FM / multiprecision

/usr/include/boost/multiprecision

Name	Size	Mode	Actions
concepts/	-	0755	rm
cpp_bin_float/	-	0755	rm
cpp_int/	-	0755	rm
detail/	-	0755	rm
traits/	-	0755	rm
complex128.hpp	707	0644	edit dl rm
complex_adaptor.hpp	26516	0644	edit dl rm
cpp_bin_float.hpp	98102	0644	edit dl rm
cpp_complex.hpp	2784	0644	edit dl rm
cpp_dec_float.hpp	141498	0644	edit dl rm
cpp_int.hpp	97009	0644	edit dl rm
debug_adaptor.hpp	27091	0644	edit dl rm
eigen.hpp	10513	0644	edit dl rm
float128.hpp	34757	0644	edit dl rm
gmp.hpp	113421	0644	edit dl rm
integer.hpp	7339	0644	edit dl rm
logged_adaptor.hpp	34770	0644	edit dl rm
miller_rabin.hpp	6285	0644	edit dl rm
mpc.hpp	51329	0644	edit dl rm
mpfi.hpp	76273	0644	edit dl rm
mpfr.hpp	128421	0644	edit dl rm
number.hpp	104027	0644	edit dl rm
random.hpp	616	0644	edit dl rm
rational_adaptor.hpp	13475	0644	edit dl rm
tommath.hpp	34140	0644	edit dl rm

Edit: /usr/include/boost/multiprecision/cpp_int.hpp (97009B)

//////////////////3/////////////////////////////////////////////
//  Copyright 2012 John Maddock. Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt

#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/multiprecision/detail/rebind.hpp>
#include <boost/core/empty_value.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/multiprecision/traits/is_byte_container.hpp>
#include <boost/predef/other/endian.h>
#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>
#include <boost/multiprecision/detail/constexpr.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
#pragma warning(push)
#pragma warning(disable : 4307) // integral constant overflow (oveflow is in a branch not taken when it would overflow)
#pragma warning(disable : 4127) // conditional expression is constant
#pragma warning(disable : 4702) // Unreachable code (reachability depends on template params)
#endif

template <unsigned MinBits = 0, unsigned MaxBits = 0, boost::multiprecision::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;

} // namespace backends

namespace detail {

template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_byte_container<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> > : public boost::false_type
{};

} // namespace detail

namespace backends {

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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void verify_new_size(unsigned /*new_size*/, unsigned /*min_size*/, const mpl::int_<unchecked>&) {}

template <class U>
inline BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void verify_limb_mask(bool /*b*/, U /*limb*/, U /*mask*/, const mpl::int_<unchecked>&) {}

} // namespace detail

//
// 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 boost::empty_value<typename detail::rebind<limb_type, Allocator>::type>
{
   typedef typename detail::rebind<limb_type, Allocator>::type allocator_type;
#ifdef BOOST_NO_CXX11_ALLOCATOR
   typedef typename allocator_type::pointer       limb_pointer;
   typedef typename allocator_type::const_pointer const_limb_pointer;
#else
   typedef typename std::allocator_traits<allocator_type>::pointer       limb_pointer;
   typedef typename std::allocator_traits<allocator_type>::const_pointer const_limb_pointer;
#endif
   typedef mpl::int_<Checked> checked_type;

//
   // Interface invariants:
   //
   BOOST_STATIC_ASSERT(!is_void<Allocator>::value);

private:
   typedef boost::empty_value<allocator_type> base_type;

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 = static_cast<limb_type>(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)) > 1 ? (sizeof(limb_data) / sizeof(limb_type)) : 2);
 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() BOOST_NOEXCEPT : first(0) {}
      BOOST_CONSTEXPR data_type(limb_type i) BOOST_NOEXCEPT : first(i) {}
      BOOST_CONSTEXPR data_type(signed_limb_type i) BOOST_NOEXCEPT : first(i < 0 ? static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
#if BOOST_ENDIAN_LITTLE_BYTE
      BOOST_CONSTEXPR data_type(double_limb_type i) BOOST_NOEXCEPT : double_first(i)
      {}
      BOOST_CONSTEXPR data_type(signed_double_limb_type i) BOOST_NOEXCEPT : double_first(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
#endif
#if !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) && !(defined(BOOST_MSVC) && (BOOST_MSVC < 1900))
      BOOST_CONSTEXPR data_type(limb_type* limbs, unsigned len) BOOST_NOEXCEPT : ld{ len, limbs }
      {}
#else
      BOOST_CONSTEXPR data_type(limb_type* limbs, unsigned len) BOOST_NOEXCEPT
      {
         ld.capacity = len;
         ld.data = limbs;
      }
#endif
   };

data_type m_data;
   unsigned  m_limbs;
   bool      m_sign, m_internal, m_alias;

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),
         m_alias(false) {}
   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),
         m_alias(false) {}
#if BOOST_ENDIAN_LITTLE_BYTE && !defined(BOOST_MP_TEST_NO_LE)
   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),
         m_alias(false)
   {}
   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),
         m_alias(false) {}
#endif
   //
   // Aliasing constructor aliases data:
   //
   struct scoped_shared_storage : private boost::empty_value<allocator_type>
   {
    private:
      limb_type*      data;
      unsigned        capacity;
      unsigned        allocated;
      bool            is_alias;
      allocator_type& allocator() BOOST_NOEXCEPT { return boost::empty_value<allocator_type>::get(); }

public:
      scoped_shared_storage(const allocator_type& a, unsigned len)
          : boost::empty_value<allocator_type>(boost::empty_init_t(), a), capacity(len), allocated(0), is_alias(false)
      {
         data = allocator().allocate(len);
      }
      scoped_shared_storage(limb_type* limbs, unsigned n) : data(limbs), capacity(n), allocated(0), is_alias(true) {}
      ~scoped_shared_storage()
      {
         if(!is_alias)
            allocator().deallocate(data, capacity);
      }
      limb_type* allocate(unsigned n) BOOST_NOEXCEPT 
      {
         limb_type* result = data + allocated;
         allocated += n;
         BOOST_ASSERT(allocated <= capacity);
         return result; 
      }
      void deallocate(unsigned n)
      {
         BOOST_ASSERT(n <= allocated);
         allocated -= n;
      }
   };
   explicit BOOST_CONSTEXPR cpp_int_base(limb_type* data, unsigned offset, unsigned len) BOOST_NOEXCEPT
       : m_data(data + offset, len),
         m_limbs(len),
         m_sign(false),
         m_internal(false),
         m_alias(true) {}
   // This next constructor is for constructing const objects from const limb_type*'s only.
   // Unfortunately we appear to have no way to assert that within the language, and the const_cast
   // is a side effect of that :(
   explicit BOOST_CONSTEXPR cpp_int_base(const limb_type* data, unsigned offset, unsigned len) BOOST_NOEXCEPT
       : m_data(const_cast<limb_type*>(data) + offset, len),
         m_limbs(len),
         m_sign(false),
         m_internal(false),
         m_alias(true) {}
   explicit BOOST_CONSTEXPR cpp_int_base(scoped_shared_storage& data, unsigned len) BOOST_NOEXCEPT
       : m_data(data.allocate(len), len),
         m_limbs(len),
         m_sign(false),
         m_internal(false),
         m_alias(true) {}
   //
   // Helper functions for getting at our internal data, and manipulating storage:
   //
   BOOST_MP_FORCEINLINE allocator_type&       allocator() BOOST_NOEXCEPT { return base_type::get(); }
   BOOST_MP_FORCEINLINE const allocator_type& allocator() const BOOST_NOEXCEPT { return base_type::get(); }
   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)
      {
         // We must not be an alias, memory allocation here defeats the whole point of aliasing:
         BOOST_ASSERT(!m_alias);
         // 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 && !m_alias)
            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), m_alias(false){}
   BOOST_MP_FORCEINLINE                 cpp_int_base(const cpp_int_base& o) : base_type(o), m_limbs(o.m_alias ? o.m_limbs : 0), m_sign(o.m_sign), m_internal(o.m_alias ? false : true), m_alias(o.m_alias)
   {
      if (m_alias)
      {
         m_data.ld = o.m_data.ld;
      }
      else
      {
         resize(o.size(), o.size());
         std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
      }
   }
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
   cpp_int_base(cpp_int_base&& o)
       : base_type(static_cast<base_type&&>(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal), m_alias(o.m_alias)
   {
      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 && !m_alias)
         allocator().deallocate(m_data.ld.data, m_data.ld.capacity);
      *static_cast<base_type*>(this) = static_cast<base_type&&>(o);
      m_limbs                        = o.m_limbs;
      m_sign                         = o.m_sign;
      m_internal                     = o.m_internal;
      m_alias                        = o.m_alias;
      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 && !m_alias)
         allocator().deallocate(limbs(), capacity());
   }
   void assign(const cpp_int_base& o)
   {
      if (this != &o)
      {
         static_cast<base_type&>(*this) = static_cast<const base_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;

#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 boost::empty_value<typename detail::rebind<limb_type, Allocator>::type>
{
   //
   // 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;

struct scoped_shared_storage {};

//
   // 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 = static_cast<limb_type>(1u) << (limb_bits - 1));
   BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
   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()
#if defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) || defined(BOOST_NO_CXX14_CONSTEXPR)
          : m_first_limb(0)
      {}
#else
          : m_data{0}
      {}
#endif
      BOOST_CONSTEXPR data_type(limb_type i)
#if defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) || defined(BOOST_NO_CXX14_CONSTEXPR)
          : m_first_limb(i)
      {}
#else
          : m_data{i}
      {}
#endif
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
      BOOST_CONSTEXPR data_type(limb_type i, limb_type j) : m_data{i, j}
      {}
#endif
      BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i)
      {
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
         if (BOOST_MP_IS_CONST_EVALUATED(m_double_first_limb))
         {
            data_type t(static_cast<limb_type>(i & max_limb_value), static_cast<limb_type>(i >> limb_bits));
            *this = t;
         }
#endif
      }
#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 BOOST_ENDIAN_LITTLE_BYTE && !defined(BOOST_MP_TEST_NO_LE)
   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
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
   //
   // These are deprecated in C++20 unless we make them explicit:
   //
   constexpr cpp_int_base& operator=(const cpp_int_base&) = default;
#endif
   //
   // Helper functions for getting at our internal data, and manipulating storage:
   //
   BOOST_MP_FORCEINLINE BOOST_CONSTEXPR unsigned              size() const BOOST_NOEXCEPT { return m_limbs; }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR assign(const cpp_int_base& o) BOOST_NOEXCEPT
   {
      if (this != &o)
      {
         m_limbs = o.m_limbs;
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
         if (BOOST_MP_IS_CONST_EVALUATED(m_limbs))
         {
            for (unsigned i = 0; i < m_limbs; ++i)
               limbs()[i] = o.limbs()[i];
         }
         else
#endif
            std::memcpy(limbs(), o.limbs(), o.size() * sizeof(o.limbs()[0]));
         m_sign = o.m_sign;
      }
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR bool isneg() const BOOST_NOEXCEPT
   {
      return m_sign;
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
   {
      for (unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
         std_constexpr::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
      std_constexpr::swap(m_sign, o.m_sign);
      std_constexpr::swap(m_limbs, o.m_limbs);
   }

protected:
   template <class A>
   BOOST_MP_CXX14_CONSTEXPR 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;

#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;

struct scoped_shared_storage {};
   //
   // 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 = static_cast<limb_type>(1u) << (limb_bits - 1));
   BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
   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;

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 BOOST_MP_CXX14_CONSTEXPR 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();
   }
#if BOOST_ENDIAN_LITTLE_BYTE && !defined(BOOST_MP_TEST_NO_LE)
   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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_CONSTEXPR unsigned              size() const BOOST_NOEXCEPT { return m_limbs; }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void         sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
   {
      if (b)
         negate();
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 {}
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
   //
   // These are deprecated in C++20 unless we make them explicit:
   //
   constexpr cpp_int_base& operator=(const cpp_int_base&) = default;
#endif

BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void assign(const cpp_int_base& o) BOOST_NOEXCEPT
   {
      if (this != &o)
      {
         m_limbs = o.m_limbs;
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
         if (BOOST_MP_IS_CONST_EVALUATED(m_limbs))
         {
            for (unsigned i = 0; i < m_limbs; ++i)
               limbs()[i] = o.limbs()[i];
         }
         else
#endif
            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."));
   }
   BOOST_MP_CXX14_CONSTEXPR void check_negate(const mpl::int_<unchecked>&) {}

public:
   BOOST_MP_CXX14_CONSTEXPR 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:
      if ((m_limbs == 1) && (m_wrapper.m_data[0] == 0))
         return; // negating zero is always zero, and always OK.
      check_negate(checked_type());
      unsigned i = m_limbs;
      for (; 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 BOOST_MP_CXX14_CONSTEXPR void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
   {
      for (unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
         std_constexpr::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
      std_constexpr::swap(m_limbs, o.m_limbs);
   }

protected:
   template <class A>
   BOOST_MP_CXX14_CONSTEXPR 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;

#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;

struct scoped_shared_storage {};
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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR void check_in_range(T, const mpl::int_<C>&) BOOST_NOEXCEPT {}

template <class T>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
   //
   // These are deprecated in C++20 unless we make them explicit:
   //
   constexpr cpp_int_base& operator=(const cpp_int_base&) = default;
#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 BOOST_MP_CXX14_CONSTEXPR 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_MP_CXX14_CONSTEXPR bool         sign() const BOOST_NOEXCEPT { return m_sign; }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void         sign(bool b) BOOST_NOEXCEPT
   {
      m_sign = b;
      // Check for zero value:
      if (m_sign && !m_data)
      {
         m_sign = false;
      }
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void resize(unsigned /* new_size */, unsigned min_size)
   {
      detail::verify_new_size(2, min_size, checked_type());
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void assign(const cpp_int_base& o) BOOST_NOEXCEPT
   {
      m_data = o.m_data;
      m_sign = o.m_sign;
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void negate() BOOST_NOEXCEPT
   {
      m_sign = !m_sign;
      // Check for zero value:
      if (m_data == 0)
      {
         m_sign = false;
      }
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR bool isneg() const BOOST_NOEXCEPT
   {
      return m_sign;
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
   {
      std_constexpr::swap(m_sign, o.m_sign);
      std_constexpr::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;

struct scoped_shared_storage {};
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;

protected:
   template <class T>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void check_in_range(T, const mpl::int_<C>&, const boost::integral_constant<bool, B>&) BOOST_NOEXCEPT {}

template <class T>
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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:
   //
#ifdef __MSVC_RUNTIME_CHECKS
   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)) & limb_mask : static_cast<local_limb_type>(i & limb_mask))
   {}
   template <class SI>
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 & limb_mask) : static_cast<local_limb_type>(i & limb_mask)) { 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 BOOST_MP_CXX14_CONSTEXPR 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)) { check_in_range(i); }
#else
   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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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); }
#endif
   template <class F>
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
   //
   // These are deprecated in C++20 unless we make them explicit:
   //
   constexpr cpp_int_base& operator=(const cpp_int_base&) = default;
#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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void         sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
   {
      if (b)
         negate();
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR void resize(unsigned, unsigned min_size)
   {
      detail::verify_new_size(2, min_size, checked_type());
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void assign(const cpp_int_base& o) BOOST_NOEXCEPT
   {
      m_data = o.m_data;
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
   {
      std_constexpr::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
#if BOOST_ENDIAN_LITTLE_BYTE && !defined(BOOST_MP_TEST_NO_LE)
                                                    || 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) {}
   //
   // Aliasing constructor: the result will alias the memory referenced, unless
   // we have fixed precision and storage, in which case we copy the memory:
   //
   explicit BOOST_CONSTEXPR cpp_int_backend(limb_type* data, unsigned offset, unsigned len) BOOST_NOEXCEPT
       : base_type(data, offset, len) {}
   explicit cpp_int_backend(const limb_type* data, unsigned offset, unsigned len) BOOST_NOEXCEPT
       : base_type(data, offset, len) { this->normalize(); }
   explicit BOOST_CONSTEXPR cpp_int_backend(typename base_type::scoped_shared_storage& data, unsigned len) BOOST_NOEXCEPT
       : base_type(data, len) {}

private:
   template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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());

unsigned count = (std::min)(other.size(), this->size());
      for (unsigned i = 0; i < count; ++i)
         this->limbs()[i] = other.limbs()[i];
      //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>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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->sign(false);
      this->normalize();
   }
   template <class A>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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);
   }
   BOOST_MP_CXX14_CONSTEXPR 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();
#ifdef __MSVC_RUNTIME_CHECKS
      *p = static_cast<limb_type>(i & ~static_cast<limb_type>(0));
#else
      *p                        = static_cast<limb_type>(i);
#endif
      p[1] = static_cast<limb_type>(i >> base_type::limb_bits);
      this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
      this->sign(false);
   }
   BOOST_MP_CXX14_CONSTEXPR 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;
      if (i < 0)
         s = true;
      double_limb_type                 ui = static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i));
      typename base_type::limb_pointer p  = this->limbs();
#ifdef __MSVC_RUNTIME_CHECKS
      *p = static_cast<limb_type>(ui & ~static_cast<limb_type>(0));
#else
      *p                        = static_cast<limb_type>(ui);
#endif
      p[1] = static_cast<limb_type>(ui >> base_type::limb_bits);
      this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
      this->sign(s);
   }

BOOST_MP_CXX14_CONSTEXPR void do_assign_arithmetic(long double a, const mpl::false_&)
   {
      using default_ops::eval_add;
      using default_ops::eval_subtract;
      using std::floor;
      using std::frexp;
      using std::ldexp;

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);
      }

if ((boost::math::isinf)(a) || (boost::math::isnan)(a))
      {
         BOOST_THROW_EXCEPTION(std::runtime_error("Cannot convert a non-finite number to an integer."));
      }

int         e = 0;
      long double f(0), term(0);
      *this = static_cast<limb_type>(0u);

f = frexp(a, &e);

#ifdef BOOST_NO_CXX11_CONSTEXPR
      static const limb_type shift = std::numeric_limits<limb_type>::digits;
#else
      constexpr limb_type shift = std::numeric_limits<limb_type>::digits;
#endif

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 BOOST_MP_CXX14_CONSTEXPR typename boost::enable_if_c<!boost::multiprecision::detail::is_byte_container<Arithmetic>::value, cpp_int_backend&>::type 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_add;
      using default_ops::eval_multiply;
      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;
         }
      }
      //
      // Exception guarantee: create the result in stack variable "result"
      // then do a swap at the end.  In the event of a throw, *this will
      // be left unchanged.
      //
      cpp_int_backend result;
      if (n)
      {
         if (radix == 16)
         {
            while (*s == '0')
               ++s;
            std::size_t bitcount = 4 * std::strlen(s);
            limb_type   val;
            std::size_t limb, shift;
            if (bitcount > 4)
               bitcount -= 4;
            else
               bitcount = 0;
            std::size_t newsize = bitcount / (sizeof(limb_type) * CHAR_BIT) + 1;
            result.resize(static_cast<unsigned>(newsize), static_cast<unsigned>(newsize)); // will throw if this is a checked integer that cannot be resized
            std::memset(result.limbs(), 0, result.size() * sizeof(limb_type));
            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
               {
                  BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
               }
               limb  = bitcount / (sizeof(limb_type) * CHAR_BIT);
               shift = bitcount % (sizeof(limb_type) * CHAR_BIT);
               val <<= shift;
               if (result.size() > limb)
               {
                  result.limbs()[limb] |= val;
               }
               ++s;
               bitcount -= 4;
            }
            result.normalize();
         }
         else if (radix == 8)
         {
            while (*s == '0')
               ++s;
            std::size_t bitcount = 3 * std::strlen(s);
            limb_type   val;
            std::size_t limb, shift;
            if (bitcount > 3)
               bitcount -= 3;
            else
               bitcount = 0;
            std::size_t newsize = bitcount / (sizeof(limb_type) * CHAR_BIT) + 1;
            result.resize(static_cast<unsigned>(newsize), static_cast<unsigned>(newsize)); // will throw if this is a checked integer that cannot be resized
            std::memset(result.limbs(), 0, result.size() * sizeof(limb_type));
            while (*s)
            {
               if (*s >= '0' && *s <= '7')
                  val = *s - '0';
               else
               {
                  BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
               }
               limb  = bitcount / (sizeof(limb_type) * CHAR_BIT);
               shift = bitcount % (sizeof(limb_type) * CHAR_BIT);
               if (result.size() > limb)
               {
                  result.limbs()[limb] |= (val << shift);
                  if (shift > sizeof(limb_type) * CHAR_BIT - 3)
                  {
                     // Deal with the bits in val that overflow into the next limb:
                     val >>= (sizeof(limb_type) * CHAR_BIT - shift);
                     if (val)
                     {
                        // If this is the most-significant-limb, we may need to allocate an extra one for the overflow:
                        if (limb + 1 == newsize)
                           result.resize(static_cast<unsigned>(newsize + 1), static_cast<unsigned>(newsize + 1));
                        if (result.size() > limb + 1)
                        {
                           result.limbs()[limb + 1] |= val;
                        }
                     }
                  }
               }
               ++s;
               bitcount -= 3;
            }
            result.normalize();
         }
         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(result, block_mult);
               eval_add(result, block);
            }
         }
      }
      if (isneg)
         result.negate();
      result.swap(*this);
   }

public:
   cpp_int_backend& operator=(const char* s)
   {
      do_assign_string(s, trivial_tag());
      return *this;
   }
   BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR 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;
         char                         letter_a = f & std::ios_base::uppercase ? 'A' : 'a';
         for (unsigned i = 0; i < Bits / shift; ++i)
         {
            char c = '0' + static_cast<char>(v & mask);
            if (c > '9')
               c += letter_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 += letter_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" : (f & std::ios_base::uppercase) ? "0X" : "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;
         char                         letter_a = f & std::ios_base::uppercase ? 'A' : 'a';
         for (unsigned i = 0; i < Bits / shift; ++i)
         {
            char c = '0' + static_cast<char>(t.limbs()[0] & mask);
            if (c > '9')
               c += letter_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 += letter_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" : (f & std::ios_base::uppercase) ? "0X" : "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());
   }

private:
   template <class Container>
   void construct_from_container(const Container& c, const mpl::false_&)
   {
      //
      // We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
      //
      unsigned newsize = static_cast<unsigned>(c.size() / sizeof(limb_type));
      if (c.size() % sizeof(limb_type))
      {
         ++newsize;
      }
      if (newsize)
      {
         this->resize(newsize, newsize); // May throw
         std::memset(this->limbs(), 0, this->size());
         typename Container::const_iterator i(c.begin()), j(c.end());
         unsigned                           byte_location = static_cast<unsigned>(c.size() - 1);
         while (i != j)
         {
            unsigned limb  = byte_location / sizeof(limb_type);
            unsigned shift = (byte_location % sizeof(limb_type)) * CHAR_BIT;
            if (this->size() > limb)
               this->limbs()[limb] |= static_cast<limb_type>(static_cast<unsigned char>(*i)) << shift;
            ++i;
            --byte_location;
         }
      }
   }
   template <class Container>
   BOOST_MP_CXX14_CONSTEXPR void construct_from_container(const Container& c, const mpl::true_&)
   {
      //
      // We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
      //
      typedef typename base_type::local_limb_type local_limb_type;
      *this->limbs() = 0;
      if (c.size())
      {
         typename Container::const_iterator i(c.begin()), j(c.end());
         unsigned                           byte_location = static_cast<unsigned>(c.size() - 1);
         while (i != j)
         {
            unsigned limb  = byte_location / sizeof(local_limb_type);
            unsigned shift = (byte_location % sizeof(local_limb_type)) * CHAR_BIT;
            if (limb == 0)
               this->limbs()[0] |= static_cast<limb_type>(static_cast<unsigned char>(*i)) << shift;
            ++i;
            --byte_location;
         }
      }
   }

public:
   template <class Container>
   BOOST_MP_CXX14_CONSTEXPR cpp_int_backend(const Container& c, typename boost::enable_if_c<boost::multiprecision::detail::is_byte_container<Container>::value>::type const* = 0)
   {
      //
      // We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
      //
      construct_from_container(c, trivial_tag());
   }
   template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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>
   BOOST_MP_CXX14_CONSTEXPR 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 BOOST_MP_CXX14_CONSTEXPR 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;
};

} // namespace default_ops

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 {

} // namespace detail
#endif

#ifdef _MSC_VER
#pragma warning(pop)
#endif

}} // namespace boost::multiprecision

//
// 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>
#include <boost/multiprecision/cpp_int/import_export.hpp>

#endif

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