text: //////////////////3/////////////////////////////////////////////
  //  Copyright 2012 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_
  
  #ifndef BOOST_MP_CPP_INT_HPP
  #define BOOST_MP_CPP_INT_HPP
  
  #include <iostream>
  #include <iomanip>
  #include <boost/cstdint.hpp>
  #include <boost/multiprecision/number.hpp>
  #include <boost/multiprecision/detail/integer_ops.hpp>
  #include <boost/array.hpp>
  #include <boost/type_traits/is_integral.hpp>
  #include <boost/type_traits/is_floating_point.hpp>
  #include <boost/multiprecision/cpp_int/cpp_int_config.hpp>
  #include <boost/multiprecision/rational_adaptor.hpp>
  #include <boost/detail/endian.hpp>
  #include <boost/integer/static_min_max.hpp>
  #include <boost/type_traits/common_type.hpp>
  #include <boost/type_traits/make_signed.hpp>
  #include <boost/multiprecision/cpp_int/checked.hpp>
  #ifdef BOOST_MP_USER_DEFINED_LITERALS
  #include <boost/multiprecision/cpp_int/value_pack.hpp>
  #endif
  
  namespace boost{
  namespace multiprecision{
  namespace backends{
  
    using boost::enable_if;
  
  
  #ifdef BOOST_MSVC
  // warning C4127: conditional expression is constant
  #pragma warning(push)
  #pragma warning(disable:4127 4351 4293 4996 4307 4702 6285)
  #endif
  
  template <unsigned MinBits = 0, unsigned MaxBits = 0, cpp_integer_type SignType = signed_magnitude, cpp_int_check_type Checked = unchecked, class Allocator = typename mpl::if_c<MinBits && (MinBits == MaxBits), void, std::allocator<limb_type> >::type >
  struct cpp_int_backend;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, bool trivial = false>
  struct cpp_int_base;
  //
  // Traits class determines the maximum and minimum precision values:
  //
  template <class T> struct max_precision;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
  {
     static const unsigned value = is_void<Allocator>::value ?
        static_unsigned_max<MinBits, MaxBits>::value
        : (((MaxBits >= MinBits) && MaxBits) ? MaxBits : UINT_MAX);
  };
  
  template <class T> struct min_precision;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct min_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
  {
     static const unsigned value = (is_void<Allocator>::value ? static_unsigned_max<MinBits, MaxBits>::value : MinBits);
  };
  //
  // Traits class determines whether the number of bits precision requested could fit in a native type,
  // we call this a "trivial" cpp_int:
  //
  template <class T>
  struct is_trivial_cpp_int
  {
     static const bool value = false;
  };
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
  {
     typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> self;
     static const bool value = is_void<Allocator>::value && (max_precision<self>::value <= (sizeof(double_limb_type) * CHAR_BIT) - (SignType == signed_packed ? 1 : 0));
  };
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct is_trivial_cpp_int<cpp_int_base<MinBits, MaxBits, SignType, Checked, Allocator, true> >
  {
     static const bool value = true;
  };
  
  } // namespace backends
  //
  // Traits class to determine whether a cpp_int_backend is signed or not:
  //
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct is_unsigned_number<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
     : public mpl::bool_<(SignType == unsigned_magnitude) || (SignType == unsigned_packed)>{};
  
  namespace backends{
  //
  // Traits class determines whether T should be implicitly convertible to U, or
  // whether the constructor should be made explicit.  The latter happens if we
  // are losing the sign, or have fewer digits precision in the target type:
  //
  template <class T, class U>
  struct is_implicit_cpp_int_conversion;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
  struct is_implicit_cpp_int_conversion<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >
  {
     typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> t1;
     typedef cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> t2;
     static const bool value =
        (is_signed_number<t2>::value || !is_signed_number<t1>::value)
        && (max_precision<t1>::value <= max_precision<t2>::value);
  };
  
  //
  // Traits class to determine whether operations on a cpp_int may throw:
  //
  template <class T>
  struct is_non_throwing_cpp_int : public mpl::false_{};
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType>
  struct is_non_throwing_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, unchecked, void> > : public mpl::true_ {};
  
  //
  // Traits class, determines whether the cpp_int is fixed precision or not:
  //
  template <class T>
  struct is_fixed_precision;
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct is_fixed_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
     : public mpl::bool_<max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value != UINT_MAX> {};
  
  namespace detail{
  
  inline void verify_new_size(unsigned new_size, unsigned min_size, const mpl::int_<checked>&)
  {
     if(new_size < min_size)
        BOOST_THROW_EXCEPTION(std::overflow_error("Unable to allocate sufficient storage for the value of the result: value overflows the maximum allowable magnitude."));
  }
  inline void verify_new_size(unsigned /*new_size*/, unsigned /*min_size*/, const mpl::int_<unchecked>&){}
  
  template <class U>
  inline void verify_limb_mask(bool b, U limb, U mask, const mpl::int_<checked>&)
  {
     // When we mask out "limb" with "mask", do we loose bits?  If so it's an overflow error:
     if(b && (limb & ~mask))
        BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in cpp_int arithmetic: there is insufficient precision in the target type to hold all of the bits of the result."));
  }
  template <class U>
  inline void verify_limb_mask(bool /*b*/, U /*limb*/, U /*mask*/, const mpl::int_<unchecked>&){}
  
  }
  
  //
  // Now define the various data layouts that are possible as partial specializations of the base class,
  // starting with the default arbitrary precision signed integer type:
  //
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  struct cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false> : private Allocator::template rebind<limb_type>::other
  {
     typedef typename Allocator::template rebind<limb_type>::other allocator_type;
     typedef typename allocator_type::pointer                      limb_pointer;
     typedef typename allocator_type::const_pointer                const_limb_pointer;
     typedef mpl::int_<Checked>                                    checked_type;
  
     //
     // Interface invariants:
     //
     BOOST_STATIC_ASSERT(!is_void<Allocator>::value);
  
  private:
     struct limb_data
     {
        unsigned capacity;
        limb_pointer data;
     };
  
  public:
     BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
     BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
     BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1));
     BOOST_STATIC_CONSTANT(unsigned, internal_limb_count =
        MinBits
           ? (MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0))
           : (sizeof(limb_data) / sizeof(limb_type)));
     BOOST_STATIC_CONSTANT(bool, variable = true);
  
  private:
     union data_type
     {
        limb_data ld;
        limb_type la[internal_limb_count];
        limb_type first;
        double_limb_type double_first;
  
        BOOST_CONSTEXPR data_type() : first(0) {}
        BOOST_CONSTEXPR data_type(limb_type i) : first(i) {}
        BOOST_CONSTEXPR data_type(signed_limb_type i) : first(i < 0 ? static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
  #ifdef BOOST_LITTLE_ENDIAN
        BOOST_CONSTEXPR data_type(double_limb_type i) : double_first(i) {}
        BOOST_CONSTEXPR data_type(signed_double_limb_type i) : double_first(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
  #endif
     };
  
     data_type   m_data;
     unsigned    m_limbs;
     bool        m_sign, m_internal;
  
  public:
     //
     // Direct construction:
     //
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
        : m_data(i), m_limbs(1), m_sign(false), m_internal(true) { }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
        : m_data(i), m_limbs(1), m_sign(i < 0), m_internal(true) { }
  #if defined(BOOST_LITTLE_ENDIAN)
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
        : m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
        : m_data(i), m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > static_cast<double_limb_type>(max_limb_value) ? 2 : 1) : (i > max_limb_value ? 2 : 1)),
          m_sign(i < 0), m_internal(true) { }
  #endif
     //
     // Helper functions for getting at our internal data, and manipulating storage:
     //
     BOOST_MP_FORCEINLINE allocator_type& allocator() BOOST_NOEXCEPT { return *this; }
     BOOST_MP_FORCEINLINE const allocator_type& allocator()const BOOST_NOEXCEPT { return *this; }
     BOOST_MP_FORCEINLINE unsigned size()const  BOOST_NOEXCEPT { return m_limbs; }
     BOOST_MP_FORCEINLINE limb_pointer limbs()  BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; }
     BOOST_MP_FORCEINLINE const_limb_pointer limbs()const  BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; }
     BOOST_MP_FORCEINLINE unsigned capacity()const  BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; }
     BOOST_MP_FORCEINLINE bool sign()const  BOOST_NOEXCEPT { return m_sign; }
     void sign(bool b)  BOOST_NOEXCEPT
     {
        m_sign = b;
        // Check for zero value:
        if(m_sign && (m_limbs == 1))
        {
           if(limbs()[0] == 0)
              m_sign = false;
        }
     }
     void resize(unsigned new_size, unsigned min_size)
     {
        static const unsigned max_limbs = MaxBits / (CHAR_BIT * sizeof(limb_type)) + ((MaxBits % (CHAR_BIT * sizeof(limb_type))) ? 1 : 0);
        // We never resize beyond MaxSize:
        if(new_size > max_limbs)
           new_size = max_limbs;
        detail::verify_new_size(new_size, min_size, checked_type());
        // See if we have enough capacity already:
        unsigned cap = capacity();
        if(new_size > cap)
        {
           // Allocate a new buffer and copy everything over:
           cap = (std::min)((std::max)(cap * 4, new_size), max_limbs);
           limb_pointer pl = allocator().allocate(cap);
           std::memcpy(pl, limbs(), size() * sizeof(limbs()[0]));
           if(!m_internal)
              allocator().deallocate(limbs(), capacity());
           else
              m_internal = false;
           m_limbs = new_size;
           m_data.ld.capacity = cap;
           m_data.ld.data = pl;
        }
        else
        {
           m_limbs = new_size;
        }
     }
     BOOST_MP_FORCEINLINE void normalize() BOOST_NOEXCEPT
     {
        limb_pointer p = limbs();
        while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
     }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {}
     BOOST_MP_FORCEINLINE cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true)
     {
        resize(o.size(), o.size());
        std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
        m_sign = o.m_sign;
     }
  #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
     cpp_int_base(cpp_int_base&& o)
        : allocator_type(static_cast<allocator_type&&>(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal)
     {
        if(m_internal)
        {
           std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
        }
        else
        {
           m_data.ld = o.m_data.ld;
           o.m_limbs = 0;
           o.m_internal = true;
        }
     }
     cpp_int_base& operator = (cpp_int_base&& o) BOOST_NOEXCEPT
     {
        if(!m_internal)
           allocator().deallocate(m_data.ld.data, m_data.ld.capacity);
        *static_cast<allocator_type*>(this) = static_cast<allocator_type&&>(o);
        m_limbs = o.m_limbs;
        m_sign = o.m_sign;
        m_internal = o.m_internal;
        if(m_internal)
        {
           std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
        }
        else
        {
           m_data.ld = o.m_data.ld;
           o.m_limbs = 0;
           o.m_internal = true;
        }
        return *this;
     }
  #endif
     BOOST_MP_FORCEINLINE ~cpp_int_base() BOOST_NOEXCEPT
     {
        if(!m_internal)
           allocator().deallocate(limbs(), capacity());
     }
     void assign(const cpp_int_base& o)
     {
        if(this != &o)
        {
           static_cast<allocator_type&>(*this) = static_cast<const allocator_type&>(o);
           m_limbs = 0;
           resize(o.size(), o.size());
           std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
           m_sign = o.m_sign;
        }
     }
     BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
     {
        m_sign = !m_sign;
        // Check for zero value:
        if(m_sign && (m_limbs == 1))
        {
           if(limbs()[0] == 0)
              m_sign = false;
        }
     }
     BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
     {
        return m_sign;
     }
     BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
     {
        std::swap(m_data, o.m_data);
        std::swap(m_sign, o.m_sign);
        std::swap(m_internal, o.m_internal);
        std::swap(m_limbs, o.m_limbs);
     }
  protected:
     template <class A>
     void check_in_range(const A&) BOOST_NOEXCEPT {}
  };
  
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  const unsigned cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::limb_bits;
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  const limb_type cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::max_limb_value;
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  const limb_type cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::sign_bit_mask;
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  const unsigned cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::internal_limb_count;
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  const bool cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::variable;
  
  #endif
  
  template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
  struct cpp_int_base<MinBits, MaxBits, unsigned_magnitude, Checked, Allocator, false> : private Allocator::template rebind<limb_type>::other
  {
     //
     // There is currently no support for unsigned arbitrary precision arithmetic, largely
     // because it's not clear what subtraction should do:
     //
     BOOST_STATIC_ASSERT_MSG(((sizeof(Allocator) == 0) && !is_void<Allocator>::value), "There is curently no support for unsigned arbitrary precision integers.");
  };
  //
  // Fixed precision (i.e. no allocator), signed-magnitude type with limb-usage count:
  //
  template <unsigned MinBits, cpp_int_check_type Checked>
  struct cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>
  {
     typedef limb_type*                      limb_pointer;
     typedef const limb_type*                const_limb_pointer;
     typedef mpl::int_<Checked>              checked_type;
  
     //
     // Interface invariants:
     //
     BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
  
  public:
     BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
     BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
     BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1));
     BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
     BOOST_STATIC_CONSTANT(bool, variable = false);
     BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (MinBits % limb_bits) ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0)));
     BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs");
  
  private:
     union data_type{
        limb_type          m_data[internal_limb_count];
        limb_type          m_first_limb;
        double_limb_type   m_double_first_limb;
  
        BOOST_CONSTEXPR data_type() : m_first_limb(0) {}
        BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {}
        BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {}
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        template <limb_type...VALUES>
        BOOST_CONSTEXPR data_type(literals::detail::value_pack<VALUES...>) : m_data{ VALUES... } {}
  #endif
     } m_wrapper;
     boost::uint16_t    m_limbs;
     bool               m_sign;
  
  public:
     //
     // Direct construction:
     //
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
        : m_wrapper(i), m_limbs(1), m_sign(false) {}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
        : m_wrapper(limb_type(i < 0 ? static_cast<limb_type>(-static_cast<signed_double_limb_type>(i)) : i)), m_limbs(1), m_sign(i < 0) {}
  #if defined(BOOST_LITTLE_ENDIAN)
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
        : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
        : m_wrapper(double_limb_type(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i)),
          m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)),
          m_sign(i < 0) {}
  #endif
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        template <limb_type...VALUES>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<VALUES...> i)
           : m_wrapper(i), m_limbs(sizeof...(VALUES)), m_sign(false) {}
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<> i)
           : m_wrapper(i), m_limbs(1), m_sign(false) {}
        BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& a, const literals::detail::negate_tag&)
           : m_wrapper(a.m_wrapper), m_limbs(a.m_limbs), m_sign((a.m_limbs == 1) && (*a.limbs() == 0) ? false : !a.m_sign) {}
  #endif
     //
     // Helper functions for getting at our internal data, and manipulating storage:
     //
     BOOST_MP_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; }
     BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return m_sign; }
     BOOST_MP_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
     {
        m_sign = b;
        // Check for zero value:
        if(m_sign && (m_limbs == 1))
        {
           if(limbs()[0] == 0)
              m_sign = false;
        }
     }
     BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        m_limbs = static_cast<boost::uint16_t>((std::min)(new_size, internal_limb_count));
        detail::verify_new_size(m_limbs, min_size, checked_type());
     }
     BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        limb_pointer p = limbs();
        detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
        p[internal_limb_count-1] &= upper_limb_mask;
        while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
        if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned
     }
  
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base()BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1), m_sign(false) {}
     // Not defaulted, it breaks constexpr support in the Intel compiler for some reason:
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o)BOOST_NOEXCEPT
        : m_wrapper(o.m_wrapper), m_limbs(o.m_limbs), m_sign(o.m_sign) {}
     // Defaulted functions:
     //~cpp_int_base() BOOST_NOEXCEPT {}
  
     void assign(const cpp_int_base& o) BOOST_NOEXCEPT
     {
        if(this != &o)
        {
           m_limbs = o.m_limbs;
           std::memcpy(limbs(), o.limbs(), o.size() * sizeof(o.limbs()[0]));
           m_sign = o.m_sign;
        }
     }
     BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
     {
        m_sign = !m_sign;
        // Check for zero value:
        if(m_sign && (m_limbs == 1))
        {
           if(limbs()[0] == 0)
              m_sign = false;
        }
     }
     BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
     {
        return m_sign;
     }
     BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
     {
        for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
           std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
        std::swap(m_sign, o.m_sign);
        std::swap(m_limbs, o.m_limbs);
     }
  protected:
     template <class A>
     void check_in_range(const A&) BOOST_NOEXCEPT {}
  };
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  
  template <unsigned MinBits, cpp_int_check_type Checked>
  const unsigned cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::limb_bits;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const limb_type cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::max_limb_value;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const limb_type cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::sign_bit_mask;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const unsigned cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::internal_limb_count;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const bool cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::variable;
  
  #endif
  //
  // Fixed precision (i.e. no allocator), unsigned type with limb-usage count:
  //
  template <unsigned MinBits, cpp_int_check_type Checked>
  struct cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>
  {
     typedef limb_type*                      limb_pointer;
     typedef const limb_type*                const_limb_pointer;
     typedef mpl::int_<Checked>              checked_type;
  
     //
     // Interface invariants:
     //
     BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
  
  public:
     BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
     BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
     BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1));
     BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
     BOOST_STATIC_CONSTANT(bool, variable = false);
     BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (MinBits % limb_bits) ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0)));
     BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs");
  
  private:
     union data_type{
        limb_type          m_data[internal_limb_count];
        limb_type          m_first_limb;
        double_limb_type   m_double_first_limb;
  
        BOOST_CONSTEXPR data_type() : m_first_limb(0) {}
        BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {}
        BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {}
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        template <limb_type...VALUES>
        BOOST_CONSTEXPR data_type(literals::detail::value_pack<VALUES...>) : m_data{ VALUES... } {}
  #endif
     } m_wrapper;
     limb_type          m_limbs;
  
  public:
     //
     // Direct construction:
     //
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
        : m_wrapper(i), m_limbs(1) {}
     BOOST_MP_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
        : m_wrapper(limb_type(i < 0 ? static_cast<limb_type>(-static_cast<signed_double_limb_type>(i)) : i)), m_limbs(1) { if(i < 0) negate(); }
  #ifdef BOOST_LITTLE_ENDIAN
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
        : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {}
     BOOST_MP_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
        : m_wrapper(double_limb_type(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i)), 
        m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) 
     {
        if (i < 0) negate();
     }
  #endif
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        template <limb_type...VALUES>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<VALUES...> i)
           : m_wrapper(i), m_limbs(sizeof...(VALUES)) {}
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>)
           : m_wrapper(static_cast<limb_type>(0u)), m_limbs(1) {}
  #endif
     //
     // Helper functions for getting at our internal data, and manipulating storage:
     //
     BOOST_MP_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; }
     BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; }
     BOOST_MP_FORCEINLINE void sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked)) {  if(b) negate(); }
     BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        m_limbs = (std::min)(new_size, internal_limb_count);
        detail::verify_new_size(m_limbs, min_size, checked_type());
     }
     BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        limb_pointer p = limbs();
        detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
        p[internal_limb_count-1] &= upper_limb_mask;
        while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
     }
  
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT
        : m_wrapper(limb_type(0u)), m_limbs(1) {}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
        : m_wrapper(o.m_wrapper), m_limbs(o.m_limbs) {}
     // Defaulted functions:
     //~cpp_int_base() BOOST_NOEXCEPT {}
  
     BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
     {
        if(this != &o)
        {
           m_limbs = o.m_limbs;
           std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
        }
     }
  private:
     void check_negate(const mpl::int_<checked>&)
     {
        BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned number."));
     }
     void check_negate(const mpl::int_<unchecked>&){}
  public:
     void negate() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        // Not so much a negate as a complement - this gets called when subtraction
        // would result in a "negative" number:
        unsigned i;
        if((m_limbs == 1) && (m_wrapper.m_data[0] == 0))
           return; // negating zero is always zero, and always OK.
        check_negate(checked_type());
        for(i = m_limbs; i < internal_limb_count; ++i)
           m_wrapper.m_data[i] = 0;
        m_limbs = internal_limb_count;
        for(i = 0; i < internal_limb_count; ++i)
           m_wrapper.m_data[i] = ~m_wrapper.m_data[i];
        normalize();
        eval_increment(static_cast<cpp_int_backend<MinBits, MinBits, unsigned_magnitude, Checked, void>& >(*this));
     }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
     {
        return false;
     }
     BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
     {
        for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
           std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
        std::swap(m_limbs, o.m_limbs);
     }
  protected:
     template <class A>
     void check_in_range(const A&) BOOST_NOEXCEPT {}
  };
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  
  template <unsigned MinBits, cpp_int_check_type Checked>
  const unsigned cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::limb_bits;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const limb_type cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::max_limb_value;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const limb_type cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::sign_bit_mask;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const unsigned cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::internal_limb_count;
  template <unsigned MinBits, cpp_int_check_type Checked>
  const bool cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::variable;
  
  #endif
  //
  // Traits classes to figure out a native type with N bits, these vary from boost::uint_t<N> only
  // because some platforms have native integer types longer than boost::long_long_type, "really boost::long_long_type" anyone??
  //
  template <unsigned N, bool s>
  struct trivial_limb_type_imp
  {
     typedef double_limb_type type;
  };
  
  template <unsigned N>
  struct trivial_limb_type_imp<N, true>
  {
     typedef typename boost::uint_t<N>::least type;
  };
  
  template <unsigned N>
  struct trivial_limb_type : public trivial_limb_type_imp<N, N <= sizeof(boost::long_long_type) * CHAR_BIT> {};
  //
  // Backend for fixed precision signed-magnitude type which will fit entirely inside a "double_limb_type":
  //
  template <unsigned MinBits, cpp_int_check_type Checked>
  struct cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, true>
  {
     typedef typename trivial_limb_type<MinBits>::type  local_limb_type;
     typedef local_limb_type*                           limb_pointer;
     typedef const local_limb_type*                     const_limb_pointer;
     typedef mpl::int_<Checked>                         checked_type;
  protected:
     BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
     BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = (MinBits < limb_bits) ? local_limb_type((local_limb_type(~local_limb_type(0))) >> (limb_bits - MinBits)) : local_limb_type(~local_limb_type(0)));
  private:
     local_limb_type    m_data;
     bool               m_sign;
  
     //
     // Interface invariants:
     //
     BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
  protected:
     template <class T>
     typename boost::disable_if_c<!boost::is_integral<T>::value || (std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits))>::type
        check_in_range(T val, const mpl::int_<checked>&)
     {
        typedef typename common_type<typename make_unsigned<T>::type, local_limb_type>::type common_type;
  
        if(static_cast<common_type>(boost::multiprecision::detail::unsigned_abs(val)) > static_cast<common_type>(limb_mask))
           BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
     }
     template <class T>
     typename boost::disable_if_c<boost::is_integral<T>::value || (std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits))>::type
        check_in_range(T val, const mpl::int_<checked>&)
     {
           using std::abs;
           typedef typename common_type<T, local_limb_type>::type common_type;
  
           if (static_cast<common_type>(abs(val)) > static_cast<common_type>(limb_mask))
              BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
     }
     template <class T, int C>
     void check_in_range(T, const mpl::int_<C>&) BOOST_NOEXCEPT {}
  
     template <class T>
     void check_in_range(T val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<T>(), checked_type())))
     {
        check_in_range(val, checked_type());
     }
  
  public:
     //
     // Direct construction:
     //
     template <class SI>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == unchecked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
        : m_data(i < 0 ? static_cast<local_limb_type>(static_cast<typename make_unsigned<SI>::type>(boost::multiprecision::detail::unsigned_abs(i)) & limb_mask) : static_cast<local_limb_type>(i)& limb_mask), m_sign(i < 0) {}
     template <class SI>
     BOOST_MP_FORCEINLINE cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
        : m_data(i < 0 ? (static_cast<local_limb_type>(static_cast<typename make_unsigned<SI>::type>(boost::multiprecision::detail::unsigned_abs(i)) & limb_mask)) : static_cast<local_limb_type>(i)& limb_mask), m_sign(i < 0) 
     { check_in_range(i); }
     template <class UI>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT
        : m_data(static_cast<local_limb_type>(i) & limb_mask), m_sign(false) {}
     template <class UI>
     BOOST_MP_FORCEINLINE cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == checked)>::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<UI>())))
        : m_data(static_cast<local_limb_type>(i) & limb_mask), m_sign(false) { check_in_range(i); }
     template <class F>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(F i, typename boost::enable_if_c<is_floating_point<F>::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT
        : m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask), m_sign(i < 0) {}
     template <class F>
     BOOST_MP_FORCEINLINE cpp_int_base(F i, typename boost::enable_if_c<is_floating_point<F>::value && (Checked == checked)>::type const* = 0)
        : m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask), m_sign(i < 0) { check_in_range(i); }
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>) BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(0u)), m_sign(false) {}
        template <limb_type a>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a>)BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(a)), m_sign(false) {}
        template <limb_type a, limb_type b>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a, b>)BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(a) | (static_cast<local_limb_type>(b) << bits_per_limb)), m_sign(false) {}
        BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& a, const literals::detail::negate_tag&)BOOST_NOEXCEPT
           : m_data(a.m_data), m_sign(a.m_data ? !a.m_sign : false) {}
  #endif
     //
     // Helper functions for getting at our internal data, and manipulating storage:
     //
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; }
     BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; }
     BOOST_MP_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; }
     BOOST_MP_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
     {
        m_sign = b;
        // Check for zero value:
        if(m_sign && !m_data)
        {
           m_sign = false;
        }
     }
     BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size)
     {
        detail::verify_new_size(2, min_size, checked_type());
     }
     BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        if(!m_data)
           m_sign = false; // zero is always unsigned
        detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
        m_data &= limb_mask;
     }
  
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(0), m_sign(false) {}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
        : m_data(o.m_data), m_sign(o.m_sign) {}
     //~cpp_int_base() BOOST_NOEXCEPT {}
     BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
     {
        m_data = o.m_data;
        m_sign = o.m_sign;
     }
     BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
     {
        m_sign = !m_sign;
        // Check for zero value:
        if(m_data == 0)
        {
           m_sign = false;
        }
     }
     BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
     {
        return m_sign;
     }
     BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
     {
        std::swap(m_sign, o.m_sign);
        std::swap(m_data, o.m_data);
     }
  };
  //
  // Backend for unsigned fixed precision (i.e. no allocator) type which will fit entirely inside a "double_limb_type":
  //
  template <unsigned MinBits, cpp_int_check_type Checked>
  struct cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, true>
  {
     typedef typename trivial_limb_type<MinBits>::type  local_limb_type;
     typedef local_limb_type*                           limb_pointer;
     typedef const local_limb_type*                     const_limb_pointer;
  private:
     BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
     BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = limb_bits != MinBits ? 
        static_cast<local_limb_type>(static_cast<local_limb_type>(~local_limb_type(0)) >> (limb_bits - MinBits))
        : static_cast<local_limb_type>(~local_limb_type(0)));
  
     local_limb_type    m_data;
  
     typedef mpl::int_<Checked>                          checked_type;
  
     //
     // Interface invariants:
     //
     BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
  protected:
     template <class T>
     typename boost::disable_if_c<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits)>::type
        check_in_range(T val, const mpl::int_<checked>&, const boost::false_type&)
     {
        typedef typename common_type<T, local_limb_type>::type common_type;
  
        if(static_cast<common_type>(val) > limb_mask)
           BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
     }
     template <class T>
     void check_in_range(T val, const mpl::int_<checked>&, const boost::true_type&)
     {
        typedef typename common_type<T, local_limb_type>::type common_type;
  
        if(static_cast<common_type>(val) > limb_mask)
           BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
        if(val < 0)
           BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative."));
     }
     template <class T, int C, bool B>
     BOOST_MP_FORCEINLINE void check_in_range(T, const mpl::int_<C>&, const boost::integral_constant<bool, B>&) BOOST_NOEXCEPT {}
  
     template <class T>
     BOOST_MP_FORCEINLINE void check_in_range(T val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<T>(), checked_type(), is_signed<T>())))
     {
        check_in_range(val, checked_type(), is_signed<T>());
     }
  
  public:
     //
     // Direct construction:
     //
     template <class SI>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
        : m_data(i < 0 ? (1 + ~static_cast<local_limb_type>(-i)) & limb_mask : static_cast<local_limb_type>(i) & limb_mask) {}
     template <class SI>
     BOOST_MP_FORCEINLINE cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
        : m_data(i < 0 ? 1 + ~static_cast<local_limb_type>(-i) : static_cast<local_limb_type>(i)) { check_in_range(i); }
     template <class UI>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
        : m_data(static_cast<local_limb_type>(i) & limb_mask) {}
     template <class UI>
     BOOST_MP_FORCEINLINE cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<UI>())))
        : m_data(static_cast<local_limb_type>(i)) { check_in_range(i); }
     template <class F>
     BOOST_MP_FORCEINLINE cpp_int_base(F i, typename boost::enable_if<is_floating_point<F> >::type const* = 0) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
        : m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask)
     {
        check_in_range(i);
        if(i < 0)
           negate();
     }
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>) BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(0u)) {}
        template <limb_type a>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a>) BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(a)) {}
        template <limb_type a, limb_type b>
        BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a, b>) BOOST_NOEXCEPT
           : m_data(static_cast<local_limb_type>(a) | (static_cast<local_limb_type>(b) << bits_per_limb)) {}
  #endif
     //
     // Helper functions for getting at our internal data, and manipulating storage:
     //
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; }
     BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; }
     BOOST_MP_FORCEINLINE void sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        if(b)
           negate();
     }
     BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size)
     {
        detail::verify_new_size(2, min_size, checked_type());
     }
     BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
        m_data &= limb_mask;
     }
  
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(0) {}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
        : m_data(o.m_data) {}
     //~cpp_int_base() BOOST_NOEXCEPT {}
     BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
     {
        m_data = o.m_data;
     }
     BOOST_MP_FORCEINLINE void negate() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
     {
        if(Checked == checked)
        {
           BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned type."));
        }
        m_data = ~m_data;
        ++m_data;
     }
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
     {
        return false;
     }
     BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
     {
        std::swap(m_data, o.m_data);
     }
  };
  //
  // Traits class, lets us know whether type T can be directly converted to the base type,
  // used to enable/disable constructors etc:
  //
  template <class Arg, class Base>
  struct is_allowed_cpp_int_base_conversion : public mpl::if_c<
        is_same<Arg, limb_type>::value || is_same<Arg, signed_limb_type>::value
  #ifdef BOOST_LITTLE_ENDIAN
        || is_same<Arg, double_limb_type>::value || is_same<Arg, signed_double_limb_type>::value
  #endif
  #if defined(BOOST_MP_USER_DEFINED_LITERALS)
        || literals::detail::is_value_pack<Arg>::value
  #endif
        || (is_trivial_cpp_int<Base>::value && is_arithmetic<Arg>::value),
        mpl::true_,
        mpl::false_
     >::type
  {};
  //
  // Now the actual backend, normalising parameters passed to the base class:
  //
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct cpp_int_backend
     : public cpp_int_base<
                 min_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
                 max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
                 SignType,
                 Checked,
                 Allocator,
                 is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value>
  {
     typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>    self_type;
     typedef cpp_int_base<
                 min_precision<self_type>::value,
                 max_precision<self_type>::value,
                 SignType,
                 Checked,
                 Allocator,
                 is_trivial_cpp_int<self_type>::value>                 base_type;
     typedef mpl::bool_<is_trivial_cpp_int<self_type>::value>          trivial_tag;
  public:
     typedef typename mpl::if_<
        trivial_tag,
        mpl::list<
        signed char, short, int, long,
        boost::long_long_type, signed_double_limb_type>,
        mpl::list<signed_limb_type, signed_double_limb_type>
     >::type                                                           signed_types;
     typedef typename mpl::if_<
        trivial_tag,
        mpl::list<unsigned char, unsigned short, unsigned,
        unsigned long, boost::ulong_long_type, double_limb_type>,
        mpl::list<limb_type, double_limb_type>
     >::type                                                           unsigned_types;
     typedef typename mpl::if_<
        trivial_tag,
        mpl::list<float, double, long double>,
        mpl::list<long double>
     >::type                                                           float_types;
     typedef mpl::int_<Checked>                                        checked_type;
  
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{}
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_MP_NOEXCEPT_IF(boost::is_void<Allocator>::value) : base_type(o) {}
  #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT
        : base_type(static_cast<base_type&&>(o)) {}
  #endif
     //
     // Direct construction from arithmetic type:
     //
     template <class Arg>
     BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(Arg i, typename boost::enable_if_c<is_allowed_cpp_int_base_conversion<Arg, base_type>::value >::type const* = 0)BOOST_MP_NOEXCEPT_IF(noexcept(base_type(std::declval<Arg>())))
        : base_type(i) {}
  
  private:
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::true_ const&, mpl::true_ const &)
     {
        // Assigning trivial type to trivial type:
        this->check_in_range(*other.limbs());
        *this->limbs() = static_cast<typename self_type::local_limb_type>(*other.limbs());
        this->sign(other.sign());
        this->normalize();
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::true_ const&, mpl::false_ const &)
     {
        // non-trivial to trivial narrowing conversion:
        double_limb_type v = *other.limbs();
        if(other.size() > 1)
        {
           v |= static_cast<double_limb_type>(other.limbs()[1]) << bits_per_limb;
           if((Checked == checked) && (other.size() > 2))
           {
              BOOST_THROW_EXCEPTION(std::range_error("Assignment of a cpp_int that is out of range for the target type."));
           }
        }
        *this = v;
        this->sign(other.sign());
        this->normalize();
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::false_ const&, mpl::true_ const &)
     {
        // trivial to non-trivial, treat the trivial argument as if it were an unsigned arithmetic type, then set the sign afterwards:
         *this = static_cast<
              typename boost::multiprecision::detail::canonical<
                 typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::local_limb_type,
                 cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>
              >::type
           >(*other.limbs());
         this->sign(other.sign());
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::false_ const&, mpl::false_ const &)
     {
        // regular non-trivial to non-trivial assign:
        this->resize(other.size(), other.size());
        std::memcpy(this->limbs(), other.limbs(), (std::min)(other.size(), this->size()) * sizeof(this->limbs()[0]));
        this->sign(other.sign());
        this->normalize();
     }
  public:
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     cpp_int_backend(
        const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other,
        typename boost::enable_if_c<is_implicit_cpp_int_conversion<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>, self_type>::value>::type* = 0)
        : base_type()
     {
        do_assign(
           other,
           mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
           mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     explicit cpp_int_backend(
        const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other,
        typename boost::disable_if_c<is_implicit_cpp_int_conversion<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>, self_type>::value>::type* = 0)
        : base_type()
     {
        do_assign(
           other,
           mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
           mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     cpp_int_backend& operator=(
        const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other)
     {
        do_assign(
           other,
           mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
           mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
        return *this;
     }
  #ifdef BOOST_MP_USER_DEFINED_LITERALS
     BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& a, const literals::detail::negate_tag& tag)
        : base_type(static_cast<const base_type&>(a), tag){}
  #endif
  
     BOOST_MP_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().assign(std::declval<const cpp_int_backend&>())))
     {
        this->assign(o);
        return *this;
     }
  #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
     BOOST_MP_FORCEINLINE cpp_int_backend& operator = (cpp_int_backend&& o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<base_type&>() = std::declval<base_type>()))
     {
        *static_cast<base_type*>(this) = static_cast<base_type&&>(o);
        return *this;
     }
  #endif
  private:
     template <class A>
     typename boost::enable_if<is_unsigned<A> >::type do_assign_arithmetic(A val, const mpl::true_&) 
           BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().check_in_range(std::declval<A>())))
     {
        this->check_in_range(val);
        *this->limbs() = static_cast<typename self_type::local_limb_type>(val);
        this->normalize();
     }
     template <class A>
     typename boost::disable_if_c<is_unsigned<A>::value || !is_integral<A>::value >::type do_assign_arithmetic(A val, const mpl::true_&) 
           BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().check_in_range(std::declval<A>())) && noexcept(std::declval<cpp_int_backend>().sign(true)))
     {
        this->check_in_range(val);
        *this->limbs() = (val < 0) ? static_cast<typename self_type::local_limb_type>(boost::multiprecision::detail::unsigned_abs(val)) : static_cast<typename self_type::local_limb_type>(val);
        this->sign(val < 0);
        this->normalize();
     }
     template <class A>
     typename boost::enable_if_c< !is_integral<A>::value>::type do_assign_arithmetic(A val, const mpl::true_&)
     {
        this->check_in_range(val);
        *this->limbs() = (val < 0) ? static_cast<typename self_type::local_limb_type>(boost::multiprecision::detail::abs(val)) : static_cast<typename self_type::local_limb_type>(val);
        this->sign(val < 0);
        this->normalize();
     }
     BOOST_MP_FORCEINLINE void do_assign_arithmetic(limb_type i, const mpl::false_&) BOOST_NOEXCEPT
     {
        this->resize(1, 1);
        *this->limbs() = i;
        this->sign(false);
     }
     BOOST_MP_FORCEINLINE void do_assign_arithmetic(signed_limb_type i, const mpl::false_&) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().sign(true)))
     {
        this->resize(1, 1);
        *this->limbs() = static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(i));
        this->sign(i < 0);
     }
     void do_assign_arithmetic(double_limb_type i, const mpl::false_&) BOOST_NOEXCEPT
     {
        BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
        BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
        typename base_type::limb_pointer p = this->limbs();
        *p = static_cast<limb_type>(i);
        p[1] = static_cast<limb_type>(i >> base_type::limb_bits);
        this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
        this->sign(false);
     }
     void do_assign_arithmetic(signed_double_limb_type i, const mpl::false_&) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().sign(true)))
     {
        BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
        BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
        bool s = false;
        double_limb_type ui;
        if(i < 0)
           s = true;
        ui = static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i));
        typename base_type::limb_pointer p = this->limbs();
        *p = static_cast<limb_type>(ui);
        p[1] = static_cast<limb_type>(ui >> base_type::limb_bits);
        this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
        this->sign(s);
     }
  
     void do_assign_arithmetic(long double a, const mpl::false_&)
     {
        using default_ops::eval_add;
        using default_ops::eval_subtract;
        using std::frexp;
        using std::ldexp;
        using std::floor;
  
        if(a < 0)
        {
           do_assign_arithmetic(-a, mpl::false_());
           this->sign(true);
           return;
        }
  
        if (a == 0) {
           *this = static_cast<limb_type>(0u);
        }
  
        if (a == 1) {
           *this = static_cast<limb_type>(1u);
        }
  
        BOOST_ASSERT(!(boost::math::isinf)(a));
        BOOST_ASSERT(!(boost::math::isnan)(a));
  
        int e;
        long double f, term;
        *this = static_cast<limb_type>(0u);
  
        f = frexp(a, &e);
  
        static const limb_type shift = std::numeric_limits<limb_type>::digits;
  
        while(f)
        {
           // extract int sized bits from f:
           f = ldexp(f, shift);
           term = floor(f);
           e -= shift;
           eval_left_shift(*this, shift);
           if(term > 0)
              eval_add(*this, static_cast<limb_type>(term));
           else
              eval_subtract(*this, static_cast<limb_type>(-term));
           f -= term;
        }
        if(e > 0)
           eval_left_shift(*this, e);
        else if(e < 0)
           eval_right_shift(*this, -e);
     }
  public:
     template <class Arithmetic>
     BOOST_MP_FORCEINLINE cpp_int_backend& operator = (Arithmetic val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().do_assign_arithmetic(std::declval<Arithmetic>(), trivial_tag())))
     {
        do_assign_arithmetic(val, trivial_tag());
        return *this;
     }
  private:
     void do_assign_string(const char* s, const mpl::true_&)
     {
        std::size_t n = s ? std::strlen(s) : 0;
        *this = 0;
        unsigned radix = 10;
        bool isneg = false;
        if(n && (*s == '-'))
        {
           --n;
           ++s;
           isneg = true;
        }
        if(n && (*s == '0'))
        {
           if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
           {
              radix = 16;
              s +=2;
              n -= 2;
           }
           else
           {
              radix = 8;
              n -= 1;
           }
        }
        if(n)
        {
           unsigned val;
           while(*s)
           {
              if(*s >= '0' && *s <= '9')
                 val = *s - '0';
              else if(*s >= 'a' && *s <= 'f')
                 val = 10 + *s - 'a';
              else if(*s >= 'A' && *s <= 'F')
                 val = 10 + *s - 'A';
              else
                 val = radix + 1;
              if(val >= radix)
              {
                 BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
              }
              *this->limbs() = detail::checked_multiply(*this->limbs(), static_cast<typename base_type::local_limb_type>(radix), checked_type());
              *this->limbs() = detail::checked_add(*this->limbs(), static_cast<typename base_type::local_limb_type>(val), checked_type());
              ++s;
           }
        }
        if(isneg)
           this->negate();
     }
     void do_assign_string(const char* s, const mpl::false_&)
     {
        using default_ops::eval_multiply;
        using default_ops::eval_add;
        std::size_t n = s ? std::strlen(s) : 0;
        *this = static_cast<limb_type>(0u);
        unsigned radix = 10;
        bool isneg = false;
        if(n && (*s == '-'))
        {
           --n;
           ++s;
           isneg = true;
        }
        if(n && (*s == '0'))
        {
           if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
           {
              radix = 16;
              s +=2;
              n -= 2;
           }
           else
           {
              radix = 8;
              n -= 1;
           }
        }
        if(n)
        {
           if(radix == 8 || radix == 16)
           {
              unsigned shift = radix == 8 ? 3 : 4;
              unsigned block_count = base_type::limb_bits / shift;
              unsigned block_shift = shift * block_count;
              limb_type val, block;
              while(*s)
              {
                 block = 0;
                 for(unsigned i = 0; (i < block_count); ++i)
                 {
                    if(*s >= '0' && *s <= '9')
                       val = *s - '0';
                    else if(*s >= 'a' && *s <= 'f')
                       val = 10 + *s - 'a';
                    else if(*s >= 'A' && *s <= 'F')
                       val = 10 + *s - 'A';
                    else
                       val = base_type::max_limb_value;
                    if(val >= radix)
                    {
                       BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
                    }
                    block <<= shift;
                    block |= val;
                    if(!*++s)
                    {
                       // final shift is different:
                       block_shift = (i + 1) * shift;
                       break;
                    }
                 }
                 eval_left_shift(*this, block_shift);
                 this->limbs()[0] |= block;
              }
           }
           else
           {
              // Base 10, we extract blocks of size 10^9 at a time, that way
              // the number of multiplications is kept to a minimum:
              limb_type block_mult = max_block_10;
              while(*s)
              {
                 limb_type block = 0;
                 for(unsigned i = 0; i < digits_per_block_10; ++i)
                 {
                    limb_type val;
                    if(*s >= '0' && *s <= '9')
                       val = *s - '0';
                    else
                       BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
                    block *= 10;
                    block += val;
                    if(!*++s)
                    {
                       block_mult = block_multiplier(i);
                       break;
                    }
                 }
                 eval_multiply(*this, block_mult);
                 eval_add(*this, block);
              }
           }
        }
        if(isneg)
           this->negate();
     }
  public:
     cpp_int_backend& operator = (const char* s)
     {
        do_assign_string(s, trivial_tag());
        return *this;
     }
     BOOST_MP_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT
     {
        this->do_swap(o);
     }
  private:
     std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::false_&)const
     {
        typedef typename mpl::if_c<sizeof(typename base_type::local_limb_type) == 1, unsigned, typename base_type::local_limb_type>::type io_type;
        if(this->sign() && (((f & std::ios_base::hex) == std::ios_base::hex) || ((f & std::ios_base::oct) == std::ios_base::oct)))
           BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
        std::stringstream ss;
        ss.flags(f & ~std::ios_base::showpos);
        ss << static_cast<io_type>(*this->limbs());
        std::string result;
        if(this->sign())
           result += '-';
        else if(f & std::ios_base::showpos)
           result += '+';
        result += ss.str();
        return result;
     }
     std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::true_&)const
     {
        // Even though we have only one limb, we can't do IO on it :-(
        int base = 10;
        if((f & std::ios_base::oct) == std::ios_base::oct)
           base = 8;
        else if((f & std::ios_base::hex) == std::ios_base::hex)
           base = 16;
        std::string result;
  
        unsigned Bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT;
  
        if(base == 8 || base == 16)
        {
           if(this->sign())
              BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
           limb_type shift = base == 8 ? 3 : 4;
           limb_type mask = static_cast<limb_type>((1u << shift) - 1);
           typename base_type::local_limb_type v = *this->limbs();
           result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0');
           std::string::difference_type pos = result.size() - 1;
           for(unsigned i = 0; i < Bits / shift; ++i)
           {
              char c = '0' + static_cast<char>(v & mask);
              if(c > '9')
                 c += 'A' - '9' - 1;
              result[pos--] = c;
              v >>= shift;
           }
           if(Bits % shift)
           {
              mask = static_cast<limb_type>((1u << (Bits % shift)) - 1);
              char c = '0' + static_cast<char>(v & mask);
              if(c > '9')
                 c += 'A' - '9';
              result[pos] = c;
           }
           //
           // Get rid of leading zeros:
           //
           std::string::size_type n = result.find_first_not_of('0');
           if(!result.empty() && (n == std::string::npos))
              n = result.size() - 1;
           result.erase(0, n);
           if(f & std::ios_base::showbase)
           {
              const char* pp = base == 8 ? "0" : "0x";
              result.insert(static_cast<std::string::size_type>(0), pp);
           }
        }
        else
        {
           result.assign(Bits / 3 + 1, '0');
           std::string::difference_type pos = result.size() - 1;
           typename base_type::local_limb_type v(*this->limbs());
           bool neg = false;
           if(this->sign())
           {
              neg = true;
           }
           while(v)
           {
              result[pos] = (v % 10) + '0';
              --pos;
              v /= 10;
           }
           std::string::size_type n = result.find_first_not_of('0');
           result.erase(0, n);
           if(result.empty())
              result = "0";
           if(neg)
              result.insert(static_cast<std::string::size_type>(0), 1, '-');
           else if(f & std::ios_base::showpos)
              result.insert(static_cast<std::string::size_type>(0), 1, '+');
        }
        return result;
     }
     std::string do_get_string(std::ios_base::fmtflags f, const mpl::true_&)const
     {
  #ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO
        return do_get_trivial_string(f, mpl::bool_<is_same<typename base_type::local_limb_type, double_limb_type>::value>());
  #else
        return do_get_trivial_string(f, mpl::bool_<false>());
  #endif
     }
     std::string do_get_string(std::ios_base::fmtflags f, const mpl::false_&)const
     {
        using default_ops::eval_get_sign;
        int base = 10;
        if((f & std::ios_base::oct) == std::ios_base::oct)
           base = 8;
        else if((f & std::ios_base::hex) == std::ios_base::hex)
           base = 16;
        std::string result;
  
        unsigned Bits = this->size() * base_type::limb_bits;
  
        if(base == 8 || base == 16)
        {
           if(this->sign())
              BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
           limb_type shift = base == 8 ? 3 : 4;
           limb_type mask = static_cast<limb_type>((1u << shift) - 1);
           cpp_int_backend t(*this);
           result.assign(Bits / shift + ((Bits % shift) ? 1 : 0), '0');
           std::string::difference_type pos = result.size() - 1;
           for(unsigned i = 0; i < Bits / shift; ++i)
           {
              char c = '0' + static_cast<char>(t.limbs()[0] & mask);
              if(c > '9')
                 c += 'A' - '9' - 1;
              result[pos--] = c;
              eval_right_shift(t, shift);
           }
           if(Bits % shift)
           {
              mask = static_cast<limb_type>((1u << (Bits % shift)) - 1);
              char c = '0' + static_cast<char>(t.limbs()[0] & mask);
              if(c > '9')
                 c += 'A' - '9';
              result[pos] = c;
           }
           //
           // Get rid of leading zeros:
           //
           std::string::size_type n = result.find_first_not_of('0');
           if(!result.empty() && (n == std::string::npos))
              n = result.size() - 1;
           result.erase(0, n);
           if(f & std::ios_base::showbase)
           {
              const char* pp = base == 8 ? "0" : "0x";
              result.insert(static_cast<std::string::size_type>(0), pp);
           }
        }
        else
        {
           result.assign(Bits / 3 + 1, '0');
           std::string::difference_type pos = result.size() - 1;
           cpp_int_backend t(*this);
           cpp_int_backend r;
           bool neg = false;
           if(t.sign())
           {
              t.negate();
              neg = true;
           }
           if(this->size() == 1)
           {
              result = boost::lexical_cast<std::string>(t.limbs()[0]);
           }
           else
           {
              cpp_int_backend block10;
              block10 = max_block_10;
              while(eval_get_sign(t) != 0)
              {
                 cpp_int_backend t2;
                 divide_unsigned_helper(&t2, t, block10, r);
                 t = t2;
                 limb_type v = r.limbs()[0];
                 for(unsigned i = 0; i < digits_per_block_10; ++i)
                 {
                    char c = '0' + v % 10;
                    v /= 10;
                    result[pos] = c;
                    if(pos-- == 0)
                       break;
                 }
              }
           }
           std::string::size_type n = result.find_first_not_of('0');
           result.erase(0, n);
           if(result.empty())
              result = "0";
           if(neg)
              result.insert(static_cast<std::string::size_type>(0), 1, '-');
           else if(f & std::ios_base::showpos)
              result.insert(static_cast<std::string::size_type>(0), 1, '+');
        }
        return result;
     }
  public:
     std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
     {
        return do_get_string(f, trivial_tag());
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::false_&, const mpl::false_&)const BOOST_NOEXCEPT
     {
        if(this->sign() != o.sign())
           return this->sign() ? -1 : 1;
  
        // Only do the compare if the same sign:
        int result = compare_unsigned(o);
  
        if(this->sign())
           result = -result;
        return result;
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::true_&, const mpl::false_&)const
     {
        cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> t(*this);
        return t.compare(o);
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::false_&, const mpl::true_&)const
     {
        cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> t(o);
        return compare(t);
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::true_&, const mpl::true_&)const BOOST_NOEXCEPT
     {
        if(this->sign())
        {
           if(o.sign())
           {
              return *this->limbs() < *o.limbs() ? 1 : (*this->limbs() > *o.limbs() ? -1 : 0);
           }
           else
              return -1;
        }
        else
        {
           if(o.sign())
              return 1;
           return *this->limbs() < *o.limbs() ? -1 : (*this->limbs() > *o.limbs() ? 1 : 0);
        }
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o)const BOOST_NOEXCEPT
     {
        typedef mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value> t1;
        typedef mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value> t2;
        return compare_imp(o, t1(), t2());
     }
     template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
     int compare_unsigned(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o)const BOOST_NOEXCEPT
     {
        if(this->size() != o.size())
        {
           return this->size() > o.size() ? 1 : -1;
        }
        typename base_type::const_limb_pointer pa = this->limbs();
        typename base_type::const_limb_pointer pb = o.limbs();
        for(int i = this->size() - 1; i >= 0; --i)
        {
           if(pa[i] != pb[i])
              return pa[i] > pb[i] ? 1 : -1;
        }
        return 0;
     }
     template <class Arithmetic>
     BOOST_MP_FORCEINLINE typename boost::enable_if<is_arithmetic<Arithmetic>, int>::type compare(Arithmetic i)const
     {
        // braindead version:
        cpp_int_backend t;
        t = i;
        return compare(t);
     }
  };
  
  } // namespace backends
  
  namespace default_ops{
  
  template <class Backend>
  struct double_precision_type;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct double_precision_type<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
  {
     typedef typename mpl::if_c<
        backends::is_fixed_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
        backends::cpp_int_backend<
           (is_void<Allocator>::value ?
              2 * backends::max_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value
              : MinBits),
           2 * backends::max_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
           SignType,
           Checked,
           Allocator>,
        backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>
     >::type type;
  };
  
  
  }
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked>
  struct expression_template_default<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, void> >
  {
     static const expression_template_option value = et_off;
  };
  
  using boost::multiprecision::backends::cpp_int_backend;
  
  template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
  struct number_category<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> > : public mpl::int_<number_kind_integer>{};
  
  typedef number<cpp_int_backend<> >                   cpp_int;
  typedef rational_adaptor<cpp_int_backend<> >         cpp_rational_backend;
  typedef number<cpp_rational_backend>                 cpp_rational;
  
  // Fixed precision unsigned types:
  typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> >   uint128_t;
  typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> >   uint256_t;
  typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> >   uint512_t;
  typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t;
  
  // Fixed precision signed types:
  typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> >    int128_t;
  typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> >    int256_t;
  typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> >    int512_t;
  typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> >  int1024_t;
  
  // Over again, but with checking enabled this time:
  typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> >               checked_cpp_int;
  typedef rational_adaptor<cpp_int_backend<0, 0, signed_magnitude, checked> >     checked_cpp_rational_backend;
  typedef number<checked_cpp_rational_backend>                                    checked_cpp_rational;
  // Fixed precision unsigned types:
  typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> >   checked_uint128_t;
  typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> >   checked_uint256_t;
  typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> >   checked_uint512_t;
  typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> > checked_uint1024_t;
  
  // Fixed precision signed types:
  typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> >    checked_int128_t;
  typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> >    checked_int256_t;
  typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> >    checked_int512_t;
  typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> >  checked_int1024_t;
  
  #ifdef BOOST_NO_SFINAE_EXPR
  
  namespace detail{
  
  template<unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
  struct is_explicitly_convertible<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> > : public mpl::true_ {};
  
  }
  #endif
  
  }} // namespaces
  
  //
  // Last of all we include the implementations of all the eval_* non member functions:
  //
  #include <boost/multiprecision/cpp_int/comparison.hpp>
  #include <boost/multiprecision/cpp_int/add.hpp>
  #include <boost/multiprecision/cpp_int/multiply.hpp>
  #include <boost/multiprecision/cpp_int/divide.hpp>
  #include <boost/multiprecision/cpp_int/bitwise.hpp>
  #include <boost/multiprecision/cpp_int/misc.hpp>
  #include <boost/multiprecision/cpp_int/limits.hpp>
  #ifdef BOOST_MP_USER_DEFINED_LITERALS
  #include <boost/multiprecision/cpp_int/literals.hpp>
  #endif
  #include <boost/multiprecision/cpp_int/serialize.hpp>
  
  #endif
  