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 ///////////////////////////////////////////////////////////////////////////////
 // Copyright Christopher Kormanyos 2002 - 2021.
 // Copyright 2011 -2021 John Maddock. Distributed under the Boost
 // Software License, Version 1.0. (See accompanying file
 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 //
 // This work is based on an earlier work:
 // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
 // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
 //
 // There are some "noexcept" specifications on the functions in this file.
 // Unlike in pre-C++11 versions, compilers can now detect noexcept misuse
 // at compile time, allowing for simple use of it here.
 //
 
 #ifndef BOOST_MP_CPP_DEC_FLOAT_HPP
 #define BOOST_MP_CPP_DEC_FLOAT_HPP
 
 #include <cmath>
 #include <cstdint>
 #include <cstdlib>
 #include <algorithm>
 #include <array>
 #include <initializer_list>
 #include <iomanip>
 #include <string>
 #include <limits>
 #include <stdexcept>
 #include <sstream>
 #include <locale>
 #include <ios>
 #include <boost/multiprecision/detail/standalone_config.hpp>
 #include <boost/multiprecision/number.hpp>
 #include <boost/multiprecision/detail/fpclassify.hpp>
 #include <boost/multiprecision/detail/dynamic_array.hpp>
 #include <boost/multiprecision/detail/hash.hpp>
 #include <boost/multiprecision/detail/float128_functions.hpp>
 #include <boost/multiprecision/detail/itos.hpp>
 #include <boost/multiprecision/detail/static_array.hpp>
 #include <boost/multiprecision/detail/tables.hpp>
 #include <boost/multiprecision/detail/no_exceptions_support.hpp>
 #include <boost/multiprecision/detail/assert.hpp>
 
 #ifdef BOOST_MP_MATH_AVAILABLE
 //
 // Headers required for Boost.Math integration:
 //
 #include <boost/math/policies/policy.hpp>
 //
 // Some includes we need from Boost.Math, since we rely on that library to provide these functions:
 //
 #include <boost/math/special_functions/acosh.hpp>
 #include <boost/math/special_functions/asinh.hpp>
 #include <boost/math/special_functions/atanh.hpp>
 #include <boost/math/special_functions/cbrt.hpp>
 #include <boost/math/special_functions/expm1.hpp>
 #include <boost/math/special_functions/gamma.hpp>
 #endif
 
 #ifdef BOOST_MSVC
 #pragma warning(push)
 #pragma warning(disable : 6326) // comparison of two constants
 #endif
 
 namespace boost {
 namespace multiprecision {
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public std::integral_constant<int, number_kind_floating_point>
 {};
 
 namespace backends {
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 class cpp_dec_float
 {
  private:
    // Perform some static sanity checks.
    static_assert(boost::multiprecision::detail::is_signed<ExponentType>::value,
                  "ExponentType must be a signed built in integer type.");
 
    static_assert(sizeof(ExponentType) > 1,
                  "ExponentType is too small.");
 
    static_assert(Digits10 < UINT32_C(0x80000000),
                  "Digits10 exceeds the maximum.");
 
    // Private class-local constants.
    static constexpr std::int32_t  cpp_dec_float_digits10_limit_lo = INT32_C(9);
    static constexpr std::int32_t  cpp_dec_float_digits10_limit_hi = static_cast<std::int32_t>((std::numeric_limits<std::int32_t>::max)() - 100);
 
    static constexpr std::int32_t cpp_dec_float_elem_digits10      = INT32_C(8);
    static constexpr std::int32_t cpp_dec_float_elem_mask          = INT32_C(100000000);
 
    static constexpr std::int32_t cpp_dec_float_elems_for_kara     = static_cast<std::int32_t>(128 + 1);
 
  public:
    using signed_types   = std::tuple<long long> ;
    using unsigned_types = std::tuple<unsigned long long>;
    using float_types    = std::tuple<double, long double>;
    using exponent_type  = ExponentType;
 
    // Public class-local constants.
    static constexpr std::int32_t  cpp_dec_float_radix             = INT32_C(10);
    static constexpr std::int32_t  cpp_dec_float_digits10          = ((static_cast<std::int32_t>(Digits10) < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((static_cast<std::int32_t>(Digits10) > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : static_cast<std::int32_t>(Digits10)));
    static constexpr exponent_type cpp_dec_float_max_exp10         = (static_cast<exponent_type>(1) << (std::numeric_limits<exponent_type>::digits - 5));
    static constexpr exponent_type cpp_dec_float_min_exp10         = -cpp_dec_float_max_exp10;
    static constexpr exponent_type cpp_dec_float_max_exp           = cpp_dec_float_max_exp10;
    static constexpr exponent_type cpp_dec_float_min_exp           = cpp_dec_float_min_exp10;
 
    static_assert(cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10, "Failed exponent range check");
 
    static_assert(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10, "Failed digit sanity check");
 
  private:
    // There are three guard limbs.
    // 1) The first limb has 'play' from 1...8 decimal digits.
    // 2) The last limb also has 'play' from 1...8 decimal digits.
    // 3) One limb can get lost when justifying after multiply.
    static constexpr std::int32_t cpp_dec_float_elem_number    = static_cast<std::int32_t>(((Digits10 / cpp_dec_float_elem_digits10) + (((Digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)) + 3);
 
  public:
    static constexpr std::int32_t cpp_dec_float_max_digits10   = static_cast<std::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10);
 
  private:
    using array_type =
       typename std::conditional<std::is_void<Allocator>::value,
                                 detail::static_array <std::uint32_t, static_cast<std::uint32_t>(cpp_dec_float_elem_number)>,
                                 detail::dynamic_array<std::uint32_t, static_cast<std::uint32_t>(cpp_dec_float_elem_number), Allocator> >::type;
 
    typedef enum enum_fpclass_type
    {
       cpp_dec_float_finite,
       cpp_dec_float_inf,
       cpp_dec_float_NaN
    } fpclass_type;
 
    array_type    data;
    exponent_type exp;
    bool          neg;
    fpclass_type  fpclass;
    std::int32_t  prec_elem;
 
    // Private constructor from the floating-point class type.
    explicit cpp_dec_float(fpclass_type c) : data(),
                                             exp(static_cast<exponent_type>(0)),
                                             neg(false),
                                             fpclass(c),
                                             prec_elem(cpp_dec_float_elem_number) {}
 
    // Constructor from an initializer_list, an optional
    // (value-aligned) exponent and a Boolean sign.
    static cpp_dec_float from_lst(std::initializer_list<std::uint32_t> lst,
                                  const exponent_type e = 0,
                                  const bool n = false)
    {
       cpp_dec_float a;
 
       a.data      = array_type(lst);
       a.exp       = e;
       a.neg       = n;
       a.fpclass   = cpp_dec_float_finite;
       a.prec_elem = cpp_dec_float_elem_number;
 
       return a;
    }
 
  public:
    // Public Constructors
    cpp_dec_float() noexcept(noexcept(array_type())) : data(),
                                                       exp(static_cast<exponent_type>(0)),
                                                       neg(false),
                                                       fpclass(cpp_dec_float_finite),
                                                       prec_elem(cpp_dec_float_elem_number) {}
 
    cpp_dec_float(const char* s) : data(),
                                   exp(static_cast<exponent_type>(0)),
                                   neg(false),
                                   fpclass(cpp_dec_float_finite),
                                   prec_elem(cpp_dec_float_elem_number)
    {
       *this = s;
    }
 
    template <class I>
    cpp_dec_float(I i,
                  typename std::enable_if<boost::multiprecision::detail::is_unsigned<I>::value && (sizeof(I) <= sizeof(long long))>::type* = nullptr)
       : data(),
         exp(static_cast<exponent_type>(0)),
         neg(false),
         fpclass(cpp_dec_float_finite),
         prec_elem(cpp_dec_float_elem_number)
    {
       from_unsigned_long_long(i);
    }
 
    template <class I>
    cpp_dec_float(I i,
                  typename std::enable_if<(   boost::multiprecision::detail::is_signed<I>::value
                                           && boost::multiprecision::detail::is_integral<I>::value
                                           && (sizeof(I) <= sizeof(long long)))>::type* = nullptr)
       : data(),
         exp(static_cast<exponent_type>(0)),
         neg(false),
         fpclass(cpp_dec_float_finite),
         prec_elem(cpp_dec_float_elem_number)
    {
       if (i < 0)
       {
          from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i));
          negate();
       }
       else
          from_unsigned_long_long(static_cast<unsigned long long>(i));
    }
 
    cpp_dec_float(const cpp_dec_float& f) noexcept(noexcept(array_type(std::declval<const array_type&>())))
       : data(f.data),
         exp(f.exp),
         neg(f.neg),
         fpclass(f.fpclass),
         prec_elem(f.prec_elem) {}
 
    template <unsigned D, class ET, class A>
    cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename std::enable_if<D <= Digits10>::type* = nullptr)
       : data(),
         exp(f.exp),
         neg(f.neg),
         fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
         prec_elem(cpp_dec_float_elem_number)
    {
       std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin());
    }
    template <unsigned D, class ET, class A>
    explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename std::enable_if< !(D <= Digits10)>::type* = nullptr)
       : data(),
         exp(f.exp),
         neg(f.neg),
         fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
         prec_elem(cpp_dec_float_elem_number)
    {
       // TODO: this doesn't round!
       std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin());
    }
 
    template <class F>
    cpp_dec_float(const F val, typename std::enable_if<std::is_floating_point<F>::value
                                                    >::type* = nullptr) : data(),
                                                                          exp(static_cast<exponent_type>(0)),
                                                                          neg(false),
                                                                          fpclass(cpp_dec_float_finite),
                                                                          prec_elem(cpp_dec_float_elem_number)
    {
       *this = val;
    }
 
    cpp_dec_float(const double mantissa, const exponent_type exponent);
 
    std::size_t hash() const
    {
       std::size_t result = 0;
       for (int i = 0; i < prec_elem; ++i)
          boost::multiprecision::detail::hash_combine(result, data[i]);
       boost::multiprecision::detail::hash_combine(result, exp, neg, static_cast<std::size_t>(fpclass));
       return result;
    }
 
    // Specific special values.
    static const cpp_dec_float&  nan () { static const cpp_dec_float val(cpp_dec_float_NaN); return val; }
    static const cpp_dec_float&  inf () { static const cpp_dec_float val(cpp_dec_float_inf); return val; }
    static const cpp_dec_float& (max)() { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) }, cpp_dec_float_max_exp10)); return val; }
    static const cpp_dec_float& (min)() { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) }, cpp_dec_float_min_exp10)); return val; }
    static const cpp_dec_float&  zero() { static const cpp_dec_float val(from_lst({ std::uint32_t(0u) })); return val; }
    static const cpp_dec_float&  one () { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) })); return val; }
    static const cpp_dec_float&  two () { static const cpp_dec_float val(from_lst({ std::uint32_t(2u) })); return val; }
    static const cpp_dec_float&  half() { static const cpp_dec_float val(from_lst({ std::uint32_t(cpp_dec_float_elem_mask / 2)}, -8)); return val; }
 
    static const cpp_dec_float& double_min() { static const cpp_dec_float val((std::numeric_limits<double>::min)()); return val; }
    static const cpp_dec_float& double_max() { static const cpp_dec_float val((std::numeric_limits<double>::max)()); return val; }
 
    static const cpp_dec_float& long_double_min()
    {
 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
       static const cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)()));
 #else
       static const cpp_dec_float val((std::numeric_limits<long double>::min)());
 #endif
       return val;
    }
 
    static const cpp_dec_float& long_double_max()
    {
 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
       static const cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)()));
 #else
       static const cpp_dec_float val((std::numeric_limits<long double>::max)());
 #endif
       return val;
    }
 
    static const cpp_dec_float& long_long_max () { static const cpp_dec_float val((std::numeric_limits<long long>::max)()); return val; }
    static const cpp_dec_float& long_long_min () { static const cpp_dec_float val((std::numeric_limits<long long>::min)()); return val; }
    static const cpp_dec_float& ulong_long_max() { static const cpp_dec_float val((std::numeric_limits<unsigned long long>::max)()); return val; }
 
    static const cpp_dec_float& eps()
    {
       static const cpp_dec_float val
       (
         from_lst
         (
           {
             (std::uint32_t) detail::pow10_maker((std::uint32_t) ((std::int32_t) (INT32_C(1) + (std::int32_t) (((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + ((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0 ? 1 : 0)) * cpp_dec_float_elem_digits10)) - cpp_dec_float_digits10))
           },
           -(exponent_type) (((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + ((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0 ? 1 : 0)) * cpp_dec_float_elem_digits10)
         )
       );
 
       return val;
    }
 
    // Basic operations.
    cpp_dec_float& operator=(const cpp_dec_float& v) noexcept(noexcept(std::declval<array_type&>() = std::declval<const array_type&>()))
    {
       data      = v.data;
       exp       = v.exp;
       neg       = v.neg;
       fpclass   = v.fpclass;
       prec_elem = v.prec_elem;
       return *this;
    }
 
    template <unsigned D>
    cpp_dec_float& operator=(const cpp_dec_float<D>& f)
    {
       exp            = f.exp;
       neg            = f.neg;
       fpclass        = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass));
       unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number);
       std::copy(f.data.begin(), f.data.begin() + elems, data.begin());
       std::fill(data.begin() + elems, data.end(), 0);
       prec_elem = cpp_dec_float_elem_number;
       return *this;
    }
 
    cpp_dec_float& operator=(long long v)
    {
       if (v < 0)
       {
          from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(v));
          negate();
       }
       else
       {
          using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type;
 
          from_unsigned_long_long(static_cast<local_ulonglong_type>(v));
       }
       return *this;
    }
 
    cpp_dec_float& operator=(unsigned long long v)
    {
       from_unsigned_long_long(v);
       return *this;
    }
 #ifdef BOOST_HAS_INT128
    cpp_dec_float& operator=(int128_type v)
    {
       *this = boost::multiprecision::detail::unsigned_abs(v);
       if (v < 0)
          negate();
       return *this;
    }
 
    cpp_dec_float& operator=(uint128_type v)
    {
       using default_ops::eval_add;
       using default_ops::eval_multiply;
 
       constexpr unsigned     bit_shift = sizeof(unsigned long long) * CHAR_BIT;
       constexpr uint128_type mask      = (static_cast<uint128_type>(1u) << bit_shift) - 1;
 
       *this = static_cast<unsigned long long>(v & mask);
 
       v >>= bit_shift;
 
       while (v)
       {
          cpp_dec_float t(static_cast<unsigned long long>(v & mask));
          eval_multiply(t, cpp_dec_float::pow2(bit_shift));
          eval_add(*this, t);
          v >>= bit_shift;
       }
       return *this;
    }
 #endif
 
    template <class Float>
    typename std::enable_if<std::is_floating_point<Float>::value, cpp_dec_float&>::type operator=(Float v);
 
    cpp_dec_float& operator=(const char* v)
    {
       rd_string(v);
       return *this;
    }
 
    cpp_dec_float& operator+=(const cpp_dec_float& v);
    cpp_dec_float& operator-=(const cpp_dec_float& v);
    cpp_dec_float& operator*=(const cpp_dec_float& v);
    cpp_dec_float& operator/=(const cpp_dec_float& v);
 
    cpp_dec_float& add_unsigned_long_long(const unsigned long long n)
    {
       cpp_dec_float t;
       t.from_unsigned_long_long(n);
       return *this += t;
    }
 
    cpp_dec_float& sub_unsigned_long_long(const unsigned long long n)
    {
       cpp_dec_float t;
       t.from_unsigned_long_long(n);
       return *this -= t;
    }
 
    cpp_dec_float& mul_unsigned_long_long(const unsigned long long n);
    cpp_dec_float& div_unsigned_long_long(const unsigned long long n);
 
    // Elementary primitives.
    cpp_dec_float& calculate_inv();
    cpp_dec_float& calculate_sqrt();
 
    void negate()
    {
       if (!iszero())
          neg = !neg;
    }
 
    // Comparison functions
    bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); }
    bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); }
    bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); }
 
    bool iszero() const
    {
       return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u));
    }
 
    bool isone() const;
    bool isint() const;
    bool isneg() const { return neg; }
 
    // Operators pre-increment and pre-decrement
    cpp_dec_float& operator++()
    {
       return *this += one();
    }
 
    cpp_dec_float& operator--()
    {
       return *this -= one();
    }
 
    std::string str(std::intmax_t digits, std::ios_base::fmtflags f) const;
 
    int compare(const cpp_dec_float& v) const;
 
    template <class V>
    int compare(const V& v) const
    {
       cpp_dec_float<Digits10, ExponentType, Allocator> t;
       t = v;
       return compare(t);
    }
 
    void swap(cpp_dec_float& v)
    {
       data.swap(v.data);
       std::swap(exp, v.exp);
       std::swap(neg, v.neg);
       std::swap(fpclass, v.fpclass);
       std::swap(prec_elem, v.prec_elem);
    }
 
    double                 extract_double() const;
    long double            extract_long_double() const;
    long long  extract_signed_long_long() const;
    unsigned long long extract_unsigned_long_long() const;
 #ifdef BOOST_HAS_INT128
    int128_type  extract_signed_int128() const;
    uint128_type extract_unsigned_int128() const;
 #endif
    void                   extract_parts(double& mantissa, exponent_type& exponent) const;
    cpp_dec_float          extract_integer_part() const;
 
    void precision(const std::int32_t prec_digits)
    {
       const std::int32_t elems =
         static_cast<std::int32_t>(    static_cast<std::int32_t>(prec_digits / cpp_dec_float_elem_digits10)
                                   +                          (((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0));
 
       prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<std::int32_t>(2)));
    }
    static cpp_dec_float pow2(long long i);
    exponent_type order() const
    {
       const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<std::uint32_t>(0u)));
       //
       // Binary search to find the order of the leading term:
       //
       exponent_type prefix = 0;
 
       if (data[0] >= 100000UL)
       {
          if (data[0] >= 10000000UL)
          {
             if (data[0] >= 100000000UL)
             {
                if (data[0] >= 1000000000UL)
                   prefix = 9;
                else
                   prefix = 8;
             }
             else
                prefix = 7;
          }
          else
          {
             if (data[0] >= 1000000UL)
                prefix = 6;
             else
                prefix = 5;
          }
       }
       else
       {
          if (data[0] >= 1000UL)
          {
             if (data[0] >= 10000UL)
                prefix = 4;
             else
                prefix = 3;
          }
          else
          {
             if (data[0] >= 100)
                prefix = 2;
             else if (data[0] >= 10)
                prefix = 1;
          }
       }
 
       return (bo_order_is_zero ? static_cast<exponent_type>(0) : static_cast<exponent_type>(exp + prefix));
    }
 
    #ifndef BOOST_MP_STANDALONE
    template <class Archive>
    void serialize(Archive& ar, const unsigned int /*version*/)
    {
       for (unsigned i = 0; i < data.size(); ++i)
          ar& boost::make_nvp("digit", data[i]);
       ar& boost::make_nvp("exponent", exp);
       ar& boost::make_nvp("sign", neg);
       ar& boost::make_nvp("class-type", fpclass);
       ar& boost::make_nvp("precision", prec_elem);
    }
    #endif
 
  private:
    static bool data_elem_is_non_zero_predicate(const std::uint32_t& d) { return (d != static_cast<std::uint32_t>(0u)); }
    static bool data_elem_is_non_nine_predicate(const std::uint32_t& d) { return (d != static_cast<std::uint32_t>(cpp_dec_float::cpp_dec_float_elem_mask - 1)); }
    static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); }
 
    void from_unsigned_long_long(const unsigned long long u);
 
    template <typename InputIteratorTypeLeft,
              typename InputIteratorTypeRight>
    static int compare_ranges(InputIteratorTypeLeft  a,
                              InputIteratorTypeRight b,
                              const std::uint32_t    count = cpp_dec_float_elem_number);
 
    static std::uint32_t eval_add_n(      std::uint32_t* r,
                                    const std::uint32_t* u,
                                    const std::uint32_t* v,
                                    const std::int32_t   count);
 
    static std::uint32_t eval_subtract_n(      std::uint32_t* r,
                                         const std::uint32_t* u,
                                         const std::uint32_t* v,
                                         const std::int32_t   count);
 
    static void eval_multiply_n_by_n_to_2n(      std::uint32_t* r,
                                           const std::uint32_t* a,
                                           const std::uint32_t* b,
                                           const std::uint32_t  count);
 
    static std::uint32_t mul_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p);
    static std::uint32_t div_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p);
 
    static void eval_multiply_kara_propagate_carry (std::uint32_t* t, const std::uint32_t n, const std::uint32_t carry);
    static void eval_multiply_kara_propagate_borrow(std::uint32_t* t, const std::uint32_t n, const bool has_borrow);
    static void eval_multiply_kara_n_by_n_to_2n    (      std::uint32_t* r,
                                                    const std::uint32_t* a,
                                                    const std::uint32_t* b,
                                                    const std::uint32_t  n,
                                                          std::uint32_t* t);
 
    template<unsigned D>
    void eval_mul_dispatch_multiplication_method(
       const cpp_dec_float<D, ExponentType, Allocator>& v,
       const std::int32_t prec_elems_for_multiply,
       const typename std::enable_if<   (D == Digits10)
                                     && (cpp_dec_float<D, ExponentType, Allocator>::cpp_dec_float_elem_number < cpp_dec_float_elems_for_kara)>::type* = nullptr)
    {
       // Use school multiplication.
 
       using array_for_mul_result_type =
          typename std::conditional<std::is_void<Allocator>::value,
                                    detail::static_array <std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2)>,
                                    detail::dynamic_array<std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2), Allocator> >::type;
 
       array_for_mul_result_type result;
 
       eval_multiply_n_by_n_to_2n(result.data(), data.data(), v.data.data(), static_cast<std::uint32_t>(prec_elems_for_multiply));
 
       // Handle a potential carry.
       if(result[0U] != static_cast<std::uint32_t>(0U))
       {
          exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10);
 
          // Shift the result of the multiplication one element to the right.
          std::copy(result.cbegin(),
                    result.cbegin() + static_cast<std::ptrdiff_t>(prec_elems_for_multiply),
                    data.begin());
       }
       else
       {
          std::copy(result.cbegin() + 1,
                    result.cbegin() + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number),
                    data.begin());
       }
    }
 
    template<unsigned D>
    void eval_mul_dispatch_multiplication_method(
       const cpp_dec_float<D, ExponentType, Allocator>& v,
       const std::int32_t prec_elems_for_multiply,
       const typename std::enable_if<    (D == Digits10)
                                     && !(cpp_dec_float<D, ExponentType, Allocator>::cpp_dec_float_elem_number < cpp_dec_float_elems_for_kara)>::type* = nullptr)
    {
       if(prec_elems_for_multiply < cpp_dec_float_elems_for_kara)
       {
          // Use school multiplication.
 
          using array_for_mul_result_type =
             typename std::conditional<std::is_void<Allocator>::value,
                                       detail::static_array <std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2)>,
                                       detail::dynamic_array<std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2), Allocator> >::type;
 
          array_for_mul_result_type result;
 
          eval_multiply_n_by_n_to_2n(result.data(), data.data(), v.data.data(), static_cast<std::uint32_t>(prec_elems_for_multiply));
 
          // Handle a potential carry.
          if(result[0U] != static_cast<std::uint32_t>(0U))
          {
             exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10);
          
             // Shift the result of the multiplication one element to the right.
             std::copy(result.cbegin(),
                       result.cbegin() + static_cast<std::ptrdiff_t>(prec_elems_for_multiply),
                       data.begin());
          }
          else
          {
             std::copy(result.cbegin() + 1,
                       result.cbegin() + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number),
                       data.begin());
          }
       }
       else
       {
          // Use Karatsuba multiplication.
 
          using array_for_kara_tmp_type =
             typename std::conditional<std::is_void<Allocator>::value,
                                       detail::static_array <std::uint32_t, detail::a029750::a029750_as_constexpr(static_cast<std::uint32_t>(cpp_dec_float_elem_number)) * 8U>,
                                       detail::dynamic_array<std::uint32_t, detail::a029750::a029750_as_constexpr(static_cast<std::uint32_t>(cpp_dec_float_elem_number)) * 8U, Allocator> >::type;
 
          // Sloanes's A029747: Numbers of the form 2^k times 1, 3 or 5.
          const std::uint32_t kara_elems_for_multiply =
             detail::a029750::a029750_as_runtime_value(static_cast<std::uint32_t>(prec_elems_for_multiply));
 
          array_for_kara_tmp_type my_kara_mul_pool;
 
          std::uint32_t* result  = my_kara_mul_pool.data() + (kara_elems_for_multiply * 0U);
          std::uint32_t* t       = my_kara_mul_pool.data() + (kara_elems_for_multiply * 2U);
          std::uint32_t* u_local = my_kara_mul_pool.data() + (kara_elems_for_multiply * 6U);
          std::uint32_t* v_local = my_kara_mul_pool.data() + (kara_elems_for_multiply * 7U);
 
          std::copy(  data.cbegin(),   data.cbegin() + prec_elems_for_multiply, u_local);
          std::copy(v.data.cbegin(), v.data.cbegin() + prec_elems_for_multiply, v_local);
 
          eval_multiply_kara_n_by_n_to_2n(result,
                                          u_local,
                                          v_local,
                                          kara_elems_for_multiply,
                                          t);
 
          // Handle a potential carry.
          if(result[0U] != static_cast<std::uint32_t>(0U))
          {
             exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10);
 
             // Shift the result of the multiplication one element to the right.
             std::copy(result,
                       result + static_cast<std::ptrdiff_t>(prec_elems_for_multiply),
                       data.begin());
          }
          else
          {
             std::copy(result + 1,
                       result + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number),
                       data.begin());
          }
       }
    }
 
    bool rd_string(const char* const s);
 
    template <unsigned D, class ET, class A>
    friend class cpp_dec_float;
 };
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number;
 template <unsigned Digits10, class ExponentType, class Allocator>
 constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask;
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 {
    if ((isnan)())
    {
       return *this;
    }
 
    if ((isinf)())
    {
       if ((v.isinf)() && (isneg() != v.isneg()))
       {
          *this = nan();
       }
       return *this;
    }
 
    if (iszero())
    {
       return operator=(v);
    }
 
    if ((v.isnan)() || (v.isinf)())
    {
       *this = v;
       return *this;
    }
 
    // Get the offset for the add/sub operation.
    constexpr exponent_type max_delta_exp =
      static_cast<exponent_type>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
 
    const exponent_type ofs_exp = static_cast<exponent_type>(exp - v.exp);
 
    // Check if the operation is out of range, requiring special handling.
    if (v.iszero() || (ofs_exp > max_delta_exp))
    {
       // Result is *this unchanged since v is negligible compared to *this.
       return *this;
    }
    else if (ofs_exp < -max_delta_exp)
    {
       // Result is *this = v since *this is negligible compared to v.
       return operator=(v);
    }
 
    // Do the add/sub operation.
 
    typename array_type::pointer       p_u    = data.data();
    typename array_type::const_pointer p_v    = v.data.data();
    bool                               b_copy = false;
    const std::int32_t                 ofs    = static_cast<std::int32_t>(static_cast<std::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10);
    array_type                         n_data;
 
    if (neg == v.neg)
    {
       // Add v to *this, where the data array of either *this or v
       // might have to be treated with a positive, negative or zero offset.
       // The result is stored in *this. The data are added one element
       // at a time, each element with carry.
       if (ofs >= static_cast<std::int32_t>(0))
       {
          std::copy(v.data.cbegin(), v.data.cend() - static_cast<std::ptrdiff_t>(ofs), n_data.begin() + static_cast<std::ptrdiff_t>(ofs));
          std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(ofs), static_cast<std::uint32_t>(0u));
          p_v = n_data.data();
       }
       else
       {
          std::copy(data.cbegin(), data.cend() - static_cast<std::ptrdiff_t>(-ofs), n_data.begin() + static_cast<std::ptrdiff_t>(-ofs));
          std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(-ofs), static_cast<std::uint32_t>(0u));
          p_u    = n_data.data();
          b_copy = true;
       }
 
       // Addition algorithm
       const std::uint32_t carry = eval_add_n(p_u, p_u, p_v, cpp_dec_float_elem_number);
 
       if (b_copy)
       {
          data = n_data;
          exp  = v.exp;
       }
 
       // There needs to be a carry into the element -1 of the array data
       if (carry != static_cast<std::uint32_t>(0u))
       {
          std::copy_backward(data.cbegin(), data.cend() - static_cast<std::size_t>(1u), data.end());
          data[0] = carry;
          exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10);
       }
    }
    else
    {
       // Subtract v from *this, where the data array of either *this or v
       // might have to be treated with a positive, negative or zero offset.
       if ((ofs > static_cast<std::int32_t>(0)) || ((ofs == static_cast<std::int32_t>(0)) && (compare_ranges(data.cbegin(), v.data.cbegin()) > static_cast<std::int32_t>(0))))
       {
          // In this case, |u| > |v| and ofs is positive.
          // Copy the data of v, shifted down to a lower value
          // into the data array m_n. Set the operand pointer p_v
          // to point to the copied, shifted data m_n.
          std::copy(v.data.cbegin(), v.data.cend() - static_cast<std::ptrdiff_t>(ofs), n_data.begin() + static_cast<std::ptrdiff_t>(ofs));
          std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(ofs), static_cast<std::uint32_t>(0u));
          p_v = n_data.data();
       }
       else
       {
          if (ofs != static_cast<std::int32_t>(0))
          {
             // In this case, |u| < |v| and ofs is negative.
             // Shift the data of u down to a lower value.
             std::copy_backward(data.cbegin(), data.cend() - static_cast<std::ptrdiff_t>(-ofs), data.end());
             std::fill(data.begin(), data.begin() + static_cast<std::ptrdiff_t>(-ofs), static_cast<std::uint32_t>(0u));
          }
 
          // Copy the data of v into the data array n_data.
          // Set the u-pointer p_u to point to m_n and the
          // operand pointer p_v to point to the shifted
          // data m_data.
          n_data = v.data;
          p_u    = n_data.data();
          p_v    = data.data();
          b_copy = true;
       }
 
       // Subtraction algorithm
       static_cast<void>(eval_subtract_n(p_u, p_u, p_v, cpp_dec_float_elem_number));
 
       if (b_copy)
       {
          data = n_data;
          exp  = v.exp;
          neg  = v.neg;
       }
 
       // Is it necessary to justify the data?
       const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
 
       if (first_nonzero_elem != data.begin())
       {
          if (first_nonzero_elem == data.end())
          {
             // This result of the subtraction is exactly zero.
             // Reset the sign and the exponent.
             neg = false;
             exp = static_cast<exponent_type>(0);
          }
          else
          {
             // Justify the data
             const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem));
 
             std::copy(data.begin() + static_cast<std::ptrdiff_t>(sj), data.end(), data.begin());
             std::fill(data.end() - static_cast<std::ptrdiff_t>(sj), data.end(), static_cast<std::uint32_t>(0u));
 
             exp -= static_cast<exponent_type>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
          }
       }
    }
 
    // Handle underflow.
    if (iszero())
       return (*this = zero());
 
    // Check for potential overflow.
    const bool b_result_might_overflow = (exp >= static_cast<exponent_type>(cpp_dec_float_max_exp10));
 
    // Handle overflow.
    if (b_result_might_overflow)
    {
       const bool b_result_is_neg = neg;
       neg                        = false;
 
       if (compare((cpp_dec_float::max)()) > 0)
          *this = inf();
 
       neg = b_result_is_neg;
    }
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 {
    // Use *this - v = -(-*this + v).
    negate();
    *this += v;
    negate();
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 {
    // Evaluate the sign of the result.
    const bool b_result_is_neg = (neg != v.neg);
 
    // Artificially set the sign of the result to be positive.
    neg = false;
 
    // Handle special cases like zero, inf and NaN.
    const bool b_u_is_inf  = (isinf)();
    const bool b_v_is_inf  = (v.isinf)();
    const bool b_u_is_zero = iszero();
    const bool b_v_is_zero = v.iszero();
 
    if (((isnan)() || (v.isnan)()) || (b_u_is_inf && b_v_is_zero) || (b_v_is_inf && b_u_is_zero))
    {
       *this = nan();
       return *this;
    }
 
    if (b_u_is_inf || b_v_is_inf)
    {
       *this = inf();
       if (b_result_is_neg)
          negate();
       return *this;
    }
 
    if (b_u_is_zero || b_v_is_zero)
    {
       return *this = zero();
    }
 
    // Check for potential overflow or underflow.
    const bool b_result_might_overflow  = ((exp + v.exp) >= static_cast<exponent_type>(cpp_dec_float_max_exp10));
    const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<exponent_type>(cpp_dec_float_min_exp10));
 
    // Set the exponent of the result.
    exp += v.exp;
 
    const std::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem);
 
    eval_mul_dispatch_multiplication_method(v, prec_mul);
 
    // Handle overflow.
    if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
    {
       *this = inf();
    }
 
    // Handle underflow.
    if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
    {
       *this = zero();
 
       return *this;
    }
 
    // Set the sign of the result.
    neg = b_result_is_neg;
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 {
    if (iszero())
    {
       if ((v.isnan)())
       {
          return *this = v;
       }
       else if (v.iszero())
       {
          return *this = nan();
       }
    }
 
    const bool u_and_v_are_finite_and_identical = ((isfinite)() && (fpclass == v.fpclass) && (exp == v.exp) && (compare_ranges(data.cbegin(), v.data.cbegin()) == static_cast<std::int32_t>(0)));
 
    if (u_and_v_are_finite_and_identical)
    {
       if (neg != v.neg)
       {
          *this = one();
          negate();
       }
       else
          *this = one();
       return *this;
    }
    else
    {
       cpp_dec_float t(v);
       t.calculate_inv();
       return operator*=(t);
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const unsigned long long n)
 {
    // Multiply *this with a constant unsigned long long.
 
    // Evaluate the sign of the result.
    const bool b_neg = neg;
 
    // Artificially set the sign of the result to be positive.
    neg = false;
 
    // Handle special cases like zero, inf and NaN.
    const bool b_u_is_inf  = (isinf)();
    const bool b_n_is_zero = (n == static_cast<std::int32_t>(0));
 
    if ((isnan)() || (b_u_is_inf && b_n_is_zero))
    {
       return (*this = nan());
    }
 
    if (b_u_is_inf)
    {
       *this = inf();
       if (b_neg)
          negate();
       return *this;
    }
 
    if (iszero() || b_n_is_zero)
    {
       // Multiplication by zero.
       return *this = zero();
    }
 
    if (n >= static_cast<unsigned long long>(cpp_dec_float_elem_mask))
    {
       neg = b_neg;
       cpp_dec_float t;
       t = n;
       return operator*=(t);
    }
 
    if (n == static_cast<unsigned long long>(1u))
    {
       neg = b_neg;
       return *this;
    }
 
    // Set up the multiplication loop.
    const std::uint32_t nn    = static_cast<std::uint32_t>(n);
    const std::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem);
 
    // Handle the carry and adjust the exponent.
    if (carry != static_cast<std::uint32_t>(0u))
    {
       exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10);
 
       // Shift the result of the multiplication one element to the right.
       std::copy_backward(data.begin(),
                          data.begin() + static_cast<std::ptrdiff_t>(prec_elem - static_cast<std::int32_t>(1)),
                          data.begin() + static_cast<std::ptrdiff_t>(prec_elem));
 
       data.front() = static_cast<std::uint32_t>(carry);
    }
 
    // Check for potential overflow.
    const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10);
 
    // Handle overflow.
    if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
    {
       *this = inf();
    }
 
    // Set the sign.
    neg = b_neg;
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const unsigned long long n)
 {
    // Divide *this by a constant unsigned long long.
 
    // Evaluate the sign of the result.
    const bool b_neg = neg;
 
    // Artificially set the sign of the result to be positive.
    neg = false;
 
    // Handle special cases like zero, inf and NaN.
    if ((isnan)())
    {
       return *this;
    }
 
    if ((isinf)())
    {
       *this = inf();
       if (b_neg)
          negate();
       return *this;
    }
 
    if (n == static_cast<unsigned long long>(0u))
    {
       // Divide by 0.
       if (iszero())
       {
          *this = nan();
          return *this;
       }
       else
       {
          *this = inf();
          if (isneg())
             negate();
          return *this;
       }
    }
 
    if (iszero())
    {
       return *this;
    }
 
    if (n >= static_cast<unsigned long long>(cpp_dec_float_elem_mask))
    {
       neg = b_neg;
       cpp_dec_float t;
       t = n;
       return operator/=(t);
    }
 
    const std::uint32_t nn = static_cast<std::uint32_t>(n);
 
    if (nn > static_cast<std::uint32_t>(1u))
    {
       // Do the division loop.
       const std::uint32_t prev = div_loop_n(data.data(), nn, prec_elem);
 
       // Determine if one leading zero is in the result data.
       if (data[0] == static_cast<std::uint32_t>(0u))
       {
          // Adjust the exponent
          exp -= static_cast<exponent_type>(cpp_dec_float_elem_digits10);
 
          // Shift result of the division one element to the left.
          std::copy(data.begin() + static_cast<std::ptrdiff_t>(1),
                    data.begin() + static_cast<std::ptrdiff_t>(prec_elem - static_cast<std::int32_t>(1)),
                    data.begin());
 
          data[static_cast<std::size_t>(prec_elem - static_cast<std::int32_t>(1))] = static_cast<std::uint32_t>(static_cast<std::uint64_t>(prev * static_cast<std::uint64_t>(cpp_dec_float_elem_mask)) / nn);
       }
    }
 
    // Check for potential underflow.
    const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10);
 
    // Handle underflow.
    if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
       return (*this = zero());
 
    // Set the sign of the result.
    neg = b_neg;
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv()
 {
    // Compute the inverse of *this.
    const bool b_neg = neg;
 
    neg = false;
 
    // Handle special cases like zero, inf and NaN.
    if (iszero())
    {
       *this = inf();
       if (b_neg)
          negate();
       return *this;
    }
 
    if ((isnan)())
    {
       return *this;
    }
 
    if ((isinf)())
    {
       return *this = zero();
    }
 
    if (isone())
    {
       if (b_neg)
          negate();
       return *this;
    }
 
    // Save the original *this.
    cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
 
    // Generate the initial estimate using division.
    // Extract the mantissa and exponent for a "manual"
    // computation of the estimate.
    double        dd;
    exponent_type ne;
    x.extract_parts(dd, ne);
 
    // Do the inverse estimate using double precision estimates of mantissa and exponent.
    operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne));
 
    // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration
    // is used. During the iterative steps, the precision of the calculation is limited
    // to the minimum required in order to minimize the run-time.
 
    constexpr std::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
 
    for (std::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_max_digits10; digits *= static_cast<std::int32_t>(2))
    {
       // Adjust precision of the terms.
       precision(static_cast<std::int32_t>((digits + 10) * static_cast<std::int32_t>(2)));
       x.precision(static_cast<std::int32_t>((digits + 10) * static_cast<std::int32_t>(2)));
 
       // Next iteration.
       cpp_dec_float t(*this);
       t *= x;
       t -= two();
       t.negate();
       *this *= t;
    }
 
    neg = b_neg;
 
    prec_elem = cpp_dec_float_elem_number;
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt()
 {
    // Compute the square root of *this.
 
    if ((isinf)() && !isneg())
    {
       return *this;
    }
 
    if (isneg() || (!(isfinite)()))
    {
       *this = nan();
       errno = EDOM;
       return *this;
    }
 
    if (iszero() || isone())
    {
       return *this;
    }
 
    // Save the original *this.
    cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
 
    // Generate the initial estimate using division.
    // Extract the mantissa and exponent for a "manual"
    // computation of the estimate.
    double        dd;
    exponent_type ne;
    extract_parts(dd, ne);
 
    // Force the exponent to be an even multiple of two.
    if ((ne % static_cast<exponent_type>(2)) != static_cast<exponent_type>(0))
    {
       ++ne;
       dd /= 10.0;
    }
 
    // Setup the iteration.
    // Estimate the square root using simple manipulations.
    const double sqd = std::sqrt(dd);
 
    *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2)));
 
    // Estimate 1.0 / (2.0 * x0) using simple manipulations.
    cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2)));
 
    // Compute the square root of x. Coupled Newton iteration
    // as described in "Pi Unleashed" is used. During the
    // iterative steps, the precision of the calculation is
    // limited to the minimum required in order to minimize
    // the run-time.
    //
    // Book reference to "Pi Unleashed:
    // https://www.springer.com/gp/book/9783642567353
 
    constexpr std::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
 
    for (std::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_max_digits10; digits *= 2)
    {
       // Adjust precision of the terms.
       precision((digits + 10) * 2);
       vi.precision((digits + 10) * 2);
 
       // Next iteration of vi
       cpp_dec_float t(*this);
       t *= vi;
       t.negate();
       t.mul_unsigned_long_long(2u);
       t += one();
       t *= vi;
       vi += t;
 
       // Next iteration of *this
       t = *this;
       t *= *this;
       t.negate();
       t += x;
       t *= vi;
       *this += t;
    }
 
    prec_elem = cpp_dec_float_elem_number;
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const
 {
    // Compare v with *this.
    // Return +1 for *this > v
    // 0 for *this = v
    // -1 for *this < v
 
    // Handle all non-finite cases.
    if ((!(isfinite)()) || (!(v.isfinite)()))
    {
       // NaN can never equal NaN. Return an implementation-dependent
       // signed result. Also note that comparison of NaN with NaN
       // using operators greater-than or less-than is undefined.
       if ((isnan)() || (v.isnan)())
       {
          return ((isnan)() ? 1 : -1);
       }
 
       if ((isinf)() && (v.isinf)())
       {
          // Both *this and v are infinite. They are equal if they have the same sign.
          // Otherwise, *this is less than v if and only if *this is negative.
          return ((neg == v.neg) ? 0 : (neg ? -1 : 1));
       }
 
       if ((isinf)())
       {
          // *this is infinite, but v is finite.
          // So negative infinite *this is less than any finite v.
          // Whereas positive infinite *this is greater than any finite v.
          return (isneg() ? -1 : 1);
       }
       else
       {
          // *this is finite, and v is infinite.
          // So any finite *this is greater than negative infinite v.
          // Whereas any finite *this is less than positive infinite v.
          return (v.neg ? 1 : -1);
       }
    }
 
    // And now handle all *finite* cases.
    if (iszero())
    {
       // The value of *this is zero and v is either zero or non-zero.
       return (v.iszero() ? 0
                          : (v.neg ? 1 : -1));
    }
    else if (v.iszero())
    {
       // The value of v is zero and *this is non-zero.
       return (neg ? -1 : 1);
    }
    else
    {
       // Both *this and v are non-zero.
 
       if (neg != v.neg)
       {
          // The signs are different.
          return (neg ? -1 : 1);
       }
       else if (exp != v.exp)
       {
          // The signs are the same and the exponents are different.
          const int val_cexpression = ((exp < v.exp) ? 1 : -1);
 
          return (neg ? val_cexpression : -val_cexpression);
       }
       else
       {
          // The signs are the same and the exponents are the same.
          // Compare the data.
          const int val_cmp_data = compare_ranges(data.cbegin(), v.data.cbegin());
 
          return ((!neg) ? val_cmp_data : -val_cmp_data);
       }
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const
 {
    // Check if the value of *this is identically 1 or very close to 1.
 
    const bool not_negative_and_is_finite = ((!neg) && (isfinite)());
 
    if (not_negative_and_is_finite)
    {
       if ((data[0u] == static_cast<std::uint32_t>(1u)) && (exp == static_cast<exponent_type>(0)))
       {
          const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
          return (it_non_zero == data.end());
       }
       else if ((data[0u] == static_cast<std::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<exponent_type>(-cpp_dec_float_elem_digits10)))
       {
          const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate);
          return (it_non_nine == data.end());
       }
    }
 
    return false;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const
 {
    if (fpclass != cpp_dec_float_finite)
    {
       return false;
    }
 
    if (iszero())
    {
       return true;
    }
 
    if (exp < static_cast<exponent_type>(0))
    {
       return false;
    } // |*this| < 1.
 
    const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u;
 
    if (offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number))
    {
       // The number is too large to resolve the integer part.
       // It considered to be a pure integer.
       return true;
    }
 
    typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + static_cast<std::ptrdiff_t>(offset_decimal_part), data.end(), data_elem_is_non_zero_predicate);
 
    return (it_non_zero == data.end());
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const
 {
    // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x.
 
    // Extracts the mantissa and exponent.
    exponent = exp;
 
    std::uint32_t p10  = static_cast<std::uint32_t>(1u);
    std::uint32_t test = data[0u];
 
    for (;;)
    {
       test /= static_cast<std::uint32_t>(10u);
 
       if (test == static_cast<std::uint32_t>(0u))
       {
          break;
       }
 
       p10 *= static_cast<std::uint32_t>(10u);
       ++exponent;
    }
 
    // Establish the upper bound of limbs for extracting the double.
    const int max_elem_in_double_count = static_cast<int>(static_cast<std::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10) + (static_cast<int>(static_cast<std::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0) + 1;
 
    // And make sure this upper bound stays within bounds of the elems.
    const std::size_t max_elem_extract_count = static_cast<std::size_t>((std::min)(static_cast<std::int32_t>(max_elem_in_double_count), cpp_dec_float_elem_number));
 
    // Extract into the mantissa the first limb, extracted as a double.
    mantissa     = static_cast<double>(data[0]);
    double scale = 1.0;
 
    // Extract the rest of the mantissa piecewise from the limbs.
    for (std::size_t i = 1u; i < max_elem_extract_count; i++)
    {
       scale /= static_cast<double>(cpp_dec_float_elem_mask);
       mantissa += (static_cast<double>(data[i]) * scale);
    }
 
    mantissa /= static_cast<double>(p10);
 
    if (neg)
    {
       mantissa = -mantissa;
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const
 {
    // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
 
    // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>.
    if (!(isfinite)())
    {
       if ((isnan)())
       {
          return std::numeric_limits<double>::quiet_NaN();
       }
       else
       {
          return ((!neg) ? std::numeric_limits<double>::infinity()
                         : -std::numeric_limits<double>::infinity());
       }
    }
 
    cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
    if (xx.isneg())
       xx.negate();
 
    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
    if (iszero() || (xx.compare(double_min()) < 0))
    {
       return 0.0;
    }
 
    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
    if (xx.compare(double_max()) > 0)
    {
       return ((!neg) ? std::numeric_limits<double>::infinity()
                      : -std::numeric_limits<double>::infinity());
    }
 
    std::stringstream ss;
    ss.imbue(std::locale::classic());
 
    ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific);
 
    double d;
    ss >> d;
 
    return d;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const
 {
    // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
 
    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal.
    if (!(isfinite)())
    {
       if ((isnan)())
       {
          return std::numeric_limits<long double>::quiet_NaN();
       }
       else
       {
          return ((!neg) ? std::numeric_limits<long double>::infinity()
                         : -std::numeric_limits<long double>::infinity());
       }
    }
 
    cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
    if (xx.isneg())
       xx.negate();
 
    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
    if (iszero() || (xx.compare(long_double_min()) < 0))
    {
       return static_cast<long double>(0.0);
    }
 
    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
    if (xx.compare(long_double_max()) > 0)
    {
       return ((!neg) ? std::numeric_limits<long double>::infinity()
                      : -std::numeric_limits<long double>::infinity());
    }
 
    std::stringstream ss;
    ss.imbue(std::locale::classic());
 
    ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific);
 
    long double ld;
    ss >> ld;
 
    return ld;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 long long cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const
 {
    // Extracts a signed long long from *this.
    // If (x > maximum of long long) or (x < minimum of long long),
    // then the maximum or minimum of long long is returned accordingly.
 
    if (exp < static_cast<exponent_type>(0))
    {
       return static_cast<long long>(0);
    }
 
    const bool b_neg = isneg();
 
    unsigned long long val;
 
    if ((!b_neg) && (compare(long_long_max()) > 0))
    {
       return (std::numeric_limits<long long>::max)();
    }
    else if (b_neg && (compare(long_long_min()) < 0))
    {
       return (std::numeric_limits<long long>::min)();
    }
    else
    {
       // Extract the data into an unsigned long long value.
       cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
       if (xn.isneg())
          xn.negate();
 
       val = static_cast<unsigned long long>(xn.data[0]);
 
       const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1)));
 
       for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++)
       {
          val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask);
          val += static_cast<unsigned long long>(xn.data[static_cast<std::size_t>(i)]);
       }
    }
 
    if (!b_neg)
    {
       return static_cast<long long>(val);
    }
    else
    {
       // This strange expression avoids a hardware trap in the corner case
       // that val is the most negative value permitted in long long.
       // See https://svn.boost.org/trac/boost/ticket/9740.
       //
       long long sval = static_cast<long long>(val - 1);
       sval                       = -sval;
       --sval;
       return sval;
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 unsigned long long cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const
 {
    // Extracts an unsigned long long from *this.
    // If x exceeds the maximum of unsigned long long,
    // then the maximum of unsigned long long is returned.
    // If x is negative, then the unsigned long long cast of
    // the long long extracted value is returned.
 
    if (isneg())
    {
       return static_cast<unsigned long long>(extract_signed_long_long());
    }
 
    if (exp < static_cast<exponent_type>(0))
    {
       return static_cast<unsigned long long>(0u);
    }
 
    const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
 
    unsigned long long val;
 
    if (xn.compare(ulong_long_max()) > 0)
    {
       return (std::numeric_limits<unsigned long long>::max)();
    }
    else
    {
       // Extract the data into an unsigned long long value.
       val = static_cast<unsigned long long>(xn.data[0]);
 
       const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1)));
 
       for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++)
       {
          val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask);
          val += static_cast<unsigned long long>(xn.data[i]);
       }
    }
 
    return val;
 }
 
 #ifdef BOOST_HAS_INT128
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 int128_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_int128() const
 {
    // Extracts a signed __int128 from *this.
    // If (x > maximum of __int128) or (x < minimum of __int128),
    // then the maximum or minimum of long long is returned accordingly.
 
    if (exp < static_cast<exponent_type>(0))
    {
       return static_cast<int128_type>(0);
    }
 
    const bool b_neg = isneg();
    cpp_dec_float<Digits10, ExponentType, Allocator> i128max;
    i128max = ((~static_cast<uint128_type>(0)) >> 1);
    cpp_dec_float<Digits10, ExponentType, Allocator> i128min;
    i128min = (-1 - static_cast<int128_type>((static_cast<uint128_type>(1) << 127) - 1));
 
    uint128_type val;
 
    if ((!b_neg) && (compare(i128max) > 0))
    {
       return ((~static_cast<uint128_type>(0)) >> 1);
    }
    else if (b_neg && (compare(i128min) < 0))
    {
       return (-1 - static_cast<int128_type>((static_cast<uint128_type>(1) << 127) - 1));
    }
    else
    {
       // Extract the data into an unsigned long long value.
       cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
       if (xn.isneg())
          xn.negate();
 
       val = static_cast<uint128_type>(xn.data[0]);
 
       const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1)));
 
       for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++)
       {
          val *= static_cast<uint128_type>(cpp_dec_float_elem_mask);
          val += static_cast<uint128_type>(xn.data[static_cast<std::size_t>(i)]);
       }
    }
 
    if (!b_neg)
    {
       return static_cast<int128_type>(val);
    }
    else
    {
       // This strange expression avoids a hardware trap in the corner case
       // that val is the most negative value permitted in long long.
       // See https://svn.boost.org/trac/boost/ticket/9740.
       //
       int128_type sval = static_cast<int128_type>(val - 1);
       sval                       = -sval;
       --sval;
       return sval;
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 uint128_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_int128() const
 {
    // Extracts an unsigned __int128 from *this.
    // If x exceeds the maximum of unsigned __int128,
    // then the maximum of unsigned __int128 is returned.
    // If x is negative, then the unsigned __int128 cast of
    // the __int128 extracted value is returned.
 
    if (isneg())
    {
       return static_cast<uint128_type>(extract_signed_int128());
    }
 
    if (exp < static_cast<exponent_type>(0))
    {
       return 0u;
    }
 
    const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
    cpp_dec_float<Digits10, ExponentType, Allocator>       i128max;
    i128max = (~static_cast<uint128_type>(0));
 
    uint128_type val;
 
    if (xn.compare(i128max) > 0)
    {
       return (~static_cast<uint128_type>(0));
    }
    else
    {
       // Extract the data into an unsigned long long value.
       val = static_cast<uint128_type>(xn.data[0]);
 
       const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1)));
 
       for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++)
       {
          val *= static_cast<uint128_type>(cpp_dec_float_elem_mask);
          val += static_cast<uint128_type>(xn.data[i]);
       }
    }
 
    return val;
 }
 
 #endif
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const
 {
    // Compute the signed integer part of x.
 
    if (!(isfinite)())
    {
       return *this;
    }
 
    if (exp < static_cast<ExponentType>(0))
    {
       // The absolute value of the number is smaller than 1.
       // Thus the integer part is zero.
       return zero();
    }
 
    // Truncate the digits from the decimal part, including guard digits
    // that do not belong to the integer part.
 
    // Make a local copy.
    cpp_dec_float<Digits10, ExponentType, Allocator> x = *this;
 
    // Clear out the decimal portion
    const std::size_t first_clear = (static_cast<std::size_t>(x.exp) / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 1u;
    const std::size_t last_clear  =  static_cast<std::size_t>(cpp_dec_float_elem_number);
 
    if (first_clear < last_clear)
       std::fill(x.data.begin() + static_cast<std::ptrdiff_t>(first_clear), x.data.begin() + static_cast<std::ptrdiff_t>(last_clear), static_cast<std::uint32_t>(0u));
 
    return x;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(std::intmax_t number_of_digits, std::ios_base::fmtflags f) const
 {
    if ((this->isinf)())
    {
       if (this->isneg())
          return "-inf";
       else if (f & std::ios_base::showpos)
          return "+inf";
       else
          return "inf";
    }
    else if ((this->isnan)())
    {
       return "nan";
    }
 
    std::string     str;
    std::intmax_t org_digits(number_of_digits);
    exponent_type    my_exp = order();
 
    if (!(f & std::ios_base::fixed) && (number_of_digits == 0))
       number_of_digits = cpp_dec_float_max_digits10;
 
    if (f & std::ios_base::fixed)
    {
       number_of_digits += my_exp + 1;
    }
    else if (f & std::ios_base::scientific)
       ++number_of_digits;
    // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>.
    const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>(static_cast<std::size_t>(number_of_digits / static_cast<std::intmax_t>(cpp_dec_float_elem_digits10)) + 2u),
                                                      static_cast<std::size_t>(cpp_dec_float_elem_number));
 
    // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point.
    std::stringstream ss;
    ss.imbue(std::locale::classic());
    ss << data[0];
    // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element.
    for (std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++)
    {
       ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10))
          << std::setfill(static_cast<char>('0'))
          << data[i];
    }
    str += ss.str();
 
    bool have_leading_zeros = false;
 
    if (number_of_digits == 0)
    {
       // We only get here if the output format is "fixed" and we just need to
       // round the first non-zero digit.
       number_of_digits -= my_exp + 1; // reset to original value
       if (number_of_digits)
       {
          str.insert(static_cast<std::string::size_type>(0), std::string::size_type(number_of_digits), '0');
          have_leading_zeros = true;
       }
    }
 
    if (number_of_digits < 0)
    {
       str = "0";
       if (isneg())
          str.insert(static_cast<std::string::size_type>(0), 1, '-');
       boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero());
       return str;
    }
    else
    {
       // Cut the output to the size of the precision.
       if (str.length() > static_cast<std::string::size_type>(number_of_digits))
       {
          // Get the digit after the last needed digit for rounding
          const std::uint32_t round = static_cast<std::uint32_t>(static_cast<std::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<std::uint32_t>('0'));
 
          bool need_round_up = round >= 5u;
 
          if (round == 5u)
          {
             const std::uint32_t ix = number_of_digits == 0 ? 0 : static_cast<std::uint32_t>(static_cast<std::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<std::uint32_t>('0'));
             if ((ix & 1u) == 0)
             {
                // We have an even digit followed by a 5, so we might not actually need to round up
                // if all the remaining digits are zero:
                if (str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos)
                {
                   bool all_zeros = true;
                   // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string:
                   for (std::size_t i = number_of_elements; i < data.size(); i++)
                   {
                      if (data[i])
                      {
                         all_zeros = false;
                         break;
                      }
                   }
                   if (all_zeros)
                      need_round_up = false; // tie break - round to even.
                }
             }
          }
 
          // Truncate the string
          str.erase(static_cast<std::string::size_type>(number_of_digits));
 
          if (need_round_up)
          {
             if (str.size())
             {
                std::size_t ix = static_cast<std::size_t>(str.length() - 1u);
 
                // Every trailing 9 must be rounded up
                while (ix && (static_cast<std::int32_t>(str.at(ix)) - static_cast<std::int32_t>('0') == static_cast<std::int32_t>(9)))
                {
                   str.at(ix) = static_cast<char>('0');
                   --ix;
                }
 
                if (!ix)
                {
                   // There were nothing but trailing nines.
                   if (static_cast<std::int32_t>(static_cast<std::int32_t>(str.at(ix)) - static_cast<std::int32_t>(0x30)) == static_cast<std::int32_t>(9))
                   {
                      // Increment up to the next order and adjust exponent.
                      str.at(ix) = static_cast<char>('1');
                      ++my_exp;
                   }
                   else
                   {
                      // Round up this digit.
                      ++str.at(ix);
                   }
                }
                else
                {
                   // Round up the last digit.
                   ++str[ix];
                }
             }
             else
             {
                str = "1";
                ++my_exp;
             }
          }
       }
    }
 
    if (have_leading_zeros)
    {
       // We need to take the zeros back out again, and correct the exponent
       // if we rounded up:
       if (str[std::string::size_type(number_of_digits - 1)] != '0')
       {
          ++my_exp;
          str.erase(0, std::string::size_type(number_of_digits - 1));
       }
       else
          str.erase(0, std::string::size_type(number_of_digits));
    }
 
    if (isneg())
       str.insert(static_cast<std::string::size_type>(0), 1, '-');
 
    boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero());
    return str;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s)
 {
 #ifndef BOOST_NO_EXCEPTIONS
    try
    {
 #endif
 
       std::string str(s);
       static const std::string valid_characters{"0123456789"};
 
       // TBD: Using several regular expressions may significantly reduce
       // the code complexity (and perhaps the run-time) of rd_string().
 
       // Get a possible exponent and remove it.
       exp = static_cast<exponent_type>(0);
 
       std::size_t pos;
 
       if (((pos = str.find('e')) != std::string::npos) || ((pos = str.find('E')) != std::string::npos))
       {
          // Remove the exponent part from the string.
 #ifndef BOOST_MP_STANDALONE
          exp = boost::lexical_cast<exponent_type>(static_cast<const char*>(str.c_str() + (pos + 1u)));
 #else
          if (str.find_first_not_of(valid_characters, ((str[pos + 1] == '+') || (str[pos + 1] == '-')) ? pos + 2 : pos + 1) != std::string::npos)
             BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with non-numeric content"));
          exp = static_cast<exponent_type>(std::atoll(static_cast<const char*>(str.c_str() + (pos + 1u))));
 #endif
          
          str = str.substr(static_cast<std::size_t>(0u), pos);
       }
 
       // Get a possible +/- sign and remove it.
       neg = false;
 
       if (str.size())
       {
          if (str[0] == '-')
          {
             neg = true;
             str.erase(0, 1);
          }
          else if (str[0] == '+')
          {
             str.erase(0, 1);
          }
       }
       //
       // Special cases for infinities and NaN's:
       //
       if ((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY"))
       {
          if (neg)
          {
             *this = this->inf();
             this->negate();
          }
          else
             *this = this->inf();
          return true;
       }
       if ((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN")))
       {
          *this = this->nan();
          return true;
       }
 
       // Remove the leading zeros for all input types.
       const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate);
 
       if (fwd_it_leading_zero != str.begin())
       {
          if (fwd_it_leading_zero == str.end())
          {
             // The string contains nothing but leading zeros.
             // This string represents zero.
             operator=(zero());
             return true;
          }
          else
          {
             str.erase(str.begin(), fwd_it_leading_zero);
          }
       }
 
       // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form
       // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an
       // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded
       // on the right-end, and n is a signed 64-bit integer which is an
       // even multiple of cpp_dec_float_elem_digits10.
 
       // Find a possible decimal point.
       pos = str.find(static_cast<char>('.'));
 
       if (pos != std::string::npos)
       {
          // Check we have only digits either side of the point:
          if (str.find_first_not_of(valid_characters) != pos)
             BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with non-numeric content"));
          if (str.find_first_not_of(valid_characters, pos + 1) != std::string::npos)
             BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with non-numeric content"));
 
          // Remove all trailing insignificant zeros.
          const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate);
 
          if (rit_non_zero != static_cast<std::string::const_reverse_iterator>(str.rbegin()))
          {
             const std::string::size_type ofs =
                static_cast<std::string::size_type>
                (
                     static_cast<std::ptrdiff_t>(str.length())
                   - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero)
                );
             str.erase(str.begin() + static_cast<std::ptrdiff_t>(ofs), str.end());
          }
 
          // Check if the input is identically zero.
          if (str == std::string("."))
          {
             operator=(zero());
             return true;
          }
 
          // Remove leading significant zeros just after the decimal point
          // and adjust the exponent accordingly.
          // Note that the while-loop operates only on strings of the form ".000abcd..."
          // and peels away the zeros just after the decimal point.
          if (str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.'))
          {
             const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate);
 
             std::size_t delta_exp = static_cast<std::size_t>(0u);
 
             if (str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0'))
             {
                delta_exp = static_cast<std::size_t>(std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero));
             }
 
             // Bring one single digit into the mantissa and adjust the exponent accordingly.
             str.erase(str.begin(), it_non_zero);
             str.insert(static_cast<std::string::size_type>(1u), ".");
             exp -= static_cast<exponent_type>(delta_exp + 1u);
          }
       }
       else
       {
          // We should have only digits:
          if (str.find_first_not_of(valid_characters) != std::string::npos)
             BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with non-numeric content"));
 
          // Input string has no decimal point: Append decimal point.
          str.append(".");
       }
 
       // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10.
       std::ptrdiff_t       n_shift   = static_cast<std::ptrdiff_t>(0);
       const std::ptrdiff_t n_exp_rem = static_cast<std::ptrdiff_t>(exp % static_cast<exponent_type>(cpp_dec_float_elem_digits10));
 
       if((exp % static_cast<exponent_type>(cpp_dec_float_elem_digits10)) != static_cast<exponent_type>(0))
       {
          n_shift = ((exp < static_cast<exponent_type>(0))
                         ? static_cast<std::ptrdiff_t>(n_exp_rem + static_cast<std::ptrdiff_t>(cpp_dec_float_elem_digits10))
                         : static_cast<std::ptrdiff_t>(n_exp_rem));
       }
 
       // Make sure that there are enough digits for the decimal point shift.
       pos = str.find(static_cast<char>('.'));
 
       std::ptrdiff_t pos_plus_one = static_cast<std::ptrdiff_t>(pos + 1);
 
       if ((static_cast<std::ptrdiff_t>(str.length()) - pos_plus_one) < n_shift)
       {
          const std::ptrdiff_t sz = static_cast<std::ptrdiff_t>(n_shift - (static_cast<std::ptrdiff_t>(str.length()) - pos_plus_one));
 
          str.append(std::string(static_cast<std::string::size_type>(sz), static_cast<char>('0')));
       }
 
       // Do the decimal point shift.
       if (n_shift != static_cast<std::ptrdiff_t>(0))
       {
          str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), ".");
 
          str.erase(pos, static_cast<std::ptrdiff_t>(1));
 
          exp -= static_cast<exponent_type>(n_shift);
       }
 
       // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10.
       pos          = str.find(static_cast<char>('.'));
       pos_plus_one = static_cast<std::ptrdiff_t>(pos + 1u);
 
       if (pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10))
       {
          const std::int32_t n_pos         = static_cast<std::int32_t>(pos);
          const std::int32_t n_rem_is_zero = ((static_cast<std::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<std::int32_t>(0)) ? static_cast<std::int32_t>(1) : static_cast<std::int32_t>(0));
          const std::int32_t n             = static_cast<std::int32_t>(static_cast<std::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero);
 
          str.insert(static_cast<std::size_t>(static_cast<std::int32_t>(n_pos - static_cast<std::int32_t>(n * cpp_dec_float_elem_digits10))), ".");
 
          str.erase(static_cast<std::size_t>(pos_plus_one), static_cast<std::size_t>(1u));
 
          exp += static_cast<exponent_type>(static_cast<exponent_type>(n) * static_cast<exponent_type>(cpp_dec_float_elem_digits10));
       }
 
       // Pad the decimal part such that its value is an even
       // multiple of cpp_dec_float_elem_digits10.
       pos          = str.find(static_cast<char>('.'));
       pos_plus_one = static_cast<std::ptrdiff_t>(pos + 1u);
 
       // Throws an error for a strange construction like 3.14L
       if(pos != std::string::npos && (str.back() == 'L' || str.back() == 'l' || str.back() == 'u' || str.back() == 'U'))
       {
          BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with an integer literal"));
       }
 
       const std::int32_t n_dec = static_cast<std::int32_t>(static_cast<std::int32_t>(str.length() - 1u) - static_cast<std::int32_t>(pos));
       const std::int32_t n_rem = static_cast<std::int32_t>(n_dec % cpp_dec_float_elem_digits10);
 
       std::int32_t n_cnt = ((n_rem != static_cast<std::int32_t>(0))
                                   ? static_cast<std::int32_t>(cpp_dec_float_elem_digits10 - n_rem)
                                   : static_cast<std::int32_t>(0));
 
       if (n_cnt != static_cast<std::int32_t>(0))
       {
          str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0'));
       }
 
       // Truncate decimal part if it is too long.
       const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
 
       if (static_cast<std::size_t>(str.length() - pos) > max_dec)
       {
          str = str.substr(static_cast<std::size_t>(0u),
                           static_cast<std::size_t>(pos_plus_one + static_cast<std::ptrdiff_t>(max_dec)));
       }
 
       // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form.
       // (See the comment above.)
 
       // Set all the data elements to 0.
       std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u));
 
       // Extract the data.
 
       // First get the digits to the left of the decimal point...
       data[0u] = static_cast<std::uint32_t>(std::stol(str.substr(static_cast<std::size_t>(0u), pos)));
 
       // ...then get the remaining digits to the right of the decimal point.
       const std::string::size_type i_end =
       (
            static_cast<std::string::size_type>(str.length() - static_cast<std::string::size_type>(pos_plus_one))
          / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)
       );
 
       for (std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++)
       {
          const std::string::const_iterator it =
               str.begin()
             + static_cast<std::ptrdiff_t>
               (
                    static_cast<std::string::size_type>(pos_plus_one)
                  + static_cast<std::string::size_type>(i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10))
               );
 
          data[i + 1u] = static_cast<std::uint32_t>(std::stol(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10))));
       }
 
       // Check for overflow...
       if (exp > cpp_dec_float_max_exp10)
       {
          const bool b_result_is_neg = neg;
 
          *this = inf();
          if (b_result_is_neg)
             negate();
       }
 
       // ...and check for underflow.
       if (exp <= cpp_dec_float_min_exp10)
       {
          if (exp == cpp_dec_float_min_exp10)
          {
             // Check for identity with the minimum value.
             cpp_dec_float<Digits10, ExponentType, Allocator> test = *this;
 
             test.exp = static_cast<exponent_type>(0);
 
             if (test.isone())
             {
                *this = zero();
             }
          }
          else
          {
             *this = zero();
          }
       }
 
 #ifndef BOOST_NO_EXCEPTIONS
    }
    #ifndef BOOST_MP_STANDALONE
    catch (const bad_lexical_cast&)
    #else
    catch (const std::exception&)
    #endif
    {
       // Rethrow with better error message:
       std::string msg = "Unable to parse the string \"";
       msg += s;
       msg += "\" as a floating point value.";
       throw std::runtime_error(msg);
    }
 #endif
    return true;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent)
     : data(),
       exp(static_cast<ExponentType>(0)),
       neg(false),
       fpclass(cpp_dec_float_finite),
       prec_elem(cpp_dec_float_elem_number)
 {
    // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent.
    // Note: This constructor does not maintain the full precision of double.
 
    const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon())));
 
    if (mantissa_is_iszero)
    {
       std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u));
       return;
    }
 
    const bool b_neg = (mantissa < 0.0);
 
    double       d = ((!b_neg) ? mantissa : -mantissa);
    exponent_type e = exponent;
 
    while (d > 10.0)
    {
       d /= 10.0;
       ++e;
    }
    while (d < 1.0)
    {
       d *= 10.0;
       --e;
    }
 
    std::int32_t shift = static_cast<std::int32_t>(e % static_cast<std::int32_t>(cpp_dec_float_elem_digits10));
 
    while (static_cast<std::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<std::int32_t>(0))
    {
       d *= 10.0;
       --e;
    }
 
    exp = e;
    neg = b_neg;
 
    std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u));
 
    constexpr std::int32_t digit_ratio = static_cast<std::int32_t>(static_cast<std::int32_t>(std::numeric_limits<double>::digits10) / static_cast<std::int32_t>(cpp_dec_float_elem_digits10));
    constexpr std::int32_t digit_loops = static_cast<std::int32_t>(digit_ratio + static_cast<std::int32_t>(2));
 
    for (std::int32_t i = static_cast<std::int32_t>(0); i < digit_loops; i++)
    {
       std::uint32_t n = static_cast<std::uint32_t>(static_cast<std::uint64_t>(d));
       data[static_cast<std::size_t>(i)] = static_cast<std::uint32_t>(n);
       d -= static_cast<double>(n);
       d *= static_cast<double>(cpp_dec_float_elem_mask);
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 template <class Float>
 typename std::enable_if<std::is_floating_point<Float>::value, cpp_dec_float<Digits10, ExponentType, Allocator>&>::type cpp_dec_float<Digits10, ExponentType, Allocator>::operator=(Float a)
 {
    // Christopher Kormanyos's original code used a cast to long long here, but that fails
    // when long double has more digits than a long long.
    BOOST_MP_FLOAT128_USING
    using std::floor;
    using std::frexp; 
    using std::ldexp;
 
    if (a == 0)
       return *this = zero();
 
    if (a == 1)
       return *this = one();
 
    if (BOOST_MP_ISINF(a))
    {
       *this = inf();
       if (a < 0)
          this->negate();
       return *this;
    }
 
    if (BOOST_MP_ISNAN(a))
       return *this = nan();
 
    int         e;
    Float f, term;
    *this = zero();
 
    f = frexp(a, &e);
    // See https://svn.boost.org/trac/boost/ticket/10924 for an example of why this may go wrong:
    BOOST_MP_ASSERT(!BOOST_MP_ISNAN(f) && !BOOST_MP_ISINF(f));
 
    constexpr int shift = std::numeric_limits<int>::digits - 1;
 
    while (f != static_cast<Float>(0.0f))
    {
       // extract int sized bits from f:
       f = ldexp(f, shift);
       BOOST_MP_ASSERT(!BOOST_MP_ISNAN(f) && !BOOST_MP_ISINF(f));
       term = floor(f);
       e -= shift;
       *this *= pow2(shift);
       if (term > 0)
          add_unsigned_long_long(static_cast<unsigned>(term));
       else
          sub_unsigned_long_long(static_cast<unsigned>(-term));
       f -= term;
    }
 
    if (e != 0)
       *this *= pow2(e);
 
    return *this;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const unsigned long long u)
 {
    std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u));
 
    exp       = static_cast<exponent_type>(0);
    neg       = false;
    fpclass   = cpp_dec_float_finite;
    prec_elem = cpp_dec_float_elem_number;
 
    if (u == 0)
    {
       return;
    }
 
    std::size_t i = static_cast<std::size_t>(0u);
 
    unsigned long long uu = u;
 
    std::uint32_t temp[(std::numeric_limits<unsigned long long>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = {static_cast<std::uint32_t>(0u)};
 
    while (uu != static_cast<unsigned long long>(0u))
    {
       temp[i] = static_cast<std::uint32_t>(uu % static_cast<unsigned long long>(cpp_dec_float_elem_mask));
       uu      = static_cast<unsigned long long>(uu / static_cast<unsigned long long>(cpp_dec_float_elem_mask));
       ++i;
    }
 
    if (i > static_cast<std::size_t>(1u))
    {
       exp += static_cast<exponent_type>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
    }
 
    std::reverse(temp, temp + i);
    std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin());
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 template <typename InputIteratorTypeLeft, typename InputIteratorTypeRight>
 int cpp_dec_float<Digits10, ExponentType, Allocator>::compare_ranges(InputIteratorTypeLeft  a,
                                                                      InputIteratorTypeRight b,
                                                                      const std::uint32_t    count)
 {
    using local_iterator_left_type  = InputIteratorTypeLeft;
    using local_iterator_right_type = InputIteratorTypeRight;
 
    local_iterator_left_type  begin_a(a);
    local_iterator_left_type  end_a  (a + static_cast<typename std::iterator_traits<local_iterator_left_type >::difference_type>(count));
    local_iterator_right_type begin_b(b);
    local_iterator_right_type end_b  (b + static_cast<typename std::iterator_traits<local_iterator_right_type>::difference_type>(count));
 
    const auto mismatch_pair = std::mismatch(begin_a, end_a, begin_b);
 
    int n_return;
 
    if((mismatch_pair.first != end_a) || (mismatch_pair.second != end_b))
    {
       const typename std::iterator_traits<local_iterator_left_type >::value_type left  = *mismatch_pair.first;
       const typename std::iterator_traits<local_iterator_right_type>::value_type right = *mismatch_pair.second;
 
       n_return = ((left > right) ?  1 : -1);
    }
    else
    {
       n_return = 0;
    }
 
    return n_return;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::eval_add_n(      std::uint32_t* r,
                                                                            const std::uint32_t* u,
                                                                            const std::uint32_t* v,
                                                                            const std::int32_t   count)
 {
    // Addition algorithm
    std::uint_fast8_t carry = static_cast<std::uint_fast8_t>(0U);
 
    for(std::int32_t j = static_cast<std::int32_t>(count - static_cast<std::int32_t>(1)); j >= static_cast<std::int32_t>(0); --j)
    {
       const std::uint32_t t = static_cast<std::uint32_t>(static_cast<std::uint32_t>(u[j] + v[j]) + carry);
 
       carry = ((t >= static_cast<std::uint32_t>(cpp_dec_float_elem_mask)) ? static_cast<std::uint_fast8_t>(1U)
                                                                    : static_cast<std::uint_fast8_t>(0U));
 
       r[j]  = static_cast<std::uint32_t>(t - ((carry != 0U) ? static_cast<std::uint32_t>(cpp_dec_float_elem_mask)
                                                             : static_cast<std::uint32_t>(0U)));
    }
 
    return static_cast<std::uint32_t>(carry);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::eval_subtract_n(      std::uint32_t* r,
                                                                                 const std::uint32_t* u,
                                                                                 const std::uint32_t* v,
                                                                                 const std::int32_t   count)
 {
    // Subtraction algorithm
    std::int_fast8_t borrow = static_cast<std::int_fast8_t>(0);
 
    for(std::uint32_t j = static_cast<std::uint32_t>(count - static_cast<std::int32_t>(1)); static_cast<std::int32_t>(j) >= static_cast<std::int32_t>(0); --j)
    {
       std::int32_t t = static_cast<std::int32_t>(  static_cast<std::int32_t>(u[j])
                                                  - static_cast<std::int32_t>(v[j])) - borrow;
 
       // Underflow? Borrow?
       if(t < 0)
       {
          // Yes, underflow and borrow
          t     += static_cast<std::int32_t>(cpp_dec_float_elem_mask);
          borrow = static_cast<std::int_fast8_t>(1);
       }
       else
       {
          borrow = static_cast<std::int_fast8_t>(0);
       }
 
       r[j] = static_cast<std::uint32_t>(t);
    }
 
    return static_cast<std::uint32_t>(borrow);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_n_by_n_to_2n(      std::uint32_t* r,
                                                                                   const std::uint32_t* a,
                                                                                   const std::uint32_t* b,
                                                                                   const std::uint32_t  count)
 {
    using local_limb_type = std::uint32_t;
 
    using local_double_limb_type = std::uint64_t;
 
    using local_reverse_iterator_type = std::reverse_iterator<local_limb_type*>;
 
    local_reverse_iterator_type ir(r + (count * 2));
 
    local_double_limb_type carry = 0U;
 
    for(std::int32_t j = static_cast<std::int32_t>(count - 1); j >= static_cast<std::int32_t>(1); --j)
    {
       local_double_limb_type sum = carry;
 
       for(std::int32_t i = static_cast<std::int32_t>(count - 1); i >= j; --i)
       {
          sum += local_double_limb_type(
                 local_double_limb_type(a[i]) * b[  static_cast<std::int32_t>(count - 1)
                                                 - static_cast<std::int32_t>(i - j)]);
       }
 
       carry = static_cast<local_double_limb_type>(sum / static_cast<local_limb_type>       (cpp_dec_float_elem_mask));
       *ir++ = static_cast<local_limb_type>       (sum - static_cast<local_double_limb_type>(static_cast<local_double_limb_type>(carry) * static_cast<local_limb_type>(cpp_dec_float_elem_mask)));
    }
 
    for(std::int32_t j = static_cast<std::int32_t>(count - 1); j >= static_cast<std::int32_t>(0); --j)
    {
       local_double_limb_type sum = carry;
 
       for(std::int32_t i = j; i >= static_cast<std::int32_t>(0); --i)
       {
          sum += static_cast<local_double_limb_type>(a[j - i] * static_cast<local_double_limb_type>(b[i]));
       }
 
       carry = static_cast<local_double_limb_type>(sum / static_cast<local_limb_type>(cpp_dec_float_elem_mask));
       *ir++ = static_cast<local_limb_type>       (sum - static_cast<local_double_limb_type>(static_cast<local_double_limb_type>(carry) * static_cast<local_limb_type>(cpp_dec_float_elem_mask)));
    }
 
    *ir = static_cast<local_limb_type>(carry);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p)
 {
    std::uint64_t carry = static_cast<std::uint64_t>(0u);
 
    // Multiplication loop.
    for (std::int32_t j = p - 1; j >= static_cast<std::int32_t>(0); j--)
    {
       const std::uint64_t t = static_cast<std::uint64_t>(carry + static_cast<std::uint64_t>(u[j] * static_cast<std::uint64_t>(n)));
       carry                 = static_cast<std::uint64_t>(t / static_cast<std::uint32_t>(cpp_dec_float_elem_mask));
       u[j]                  = static_cast<std::uint32_t>(t - static_cast<std::uint64_t>(static_cast<std::uint32_t>(cpp_dec_float_elem_mask) * static_cast<std::uint64_t>(carry)));
    }
 
    return static_cast<std::uint32_t>(carry);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p)
 {
    std::uint64_t prev = static_cast<std::uint64_t>(0u);
 
    for (std::int32_t j = static_cast<std::int32_t>(0); j < p; j++)
    {
       const std::uint64_t t = static_cast<std::uint64_t>(u[j] + static_cast<std::uint64_t>(prev * static_cast<std::uint32_t>(cpp_dec_float_elem_mask)));
       u[j]                    = static_cast<std::uint32_t>(t / n);
       prev                    = static_cast<std::uint64_t>(t - static_cast<std::uint64_t>(n * static_cast<std::uint64_t>(u[j])));
    }
 
    return static_cast<std::uint32_t>(prev);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_propagate_carry(std::uint32_t* t, const std::uint32_t n, const std::uint32_t carry)
 {
    std::uint_fast8_t carry_out = ((carry != 0U) ? static_cast<std::uint_fast8_t>(1U)
                                                 : static_cast<std::uint_fast8_t>(0U));
 
    using local_reverse_iterator_type = std::reverse_iterator<std::uint32_t*>;
 
    local_reverse_iterator_type ri_t  (t + n);
    local_reverse_iterator_type rend_t(t);
 
    while((carry_out != 0U) && (ri_t != rend_t))
    {
       const std::uint64_t tt = *ri_t + carry_out;
 
       carry_out = ((tt >= static_cast<std::uint32_t>(cpp_dec_float_elem_mask)) ? static_cast<std::uint_fast8_t>(1U)
                                                                                : static_cast<std::uint_fast8_t>(0U));
 
       *ri_t++    = static_cast<std::uint32_t>(tt - ((carry_out != 0U) ? static_cast<std::uint32_t>(cpp_dec_float_elem_mask)
                                                                       : static_cast<std::uint32_t>(0U)));
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_propagate_borrow(std::uint32_t* t, const std::uint32_t n, const bool has_borrow)
 {
    std::int_fast8_t borrow = (has_borrow ? static_cast<std::int_fast8_t>(1)
                                          : static_cast<std::int_fast8_t>(0));
 
    using local_reverse_iterator_type = std::reverse_iterator<std::uint32_t*>;
 
    local_reverse_iterator_type ri_t  (t + n);
    local_reverse_iterator_type rend_t(t);
 
    while((borrow != 0U) && (ri_t != rend_t))
    {
       std::int32_t tt = static_cast<std::int32_t>(static_cast<std::int32_t>(*ri_t) - borrow);
 
       // Underflow? Borrow?
       if(tt < 0)
       {
          // Yes, underflow and borrow
          tt     += static_cast<std::int32_t>(cpp_dec_float_elem_mask);
          borrow  = static_cast<int_fast8_t>(1);
       }
       else
       {
          borrow = static_cast<int_fast8_t>(0);
       }
 
       *ri_t++ = static_cast<std::uint32_t>(tt);
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_n_by_n_to_2n(      std::uint32_t* r,
                                                                                        const std::uint32_t* a,
                                                                                        const std::uint32_t* b,
                                                                                        const std::uint32_t  n,
                                                                                              std::uint32_t* t)
 {
    if(n <= 32U)
    {
       static_cast<void>(t);
 
       eval_multiply_n_by_n_to_2n(r, a, b, n);
    }
    else
    {
       // Based on "Algorithm 1.3 KaratsubaMultiply", Sect. 1.3.2, page 5
       // of R.P. Brent and P. Zimmermann, "Modern Computer Arithmetic",
       // Cambridge University Press (2011).
 
       // The Karatsuba multipliation computes the product of a*b as:
       // [b^N + b^(N/2)] a1*b1 + [b^(N/2)](a1 - a0)(b0 - b1) + [b^(N/2) + 1] a0*b0
 
       // Here we visualize a and b in two components 1,0 corresponding
       // to the high and low order parts, respectively.
 
       // Step 1
       // Calculate a1*b1 and store it in the upper-order part of r.
       // Calculate a0*b0 and store it in the lower-order part of r.
       // copy r to t0.
 
       // Step 2
       // Add a1*b1 (which is t2) to the middle two-quarters of r (which is r1)
       // Add a0*b0 (which is t0) to the middle two-quarters of r (which is r1)
 
       // Step 3
       // Calculate |a1-a0| in t0 and note the sign (i.e., the borrow flag)
 
       // Step 4
       // Calculate |b0-b1| in t1 and note the sign (i.e., the borrow flag)
 
       // Step 5
       // Call kara mul to calculate |a1-a0|*|b0-b1| in (t2),
       // while using temporary storage in t4 along the way.
 
       // Step 6
       // Check the borrow signs. If a1-a0 and b0-b1 have the same signs,
       // then add |a1-a0|*|b0-b1| to r1, otherwise subtract it from r1.
 
       const std::uint_fast32_t  nh = n / 2U;
 
       const std::uint32_t* a0 = a + nh;
       const std::uint32_t* a1 = a + 0U;
 
       const std::uint32_t* b0 = b + nh;
       const std::uint32_t* b1 = b + 0U;
 
             std::uint32_t* r0 = r + 0U;
             std::uint32_t* r1 = r + nh;
             std::uint32_t* r2 = r + n;
 
             std::uint32_t* t0 = t + 0U;
             std::uint32_t* t1 = t + nh;
             std::uint32_t* t2 = t + n;
             std::uint32_t* t4 = t + (n + n);
 
       // Step 1
       eval_multiply_kara_n_by_n_to_2n(r0, a1, b1, static_cast<std::uint32_t>(nh), t);
       eval_multiply_kara_n_by_n_to_2n(r2, a0, b0, static_cast<std::uint32_t>(nh), t);
       std::copy(r0, r0 + (2U * n), t0);
 
       // Step 2
       std::uint32_t carry;
       carry = eval_add_n(r1, r1, t0, static_cast<std::int32_t>(n));
       eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry);
       carry = eval_add_n(r1, r1, t2, static_cast<std::int32_t>(n));
       eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry);
 
       // Step 3
       const int cmp_result_a1a0 = compare_ranges(a1, a0, static_cast<std::uint32_t>(nh));
 
       if(cmp_result_a1a0 == 1)
          static_cast<void>(eval_subtract_n(t0, a1, a0, static_cast<std::int32_t>(nh)));
       else if(cmp_result_a1a0 == -1)
          static_cast<void>(eval_subtract_n(t0, a0, a1, static_cast<std::int32_t>(nh)));
 
       // Step 4
       const int cmp_result_b0b1 = compare_ranges(b0, b1, static_cast<std::uint32_t>(nh));
 
       if(cmp_result_b0b1 == 1)
          static_cast<void>(eval_subtract_n(t1, b0, b1, static_cast<std::int32_t>(nh)));
       else if(cmp_result_b0b1 == -1)
          static_cast<void>(eval_subtract_n(t1, b1, b0, static_cast<std::int32_t>(nh)));
 
       // Step 5
       eval_multiply_kara_n_by_n_to_2n(t2, t0, t1, static_cast<std::uint32_t>(nh), t4);
 
       // Step 6
       if((cmp_result_a1a0 * cmp_result_b0b1) == 1)
       {
          carry = eval_add_n(r1, r1, t2, static_cast<std::int32_t>(n));
 
          eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry);
       }
       else if((cmp_result_a1a0 * cmp_result_b0b1) == -1)
       {
          const bool has_borrow = eval_subtract_n(r1, r1, t2, static_cast<std::int32_t>(n));
 
          eval_multiply_kara_propagate_borrow(r0, static_cast<std::uint32_t>(nh), has_borrow);
       }
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const long long p)
 {
    static const std::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 256u> local_pow2_data =
    {{
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       29u, 38735877u,  5571876u, 99218413u, 43055614u, 19454666u, 38919302u, 18803771u, 87926569u, 60431486u, 36817932u, 12890625u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       58u, 77471754u, 11143753u, 98436826u, 86111228u, 38909332u, 77838604u, 37607543u, 75853139u, 20862972u, 73635864u, 25781250u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      117u, 54943508u, 22287507u, 96873653u, 72222456u, 77818665u, 55677208u, 75215087u, 51706278u, 41725945u, 47271728u, 51562500u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      235u,  9887016u, 44575015u, 93747307u, 44444913u, 55637331u, 11354417u, 50430175u,  3412556u, 83451890u, 94543457u,  3125000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      470u, 19774032u, 89150031u, 87494614u, 88889827u, 11274662u, 22708835u,   860350u,  6825113u, 66903781u, 89086914u,  6250000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      940u, 39548065u, 78300063u, 74989229u, 77779654u, 22549324u, 45417670u,  1720700u, 13650227u, 33807563u, 78173828u, 12500000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1880u, 79096131u, 56600127u, 49978459u, 55559308u, 45098648u, 90835340u,  3441400u, 27300454u, 67615127u, 56347656u, 25000000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     3761u, 58192263u, 13200254u, 99956919u, 11118616u, 90197297u, 81670680u,  6882800u, 54600909u, 35230255u, 12695312u, 50000000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     7523u, 16384526u, 26400509u, 99913838u, 22237233u, 80394595u, 63341360u, 13765601u,  9201818u, 70460510u, 25390625u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    15046u, 32769052u, 52801019u, 99827676u, 44474467u, 60789191u, 26682720u, 27531202u, 18403637u, 40921020u, 50781250u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    30092u, 65538105u,  5602039u, 99655352u, 88948935u, 21578382u, 53365440u, 55062404u, 36807274u, 81842041u,  1562500u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    60185u, 31076210u, 11204079u, 99310705u, 77897870u, 43156765u,  6730881u, 10124808u, 73614549u, 63684082u,  3125000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   120370u, 62152420u, 22408159u, 98621411u, 55795740u, 86313530u, 13461762u, 20249617u, 47229099u, 27368164u,  6250000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   240741u, 24304840u, 44816319u, 97242823u, 11591481u, 72627060u, 26923524u, 40499234u, 94458198u, 54736328u, 12500000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   481482u, 48609680u, 89632639u, 94485646u, 23182963u, 45254120u, 53847048u, 80998469u, 88916397u,  9472656u, 25000000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   962964u, 97219361u, 79265279u, 88971292u, 46365926u, 90508241u,  7694097u, 61996939u, 77832794u, 18945312u, 50000000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1925929u, 94438723u, 58530559u, 77942584u, 92731853u, 81016482u, 15388195u, 23993879u, 55665588u, 37890625u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  3851859u, 88877447u, 17061119u, 55885169u, 85463707u, 62032964u, 30776390u, 47987759u, 11331176u, 75781250u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  7703719u, 77754894u, 34122239u, 11770339u, 70927415u, 24065928u, 61552780u, 95975518u, 22662353u, 51562500u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 15407439u, 55509788u, 68244478u, 23540679u, 41854830u, 48131857u, 23105561u, 91951036u, 45324707u,  3125000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 30814879u, 11019577u, 36488956u, 47081358u, 83709660u, 96263714u, 46211123u, 83902072u, 90649414u,  6250000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 61629758u, 22039154u, 72977912u, 94162717u, 67419321u, 92527428u, 92422247u, 67804145u, 81298828u, 12500000u }, -40 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 23259516u, 44078309u, 45955825u, 88325435u, 34838643u, 85054857u, 84844495u, 35608291u, 62597656u, 25000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u, 46519032u, 88156618u, 91911651u, 76650870u, 69677287u, 70109715u, 69688990u, 71216583u, 25195312u, 50000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        4u, 93038065u, 76313237u, 83823303u, 53301741u, 39354575u, 40219431u, 39377981u, 42433166u, 50390625u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        9u, 86076131u, 52626475u, 67646607u,  6603482u, 78709150u, 80438862u, 78755962u, 84866333u,   781250u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       19u, 72152263u,  5252951u, 35293214u, 13206965u, 57418301u, 60877725u, 57511925u, 69732666u,  1562500u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       39u, 44304526u, 10505902u, 70586428u, 26413931u, 14836603u, 21755451u, 15023851u, 39465332u,  3125000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       78u, 88609052u, 21011805u, 41172856u, 52827862u, 29673206u, 43510902u, 30047702u, 78930664u,  6250000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      157u, 77218104u, 42023610u, 82345713u,  5655724u, 59346412u, 87021804u, 60095405u, 57861328u, 12500000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      315u, 54436208u, 84047221u, 64691426u, 11311449u, 18692825u, 74043609u, 20190811u, 15722656u, 25000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      631u,  8872417u, 68094443u, 29382852u, 22622898u, 37385651u, 48087218u, 40381622u, 31445312u, 50000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1262u, 17744835u, 36188886u, 58765704u, 45245796u, 74771302u, 96174436u, 80763244u, 62890625u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     2524u, 35489670u, 72377773u, 17531408u, 90491593u, 49542605u, 92348873u, 61526489u, 25781250u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     5048u, 70979341u, 44755546u, 35062817u, 80983186u, 99085211u, 84697747u, 23052978u, 51562500u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    10097u, 41958682u, 89511092u, 70125635u, 61966373u, 98170423u, 69395494u, 46105957u,  3125000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    20194u, 83917365u, 79022185u, 40251271u, 23932747u, 96340847u, 38790988u, 92211914u,  6250000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    40389u, 67834731u, 58044370u, 80502542u, 47865495u, 92681694u, 77581977u, 84423828u, 12500000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    80779u, 35669463u, 16088741u, 61005084u, 95730991u, 85363389u, 55163955u, 68847656u, 25000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   161558u, 71338926u, 32177483u, 22010169u, 91461983u, 70726779u, 10327911u, 37695312u, 50000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   323117u, 42677852u, 64354966u, 44020339u, 82923967u, 41453558u, 20655822u, 75390625u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   646234u, 85355705u, 28709932u, 88040679u, 65847934u, 82907116u, 41311645u, 50781250u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1292469u, 70711410u, 57419865u, 76081359u, 31695869u, 65814232u, 82623291u,  1562500u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  2584939u, 41422821u, 14839731u, 52162718u, 63391739u, 31628465u, 65246582u,  3125000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  5169878u, 82845642u, 29679463u,  4325437u, 26783478u, 63256931u, 30493164u,  6250000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10339757u, 65691284u, 59358926u,  8650874u, 53566957u, 26513862u, 60986328u, 12500000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 20679515u, 31382569u, 18717852u, 17301749u,  7133914u, 53027725u, 21972656u, 25000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 41359030u, 62765138u, 37435704u, 34603498u, 14267829u,  6055450u, 43945312u, 50000000u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 82718061u, 25530276u, 74871408u, 69206996u, 28535658u, 12110900u, 87890625u }, -32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 65436122u, 51060553u, 49742817u, 38413992u, 57071316u, 24221801u, 75781250u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        3u, 30872245u,  2121106u, 99485634u, 76827985u, 14142632u, 48443603u, 51562500u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        6u, 61744490u,  4242213u, 98971269u, 53655970u, 28285264u, 96887207u,  3125000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       13u, 23488980u,  8484427u, 97942539u,  7311940u, 56570529u, 93774414u,  6250000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       26u, 46977960u, 16968855u, 95885078u, 14623881u, 13141059u, 87548828u, 12500000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       52u, 93955920u, 33937711u, 91770156u, 29247762u, 26282119u, 75097656u, 25000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      105u, 87911840u, 67875423u, 83540312u, 58495524u, 52564239u, 50195312u, 50000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      211u, 75823681u, 35750847u, 67080625u, 16991049u,  5128479u,   390625u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      423u, 51647362u, 71501695u, 34161250u, 33982098u, 10256958u,   781250u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      847u,  3294725u, 43003390u, 68322500u, 67964196u, 20513916u,  1562500u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1694u,  6589450u, 86006781u, 36645001u, 35928392u, 41027832u,  3125000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     3388u, 13178901u, 72013562u, 73290002u, 71856784u, 82055664u,  6250000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     6776u, 26357803u, 44027125u, 46580005u, 43713569u, 64111328u, 12500000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    13552u, 52715606u, 88054250u, 93160010u, 87427139u, 28222656u, 25000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    27105u,  5431213u, 76108501u, 86320021u, 74854278u, 56445312u, 50000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    54210u, 10862427u, 52217003u, 72640043u, 49708557u, 12890625u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   108420u, 21724855u,  4434007u, 45280086u, 99417114u, 25781250u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   216840u, 43449710u,  8868014u, 90560173u, 98834228u, 51562500u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   433680u, 86899420u, 17736029u, 81120347u, 97668457u,  3125000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   867361u, 73798840u, 35472059u, 62240695u, 95336914u,  6250000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1734723u, 47597680u, 70944119u, 24481391u, 90673828u, 12500000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  3469446u, 95195361u, 41888238u, 48962783u, 81347656u, 25000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  6938893u, 90390722u, 83776476u, 97925567u, 62695312u, 50000000u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 13877787u, 80781445u, 67552953u, 95851135u, 25390625u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 27755575u, 61562891u, 35105907u, 91702270u, 50781250u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 55511151u, 23125782u, 70211815u, 83404541u,  1562500u }, -24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 11022302u, 46251565u, 40423631u, 66809082u,  3125000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u, 22044604u, 92503130u, 80847263u, 33618164u,  6250000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        4u, 44089209u, 85006261u, 61694526u, 67236328u, 12500000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        8u, 88178419u, 70012523u, 23389053u, 34472656u, 25000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       17u, 76356839u, 40025046u, 46778106u, 68945312u, 50000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       35u, 52713678u, 80050092u, 93556213u, 37890625u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       71u,  5427357u, 60100185u, 87112426u, 75781250u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      142u, 10854715u, 20200371u, 74224853u, 51562500u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      284u, 21709430u, 40400743u, 48449707u,  3125000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      568u, 43418860u, 80801486u, 96899414u,  6250000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1136u, 86837721u, 61602973u, 93798828u, 12500000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     2273u, 73675443u, 23205947u, 87597656u, 25000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     4547u, 47350886u, 46411895u, 75195312u, 50000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     9094u, 94701772u, 92823791u, 50390625u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    18189u, 89403545u, 85647583u,   781250u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    36379u, 78807091u, 71295166u,  1562500u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    72759u, 57614183u, 42590332u,  3125000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   145519u, 15228366u, 85180664u,  6250000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   291038u, 30456733u, 70361328u, 12500000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   582076u, 60913467u, 40722656u, 25000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1164153u, 21826934u, 81445312u, 50000000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  2328306u, 43653869u, 62890625u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  4656612u, 87307739u, 25781250u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  9313225u, 74615478u, 51562500u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 18626451u, 49230957u,  3125000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 37252902u, 98461914u,  6250000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 74505805u, 96923828u, 12500000u }, -16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 49011611u, 93847656u, 25000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u, 98023223u, 87695312u, 50000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        5u, 96046447u, 75390625u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       11u, 92092895u, 50781250u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       23u, 84185791u,  1562500u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       47u, 68371582u,  3125000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       95u, 36743164u,  6250000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      190u, 73486328u, 12500000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      381u, 46972656u, 25000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      762u, 93945312u, 50000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1525u, 87890625u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     3051u, 75781250u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     6103u, 51562500u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    12207u,  3125000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    24414u,  6250000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    48828u, 12500000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    97656u, 25000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   195312u, 50000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   390625u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   781250u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1562500u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  3125000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  6250000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 12500000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 25000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 50000000u }, -8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        4u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        8u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       16u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       32u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       64u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      128u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      256u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      512u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1024u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     2048u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     4096u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     8192u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    16384u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    32768u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    65536u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   131072u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   262144u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   524288u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1048576u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  2097152u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  4194304u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  8388608u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 16777216u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 33554432u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 67108864u },  0 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 34217728u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u, 68435456u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        5u, 36870912u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       10u, 73741824u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       21u, 47483648u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       42u, 94967296u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       85u, 89934592u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      171u, 79869184u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      343u, 59738368u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      687u, 19476736u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1374u, 38953472u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     2748u, 77906944u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     5497u, 55813888u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    10995u, 11627776u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    21990u, 23255552u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    43980u, 46511104u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    87960u, 93022208u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   175921u, 86044416u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   351843u, 72088832u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   703687u, 44177664u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1407374u, 88355328u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  2814749u, 76710656u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  5629499u, 53421312u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 11258999u,  6842624u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 22517998u, 13685248u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 45035996u, 27370496u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 90071992u, 54740992u },  8 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 80143985u,  9481984u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        3u, 60287970u, 18963968u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        7u, 20575940u, 37927936u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       14u, 41151880u, 75855872u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       28u, 82303761u, 51711744u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       57u, 64607523u,  3423488u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      115u, 29215046u,  6846976u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      230u, 58430092u, 13693952u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      461u, 16860184u, 27387904u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      922u, 33720368u, 54775808u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1844u, 67440737u,  9551616u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     3689u, 34881474u, 19103232u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     7378u, 69762948u, 38206464u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    14757u, 39525896u, 76412928u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    29514u, 79051793u, 52825856u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    59029u, 58103587u,  5651712u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   118059u, 16207174u, 11303424u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   236118u, 32414348u, 22606848u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   472236u, 64828696u, 45213696u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   944473u, 29657392u, 90427392u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1888946u, 59314785u, 80854784u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  3777893u, 18629571u, 61709568u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  7555786u, 37259143u, 23419136u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 15111572u, 74518286u, 46838272u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 30223145u, 49036572u, 93676544u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 60446290u, 98073145u, 87353088u }, 16 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 20892581u, 96146291u, 74706176u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        2u, 41785163u, 92292583u, 49412352u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        4u, 83570327u, 84585166u, 98824704u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        9u, 67140655u, 69170333u, 97649408u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       19u, 34281311u, 38340667u, 95298816u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       38u, 68562622u, 76681335u, 90597632u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       77u, 37125245u, 53362671u, 81195264u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      154u, 74250491u,  6725343u, 62390528u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      309u, 48500982u, 13450687u, 24781056u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      618u, 97001964u, 26901374u, 49562112u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1237u, 94003928u, 53802748u, 99124224u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     2475u, 88007857u,  7605497u, 98248448u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     4951u, 76015714u, 15210995u, 96496896u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     9903u, 52031428u, 30421991u, 92993792u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    19807u,  4062856u, 60843983u, 85987584u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    39614u,  8125713u, 21687967u, 71975168u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    79228u, 16251426u, 43375935u, 43950336u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   158456u, 32502852u, 86751870u, 87900672u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   316912u, 65005705u, 73503741u, 75801344u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   633825u, 30011411u, 47007483u, 51602688u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1267650u, 60022822u, 94014967u,  3205376u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  2535301u, 20045645u, 88029934u,  6410752u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  5070602u, 40091291u, 76059868u, 12821504u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10141204u, 80182583u, 52119736u, 25643008u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 20282409u, 60365167u,  4239472u, 51286016u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 40564819u, 20730334u,  8478945u,  2572032u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 81129638u, 41460668u, 16957890u,  5144064u }, 24 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        1u, 62259276u, 82921336u, 33915780u, 10288128u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        3u, 24518553u, 65842672u, 67831560u, 20576256u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {        6u, 49037107u, 31685345u, 35663120u, 41152512u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       12u, 98074214u, 63370690u, 71326240u, 82305024u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       25u, 96148429u, 26741381u, 42652481u, 64610048u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {       51u, 92296858u, 53482762u, 85304963u, 29220096u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      103u, 84593717u,  6965525u, 70609926u, 58440192u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      207u, 69187434u, 13931051u, 41219853u, 16880384u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      415u, 38374868u, 27862102u, 82439706u, 33760768u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {      830u, 76749736u, 55724205u, 64879412u, 67521536u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     1661u, 53499473u, 11448411u, 29758825u, 35043072u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     3323u,  6998946u, 22896822u, 59517650u, 70086144u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {     6646u, 13997892u, 45793645u, 19035301u, 40172288u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    13292u, 27995784u, 91587290u, 38070602u, 80344576u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    26584u, 55991569u, 83174580u, 76141205u, 60689152u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {    53169u, 11983139u, 66349161u, 52282411u, 21378304u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   106338u, 23966279u, 32698323u,  4564822u, 42756608u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   212676u, 47932558u, 65396646u,  9129644u, 85513216u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   425352u, 95865117u, 30793292u, 18259289u, 71026432u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {   850705u, 91730234u, 61586584u, 36518579u, 42052864u }, 32 ),
       cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( {  1701411u, 83460469u, 23173168u, 73037158u, 84105728u }, 32 ),
    }};
 
    cpp_dec_float<Digits10, ExponentType, Allocator> t;
 
    if(p < -128L)
       default_ops::detail::pow_imp(t, cpp_dec_float<Digits10, ExponentType, Allocator>::half(), static_cast<unsigned long long>(-p), std::integral_constant<bool, false>());
    else if ((p >= -128L) && (p <= 127L))
       t = local_pow2_data[std::size_t(p + 128)];
    else
       default_ops::detail::pow_imp(t, cpp_dec_float<Digits10, ExponentType, Allocator>::two(), static_cast<unsigned long long>(p), std::integral_constant<bool, false>());
 
    return t;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
 {
    result += o;
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
 {
    result -= o;
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
 {
    result *= o;
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
 {
    result /= o;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o)
 {
    result.add_unsigned_long_long(o);
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o)
 {
    result.sub_unsigned_long_long(o);
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o)
 {
    result.mul_unsigned_long_long(o);
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o)
 {
    result.div_unsigned_long_long(o);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o)
 {
    if (o < 0)
       result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
    else
    {
       using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type;
 
       result.add_unsigned_long_long(static_cast<local_ulonglong_type>(o));
    }
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o)
 {
    if (o < 0)
       result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
    else
    {
       using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type;
 
       result.sub_unsigned_long_long(static_cast<local_ulonglong_type>(o));
    }
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o)
 {
    if (o < 0)
    {
       result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
       result.negate();
    }
    else
    {
       using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type;
 
       result.mul_unsigned_long_long(static_cast<local_ulonglong_type>(o));
    }
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o)
 {
    if (o < 0)
    {
       result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
       result.negate();
    }
    else
    {
       using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type;
 
       result.div_unsigned_long_long(static_cast<local_ulonglong_type>(o));
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(unsigned long long* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_unsigned_long_long();
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(long long* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_signed_long_long();
 }
 #ifdef BOOST_HAS_INT128
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(uint128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_unsigned_int128();
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(int128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_signed_int128();
 }
 #endif
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(long double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_long_double();
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = val.extract_double();
 }
 #if defined(BOOST_HAS_FLOAT128)
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_convert_to(float128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    *result = float128_procs::strtoflt128(val.str(0, std::ios_base::scientific).c_str(), nullptr);
 }
 #endif
 
 //
 // Non member function support:
 //
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    if ((x.isinf)())
       return FP_INFINITE;
    if ((x.isnan)())
       return FP_NAN;
    if (x.iszero())
       return FP_ZERO;
    return FP_NORMAL;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    result = x;
    if (x.isneg())
       result.negate();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    result = x;
    if (x.isneg())
       result.negate();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    result = x;
    result.calculate_sqrt();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    result = x;
    if (!(x.isfinite)() || x.isint())
    {
       if ((x.isnan)())
          errno = EDOM;
       return;
    }
 
    if (x.isneg())
       result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one();
    result = result.extract_integer_part();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    result = x;
    if (!(x.isfinite)() || x.isint())
    {
       if ((x.isnan)())
          errno = EDOM;
       return;
    }
 
    if (!x.isneg())
       result += cpp_dec_float<Digits10, ExponentType, Allocator>::one();
    result = result.extract_integer_part();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
 {
    if (x.isint() || !(x.isfinite)())
    {
       result = x;
       if ((x.isnan)())
          errno = EDOM;
       return;
    }
    result = x.extract_integer_part();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    if (val.iszero())
       return (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::min)();
    if ((val.isinf)())
       return INT_MAX;
    if ((val.isnan)())
 #ifdef FP_ILOGBNAN
       return FP_ILOGBNAN;
 #else
       return INT_MAX;
 #endif
    // Set result, to the exponent of val:
    return val.order();
 }
 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
 inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_)
 {
    using default_ops::eval_multiply;
    const typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type e = static_cast<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>(e_);
    cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e);
    eval_multiply(result, val, t);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
 inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e)
 {
    const long long the_exp = static_cast<long long>(e);
 
    if ((the_exp > (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::max)()) || (the_exp < (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::min)()))
       BOOST_MP_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range.")));
 
    result = x;
 
    if ((the_exp > static_cast<long long>(-std::numeric_limits<long long>::digits)) && (the_exp < static_cast<long long>(0)))
       result.div_unsigned_long_long(1ULL << static_cast<long long>(-the_exp));
    else if ((the_exp < static_cast<long long>(std::numeric_limits<long long>::digits)) && (the_exp > static_cast<long long>(0)))
       result.mul_unsigned_long_long(1ULL << the_exp);
    else if (the_exp != static_cast<long long>(0))
    {
       if ((the_exp < cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp / 2) && (x.order() > 0))
       {
          long long half_exp = e / 2;
          cpp_dec_float<Digits10, ExponentType, Allocator> t = cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(half_exp);
          result *= t;
          if (2 * half_exp != e)
             t *= 2;
          result *= t;
       }
       else
          result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e);
    }
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e)
 {
    result = x;
 
    if (result.iszero() || (result.isinf)() || (result.isnan)())
    {
       *e = 0;
       return;
    }
 
    if (result.isneg())
       result.negate();
 
    typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type t = result.order();
    BOOST_MP_USING_ABS
    if (abs(t) < ((std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::max)() / 1000))
    {
       t *= 1000;
       t /= 301;
    }
    else
    {
       t /= 301;
       t *= 1000;
    }
 
    result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
 
    if (result.iszero() || (result.isinf)() || (result.isnan)())
    {
       // pow2 overflowed, slip the calculation up:
       result = x;
       if (result.isneg())
          result.negate();
       t /= 2;
       result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
    }
    BOOST_MP_USING_ABS
    if (abs(result.order()) > 5)
    {
       // If our first estimate doesn't get close enough then try recursion until we do:
       typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type e2;
       cpp_dec_float<Digits10, ExponentType, Allocator>                         r2;
       eval_frexp(r2, result, &e2);
       // overflow protection:
       if ((t > 0) && (e2 > 0) && (t > (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::max)() - e2))
          BOOST_MP_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
       if ((t < 0) && (e2 < 0) && (t < (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::min)() - e2))
          BOOST_MP_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
       t += e2;
       result = r2;
    }
 
    while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0)
    {
       result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
       ++t;
    }
    while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0)
    {
       result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
       --t;
    }
    *e = t;
    if (x.isneg())
       result.negate();
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline typename std::enable_if< !std::is_same<ExponentType, int>::value>::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e)
 {
    typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type t;
    eval_frexp(result, x, &t);
    if ((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)()))
       BOOST_MP_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int"));
    *e = static_cast<int>(t);
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    return val.iszero();
 }
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    return val.iszero() ? 0 : val.isneg() ? -1 : 1;
 }
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 inline std::size_t hash_value(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
 {
    return val.hash();
 }
 
 } // namespace backends
 
 namespace detail {
 
 template <unsigned Digits10, class ExponentType, class Allocator>
 struct transcendental_reduction_type<boost::multiprecision::backends::cpp_dec_float<Digits10, ExponentType, Allocator> >
 {
    //
    // The type used for trigonometric reduction needs 3 times the precision of the base type.
    // This is double the precision of the original type, plus the largest exponent supported.
    // As a practical measure the largest argument supported is 1/eps, as supporting larger
    // arguments requires the division of argument by PI/2 to also be done at higher precision,
    // otherwise the result (an integer) can not be represented exactly.
    // 
    // See ARGUMENT REDUCTION FOR HUGE ARGUMENTS. K C Ng.
    //
    using type = boost::multiprecision::backends::cpp_dec_float<Digits10 * 3, ExponentType, Allocator>;
 };
 
 } // namespace detail
 
 
 }} // namespace boost::multiprecision
 
 namespace std {
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >
 {
  public:
    static constexpr bool                    is_specialized    = true;
    static constexpr bool                    is_signed         = true;
    static constexpr bool                    is_integer        = false;
    static constexpr bool                    is_exact          = false;
    static constexpr bool                    is_bounded        = true;
    static constexpr bool                    is_modulo         = false;
    static constexpr bool                    is_iec559         = false;
    static constexpr int                     digits            = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
    static constexpr int                     digits10          = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
    static constexpr int                     max_digits10      = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_digits10;
    static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type min_exponent                = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp;   // Type differs from int.
    static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type min_exponent10              = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int.
    static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type max_exponent                = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp;   // Type differs from int.
    static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type max_exponent10              = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int.
    static constexpr int                     radix             = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
    static constexpr std::float_round_style  round_style       = std::round_indeterminate;
    static constexpr bool                    has_infinity      = true;
    static constexpr bool                    has_quiet_NaN     = true;
    static constexpr bool                    has_signaling_NaN = false;
    static constexpr std::float_denorm_style has_denorm        = std::denorm_absent;
    static constexpr bool                    has_denorm_loss   = false;
    static constexpr bool                    traps             = false;
    static constexpr bool                    tinyness_before   = false;
 
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>(min)() { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>(max)() { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> lowest() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> epsilon() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error() { return 0.5L; }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> infinity() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> quiet_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> signaling_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); }
    static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> denorm_min() { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); }
 };
 
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before;
 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
 constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style;
 
 } // namespace std
 
 #ifdef BOOST_MP_MATH_AVAILABLE
 namespace boost {
 namespace math {
 
 namespace policies {
 
 template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates>
 struct precision<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy>
 {
    // Define a local copy of cpp_dec_float_digits10 because it might differ
    // from the template parameter Digits10 for small or large digit counts.
    static constexpr std::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
 
    using precision_type = typename Policy::precision_type                           ;
    using digits_2 = digits2<static_cast<int>(((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL)>;
    using type = typename std::conditional<
        ((digits_2::value <= precision_type::value) || (Policy::precision_type::value <= 0)),
        // Default case, full precision for RealType:
        digits_2,
        // User customized precision:
        precision_type>::type;
 };
 
 }
 
 }} // namespace boost::math::policies
 #endif
 
 #ifdef BOOST_MSVC
 #pragma warning(pop)
 #endif
 
 #endif