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+//  ratio.hpp  ---------------------------------------------------------------//
+
+//  Copyright 2008 Howard Hinnant
+//  Copyright 2008 Beman Dawes
+//  Copyright 2009 Vicente J. Botet Escriba
+
+//  Distributed under the Boost Software License, Version 1.0.
+//  See http://www.boost.org/LICENSE_1_0.txt
+
+/*
+
+This code was derived by Beman Dawes from Howard Hinnant's time2_demo prototype.
+Many thanks to Howard for making his code available under the Boost license.
+The original code was modified to conform to Boost conventions and to section
+20.4 Compile-time rational arithmetic [ratio], of the C++ committee working
+paper N2798.
+See http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2798.pdf.
+
+time2_demo contained this comment:
+
+    Much thanks to Andrei Alexandrescu,
+                   Walter Brown,
+                   Peter Dimov,
+                   Jeff Garland,
+                   Terry Golubiewski,
+                   Daniel Krugler,
+                   Anthony Williams.
+*/
+
+// The way overflow is managed for ratio_less is taken from llvm/libcxx/include/ratio
+
+#ifndef BOOST_RATIO_RATIO_HPP
+#define BOOST_RATIO_RATIO_HPP
+
+#include <boost/ratio/config.hpp>
+#include <boost/ratio/detail/mpl/abs.hpp>
+#include <boost/ratio/detail/mpl/sign.hpp>
+#include <boost/ratio/detail/mpl/gcd.hpp>
+#include <boost/ratio/detail/mpl/lcm.hpp>
+#include <cstdlib>
+#include <climits>
+#include <limits>
+#include <boost/cstdint.hpp>
+#include <boost/type_traits/integral_constant.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <boost/integer_traits.hpp>
+#include <boost/ratio/ratio_fwd.hpp>
+#include <boost/ratio/detail/overflow_helpers.hpp>
+#ifdef BOOST_RATIO_EXTENSIONS
+#include <boost/rational.hpp>
+#include <boost/ratio/mpl/rational_c_tag.hpp>
+#endif
+
+//
+// We simply cannot include this header on gcc without getting copious warnings of the kind:
+//
+// boost/integer.hpp:77:30: warning: use of C99 long long integer constant
+//
+// And yet there is no other reasonable implementation, so we declare this a system header
+// to suppress these warnings.
+//
+#if defined(__GNUC__) && (__GNUC__ >= 4)
+#pragma GCC system_header
+#endif
+
+namespace boost
+{
+
+
+//----------------------------------------------------------------------------//
+//                                                                            //
+//                20.6.1 Class template ratio [ratio.ratio]                   //
+//                                                                            //
+//----------------------------------------------------------------------------//
+
+template <boost::intmax_t N, boost::intmax_t D>
+class ratio
+{
+    static const boost::intmax_t ABS_N = mpl::abs_c<boost::intmax_t, N>::value;
+    static const boost::intmax_t ABS_D = mpl::abs_c<boost::intmax_t, D>::value;
+    BOOST_RATIO_STATIC_ASSERT(ABS_N >= 0, BOOST_RATIO_NUMERATOR_IS_OUT_OF_RANGE, ());
+    BOOST_RATIO_STATIC_ASSERT(ABS_D > 0, BOOST_RATIO_DENOMINATOR_IS_OUT_OF_RANGE, ());
+    BOOST_RATIO_STATIC_ASSERT(D != 0, BOOST_RATIO_DIVIDE_BY_0 , ());
+    static const boost::intmax_t SIGN_N = mpl::sign_c<boost::intmax_t,N>::value
+      * mpl::sign_c<boost::intmax_t,D>::value;
+    static const boost::intmax_t GCD = mpl::gcd_c<boost::intmax_t, ABS_N, ABS_D>::value;
+public:
+    BOOST_STATIC_CONSTEXPR boost::intmax_t num = SIGN_N * ABS_N / GCD;
+    BOOST_STATIC_CONSTEXPR boost::intmax_t den = ABS_D / GCD;
+
+#ifdef BOOST_RATIO_EXTENSIONS
+    typedef mpl::rational_c_tag tag;
+    typedef boost::rational<boost::intmax_t> value_type;
+    typedef boost::intmax_t num_type;
+    typedef boost::intmax_t den_type;
+    ratio()
+    {}
+    template <boost::intmax_t _N2, boost::intmax_t _D2>
+    ratio(const ratio<_N2, _D2>&,
+        typename enable_if_c
+            <
+                (ratio<_N2, _D2>::num == num &&
+                ratio<_N2, _D2>::den == den)
+            >::type* = 0)
+    {}
+
+    template <boost::intmax_t _N2, boost::intmax_t _D2>
+        typename enable_if_c
+        <
+            (ratio<_N2, _D2>::num == num &&
+            ratio<_N2, _D2>::den == den),
+            ratio&
+        >::type
+    operator=(const ratio<_N2, _D2>&) {return *this;}
+
+    static value_type value() {return value_type(num,den);}
+    value_type operator()() const {return value();}
+#endif
+    typedef ratio<num, den> type;
+};
+
+#if defined(BOOST_NO_CXX11_CONSTEXPR)
+template <boost::intmax_t N, boost::intmax_t D>
+const    boost::intmax_t ratio<N, D>::num;
+template <boost::intmax_t N, boost::intmax_t D>
+const    boost::intmax_t ratio<N, D>::den;
+#endif
+
+//----------------------------------------------------------------------------//
+//                                                                            //
+//                20.6.2 Arithmetic on ratio types [ratio.arithmetic]                   //
+//                                                                            //
+//----------------------------------------------------------------------------//
+
+template <class R1, class R2>
+struct ratio_add
+: boost::ratio_detail::ratio_add<R1, R2>::type
+{
+};
+
+template <class R1, class R2>
+struct ratio_subtract
+: boost::ratio_detail::ratio_subtract<R1, R2>::type
+{
+};
+
+template <class R1, class R2>
+struct ratio_multiply
+: boost::ratio_detail::ratio_multiply<R1, R2>::type
+{
+};
+
+template <class R1, class R2>
+struct ratio_divide
+: boost::ratio_detail::ratio_divide<R1, R2>::type
+{
+};
+
+//----------------------------------------------------------------------------//
+//                                                                            //
+//                20.6.3 Comparasion of ratio types [ratio.comparison]                   //
+//                                                                            //
+//----------------------------------------------------------------------------//
+
+// ratio_equal
+
+template <class R1, class R2>
+struct ratio_equal
+    : public boost::integral_constant<bool,
+                               (R1::num == R2::num && R1::den == R2::den)>
+{};
+
+template <class R1, class R2>
+struct ratio_not_equal
+    : public boost::integral_constant<bool, !ratio_equal<R1, R2>::value>
+{};
+
+// ratio_less
+
+template <class R1, class R2>
+struct ratio_less
+    : boost::integral_constant<bool, boost::ratio_detail::ratio_less<R1, R2>::value>
+{};
+
+template <class R1, class R2>
+struct ratio_less_equal
+    : boost::integral_constant<bool, !ratio_less<R2, R1>::value>
+{};
+
+template <class R1, class R2>
+struct ratio_greater
+    : boost::integral_constant<bool, ratio_less<R2, R1>::value>
+{};
+
+template <class R1, class R2>
+struct ratio_greater_equal
+    : boost::integral_constant<bool, !ratio_less<R1, R2>::value>
+{};
+
+template <class R1, class R2>
+struct ratio_gcd :
+    ratio<mpl::gcd_c<boost::intmax_t, R1::num, R2::num>::value,
+        mpl::lcm_c<boost::intmax_t, R1::den, R2::den>::value>::type
+{
+};
+
+#ifdef BOOST_RATIO_EXTENSIONS
+template <class R>
+struct ratio_negate
+    : ratio<-R::num, R::den>::type
+{
+};
+template <class R>
+struct ratio_abs
+    : ratio<mpl::abs_c<boost::intmax_t, R::num>::value, R::den>::type
+{
+};
+template <class R>
+struct ratio_sign
+    : mpl::sign_c<boost::intmax_t, R::num>
+{
+};
+template <class R1, class R2>
+struct ratio_lcm :
+    ratio<mpl::lcm_c<boost::intmax_t, R1::num, R2::num>::value,
+        mpl::gcd_c<boost::intmax_t, R1::den, R2::den>::value>::type
+{
+};
+#endif
+}  // namespace boost
+
+
+#endif  // BOOST_RATIO_RATIO_HPP