OTS/OTSCPP/Tools/boost/multiprecision/detail/number_base.hpp

///////////////////////////////////////////////////////////////////////////////
//  Copyright 2011 John Maddock. 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)

#ifndef BOOST_MATH_BIG_NUM_BASE_HPP
#define BOOST_MATH_BIG_NUM_BASE_HPP

#include <limits>
#include <boost/utility/enable_if.hpp>
#include <boost/core/nvp.hpp>
#include <boost/type_traits/is_convertible.hpp>
#include <boost/type_traits/is_constructible.hpp>
#include <boost/type_traits/decay.hpp>
#include <boost/math/tools/complex.hpp>
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 4307)
#endif
#include <boost/lexical_cast.hpp>
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif

#if defined(BOOST_NO_CXX11_RVALUE_REFERENCES) || defined(BOOST_NO_CXX11_TEMPLATE_ALIASES) || defined(BOOST_NO_CXX11_HDR_ARRAY)\
      || defined(BOOST_NO_CXX11_ALLOCATOR) || defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) || defined(BOOST_NO_CXX11_CONSTEXPR)\
      || defined(BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS) || defined(BOOST_NO_CXX11_REF_QUALIFIERS) || defined(BOOST_NO_CXX11_HDR_FUNCTIONAL)\
      || defined(BOOST_NO_CXX11_VARIADIC_TEMPLATES) || defined(BOOST_NO_CXX11_USER_DEFINED_LITERALS) || defined(BOOST_NO_CXX11_THREAD_LOCAL)\
      || defined(BOOST_NO_CXX11_DECLTYPE) || defined(BOOST_NO_CXX11_STATIC_ASSERT) || defined(BOOST_NO_CXX11_DEFAULTED_FUNCTIONS)\
      || defined(BOOST_NO_CXX11_NOEXCEPT) || defined(BOOST_NO_CXX11_REF_QUALIFIERS)
//
// The above list includes everything we use, plus a few we're likely to use soon.
// As from March 2020, C++03 support is deprecated, and as from March 2021 will be removed,
// so mark up as such:
//
#if (defined(_MSC_VER) || defined(__GNUC__)) && !defined(BOOST_MP_DISABLE_DEPRECATE_03_WARNING)
#pragma message("CAUTION: One or more C++11 features were found to be unavailable")
#pragma message("CAUTION: Compiling Boost.Multiprecision in non-C++11 or later conformance modes is now deprecated and will be removed from March 2021.")
#pragma message("CAUTION: Define BOOST_MP_DISABLE_DEPRECATE_03_WARNING to suppress this message.")
#endif
#endif

#if defined(NDEBUG) && !defined(_DEBUG)
#define BOOST_MP_FORCEINLINE BOOST_FORCEINLINE
#else
#define BOOST_MP_FORCEINLINE inline
#endif

#if (defined(BOOST_GCC) && (BOOST_GCC <= 40700)) || BOOST_WORKAROUND(__SUNPRO_CC, < 0x5140) || (defined(__clang_major__) && (__clang_major__ == 3) && (__clang_minor__ < 5))
#define BOOST_MP_NOEXCEPT_IF(x)
#else
#define BOOST_MP_NOEXCEPT_IF(x) BOOST_NOEXCEPT_IF(x)
#endif

#if defined(BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS) || BOOST_WORKAROUND(__SUNPRO_CC, < 0x5140)
#define BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#endif

//
// Thread local storage:
// Note fails on Mingw, see https://sourceforge.net/p/mingw-w64/bugs/527/
//
#if !defined(BOOST_NO_CXX11_THREAD_LOCAL) && !defined(BOOST_INTEL) && !defined(__MINGW32__)
#define BOOST_MP_THREAD_LOCAL thread_local
#define BOOST_MP_USING_THREAD_LOCAL
#else
#define BOOST_MP_THREAD_LOCAL
#endif

#ifdef __has_include
# if __has_include(<version>)
#  include <version>
#  ifdef __cpp_lib_is_constant_evaluated
#   include <type_traits>
#   define BOOST_MP_HAS_IS_CONSTANT_EVALUATED
#  endif
# endif
#endif

#ifdef __has_builtin
#if __has_builtin(__builtin_is_constant_evaluated) && !defined(BOOST_NO_CXX14_CONSTEXPR) && !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX)
#define BOOST_MP_HAS_BUILTIN_IS_CONSTANT_EVALUATED
#endif
#endif
//
// MSVC also supports __builtin_is_constant_evaluated if it's recent enough:
//
#if defined(_MSC_FULL_VER) && (_MSC_FULL_VER >= 192528326)
#  define BOOST_MP_HAS_BUILTIN_IS_CONSTANT_EVALUATED
#endif
//
// As does GCC-9:
//
#if defined(BOOST_GCC) && !defined(BOOST_NO_CXX14_CONSTEXPR) && (__GNUC__ >= 9) && !defined(BOOST_MP_HAS_BUILTIN_IS_CONSTANT_EVALUATED)
#  define BOOST_MP_HAS_BUILTIN_IS_CONSTANT_EVALUATED
#endif

#if defined(BOOST_MP_HAS_IS_CONSTANT_EVALUATED) && !defined(BOOST_NO_CXX14_CONSTEXPR)
#  define BOOST_MP_IS_CONST_EVALUATED(x) std::is_constant_evaluated()
#elif defined(BOOST_MP_HAS_BUILTIN_IS_CONSTANT_EVALUATED)
#  define BOOST_MP_IS_CONST_EVALUATED(x) __builtin_is_constant_evaluated()
#elif !defined(BOOST_NO_CXX14_CONSTEXPR) && defined(BOOST_GCC) && (__GNUC__ >= 6)
#  define BOOST_MP_IS_CONST_EVALUATED(x) __builtin_constant_p(x)
#else
#  define BOOST_MP_NO_CONSTEXPR_DETECTION
#endif

#define BOOST_MP_CXX14_CONSTEXPR BOOST_CXX14_CONSTEXPR
//
// Early compiler versions trip over the constexpr code:
//
#if defined(__clang__) && (__clang_major__ < 5)
#undef BOOST_MP_CXX14_CONSTEXPR
#define BOOST_MP_CXX14_CONSTEXPR
#endif
#if defined(__apple_build_version__) && (__clang_major__ < 9)
#undef BOOST_MP_CXX14_CONSTEXPR
#define BOOST_MP_CXX14_CONSTEXPR
#endif
#if defined(BOOST_GCC) && (__GNUC__ < 6)
#undef BOOST_MP_CXX14_CONSTEXPR
#define BOOST_MP_CXX14_CONSTEXPR
#endif
#if defined(BOOST_INTEL)
#undef BOOST_MP_CXX14_CONSTEXPR
#define BOOST_MP_CXX14_CONSTEXPR
#define BOOST_MP_NO_CONSTEXPR_DETECTION
#endif

#ifdef BOOST_MP_NO_CONSTEXPR_DETECTION
#  define BOOST_CXX14_CONSTEXPR_IF_DETECTION
#else
#  define BOOST_CXX14_CONSTEXPR_IF_DETECTION constexpr
#endif

#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 6326)
#endif

namespace boost {
namespace multiprecision {

enum expression_template_option
{
   et_off = 0,
   et_on  = 1
};

template <class Backend>
struct expression_template_default
{
   static const expression_template_option value = et_on;
};

template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value>
class number;

template <class T>
struct is_number : public mpl::false_
{};

template <class Backend, expression_template_option ExpressionTemplates>
struct is_number<number<Backend, ExpressionTemplates> > : public mpl::true_
{};

template <class T>
struct is_et_number : public mpl::false_
{};

template <class Backend>
struct is_et_number<number<Backend, et_on> > : public mpl::true_
{};

template <class T>
struct is_no_et_number : public mpl::false_
{};

template <class Backend>
struct is_no_et_number<number<Backend, et_off> > : public mpl::true_
{};

namespace detail {

// Forward-declare an expression wrapper
template <class tag, class Arg1 = void, class Arg2 = void, class Arg3 = void, class Arg4 = void>
struct expression;

} // namespace detail

template <class T>
struct is_number_expression : public mpl::false_
{};

template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
struct is_number_expression<detail::expression<tag, Arg1, Arg2, Arg3, Arg4> > : public mpl::true_
{};

template <class T, class Num>
struct is_compatible_arithmetic_type
    : public mpl::bool_<
          is_convertible<T, Num>::value && !is_same<T, Num>::value && !is_number_expression<T>::value>
{};

namespace detail {
//
// Workaround for missing abs(boost::long_long_type) and abs(__int128) on some compilers:
//
template <class T>
BOOST_CONSTEXPR typename enable_if_c<(is_signed<T>::value || is_floating_point<T>::value), T>::type abs(T t) BOOST_NOEXCEPT
{
   // This strange expression avoids a hardware trap in the corner case
   // that val is the most negative value permitted in boost::long_long_type.
   // See https://svn.boost.org/trac/boost/ticket/9740.
   return t < 0 ? T(1u) + T(-(t + 1)) : t;
}
template <class T>
BOOST_CONSTEXPR typename enable_if_c<(is_unsigned<T>::value), T>::type abs(T t) BOOST_NOEXCEPT
{
   return t;
}

#define BOOST_MP_USING_ABS using boost::multiprecision::detail::abs;

template <class T>
BOOST_CONSTEXPR typename enable_if_c<(is_signed<T>::value || is_floating_point<T>::value), typename make_unsigned<T>::type>::type unsigned_abs(T t) BOOST_NOEXCEPT
{
   // This strange expression avoids a hardware trap in the corner case
   // that val is the most negative value permitted in boost::long_long_type.
   // See https://svn.boost.org/trac/boost/ticket/9740.
   return t < 0 ? static_cast<typename make_unsigned<T>::type>(1u) + static_cast<typename make_unsigned<T>::type>(-(t + 1)) : static_cast<typename make_unsigned<T>::type>(t);
}
template <class T>
BOOST_CONSTEXPR typename enable_if_c<(is_unsigned<T>::value), T>::type unsigned_abs(T t) BOOST_NOEXCEPT
{
   return t;
}

//
// Move support:
//
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
#define BOOST_MP_MOVE(x) std::move(x)
#else
#define BOOST_MP_MOVE(x) x
#endif

template <class T>
struct bits_of
{
   BOOST_STATIC_ASSERT(is_integral<T>::value || is_enum<T>::value || std::numeric_limits<T>::is_specialized);
   static const unsigned value =
       std::numeric_limits<T>::is_specialized ? std::numeric_limits<T>::digits
                                              : sizeof(T) * CHAR_BIT - (is_signed<T>::value ? 1 : 0);
};

#if defined(_GLIBCXX_USE_FLOAT128) && defined(BOOST_GCC) && !defined(__STRICT_ANSI__)
#define BOOST_MP_BITS_OF_FLOAT128_DEFINED
template <>
struct bits_of<__float128>
{
   static const unsigned value = 113;
};
#endif

template <int b>
struct has_enough_bits
{
   template <class T>
   struct type : public mpl::bool_<bits_of<T>::value >= b>
   {};
};

template <class Val, class Backend, class Tag>
struct canonical_imp
{
   typedef typename remove_cv<typename decay<const Val>::type>::type type;
};
template <class B, class Backend, class Tag>
struct canonical_imp<number<B, et_on>, Backend, Tag>
{
   typedef B type;
};
template <class B, class Backend, class Tag>
struct canonical_imp<number<B, et_off>, Backend, Tag>
{
   typedef B type;
};
#ifdef __SUNPRO_CC
template <class B, class Backend>
struct canonical_imp<number<B, et_on>, Backend, mpl::int_<3> >
{
   typedef B type;
};
template <class B, class Backend>
struct canonical_imp<number<B, et_off>, Backend, mpl::int_<3> >
{
   typedef B type;
};
#endif
template <class Val, class Backend>
struct canonical_imp<Val, Backend, mpl::int_<0> >
{
   typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
   typedef typename mpl::find_if<
       typename Backend::signed_types,
       pred_type>::type                                                                                                 iter_type;
   typedef typename mpl::end<typename Backend::signed_types>::type                                                      end_type;
   typedef typename mpl::eval_if<boost::is_same<iter_type, end_type>, mpl::identity<Val>, mpl::deref<iter_type> >::type type;
};
template <class Val, class Backend>
struct canonical_imp<Val, Backend, mpl::int_<1> >
{
   typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
   typedef typename mpl::find_if<
       typename Backend::unsigned_types,
       pred_type>::type                                                                                                 iter_type;
   typedef typename mpl::end<typename Backend::unsigned_types>::type                                                    end_type;
   typedef typename mpl::eval_if<boost::is_same<iter_type, end_type>, mpl::identity<Val>, mpl::deref<iter_type> >::type type;
};
template <class Val, class Backend>
struct canonical_imp<Val, Backend, mpl::int_<2> >
{
   typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
   typedef typename mpl::find_if<
       typename Backend::float_types,
       pred_type>::type                                                                                                 iter_type;
   typedef typename mpl::end<typename Backend::float_types>::type                                                       end_type;
   typedef typename mpl::eval_if<boost::is_same<iter_type, end_type>, mpl::identity<Val>, mpl::deref<iter_type> >::type type;
};
template <class Val, class Backend>
struct canonical_imp<Val, Backend, mpl::int_<3> >
{
   typedef const char* type;
};

template <class Val, class Backend>
struct canonical
{
   typedef typename mpl::if_<
       is_signed<Val>,
       mpl::int_<0>,
       typename mpl::if_<
           is_unsigned<Val>,
           mpl::int_<1>,
           typename mpl::if_<
               is_floating_point<Val>,
               mpl::int_<2>,
               typename mpl::if_<
                   mpl::or_<
                       is_convertible<Val, const char*>,
                       is_same<Val, std::string> >,
                   mpl::int_<3>,
                   mpl::int_<4> >::type>::type>::type>::type tag_type;

   typedef typename canonical_imp<Val, Backend, tag_type>::type type;
};

struct terminal
{};
struct negate
{};
struct plus
{};
struct minus
{};
struct multiplies
{};
struct divides
{};
struct modulus
{};
struct shift_left
{};
struct shift_right
{};
struct bitwise_and
{};
struct bitwise_or
{};
struct bitwise_xor
{};
struct bitwise_complement
{};
struct add_immediates
{};
struct subtract_immediates
{};
struct multiply_immediates
{};
struct divide_immediates
{};
struct modulus_immediates
{};
struct bitwise_and_immediates
{};
struct bitwise_or_immediates
{};
struct bitwise_xor_immediates
{};
struct complement_immediates
{};
struct function
{};
struct multiply_add
{};
struct multiply_subtract
{};

template <class T>
struct backend_type;

template <class T, expression_template_option ExpressionTemplates>
struct backend_type<number<T, ExpressionTemplates> >
{
   typedef T type;
};

template <class tag, class A1, class A2, class A3, class A4>
struct backend_type<expression<tag, A1, A2, A3, A4> >
{
   typedef typename backend_type<typename expression<tag, A1, A2, A3, A4>::result_type>::type type;
};

template <class T1, class T2>
struct combine_expression
{
#ifdef BOOST_NO_CXX11_DECLTYPE
   typedef typename mpl::if_c<(sizeof(T1() + T2()) == sizeof(T1)), T1, T2>::type type;
#else
   typedef decltype(T1() + T2()) type;
#endif
};

template <class T1, expression_template_option ExpressionTemplates, class T2>
struct combine_expression<number<T1, ExpressionTemplates>, T2>
{
   typedef number<T1, ExpressionTemplates> type;
};

template <class T1, class T2, expression_template_option ExpressionTemplates>
struct combine_expression<T1, number<T2, ExpressionTemplates> >
{
   typedef number<T2, ExpressionTemplates> type;
};

template <class T, expression_template_option ExpressionTemplates>
struct combine_expression<number<T, ExpressionTemplates>, number<T, ExpressionTemplates> >
{
   typedef number<T, ExpressionTemplates> type;
};

template <class T1, expression_template_option ExpressionTemplates1, class T2, expression_template_option ExpressionTemplates2>
struct combine_expression<number<T1, ExpressionTemplates1>, number<T2, ExpressionTemplates2> >
{
   typedef typename mpl::if_c<
       is_convertible<number<T2, ExpressionTemplates2>, number<T1, ExpressionTemplates2> >::value,
       number<T1, ExpressionTemplates1>,
       number<T2, ExpressionTemplates2> >::type type;
};

template <class T>
struct arg_type
{
   typedef expression<terminal, T> type;
};

template <class Tag, class Arg1, class Arg2, class Arg3, class Arg4>
struct arg_type<expression<Tag, Arg1, Arg2, Arg3, Arg4> >
{
   typedef expression<Tag, Arg1, Arg2, Arg3, Arg4> type;
};

struct unmentionable
{
   unmentionable* proc() { return 0; }
};

typedef unmentionable* (unmentionable::*unmentionable_type)();

template <class T, bool b>
struct expression_storage_base
{
   typedef const T& type;
};

template <class T>
struct expression_storage_base<T, true>
{
   typedef T type;
};

template <class T>
struct expression_storage : public expression_storage_base<T, boost::is_arithmetic<T>::value>
{};

template <class T>
struct expression_storage<T*>
{
   typedef T* type;
};

template <class T>
struct expression_storage<const T*>
{
   typedef const T* type;
};

template <class tag, class A1, class A2, class A3, class A4>
struct expression_storage<expression<tag, A1, A2, A3, A4> >
{
   typedef expression<tag, A1, A2, A3, A4> type;
};

template <class tag, class Arg1>
struct expression<tag, Arg1, void, void, void>
{
   typedef mpl::int_<1>                    arity;
   typedef typename arg_type<Arg1>::type   left_type;
   typedef typename left_type::result_type left_result_type;
   typedef typename left_type::result_type result_type;
   typedef tag                             tag_type;

   explicit BOOST_MP_CXX14_CONSTEXPR expression(const Arg1& a) : arg(a) {}
   BOOST_MP_CXX14_CONSTEXPR expression(const expression& e) : arg(e.arg) {}

#ifndef BOOST_NO_CXX11_STATIC_ASSERT
   //
   // If we have static_assert we can give a more useful error message
   // than if we simply have no operator defined at all:
   //
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not assign to a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator+=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator+= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator-=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator-= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator*=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator*= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator/=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator/= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator%=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator%= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator|=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator|= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator&=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator&= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator^=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator^= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator<<=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator<<= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator>>=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator>>= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
#endif

   BOOST_MP_CXX14_CONSTEXPR left_type left() const
   {
      return left_type(arg);
   }

   BOOST_MP_CXX14_CONSTEXPR const Arg1& left_ref() const BOOST_NOEXCEPT { return arg; }

   static const unsigned depth = left_type::depth + 1;
#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) && !defined(__clang__)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500))
   //
   // Horrible workaround for gcc-4.6.x which always prefers the template
   // operator bool() rather than the non-template operator when converting to
   // an arithmetic type:
   //
   template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0>
   explicit operator T() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
   template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value || is_number<T>::value, int>::type = 0>
   explicit operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
#else
   template <class T
#ifndef __SUNPRO_CC
             ,
             typename boost::disable_if_c<is_number<T>::value || is_constructible<T const&, result_type>::value || !is_constructible<T, result_type>::value, int>::type = 0
#endif
             >
   explicit BOOST_MP_CXX14_CONSTEXPR operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
   BOOST_MP_FORCEINLINE explicit BOOST_MP_CXX14_CONSTEXPR operator bool() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800)
   BOOST_MP_FORCEINLINE explicit operator void() const
   {}
#endif
#endif
#else
   operator unmentionable_type() const
   {
      result_type r(*this);
      return r ? &unmentionable::proc : 0;
   }
#endif

   template <class T>
   BOOST_MP_CXX14_CONSTEXPR T convert_to()
   {
      result_type r(*this);
      return r.template convert_to<T>();
   }

 private:
   typename expression_storage<Arg1>::type arg;
   expression&                             operator=(const expression&);
};

template <class Arg1>
struct expression<terminal, Arg1, void, void, void>
{
   typedef mpl::int_<0> arity;
   typedef Arg1         result_type;
   typedef terminal     tag_type;

   explicit BOOST_MP_CXX14_CONSTEXPR expression(const Arg1& a) : arg(a) {}
   BOOST_MP_CXX14_CONSTEXPR expression(const expression& e) : arg(e.arg) {}

#ifndef BOOST_NO_CXX11_STATIC_ASSERT
   //
   // If we have static_assert we can give a more useful error message
   // than if we simply have no operator defined at all:
   //
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not assign to a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator+=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator+= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator-=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator-= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator*=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator*= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator/=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator/= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator%=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator%= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator|=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator|= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator&=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator&= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator^=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator^= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator<<=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator<<= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator>>=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator>>= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
#endif

   BOOST_MP_CXX14_CONSTEXPR const Arg1& value() const BOOST_NOEXCEPT
   {
      return arg;
   }

   static const unsigned depth = 0;

#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) && !defined(__clang__)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500))
   //
   // Horrible workaround for gcc-4.6.x which always prefers the template
   // operator bool() rather than the non-template operator when converting to
   // an arithmetic type:
   //
   template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0>
   explicit operator T() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
   template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value || is_number<T>::value, int>::type = 0>
   explicit operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
#else
   template <class T
#ifndef __SUNPRO_CC
             ,
             typename boost::disable_if_c<is_number<T>::value || is_constructible<T const&, result_type>::value || !is_constructible<T, result_type>::value, int>::type = 0
#endif
             >
   explicit BOOST_MP_CXX14_CONSTEXPR operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
   BOOST_MP_FORCEINLINE explicit BOOST_MP_CXX14_CONSTEXPR operator bool() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800)
   BOOST_MP_FORCEINLINE explicit operator void() const
   {}
#endif
#endif
#else
   operator unmentionable_type() const
   {
      return arg ? &unmentionable::proc : 0;
   }
#endif

   template <class T>
   BOOST_MP_CXX14_CONSTEXPR T convert_to()
   {
      result_type r(*this);
      return r.template convert_to<T>();
   }

 private:
   typename expression_storage<Arg1>::type arg;
   expression&                             operator=(const expression&);
};

template <class tag, class Arg1, class Arg2>
struct expression<tag, Arg1, Arg2, void, void>
{
   typedef mpl::int_<2>                                                           arity;
   typedef typename arg_type<Arg1>::type                                          left_type;
   typedef typename arg_type<Arg2>::type                                          right_type;
   typedef typename left_type::result_type                                        left_result_type;
   typedef typename right_type::result_type                                       right_result_type;
   typedef typename combine_expression<left_result_type, right_result_type>::type result_type;
   typedef tag                                                                    tag_type;

   BOOST_MP_CXX14_CONSTEXPR expression(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {}
   BOOST_MP_CXX14_CONSTEXPR expression(const expression& e) : arg1(e.arg1), arg2(e.arg2) {}

#ifndef BOOST_NO_CXX11_STATIC_ASSERT
   //
   // If we have static_assert we can give a more useful error message
   // than if we simply have no operator defined at all:
   //
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not assign to a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator+=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator+= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator-=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator-= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator*=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator*= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator/=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator/= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator%=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator%= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator|=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator|= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator&=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator&= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator^=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator^= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator<<=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator<<= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator>>=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator>>= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
#endif

   BOOST_MP_CXX14_CONSTEXPR left_type left() const
   {
      return left_type(arg1);
   }
   BOOST_MP_CXX14_CONSTEXPR right_type  right() const { return right_type(arg2); }
   BOOST_MP_CXX14_CONSTEXPR const Arg1& left_ref() const BOOST_NOEXCEPT { return arg1; }
   BOOST_MP_CXX14_CONSTEXPR const Arg2& right_ref() const BOOST_NOEXCEPT { return arg2; }

#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) && !defined(__clang__)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500))
   //
   // Horrible workaround for gcc-4.6.x which always prefers the template
   // operator bool() rather than the non-template operator when converting to
   // an arithmetic type:
   //
   template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0>
   explicit operator T() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
   template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value || is_number<T>::value, int>::type = 0>
   explicit operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
#else
   template <class T
#ifndef __SUNPRO_CC
             ,
             typename boost::disable_if_c<is_number<T>::value || is_constructible<T const&, result_type>::value || !is_constructible<T, result_type>::value, int>::type = 0
#endif
             >
   explicit BOOST_MP_CXX14_CONSTEXPR operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
   BOOST_MP_FORCEINLINE explicit BOOST_MP_CXX14_CONSTEXPR operator bool() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800)
   BOOST_MP_FORCEINLINE explicit operator void() const
   {}
#endif
#endif
#else
   operator unmentionable_type() const
   {
      result_type r(*this);
      return r ? &unmentionable::proc : 0;
   }
#endif
   template <class T>
   BOOST_MP_CXX14_CONSTEXPR T convert_to()
   {
      result_type r(*this);
      return r.template convert_to<T>();
   }

   static const BOOST_MP_CXX14_CONSTEXPR unsigned left_depth  = left_type::depth + 1;
   static const BOOST_MP_CXX14_CONSTEXPR unsigned right_depth = right_type::depth + 1;
   static const BOOST_MP_CXX14_CONSTEXPR unsigned depth       = left_depth > right_depth ? left_depth : right_depth;

 private:
   typename expression_storage<Arg1>::type arg1;
   typename expression_storage<Arg2>::type arg2;
   expression&                             operator=(const expression&);
};

template <class tag, class Arg1, class Arg2, class Arg3>
struct expression<tag, Arg1, Arg2, Arg3, void>
{
   typedef mpl::int_<3>                      arity;
   typedef typename arg_type<Arg1>::type     left_type;
   typedef typename arg_type<Arg2>::type     middle_type;
   typedef typename arg_type<Arg3>::type     right_type;
   typedef typename left_type::result_type   left_result_type;
   typedef typename middle_type::result_type middle_result_type;
   typedef typename right_type::result_type  right_result_type;
   typedef typename combine_expression<
       left_result_type,
       typename combine_expression<right_result_type, middle_result_type>::type>::type result_type;
   typedef tag                                                                         tag_type;

   BOOST_MP_CXX14_CONSTEXPR expression(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {}
   BOOST_MP_CXX14_CONSTEXPR expression(const expression& e) : arg1(e.arg1), arg2(e.arg2), arg3(e.arg3) {}

#ifndef BOOST_NO_CXX11_STATIC_ASSERT
   //
   // If we have static_assert we can give a more useful error message
   // than if we simply have no operator defined at all:
   //
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not assign to a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator+=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator+= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator-=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator-= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator*=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator*= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator/=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator/= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator%=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator%= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator|=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator|= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator&=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator&= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator^=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator^= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator<<=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator<<= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator>>=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator>>= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
#endif

   BOOST_MP_CXX14_CONSTEXPR left_type left() const
   {
      return left_type(arg1);
   }
   BOOST_MP_CXX14_CONSTEXPR middle_type middle() const { return middle_type(arg2); }
   BOOST_MP_CXX14_CONSTEXPR right_type  right() const { return right_type(arg3); }
   BOOST_MP_CXX14_CONSTEXPR const Arg1& left_ref() const BOOST_NOEXCEPT { return arg1; }
   BOOST_MP_CXX14_CONSTEXPR const Arg2& middle_ref() const BOOST_NOEXCEPT { return arg2; }
   BOOST_MP_CXX14_CONSTEXPR const Arg3& right_ref() const BOOST_NOEXCEPT { return arg3; }

#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) && !defined(__clang__)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500))
   //
   // Horrible workaround for gcc-4.6.x which always prefers the template
   // operator bool() rather than the non-template operator when converting to
   // an arithmetic type:
   //
   template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0>
   explicit operator T() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
   template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value || is_number<T>::value, int>::type = 0>
   explicit operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
#else
   template <class T
#ifndef __SUNPRO_CC
             ,
             typename boost::disable_if_c<is_number<T>::value || is_constructible<T const&, result_type>::value || !is_constructible<T, result_type>::value, int>::type = 0
#endif
             >
   explicit BOOST_MP_CXX14_CONSTEXPR operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
   BOOST_MP_FORCEINLINE explicit BOOST_MP_CXX14_CONSTEXPR operator bool() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800)
   BOOST_MP_FORCEINLINE explicit operator void() const
   {}
#endif
#endif
#else
   operator unmentionable_type() const
   {
      result_type r(*this);
      return r ? &unmentionable::proc : 0;
   }
#endif
   template <class T>
   BOOST_MP_CXX14_CONSTEXPR T convert_to()
   {
      result_type r(*this);
      return r.template convert_to<T>();
   }

   static const unsigned left_depth   = left_type::depth + 1;
   static const unsigned middle_depth = middle_type::depth + 1;
   static const unsigned right_depth  = right_type::depth + 1;
   static const unsigned depth        = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth);

 private:
   typename expression_storage<Arg1>::type arg1;
   typename expression_storage<Arg2>::type arg2;
   typename expression_storage<Arg3>::type arg3;
   expression&                             operator=(const expression&);
};

template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
struct expression
{
   typedef mpl::int_<4>                            arity;
   typedef typename arg_type<Arg1>::type           left_type;
   typedef typename arg_type<Arg2>::type           left_middle_type;
   typedef typename arg_type<Arg3>::type           right_middle_type;
   typedef typename arg_type<Arg4>::type           right_type;
   typedef typename left_type::result_type         left_result_type;
   typedef typename left_middle_type::result_type  left_middle_result_type;
   typedef typename right_middle_type::result_type right_middle_result_type;
   typedef typename right_type::result_type        right_result_type;
   typedef typename combine_expression<
       left_result_type,
       typename combine_expression<
           left_middle_result_type,
           typename combine_expression<right_middle_result_type, right_result_type>::type>::type>::type result_type;
   typedef tag                                                                                          tag_type;

   BOOST_MP_CXX14_CONSTEXPR expression(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {}
   BOOST_MP_CXX14_CONSTEXPR expression(const expression& e) : arg1(e.arg1), arg2(e.arg2), arg3(e.arg3), arg4(e.arg4) {}

#ifndef BOOST_NO_CXX11_STATIC_ASSERT
   //
   // If we have static_assert we can give a more useful error message
   // than if we simply have no operator defined at all:
   //
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not assign to a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator++(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not increment a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--()
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   BOOST_MP_CXX14_CONSTEXPR expression& operator--(int)
   {
      // This should always fail:
      static_assert(sizeof(*this) == INT_MAX, "You can not decrement a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator+=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator+= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator-=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator-= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator*=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator*= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator/=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator/= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator%=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator%= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator|=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator|= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator&=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator&= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator^=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator^= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator<<=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator<<= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
   template <class Other>
   BOOST_MP_CXX14_CONSTEXPR expression& operator>>=(const Other&)
   {
      // This should always fail:
      static_assert(sizeof(Other) == INT_MAX, "You can not use operator>>= on a Boost.Multiprecision expression template: did you inadvertantly store an expression template in a \"auto\" variable?  Or pass an expression to a template function with deduced temnplate arguments?");
      return *this;
   }
#endif

   BOOST_MP_CXX14_CONSTEXPR left_type left() const
   {
      return left_type(arg1);
   }
   BOOST_MP_CXX14_CONSTEXPR left_middle_type  left_middle() const { return left_middle_type(arg2); }
   BOOST_MP_CXX14_CONSTEXPR right_middle_type right_middle() const { return right_middle_type(arg3); }
   BOOST_MP_CXX14_CONSTEXPR right_type        right() const { return right_type(arg4); }
   BOOST_MP_CXX14_CONSTEXPR const Arg1&       left_ref() const BOOST_NOEXCEPT { return arg1; }
   BOOST_MP_CXX14_CONSTEXPR const Arg2&       left_middle_ref() const BOOST_NOEXCEPT { return arg2; }
   BOOST_MP_CXX14_CONSTEXPR const Arg3&       right_middle_ref() const BOOST_NOEXCEPT { return arg3; }
   BOOST_MP_CXX14_CONSTEXPR const Arg4&       right_ref() const BOOST_NOEXCEPT { return arg4; }

#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
#if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) && !defined(__clang__)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500))
   //
   // Horrible workaround for gcc-4.6.x which always prefers the template
   // operator bool() rather than the non-template operator when converting to
   // an arithmetic type:
   //
   template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0>
   explicit operator T() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
   template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value || is_number<T>::value, int>::type = 0>
   explicit operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
#else
   template <class T
#ifndef __SUNPRO_CC
             ,
             typename boost::disable_if_c<is_number<T>::value || is_constructible<T const&, result_type>::value || !is_constructible<T, result_type>::value, int>::type = 0
#endif
             >
   explicit BOOST_MP_CXX14_CONSTEXPR operator T() const
   {
      return static_cast<T>(static_cast<result_type>(*this));
   }
   BOOST_MP_FORCEINLINE explicit BOOST_MP_CXX14_CONSTEXPR operator bool() const
   {
      result_type r(*this);
      return static_cast<bool>(r);
   }
#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800)
   BOOST_MP_FORCEINLINE explicit operator void() const
   {}
#endif
#endif
#else
   operator unmentionable_type() const
   {
      result_type r(*this);
      return r ? &unmentionable::proc : 0;
   }
#endif
   template <class T>
   BOOST_MP_CXX14_CONSTEXPR T convert_to()
   {
      result_type r(*this);
      return r.template convert_to<T>();
   }

   static const unsigned left_depth         = left_type::depth + 1;
   static const unsigned left_middle_depth  = left_middle_type::depth + 1;
   static const unsigned right_middle_depth = right_middle_type::depth + 1;
   static const unsigned right_depth        = right_type::depth + 1;

   static const unsigned left_max_depth  = left_depth > left_middle_depth ? left_depth : left_middle_depth;
   static const unsigned right_max_depth = right_depth > right_middle_depth ? right_depth : right_middle_depth;

   static const unsigned depth = left_max_depth > right_max_depth ? left_max_depth : right_max_depth;

 private:
   typename expression_storage<Arg1>::type arg1;
   typename expression_storage<Arg2>::type arg2;
   typename expression_storage<Arg3>::type arg3;
   typename expression_storage<Arg4>::type arg4;
   expression&                             operator=(const expression&);
};

template <class T>
struct digits2
{
   BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
   BOOST_STATIC_ASSERT((std::numeric_limits<T>::radix == 2) || (std::numeric_limits<T>::radix == 10));
   // If we really have so many digits that this fails, then we're probably going to hit other problems anyway:
   BOOST_STATIC_ASSERT(LONG_MAX / 1000 > (std::numeric_limits<T>::digits + 1));
   static const long                  m_value = std::numeric_limits<T>::radix == 10 ? (((std::numeric_limits<T>::digits + 1) * 1000L) / 301L) : std::numeric_limits<T>::digits;
   static inline BOOST_CONSTEXPR long value() BOOST_NOEXCEPT { return m_value; }
};

#ifndef BOOST_MP_MIN_EXPONENT_DIGITS
#ifdef _MSC_VER
#define BOOST_MP_MIN_EXPONENT_DIGITS 2
#else
#define BOOST_MP_MIN_EXPONENT_DIGITS 2
#endif
#endif

template <class S>
void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, std::ios_base::fmtflags f, bool iszero)
{
   typedef typename S::size_type size_type;
   bool                          scientific = (f & std::ios_base::scientific) == std::ios_base::scientific;
   bool                          fixed      = (f & std::ios_base::fixed) == std::ios_base::fixed;
   bool                          showpoint  = (f & std::ios_base::showpoint) == std::ios_base::showpoint;
   bool                          showpos    = (f & std::ios_base::showpos) == std::ios_base::showpos;

   bool neg = str.size() && (str[0] == '-');

   if (neg)
      str.erase(0, 1);

   if (digits == 0)
   {
      digits = (std::max)(str.size(), size_type(16));
   }

   if (iszero || str.empty() || (str.find_first_not_of('0') == S::npos))
   {
      // We will be printing zero, even though the value might not
      // actually be zero (it just may have been rounded to zero).
      str = "0";
      if (scientific || fixed)
      {
         str.append(1, '.');
         str.append(size_type(digits), '0');
         if (scientific)
            str.append("e+00");
      }
      else
      {
         if (showpoint)
         {
            str.append(1, '.');
            if (digits > 1)
               str.append(size_type(digits - 1), '0');
         }
      }
      if (neg)
         str.insert(static_cast<std::string::size_type>(0), 1, '-');
      else if (showpos)
         str.insert(static_cast<std::string::size_type>(0), 1, '+');
      return;
   }

   if (!fixed && !scientific && !showpoint)
   {
      //
      // Suppress trailing zeros:
      //
      std::string::iterator pos = str.end();
      while (pos != str.begin() && *--pos == '0')
      {
      }
      if (pos != str.end())
         ++pos;
      str.erase(pos, str.end());
      if (str.empty())
         str = '0';
   }
   else if (!fixed || (my_exp >= 0))
   {
      //
      // Pad out the end with zero's if we need to:
      //
      boost::intmax_t chars = str.size();
      chars                 = digits - chars;
      if (scientific)
         ++chars;
      if (chars > 0)
      {
         str.append(static_cast<std::string::size_type>(chars), '0');
      }
   }

   if (fixed || (!scientific && (my_exp >= -4) && (my_exp < digits)))
   {
      if (1 + my_exp > static_cast<boost::intmax_t>(str.size()))
      {
         // Just pad out the end with zeros:
         str.append(static_cast<std::string::size_type>(1 + my_exp - str.size()), '0');
         if (showpoint || fixed)
            str.append(".");
      }
      else if (my_exp + 1 < static_cast<boost::intmax_t>(str.size()))
      {
         if (my_exp < 0)
         {
            str.insert(static_cast<std::string::size_type>(0), static_cast<std::string::size_type>(-1 - my_exp), '0');
            str.insert(static_cast<std::string::size_type>(0), "0.");
         }
         else
         {
            // Insert the decimal point:
            str.insert(static_cast<std::string::size_type>(my_exp + 1), 1, '.');
         }
      }
      else if (showpoint || fixed) // we have exactly the digits we require to left of the point
         str += ".";

      if (fixed)
      {
         // We may need to add trailing zeros:
         boost::intmax_t l = str.find('.') + 1;
         l                 = digits - (str.size() - l);
         if (l > 0)
            str.append(size_type(l), '0');
      }
   }
   else
   {
      BOOST_MP_USING_ABS
      // Scientific format:
      if (showpoint || (str.size() > 1))
         str.insert(static_cast<std::string::size_type>(1u), 1, '.');
      str.append(static_cast<std::string::size_type>(1u), 'e');
      S e = boost::lexical_cast<S>(abs(my_exp));
      if (e.size() < BOOST_MP_MIN_EXPONENT_DIGITS)
         e.insert(static_cast<std::string::size_type>(0), BOOST_MP_MIN_EXPONENT_DIGITS - e.size(), '0');
      if (my_exp < 0)
         e.insert(static_cast<std::string::size_type>(0), 1, '-');
      else
         e.insert(static_cast<std::string::size_type>(0), 1, '+');
      str.append(e);
   }
   if (neg)
      str.insert(static_cast<std::string::size_type>(0), 1, '-');
   else if (showpos)
      str.insert(static_cast<std::string::size_type>(0), 1, '+');
}

template <class V>
BOOST_MP_CXX14_CONSTEXPR void check_shift_range(V val, const mpl::true_&, const mpl::true_&)
{
   if (val > (std::numeric_limits<std::size_t>::max)())
      BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits<std::size_t>::max()."));
   if (val < 0)
      BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value."));
}
template <class V>
BOOST_MP_CXX14_CONSTEXPR void check_shift_range(V val, const mpl::false_&, const mpl::true_&)
{
   if (val < 0)
      BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value."));
}
template <class V>
BOOST_MP_CXX14_CONSTEXPR void check_shift_range(V val, const mpl::true_&, const mpl::false_&)
{
   if (val > (std::numeric_limits<std::size_t>::max)())
      BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits<std::size_t>::max()."));
}
template <class V>
BOOST_MP_CXX14_CONSTEXPR void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT {}

template <class T>
BOOST_MP_CXX14_CONSTEXPR const T& evaluate_if_expression(const T& val) { return val; }
template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
BOOST_MP_CXX14_CONSTEXPR typename expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type evaluate_if_expression(const expression<tag, Arg1, Arg2, Arg3, Arg4>& val) { return val; }

} // namespace detail

//
// Traits class, lets us know what kind of number we have, defaults to a floating point type:
//
enum number_category_type
{
   number_kind_unknown        = -1,
   number_kind_integer        = 0,
   number_kind_floating_point = 1,
   number_kind_rational       = 2,
   number_kind_fixed_point    = 3,
   number_kind_complex        = 4
};

template <class Num, bool, bool>
struct number_category_base : public mpl::int_<number_kind_unknown>
{};
template <class Num>
struct number_category_base<Num, true, false> : public mpl::int_<std::numeric_limits<Num>::is_integer ? number_kind_integer : (std::numeric_limits<Num>::max_exponent ? number_kind_floating_point : number_kind_unknown)>
{};
template <class Num>
struct number_category : public number_category_base<Num, boost::is_class<Num>::value || boost::is_arithmetic<Num>::value, boost::is_abstract<Num>::value>
{};
template <class Backend, expression_template_option ExpressionTemplates>
struct number_category<number<Backend, ExpressionTemplates> > : public number_category<Backend>
{};
template <class tag, class A1, class A2, class A3, class A4>
struct number_category<detail::expression<tag, A1, A2, A3, A4> > : public number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>
{};
//
// Specializations for types which do not always have numberic_limits specializations:
//
#ifdef BOOST_HAS_INT128
template <>
struct number_category<boost::int128_type> : public mpl::int_<number_kind_integer>
{};
template <>
struct number_category<boost::uint128_type> : public mpl::int_<number_kind_integer>
{};
#endif
#ifdef BOOST_HAS_FLOAT128
template <>
struct number_category<__float128> : public mpl::int_<number_kind_floating_point>
{};
#endif

template <class T>
struct component_type
{
   typedef T type;
};
template <class tag, class A1, class A2, class A3, class A4>
struct component_type<detail::expression<tag, A1, A2, A3, A4> > : public component_type<typename detail::expression<tag, A1, A2, A3, A4>::result_type>
{};

template <class T>
struct scalar_result_from_possible_complex
{
   typedef typename mpl::if_c<number_category<T>::value == number_kind_complex,
                              typename component_type<T>::type, T>::type type;
};

template <class T>
struct complex_result_from_scalar; // individual backends must specialize this trait.

template <class T>
struct is_unsigned_number : public mpl::false_
{};
template <class Backend, expression_template_option ExpressionTemplates>
struct is_unsigned_number<number<Backend, ExpressionTemplates> > : public is_unsigned_number<Backend>
{};
template <class T>
struct is_signed_number : public mpl::bool_<!is_unsigned_number<T>::value>
{};
template <class T>
struct is_interval_number : public mpl::false_
{};
template <class Backend, expression_template_option ExpressionTemplates>
struct is_interval_number<number<Backend, ExpressionTemplates> > : public is_interval_number<Backend>
{};

} // namespace multiprecision
} // namespace boost

namespace boost { namespace math {
   namespace tools {

      template <class T>
      struct promote_arg;

      template <class tag, class A1, class A2, class A3, class A4>
      struct promote_arg<boost::multiprecision::detail::expression<tag, A1, A2, A3, A4> >
      {
         typedef typename boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type type;
      };

      template <class R, class B, boost::multiprecision::expression_template_option ET>
      inline R real_cast(const boost::multiprecision::number<B, ET>& val)
      {
         return val.template convert_to<R>();
      }

      template <class R, class tag, class A1, class A2, class A3, class A4>
      inline R real_cast(const boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>& val)
      {
         typedef typename boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type val_type;
         return val_type(val).template convert_to<R>();
      }

      template <class B, boost::multiprecision::expression_template_option ET>
      struct is_complex_type<boost::multiprecision::number<B, ET> > : public boost::mpl::bool_<boost::multiprecision::number_category<B>::value == boost::multiprecision::number_kind_complex> {};

} // namespace tools

namespace constants {

template <class T>
struct is_explicitly_convertible_from_string;

template <class B, boost::multiprecision::expression_template_option ET>
struct is_explicitly_convertible_from_string<boost::multiprecision::number<B, ET> >
{
   static const bool value = true;
};

} // namespace constants

}} // namespace boost::math

#ifdef BOOST_MSVC
#pragma warning(pop)
#endif

#endif // BOOST_MATH_BIG_NUM_BASE_HPP