Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: //  Copyright 2011 John Maddock. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_BIG_NUM_BASE_HPP
Chris@16: #define BOOST_MATH_BIG_NUM_BASE_HPP
Chris@16: 
Chris@16: #include <limits>
Chris@16: #include <boost/utility/enable_if.hpp>
Chris@16: #include <boost/type_traits/is_convertible.hpp>
Chris@16: #include <boost/type_traits/decay.hpp>
Chris@16: #ifdef BOOST_MSVC
Chris@16: #  pragma warning(push)
Chris@16: #  pragma warning(disable:4307)
Chris@16: #endif
Chris@16: #include <boost/lexical_cast.hpp>
Chris@16: #ifdef BOOST_MSVC
Chris@16: #  pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: #if defined(NDEBUG) && !defined(_DEBUG)
Chris@16: #  define BOOST_MP_FORCEINLINE BOOST_FORCEINLINE
Chris@16: #else
Chris@16: #  define BOOST_MP_FORCEINLINE inline
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost{ namespace multiprecision{
Chris@16: 
Chris@16: enum expression_template_option
Chris@16: {
Chris@16:    et_off  = 0,
Chris@16:    et_on   = 1
Chris@16: };
Chris@16: 
Chris@16: template <class Backend>
Chris@16: struct expression_template_default
Chris@16: {
Chris@16:    static const expression_template_option value = et_on;
Chris@16: };
Chris@16: 
Chris@16: template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value>
Chris@16: class number;
Chris@16: 
Chris@16: template <class T>
Chris@16: struct is_number : public mpl::false_ {};
Chris@16: 
Chris@16: template <class Backend, expression_template_option ExpressionTemplates>
Chris@16: struct is_number<number<Backend, ExpressionTemplates> > : public mpl::true_ {};
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: // Forward-declare an expression wrapper
Chris@16: template<class tag, class Arg1 = void, class Arg2 = void, class Arg3 = void, class Arg4 = void>
Chris@16: struct expression;
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class T>
Chris@16: struct is_number_expression : public mpl::false_ {};
Chris@16: 
Chris@16: template<class tag, class Arg1, class Arg2, class Arg3, class Arg4>
Chris@16: struct is_number_expression<detail::expression<tag, Arg1, Arg2, Arg3, Arg4> > : public mpl::true_ {};
Chris@16: 
Chris@16: template <class T, class Num>
Chris@16: struct is_compatible_arithmetic_type
Chris@16:    : public mpl::bool_<
Chris@16:          is_convertible<T, Num>::value
Chris@16:          && !is_same<T, Num>::value
Chris@16:          && !is_number_expression<T>::value>
Chris@16: {};
Chris@16: 
Chris@16: namespace detail{
Chris@16: //
Chris@16: // Workaround for missing abs(long long) and abs(__int128) on some compilers:
Chris@16: //
Chris@16: template <class T>
Chris@101: BOOST_CONSTEXPR typename enable_if_c<(is_signed<T>::value || is_floating_point<T>::value), T>::type abs(T t) BOOST_NOEXCEPT
Chris@16: {
Chris@101:    // This strange expression avoids a hardware trap in the corner case
Chris@101:    // that val is the most negative value permitted in long long.
Chris@101:    // See https://svn.boost.org/trac/boost/ticket/9740.
Chris@101:    return t < 0 ? T(1u) + T(-(t + 1)) : t;
Chris@16: }
Chris@16: template <class T>
Chris@101: BOOST_CONSTEXPR typename enable_if_c<(is_unsigned<T>::value), T>::type abs(T t) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return t;
Chris@16: }
Chris@16: 
Chris@16: #define BOOST_MP_USING_ABS using boost::multiprecision::detail::abs;
Chris@16: 
Chris@101: template <class T>
Chris@101: 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
Chris@101: {
Chris@101:    // This strange expression avoids a hardware trap in the corner case
Chris@101:    // that val is the most negative value permitted in long long.
Chris@101:    // See https://svn.boost.org/trac/boost/ticket/9740.
Chris@101:    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);
Chris@101: }
Chris@101: template <class T>
Chris@101: BOOST_CONSTEXPR typename enable_if_c<(is_unsigned<T>::value), T>::type unsigned_abs(T t) BOOST_NOEXCEPT
Chris@101: {
Chris@101:    return t;
Chris@101: }
Chris@101: 
Chris@16: //
Chris@16: // Move support:
Chris@16: //
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16: #  define BOOST_MP_MOVE(x) std::move(x)
Chris@16: #else
Chris@16: #  define BOOST_MP_MOVE(x) x
Chris@16: #endif
Chris@16: 
Chris@16: template <class T>
Chris@16: struct bits_of
Chris@16: {
Chris@16:    BOOST_STATIC_ASSERT(is_integral<T>::value || is_enum<T>::value || std::numeric_limits<T>::is_specialized);
Chris@16:    static const unsigned value =
Chris@16:       std::numeric_limits<T>::is_specialized ?
Chris@16:          std::numeric_limits<T>::digits
Chris@16:          : sizeof(T) * CHAR_BIT - (is_signed<T>::value ? 1 : 0);
Chris@16: };
Chris@16: 
Chris@16: template <int b>
Chris@16: struct has_enough_bits
Chris@16: {
Chris@16:    template <class T>
Chris@16:    struct type : public mpl::bool_<bits_of<T>::value>= b>{};
Chris@16: };
Chris@16: 
Chris@16: template <class Val, class Backend, class Tag>
Chris@16: struct canonical_imp
Chris@16: {
Chris@16:    typedef typename remove_cv<typename decay<const Val>::type>::type type;
Chris@16: };
Chris@16: template <class B, class Backend, class Tag>
Chris@16: struct canonical_imp<number<B, et_on>, Backend, Tag>
Chris@16: {
Chris@16:    typedef B type;
Chris@16: };
Chris@16: template <class B, class Backend, class Tag>
Chris@16: struct canonical_imp<number<B, et_off>, Backend, Tag>
Chris@16: {
Chris@16:    typedef B type;
Chris@16: };
Chris@101: #ifdef __SUNPRO_CC
Chris@101: template <class B, class Backend>
Chris@101: struct canonical_imp<number<B, et_on>, Backend, mpl::int_<3> >
Chris@101: {
Chris@101:    typedef B type;
Chris@101: };
Chris@101: template <class B, class Backend>
Chris@101: struct canonical_imp<number<B, et_off>, Backend, mpl::int_<3> >
Chris@101: {
Chris@101:    typedef B type;
Chris@101: };
Chris@101: #endif
Chris@16: template <class Val, class Backend>
Chris@16: struct canonical_imp<Val, Backend, mpl::int_<0> >
Chris@16: {
Chris@16:    typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
Chris@16:    typedef typename mpl::find_if<
Chris@16:       typename Backend::signed_types,
Chris@16:       pred_type
Chris@16:    >::type iter_type;
Chris@16:    typedef typename mpl::deref<iter_type>::type type;
Chris@16: };
Chris@16: template <class Val, class Backend>
Chris@16: struct canonical_imp<Val, Backend, mpl::int_<1> >
Chris@16: {
Chris@16:    typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
Chris@16:    typedef typename mpl::find_if<
Chris@16:       typename Backend::unsigned_types,
Chris@16:       pred_type
Chris@16:    >::type iter_type;
Chris@16:    typedef typename mpl::deref<iter_type>::type type;
Chris@16: };
Chris@16: template <class Val, class Backend>
Chris@16: struct canonical_imp<Val, Backend, mpl::int_<2> >
Chris@16: {
Chris@16:    typedef typename has_enough_bits<bits_of<Val>::value>::template type<mpl::_> pred_type;
Chris@16:    typedef typename mpl::find_if<
Chris@16:       typename Backend::float_types,
Chris@16:       pred_type
Chris@16:    >::type iter_type;
Chris@16:    typedef typename mpl::deref<iter_type>::type type;
Chris@16: };
Chris@16: template <class Val, class Backend>
Chris@16: struct canonical_imp<Val, Backend, mpl::int_<3> >
Chris@16: {
Chris@16:    typedef const char* type;
Chris@16: };
Chris@16: 
Chris@16: template <class Val, class Backend>
Chris@16: struct canonical
Chris@16: {
Chris@16:    typedef typename mpl::if_<
Chris@16:       is_signed<Val>,
Chris@16:       mpl::int_<0>,
Chris@16:       typename mpl::if_<
Chris@16:          is_unsigned<Val>,
Chris@16:          mpl::int_<1>,
Chris@16:          typename mpl::if_<
Chris@16:             is_floating_point<Val>,
Chris@16:             mpl::int_<2>,
Chris@16:             typename mpl::if_<
Chris@16:                mpl::or_<
Chris@16:                   is_convertible<Val, const char*>,
Chris@16:                   is_same<Val, std::string>
Chris@16:                >,
Chris@16:                mpl::int_<3>,
Chris@16:                mpl::int_<4>
Chris@16:             >::type
Chris@16:          >::type
Chris@16:       >::type
Chris@16:    >::type tag_type;
Chris@16: 
Chris@16:    typedef typename canonical_imp<Val, Backend, tag_type>::type type;
Chris@16: };
Chris@16: 
Chris@16: struct terminal{};
Chris@16: struct negate{};
Chris@16: struct plus{};
Chris@16: struct minus{};
Chris@16: struct multiplies{};
Chris@16: struct divides{};
Chris@16: struct modulus{};
Chris@16: struct shift_left{};
Chris@16: struct shift_right{};
Chris@16: struct bitwise_and{};
Chris@16: struct bitwise_or{};
Chris@16: struct bitwise_xor{};
Chris@16: struct bitwise_complement{};
Chris@16: struct add_immediates{};
Chris@16: struct subtract_immediates{};
Chris@16: struct multiply_immediates{};
Chris@16: struct divide_immediates{};
Chris@16: struct modulus_immediates{};
Chris@16: struct bitwise_and_immediates{};
Chris@16: struct bitwise_or_immediates{};
Chris@16: struct bitwise_xor_immediates{};
Chris@16: struct complement_immediates{};
Chris@16: struct function{};
Chris@16: struct multiply_add{};
Chris@16: struct multiply_subtract{};
Chris@16: 
Chris@16: template <class T>
Chris@16: struct backend_type;
Chris@16: 
Chris@16: template <class T, expression_template_option ExpressionTemplates>
Chris@16: struct backend_type<number<T, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef T type;
Chris@16: };
Chris@16: 
Chris@16: template <class tag, class A1, class A2, class A3, class A4>
Chris@16: struct backend_type<expression<tag, A1, A2, A3, A4> >
Chris@16: {
Chris@16:    typedef typename backend_type<typename expression<tag, A1, A2, A3, A4>::result_type>::type type;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: template <class T1, class T2>
Chris@16: struct combine_expression
Chris@16: {
Chris@16: #ifdef BOOST_NO_CXX11_DECLTYPE
Chris@16:    typedef typename mpl::if_c<(sizeof(T1() + T2()) == sizeof(T1)), T1, T2>::type type;
Chris@16: #else
Chris@16:    typedef decltype(T1() + T2()) type;
Chris@16: #endif
Chris@16: };
Chris@16: 
Chris@16: template <class T1, expression_template_option ExpressionTemplates, class T2>
Chris@16: struct combine_expression<number<T1, ExpressionTemplates>, T2>
Chris@16: {
Chris@16:    typedef number<T1, ExpressionTemplates> type;
Chris@16: };
Chris@16: 
Chris@16: template <class T1, class T2, expression_template_option ExpressionTemplates>
Chris@16: struct combine_expression<T1, number<T2, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef number<T2, ExpressionTemplates> type;
Chris@16: };
Chris@16: 
Chris@16: template <class T, expression_template_option ExpressionTemplates>
Chris@16: struct combine_expression<number<T, ExpressionTemplates>, number<T, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef number<T, ExpressionTemplates> type;
Chris@16: };
Chris@16: 
Chris@16: template <class T1, expression_template_option ExpressionTemplates1, class T2, expression_template_option ExpressionTemplates2>
Chris@16: struct combine_expression<number<T1, ExpressionTemplates1>, number<T2, ExpressionTemplates2> >
Chris@16: {
Chris@16:    typedef typename mpl::if_c<
Chris@16:       is_convertible<number<T2, ExpressionTemplates2>, number<T1, ExpressionTemplates2> >::value,
Chris@16:       number<T1, ExpressionTemplates1>,
Chris@16:       number<T2, ExpressionTemplates2>
Chris@16:       >::type type;
Chris@16: };
Chris@16: 
Chris@16: template <class T>
Chris@16: struct arg_type
Chris@16: {
Chris@16:    typedef expression<terminal, T> type;
Chris@16: };
Chris@16: 
Chris@16: template <class Tag, class Arg1, class Arg2, class Arg3, class Arg4>
Chris@16: struct arg_type<expression<Tag, Arg1, Arg2, Arg3, Arg4> >
Chris@16: {
Chris@16:    typedef expression<Tag, Arg1, Arg2, Arg3, Arg4> type;
Chris@16: };
Chris@16: 
Chris@16: struct unmentionable
Chris@16: {
Chris@16:    unmentionable* proc(){ return 0; }
Chris@16: };
Chris@16: 
Chris@16: typedef unmentionable* (unmentionable::*unmentionable_type)();
Chris@16: 
Chris@16: template <class T>
Chris@16: struct expression_storage
Chris@16: {
Chris@16:    typedef const T& type;
Chris@16: };
Chris@16: 
Chris@16: template <class T>
Chris@16: struct expression_storage<T*>
Chris@16: {
Chris@16:    typedef T* type;
Chris@16: };
Chris@16: 
Chris@16: template <class T>
Chris@16: struct expression_storage<const T*>
Chris@16: {
Chris@16:    typedef const T* type;
Chris@16: };
Chris@16: 
Chris@16: template <class tag, class A1, class A2, class A3, class A4>
Chris@16: struct expression_storage<expression<tag, A1, A2, A3, A4> >
Chris@16: {
Chris@16:    typedef expression<tag, A1, A2, A3, A4> type;
Chris@16: };
Chris@16: 
Chris@16: template<class tag, class Arg1>
Chris@16: struct expression<tag, Arg1, void, void, void>
Chris@16: {
Chris@16:    typedef mpl::int_<1> arity;
Chris@16:    typedef typename arg_type<Arg1>::type left_type;
Chris@16:    typedef typename left_type::result_type left_result_type;
Chris@16:    typedef typename left_type::result_type result_type;
Chris@16:    typedef tag tag_type;
Chris@16: 
Chris@16:    explicit expression(const Arg1& a) : arg(a) {}
Chris@16: 
Chris@16:    left_type left()const { return left_type(arg); }
Chris@16: 
Chris@16:    const Arg1& left_ref()const BOOST_NOEXCEPT { return arg; }
Chris@16: 
Chris@16:    static const unsigned depth = left_type::depth + 1;
Chris@16: #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
Chris@16:    explicit operator bool()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return static_cast<bool>(r);
Chris@16:    }
Chris@16: #else
Chris@16:    operator unmentionable_type()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return r ? &unmentionable::proc : 0;
Chris@16:    }
Chris@16: #endif
Chris@16: 
Chris@16: private:
Chris@16:    typename expression_storage<Arg1>::type arg;
Chris@16:    expression& operator=(const expression&);
Chris@16: };
Chris@16: 
Chris@16: template<class Arg1>
Chris@16: struct expression<terminal, Arg1, void, void, void>
Chris@16: {
Chris@16:    typedef mpl::int_<0> arity;
Chris@16:    typedef Arg1 result_type;
Chris@16:    typedef terminal tag_type;
Chris@16: 
Chris@16:    explicit expression(const Arg1& a) : arg(a) {}
Chris@16: 
Chris@16:    const Arg1& value()const BOOST_NOEXCEPT { return arg; }
Chris@16: 
Chris@16:    static const unsigned depth = 0;
Chris@16: 
Chris@16: #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
Chris@16:    explicit operator bool()const
Chris@16:    {
Chris@16:       return static_cast<bool>(arg);
Chris@16:    }
Chris@16: #else
Chris@16:    operator unmentionable_type()const
Chris@16:    {
Chris@16:       return arg ? &unmentionable::proc : 0;
Chris@16:    }
Chris@16: #endif
Chris@16: 
Chris@16: private:
Chris@16:    typename expression_storage<Arg1>::type arg;
Chris@16:    expression& operator=(const expression&);
Chris@16: };
Chris@16: 
Chris@16: template <class tag, class Arg1, class Arg2>
Chris@16: struct expression<tag, Arg1, Arg2, void, void>
Chris@16: {
Chris@16:    typedef mpl::int_<2> arity;
Chris@16:    typedef typename arg_type<Arg1>::type left_type;
Chris@16:    typedef typename arg_type<Arg2>::type right_type;
Chris@16:    typedef typename left_type::result_type left_result_type;
Chris@16:    typedef typename right_type::result_type right_result_type;
Chris@16:    typedef typename combine_expression<left_result_type, right_result_type>::type result_type;
Chris@16:    typedef tag tag_type;
Chris@16: 
Chris@16:    expression(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {}
Chris@16: 
Chris@16:    left_type left()const { return left_type(arg1); }
Chris@16:    right_type right()const { return right_type(arg2); }
Chris@16:    const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
Chris@16:    const Arg2& right_ref()const BOOST_NOEXCEPT { return arg2; }
Chris@16: 
Chris@16: #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
Chris@16:    explicit operator bool()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return static_cast<bool>(r);
Chris@16:    }
Chris@16: #else
Chris@16:    operator unmentionable_type()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return r ? &unmentionable::proc : 0;
Chris@16:    }
Chris@16: #endif
Chris@16:    static const unsigned left_depth = left_type::depth + 1;
Chris@16:    static const unsigned right_depth = right_type::depth + 1;
Chris@16:    static const unsigned depth = left_depth > right_depth ? left_depth : right_depth;
Chris@16: private:
Chris@16:    typename expression_storage<Arg1>::type arg1;
Chris@16:    typename expression_storage<Arg2>::type arg2;
Chris@16:    expression& operator=(const expression&);
Chris@16: };
Chris@16: 
Chris@16: template <class tag, class Arg1, class Arg2, class Arg3>
Chris@16: struct expression<tag, Arg1, Arg2, Arg3, void>
Chris@16: {
Chris@16:    typedef mpl::int_<3> arity;
Chris@16:    typedef typename arg_type<Arg1>::type left_type;
Chris@16:    typedef typename arg_type<Arg2>::type middle_type;
Chris@16:    typedef typename arg_type<Arg3>::type right_type;
Chris@16:    typedef typename left_type::result_type left_result_type;
Chris@16:    typedef typename middle_type::result_type middle_result_type;
Chris@16:    typedef typename right_type::result_type right_result_type;
Chris@16:    typedef typename combine_expression<
Chris@16:       left_result_type,
Chris@16:       typename combine_expression<right_result_type, middle_result_type>::type
Chris@16:    >::type result_type;
Chris@16:    typedef tag tag_type;
Chris@16: 
Chris@16:    expression(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {}
Chris@16: 
Chris@16:    left_type left()const { return left_type(arg1); }
Chris@16:    middle_type middle()const { return middle_type(arg2); }
Chris@16:    right_type right()const { return right_type(arg3); }
Chris@16:    const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
Chris@16:    const Arg2& middle_ref()const BOOST_NOEXCEPT { return arg2; }
Chris@16:    const Arg3& right_ref()const BOOST_NOEXCEPT { return arg3; }
Chris@16: 
Chris@16: #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
Chris@16:    explicit operator bool()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return static_cast<bool>(r);
Chris@16:    }
Chris@16: #else
Chris@16:    operator unmentionable_type()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return r ? &unmentionable::proc : 0;
Chris@16:    }
Chris@16: #endif
Chris@16:    static const unsigned left_depth = left_type::depth + 1;
Chris@16:    static const unsigned middle_depth = middle_type::depth + 1;
Chris@16:    static const unsigned right_depth = right_type::depth + 1;
Chris@16:    static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth);
Chris@16: private:
Chris@16:    typename expression_storage<Arg1>::type arg1;
Chris@16:    typename expression_storage<Arg2>::type arg2;
Chris@16:    typename expression_storage<Arg3>::type arg3;
Chris@16:    expression& operator=(const expression&);
Chris@16: };
Chris@16: 
Chris@16: template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
Chris@16: struct expression
Chris@16: {
Chris@16:    typedef mpl::int_<4> arity;
Chris@16:    typedef typename arg_type<Arg1>::type left_type;
Chris@16:    typedef typename arg_type<Arg2>::type left_middle_type;
Chris@16:    typedef typename arg_type<Arg3>::type right_middle_type;
Chris@16:    typedef typename arg_type<Arg4>::type right_type;
Chris@16:    typedef typename left_type::result_type left_result_type;
Chris@16:    typedef typename left_middle_type::result_type left_middle_result_type;
Chris@16:    typedef typename right_middle_type::result_type right_middle_result_type;
Chris@16:    typedef typename right_type::result_type right_result_type;
Chris@16:    typedef typename combine_expression<
Chris@16:       typename combine_expression<
Chris@16:          typename combine_expression<left_result_type, left_middle_result_type>::type,
Chris@16:          right_middle_result_type
Chris@16:       >::type,
Chris@16:       right_result_type
Chris@16:    >::type result_type;
Chris@16:    typedef tag tag_type;
Chris@16: 
Chris@16:    expression(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {}
Chris@16: 
Chris@16:    left_type left()const { return left_type(arg1); }
Chris@16:    left_middle_type left_middle()const { return left_middle_type(arg2); }
Chris@16:    right_middle_type right_middle()const { return right_middle_type(arg3); }
Chris@16:    right_type right()const { return right_type(arg4); }
Chris@16:    const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; }
Chris@16:    const Arg2& left_middle_ref()const BOOST_NOEXCEPT { return arg2; }
Chris@16:    const Arg3& right_middle_ref()const BOOST_NOEXCEPT { return arg3; }
Chris@16:    const Arg4& right_ref()const BOOST_NOEXCEPT { return arg4; }
Chris@16: 
Chris@16: #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
Chris@16:    explicit operator bool()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return static_cast<bool>(r);
Chris@16:    }
Chris@16: #else
Chris@16:    operator unmentionable_type()const
Chris@16:    {
Chris@16:       result_type r(*this);
Chris@16:       return r ? &unmentionable::proc : 0;
Chris@16:    }
Chris@16: #endif
Chris@16:    static const unsigned left_depth = left_type::depth + 1;
Chris@16:    static const unsigned left_middle_depth = left_middle_type::depth + 1;
Chris@16:    static const unsigned right_middle_depth = right_middle_type::depth + 1;
Chris@16:    static const unsigned right_depth = right_type::depth + 1;
Chris@16: 
Chris@16:    static const unsigned left_max_depth = left_depth > left_middle_depth ? left_depth : left_middle_depth;
Chris@16:    static const unsigned right_max_depth = right_depth > right_middle_depth ? right_depth : right_middle_depth;
Chris@16: 
Chris@16:    static const unsigned depth = left_max_depth > right_max_depth ? left_max_depth : right_max_depth;
Chris@16: private:
Chris@16:    typename expression_storage<Arg1>::type arg1;
Chris@16:    typename expression_storage<Arg2>::type arg2;
Chris@16:    typename expression_storage<Arg3>::type arg3;
Chris@16:    typename expression_storage<Arg4>::type arg4;
Chris@16:    expression& operator=(const expression&);
Chris@16: };
Chris@16: 
Chris@16: template <class T>
Chris@16: struct digits2
Chris@16: {
Chris@16:    BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized);
Chris@16:    BOOST_STATIC_ASSERT((std::numeric_limits<T>::radix == 2) || (std::numeric_limits<T>::radix == 10));
Chris@16:    // If we really have so many digits that this fails, then we're probably going to hit other problems anyway:
Chris@16:    BOOST_STATIC_ASSERT(LONG_MAX / 1000 > (std::numeric_limits<T>::digits + 1));
Chris@16:    static const long value = std::numeric_limits<T>::radix == 10 ?  (((std::numeric_limits<T>::digits + 1) * 1000L) / 301L) : std::numeric_limits<T>::digits;
Chris@16: };
Chris@16: 
Chris@16: #ifndef BOOST_MP_MIN_EXPONENT_DIGITS
Chris@16: #ifdef _MSC_VER
Chris@16: #  define BOOST_MP_MIN_EXPONENT_DIGITS 2
Chris@16: #else
Chris@16: #  define BOOST_MP_MIN_EXPONENT_DIGITS 2
Chris@16: #endif
Chris@16: #endif
Chris@16: 
Chris@16: template <class S>
Chris@16: void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, std::ios_base::fmtflags f, bool iszero)
Chris@16: {
Chris@16:    typedef typename S::size_type size_type;
Chris@16:    bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific;
Chris@16:    bool fixed      = (f & std::ios_base::fixed) == std::ios_base::fixed;
Chris@16:    bool showpoint  = (f & std::ios_base::showpoint) == std::ios_base::showpoint;
Chris@16:    bool showpos     = (f & std::ios_base::showpos) == std::ios_base::showpos;
Chris@16: 
Chris@16:    bool neg = str.size() && (str[0] == '-');
Chris@16: 
Chris@16:    if(neg)
Chris@16:       str.erase(0, 1);
Chris@16: 
Chris@16:    if(digits == 0)
Chris@16:    {
Chris@16:       digits = (std::max)(str.size(), size_type(16));
Chris@16:    }
Chris@16: 
Chris@16:    if(iszero || str.empty() || (str.find_first_not_of('0') == S::npos))
Chris@16:    {
Chris@16:       // We will be printing zero, even though the value might not
Chris@16:       // actually be zero (it just may have been rounded to zero).
Chris@16:       str = "0";
Chris@16:       if(scientific || fixed)
Chris@16:       {
Chris@16:          str.append(1, '.');
Chris@16:          str.append(size_type(digits), '0');
Chris@16:          if(scientific)
Chris@16:             str.append("e+00");
Chris@16:       }
Chris@16:       else
Chris@16:       {
Chris@16:          if(showpoint)
Chris@16:          {
Chris@16:             str.append(1, '.');
Chris@16:             if(digits > 1)
Chris@16:                str.append(size_type(digits - 1), '0');
Chris@16:          }
Chris@16:       }
Chris@16:       if(neg)
Chris@101:          str.insert(static_cast<std::string::size_type>(0), 1, '-');
Chris@16:       else if(showpos)
Chris@101:          str.insert(static_cast<std::string::size_type>(0), 1, '+');
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    if(!fixed && !scientific && !showpoint)
Chris@16:    {
Chris@16:       //
Chris@16:       // Suppress trailing zeros:
Chris@16:       //
Chris@16:       std::string::iterator pos = str.end();
Chris@16:       while(pos != str.begin() && *--pos == '0'){}
Chris@16:       if(pos != str.end())
Chris@16:          ++pos;
Chris@16:       str.erase(pos, str.end());
Chris@16:       if(str.empty())
Chris@16:          str = '0';
Chris@16:    }
Chris@16:    else if(!fixed || (my_exp >= 0))
Chris@16:    {
Chris@16:       //
Chris@16:       // Pad out the end with zero's if we need to:
Chris@16:       //
Chris@16:       boost::intmax_t chars = str.size();
Chris@16:       chars = digits - chars;
Chris@16:       if(scientific)
Chris@16:          ++chars;
Chris@16:       if(chars > 0)
Chris@16:       {
Chris@16:          str.append(static_cast<std::string::size_type>(chars), '0');
Chris@16:       }
Chris@16:    }
Chris@16: 
Chris@16:    if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits)))
Chris@16:    {
Chris@16:       if(1 + my_exp > static_cast<boost::intmax_t>(str.size()))
Chris@16:       {
Chris@16:          // Just pad out the end with zeros:
Chris@16:          str.append(static_cast<std::string::size_type>(1 + my_exp - str.size()), '0');
Chris@16:          if(showpoint || fixed)
Chris@16:             str.append(".");
Chris@16:       }
Chris@16:       else if(my_exp + 1 < static_cast<boost::intmax_t>(str.size()))
Chris@16:       {
Chris@16:          if(my_exp < 0)
Chris@16:          {
Chris@101:             str.insert(static_cast<std::string::size_type>(0), static_cast<std::string::size_type>(-1 - my_exp), '0');
Chris@101:             str.insert(static_cast<std::string::size_type>(0), "0.");
Chris@16:          }
Chris@16:          else
Chris@16:          {
Chris@16:             // Insert the decimal point:
Chris@16:             str.insert(static_cast<std::string::size_type>(my_exp + 1), 1, '.');
Chris@16:          }
Chris@16:       }
Chris@16:       else if(showpoint || fixed) // we have exactly the digits we require to left of the point
Chris@16:          str += ".";
Chris@16: 
Chris@16:       if(fixed)
Chris@16:       {
Chris@16:          // We may need to add trailing zeros:
Chris@16:          boost::intmax_t l = str.find('.') + 1;
Chris@16:          l = digits - (str.size() - l);
Chris@16:          if(l > 0)
Chris@16:             str.append(size_type(l), '0');
Chris@16:       }
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       BOOST_MP_USING_ABS
Chris@16:       // Scientific format:
Chris@16:       if(showpoint || (str.size() > 1))
Chris@101:          str.insert(static_cast<std::string::size_type>(1u), 1, '.');
Chris@101:       str.append(static_cast<std::string::size_type>(1u), 'e');
Chris@16:       S e = boost::lexical_cast<S>(abs(my_exp));
Chris@16:       if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS)
Chris@101:          e.insert(static_cast<std::string::size_type>(0), BOOST_MP_MIN_EXPONENT_DIGITS - e.size(), '0');
Chris@16:       if(my_exp < 0)
Chris@101:          e.insert(static_cast<std::string::size_type>(0), 1, '-');
Chris@16:       else
Chris@101:          e.insert(static_cast<std::string::size_type>(0), 1, '+');
Chris@16:       str.append(e);
Chris@16:    }
Chris@16:    if(neg)
Chris@101:       str.insert(static_cast<std::string::size_type>(0), 1, '-');
Chris@16:    else if(showpos)
Chris@101:       str.insert(static_cast<std::string::size_type>(0), 1, '+');
Chris@16: }
Chris@16: 
Chris@16: template <class V>
Chris@16: void check_shift_range(V val, const mpl::true_&, const mpl::true_&)
Chris@16: {
Chris@16:    if(val > (std::numeric_limits<std::size_t>::max)())
Chris@16:       BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits<std::size_t>::max()."));
Chris@16:    if(val < 0)
Chris@16:       BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value."));
Chris@16: }
Chris@16: template <class V>
Chris@16: void check_shift_range(V val, const mpl::false_&, const mpl::true_&)
Chris@16: {
Chris@16:    if(val < 0)
Chris@16:       BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value."));
Chris@16: }
Chris@16: template <class V>
Chris@16: void check_shift_range(V val, const mpl::true_&, const mpl::false_&)
Chris@16: {
Chris@16:    if(val > (std::numeric_limits<std::size_t>::max)())
Chris@16:       BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits<std::size_t>::max()."));
Chris@16: }
Chris@16: template <class V>
Chris@16: void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT{}
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: //
Chris@16: // Traits class, lets us know what kind of number we have, defaults to a floating point type:
Chris@16: //
Chris@16: enum number_category_type
Chris@16: {
Chris@16:    number_kind_unknown = -1,
Chris@16:    number_kind_integer = 0,
Chris@16:    number_kind_floating_point = 1,
Chris@16:    number_kind_rational = 2,
Chris@16:    number_kind_fixed_point = 3
Chris@16: };
Chris@16: 
Chris@16: template <class Num>
Chris@16: 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)> {};
Chris@16: template <class Backend, expression_template_option ExpressionTemplates>
Chris@16: struct number_category<number<Backend, ExpressionTemplates> > : public number_category<Backend>{};
Chris@16: template <class tag, class A1, class A2, class A3, class A4>
Chris@16: struct number_category<detail::expression<tag, A1, A2, A3, A4> > : public number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>{};
Chris@16: 
Chris@16: template <class T>
Chris@16: struct component_type;
Chris@16: template <class T, expression_template_option ExpressionTemplates>
Chris@16: struct component_type<number<T, ExpressionTemplates> > : public component_type<T>{};
Chris@16: template <class tag, class A1, class A2, class A3, class A4>
Chris@16: struct component_type<detail::expression<tag, A1, A2, A3, A4> > : public component_type<typename detail::expression<tag, A1, A2, A3, A4>::result_type>{};
Chris@16: 
Chris@16: template <class T>
Chris@16: struct is_unsigned_number : public mpl::false_{};
Chris@16: template <class Backend, expression_template_option ExpressionTemplates>
Chris@16: struct is_unsigned_number<number<Backend, ExpressionTemplates> > : public is_unsigned_number<Backend> {};
Chris@16: template <class T>
Chris@16: struct is_signed_number : public mpl::bool_<!is_unsigned_number<T>::value> {};
Chris@16: template <class T>
Chris@16: struct is_interval_number : public mpl::false_ {};
Chris@16: template <class Backend, expression_template_option ExpressionTemplates>
Chris@16: struct is_interval_number<number<Backend, ExpressionTemplates> > : public is_interval_number<Backend>{};
Chris@16: 
Chris@16: }} // namespaces
Chris@16: 
Chris@16: namespace boost{ namespace math{ namespace tools{
Chris@16: 
Chris@16: template <class T>
Chris@16: struct promote_arg;
Chris@16: 
Chris@16: template <class tag, class A1, class A2, class A3, class A4>
Chris@16: struct promote_arg<boost::multiprecision::detail::expression<tag, A1, A2, A3, A4> >
Chris@16: {
Chris@16:    typedef typename boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type type;
Chris@16: };
Chris@16: 
Chris@16: template <class R, class B, boost::multiprecision::expression_template_option ET>
Chris@16: inline R real_cast(const boost::multiprecision::number<B, ET>& val)
Chris@16: {
Chris@16:    return val.template convert_to<R>();
Chris@16: }
Chris@16: 
Chris@16: template <class R, class tag, class A1, class A2, class A3, class A4>
Chris@16: inline R real_cast(const boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>& val)
Chris@16: {
Chris@16:    typedef typename boost::multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type val_type;
Chris@16:    return val_type(val).template convert_to<R>();
Chris@16: }
Chris@16: 
Chris@16: 
Chris@101: }
Chris@101: 
Chris@101: namespace constants{
Chris@101: 
Chris@101:    template <class T>
Chris@101:    struct is_explicitly_convertible_from_string;
Chris@101: 
Chris@101:    template <class B, boost::multiprecision::expression_template_option ET>
Chris@101:    struct is_explicitly_convertible_from_string<boost::multiprecision::number<B, ET> >
Chris@101:    {
Chris@101:       static const bool value = true;
Chris@101:    };
Chris@101: 
Chris@101: }
Chris@101: 
Chris@101: }}
Chris@16: 
Chris@16: #endif // BOOST_MATH_BIG_NUM_BASE_HPP
Chris@16: 
Chris@16: