Imported Upstream version 1.57.0upstream/1.57.0

1 files changed, 807 insertions, 0 deletions

diff --git a/boost/multiprecision/detail/number_base.hpp b/boost/multiprecision/detail/number_base.hpp
new file mode 100644
index 0000000000..9353082d37
--- /dev/null
+++ b/boost/multiprecision/detail/number_base.hpp
@@ -0,0 +1,807 @@
+///////////////////////////////////////////////////////////////////////////////
+//  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/type_traits/is_convertible.hpp>
+#include <boost/type_traits/decay.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(NDEBUG) && !defined(_DEBUG)
+#  define BOOST_MP_FORCEINLINE BOOST_FORCEINLINE
+#else
+#  define BOOST_MP_FORCEINLINE inline
+#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_ {};
+
+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(long long) 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 long long.
+   // 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 long long.
+   // 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);
+};
+
+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;
+};
+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::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::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::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>
+struct expression_storage
+{
+   typedef const T& type;
+};
+
+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 expression(const Arg1& a) : arg(a) {}
+
+   left_type left()const { return left_type(arg); }
+
+   const Arg1& left_ref()const BOOST_NOEXCEPT { return arg; }
+
+   static const unsigned depth = left_type::depth + 1;
+#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   explicit operator bool()const
+   {
+      result_type r(*this);
+      return static_cast<bool>(r);
+   }
+#else
+   operator unmentionable_type()const
+   {
+      result_type r(*this);
+      return r ? &unmentionable::proc : 0;
+   }
+#endif
+
+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 expression(const Arg1& a) : arg(a) {}
+
+   const Arg1& value()const BOOST_NOEXCEPT { return arg; }
+
+   static const unsigned depth = 0;
+
+#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   explicit operator bool()const
+   {
+      return static_cast<bool>(arg);
+   }
+#else
+   operator unmentionable_type()const
+   {
+      return arg ? &unmentionable::proc : 0;
+   }
+#endif
+
+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;
+
+   expression(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {}
+
+   left_type left()const { return left_type(arg1); }
+   right_type right()const { return right_type(arg2); }
+   const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
+   const Arg2& right_ref()const BOOST_NOEXCEPT { return arg2; }
+
+#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   explicit operator bool()const
+   {
+      result_type r(*this);
+      return static_cast<bool>(r);
+   }
+#else
+   operator unmentionable_type()const
+   {
+      result_type r(*this);
+      return r ? &unmentionable::proc : 0;
+   }
+#endif
+   static const unsigned left_depth = left_type::depth + 1;
+   static const unsigned right_depth = right_type::depth + 1;
+   static const 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;
+
+   expression(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {}
+
+   left_type left()const { return left_type(arg1); }
+   middle_type middle()const { return middle_type(arg2); }
+   right_type right()const { return right_type(arg3); }
+   const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
+   const Arg2& middle_ref()const BOOST_NOEXCEPT { return arg2; }
+   const Arg3& right_ref()const BOOST_NOEXCEPT { return arg3; }
+
+#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   explicit operator bool()const
+   {
+      result_type r(*this);
+      return static_cast<bool>(r);
+   }
+#else
+   operator unmentionable_type()const
+   {
+      result_type r(*this);
+      return r ? &unmentionable::proc : 0;
+   }
+#endif
+   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<
+      typename combine_expression<
+         typename combine_expression<left_result_type, left_middle_result_type>::type,
+         right_middle_result_type
+      >::type,
+      right_result_type
+   >::type result_type;
+   typedef tag tag_type;
+
+   expression(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {}
+
+   left_type left()const { return left_type(arg1); }
+   left_middle_type left_middle()const { return left_middle_type(arg2); }
+   right_middle_type right_middle()const { return right_middle_type(arg3); }
+   right_type right()const { return right_type(arg4); }
+   const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
+   const Arg2& left_middle_ref()const BOOST_NOEXCEPT { return arg2; }
+   const Arg3& right_middle_ref()const BOOST_NOEXCEPT { return arg3; }
+   const Arg4& right_ref()const BOOST_NOEXCEPT { return arg4; }
+
+#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   explicit operator bool()const
+   {
+      result_type r(*this);
+      return static_cast<bool>(r);
+   }
+#else
+   operator unmentionable_type()const
+   {
+      result_type r(*this);
+      return r ? &unmentionable::proc : 0;
+   }
+#endif
+   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 value = std::numeric_limits<T>::radix == 10 ?  (((std::numeric_limits<T>::digits + 1) * 1000L) / 301L) : std::numeric_limits<T>::digits;
+};
+
+#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(0, 1, '-');
+      else if(showpos)
+         str.insert(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(0, static_cast<std::string::size_type>(-1 - my_exp), '0');
+            str.insert(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(1, 1, '.');
+      str.append(1, 'e');
+      S e = boost::lexical_cast<S>(abs(my_exp));
+      if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS)
+         e.insert(0, BOOST_MP_MIN_EXPONENT_DIGITS-e.size(), '0');
+      if(my_exp < 0)
+         e.insert(0, 1, '-');
+      else
+         e.insert(0, 1, '+');
+      str.append(e);
+   }
+   if(neg)
+      str.insert(0, 1, '-');
+   else if(showpos)
+      str.insert(0, 1, '+');
+}
+
+template <class V>
+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>
+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>
+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>
+void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT{}
+
+} // 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
+};
+
+template <class Num>
+struct number_category : 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 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>{};
+
+template <class T>
+struct component_type;
+template <class T, expression_template_option ExpressionTemplates>
+struct component_type<number<T, ExpressionTemplates> > : public component_type<T>{};
+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 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>{};
+
+}} // namespaces
+
+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>();
+}
+
+
+}
+
+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;
+   };
+
+}
+
+}}
+
+#endif // BOOST_MATH_BIG_NUM_BASE_HPP
+
+