@16: 
Chris@16: 
Chris@16: }  // namespace ratio_detail
Chris@16: 
Chris@16: }  // namespace boost
Chris@16: 
Chris@16: #endif  // BOOST_RATIO_HPP