[Boost-commit] svn:boost r75454 - sandbox/big_number/boost/multiprecision

Subject: [Boost-commit] svn:boost r75454 - sandbox/big_number/boost/multiprecision
From: john_at_[hidden]
Date: 2011-11-12 08:16:40

Author: johnmaddock
Date: 2011-11-12 08:16:39 EST (Sat, 12 Nov 2011)
New Revision: 75454
URL: http://svn.boost.org/trac/boost/changeset/75454

Log:
Remove dead file.
Removed:
   sandbox/big_number/boost/multiprecision/mp_float.hpp

Deleted: sandbox/big_number/boost/multiprecision/mp_float.hpp
==============================================================================
--- sandbox/big_number/boost/multiprecision/mp_float.hpp	2011-11-12 08:16:39 EST (Sat, 12 Nov 2011)
+++ (empty file)
@@ -1,2726 +0,0 @@
-///////////////////////////////////////////////////////////////////////////////
-//  Copyright Christopher Kormanyos 2002 - 2011.
-//  Copyright 2011 John Maddock. Distributed under the Boost
-//  Software License, Version 1.0. (See accompanying file
-//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-//
-// 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
-//
-
-#ifndef BOOST_MP_EFX_BACKEND_HPP
-#define BOOST_MP_EFX_BACKEND_HPP
-
-#include <boost/cstdint.hpp>
-#include <boost/array.hpp>
-#include <boost/multiprecision/mp_number.hpp>
-
-//
-// Headers required for Boost.Math integration:
-//
-#include <boost/math/policies/policy.hpp>
-
-namespace boost{
-namespace multiprecision{
-
-template <unsigned Digits10>
-class cpp_float
-{
-public:
-   typedef mpl::list<long long>                    signed_types;
-   typedef mpl::list<unsigned long long>           unsigned_types;
-   typedef mpl::list<long double>                  real_types;
-   typedef boost::int64_t                          exponent_type;
-
-
-   static const boost::int32_t mp_radix        = 10;
-   static const boost::int32_t cpp_float_digits = Digits10;
-
-   static const boost::int32_t cpp_float_digits10_setting = Digits10;
-   static const boost::int32_t cpp_float_digits10_limit   = boost::integer_traits<boost::int32_t>::const_max;
-   static const boost::int32_t cpp_float_digits10         = ((cpp_float_digits10_setting < static_cast<boost::int32_t>(30)) ? static_cast<boost::int32_t>(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting));
-   static const boost::int32_t cpp_float_digits10_extra   = static_cast<boost::int32_t>(((static_cast<boost::int64_t>(cpp_float_digits10) * 15LL) + 50LL) / 100LL);
-   static const boost::int32_t cpp_float_max_digits10     = static_cast<boost::int32_t>(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast<boost::int32_t>(5)) ? static_cast<boost::int32_t>(5) : ((cpp_float_digits10_extra > static_cast<boost::int32_t>(30)) ? static_cast<boost::int32_t>(30) : cpp_float_digits10_extra)));
-   static const boost::int64_t cpp_float_max_exp   = static_cast<boost::int64_t>(+9223372036854775795LL);
-   static const boost::int64_t cpp_float_min_exp   = static_cast<boost::int64_t>(-9223372036854775795LL);
-   static const boost::int64_t cpp_float_max_exp10 = static_cast<boost::int64_t>(+3063937869882635616LL); // Approx. [cpp_float_max_exp / log10(2)], also an even multiple of 8
-   static const boost::int64_t cpp_float_min_exp10 = static_cast<boost::int64_t>(-3063937869882635616LL);
-   static const boost::int32_t mp_elem_digits10   = static_cast<boost::int32_t>(8);
-
-private:
-   static const boost::int32_t cpp_float_digits10_num_base = static_cast<boost::int32_t>((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0));
-   static const boost::int32_t mp_elem_number       = static_cast<boost::int32_t>(cpp_float_digits10_num_base + 2);
-   static const boost::int32_t mp_elem_mask = static_cast<boost::int32_t>(100000000);
-
-   typedef enum enum_fpclass
-   {
-      mp_finite,
-      mp_inf,
-      mp_NaN
-   }
-   t_fpclass;
-
-   typedef boost::array<boost::uint32_t, mp_elem_number> array_type;
-
-   array_type          data;
-   boost::int64_t      exp;
-   bool                neg;
-   t_fpclass           fpclass;
-   boost::int32_t      prec_elem;
-
-   //
-   // Special values constructor:
-   //
-   cpp_float(t_fpclass c) : 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (c),
-      prec_elem(mp_elem_number) { }
-
-      //
-      // Static data initializer:
-      //
-      struct initializer
-      {
-         initializer()
-         {
-            cpp_float<Digits10>::nan();
-            cpp_float<Digits10>::inf();
-            (cpp_float<Digits10>::min)();
-            (cpp_float<Digits10>::max)();
-            cpp_float<Digits10>::zero();
-            cpp_float<Digits10>::one();
-            cpp_float<Digits10>::two();
-            cpp_float<Digits10>::half();
-            cpp_float<Digits10>::double_min();
-            cpp_float<Digits10>::double_max();
-            cpp_float<Digits10>::long_double_max();
-            cpp_float<Digits10>::long_double_min();
-            cpp_float<Digits10>::long_long_max();
-            cpp_float<Digits10>::long_long_min();
-            cpp_float<Digits10>::ulong_long_max();
-            cpp_float<Digits10>::eps();
-            cpp_float<Digits10>::pow2(0);
-         }
-         void do_nothing(){}
-      };
-
-      static initializer init;
-
-public:
-   // Constructors
-   cpp_float() : 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (mp_finite),
-      prec_elem(mp_elem_number) { }
-
-   cpp_float(const char* s) : 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (mp_finite),
-      prec_elem(mp_elem_number) 
-      {
-         *this = s;
-      }
-
-   template<class I>
-   cpp_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) : 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (mp_finite),
-      prec_elem(mp_elem_number) 
-      {
-         from_unsigned_long_long(i);
-      }
-
-   template <class I>
-   cpp_float(I i, typename enable_if<is_signed<I> >::type* = 0) : 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (mp_finite),
-      prec_elem(mp_elem_number) 
-      {
-         if(i < 0)
-         {
-            from_unsigned_long_long(-i);
-            negate();
-         }
-         else
-            from_unsigned_long_long(i);
-      }
-
-   cpp_float(const cpp_float& f) : 
-      data     (f.data),
-      exp      (f.exp),
-      neg      (f.neg),
-      fpclass  (f.fpclass),
-      prec_elem(f.prec_elem) { }
-
-   template <class F>
-   cpp_float(const F val, typename enable_if<is_floating_point<F> >::type* = 0): 
-      data(),
-      exp      (static_cast<boost::int64_t>(0)),
-      neg      (false),
-      fpclass  (mp_finite),
-      prec_elem(mp_elem_number) 
-   {
-      *this = val;
-   }
-
-   cpp_float(const double val, long long exponent);
-
-   // Specific special values.
-   static const cpp_float& nan()
-   {
-      static const cpp_float val(mp_NaN);
-      init.do_nothing();
-      return val;
-   }
-   static const cpp_float& inf()
-   {
-      static const cpp_float val(mp_inf);
-      init.do_nothing();
-      return val;
-   }
-   static const cpp_float& (max)()
-   {
-      init.do_nothing();
-      static bool init = false;
-      static const std::string str_max =   std::string("9." + std::string(static_cast<std::size_t>(cpp_float_max_digits10), static_cast<char>('9')))
-         + std::string("e+" + boost::lexical_cast<std::string>(cpp_float_max_exp10));
-      static cpp_float val_max;
-      if(!init)
-      {
-         init = true;
-         val_max = str_max.c_str();
-      }
-      return val_max;
-   }
-
-   static const cpp_float& (min)()
-   {
-      init.do_nothing();
-      static bool init = false;
-      static cpp_float val_min;
-      if(!init)
-      {
-         init = true;
-         val_min = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_float_min_exp10)).c_str();
-      }
-      return val_min;
-   }
-   static const cpp_float& zero()
-   {
-      init.do_nothing();
-      static cpp_float val(static_cast<unsigned long long>(0u));
-      return val;
-   }
-   static const cpp_float& one()
-   {
-      init.do_nothing();
-      static cpp_float val(static_cast<unsigned long long>(1u));
-      return val;
-   }
-   static const cpp_float& two()
-   {
-      init.do_nothing();
-      static cpp_float val(static_cast<unsigned long long>(2u));
-      return val;
-   }
-   static const cpp_float& half()
-   {
-      init.do_nothing();
-      static cpp_float val(0.5L);
-      return val;
-   }
-   static const cpp_float& double_min()
-   {
-      init.do_nothing();
-      static cpp_float val(static_cast<long double>((std::numeric_limits<double>::min)()));
-      return val;
-   }
-   static const cpp_float& double_max()
-   {
-      init.do_nothing();
-      static cpp_float val(static_cast<long double>((std::numeric_limits<double>::max)()));
-      return val;
-   }
-   static const cpp_float& long_double_min()
-   {
-      init.do_nothing();
-      static cpp_float val((std::numeric_limits<long double>::min)());
-      return val;
-   }
-   static const cpp_float& long_double_max()
-   {
-      init.do_nothing();
-      static cpp_float val((std::numeric_limits<long double>::max)());
-      return val;
-   }
-   static const cpp_float& long_long_max()
-   {
-      init.do_nothing();
-      static cpp_float val((std::numeric_limits<long long>::max)());
-      return val;
-   }
-   static const cpp_float& long_long_min()
-   {
-      init.do_nothing();
-      static cpp_float val((std::numeric_limits<long long>::min)());
-      return val;
-   }
-   static const cpp_float& ulong_long_max()
-   {
-      init.do_nothing();
-      static cpp_float val((std::numeric_limits<unsigned long long>::max)());
-      return val;
-   }
-   static const cpp_float& eps()
-   {
-      init.do_nothing();
-      static cpp_float val(1.0, 1 - (int)Digits10);
-      return val;
-   }
-
-   // Basic operations.
-   cpp_float& operator= (const cpp_float& v)
-   {
-      data = v.data;
-      exp = v.exp;
-      neg = v.neg;
-      fpclass = v.fpclass;
-      prec_elem = v.prec_elem;
-      return *this;
-   }
-   cpp_float& operator= (long long v)
-   {
-      if(v < 0)
-      {
-         from_unsigned_long_long(-v);
-         negate();
-      }
-      else
-         from_unsigned_long_long(v);
-      return *this;
-   }
-   cpp_float& operator= (unsigned long long v)
-   {
-      from_unsigned_long_long(v);
-      return *this;
-   }
-   cpp_float& operator= (long double v);
-   cpp_float& operator= (const char* v)
-   {
-      rd_string(v);
-      return *this;
-   }
-
-   cpp_float& operator+=(const cpp_float& v);
-   cpp_float& operator-=(const cpp_float& v);
-   cpp_float& operator*=(const cpp_float& v);
-   cpp_float& operator/=(const cpp_float& v);
-   
-   cpp_float& add_unsigned_long_long(const unsigned long long n)
-   {
-      cpp_float t;
-      t.from_unsigned_long_long(n);
-      return *this += t;
-   }
-   cpp_float& sub_unsigned_long_long(const unsigned long long n)
-   {
-      cpp_float t;
-      t.from_unsigned_long_long(n);
-      return *this -= t;
-   }
-   cpp_float& mul_unsigned_long_long(const unsigned long long n);
-   cpp_float& div_unsigned_long_long(const unsigned long long n);
-
-   // Elementary primitives.
-   cpp_float& calculate_inv (void);
-   cpp_float& calculate_sqrt(void);
-   void negate() 
-   { 
-      if(!iszero())
-         neg = !neg;
-   }
-
-   // Comparison functions
-   bool isnan   (void) const { return (fpclass == mp_NaN); }
-   bool isinf   (void) const { return (fpclass == mp_inf); }
-   bool isfinite(void) const { return (fpclass == mp_finite); }
-
-   bool iszero (void) const
-   {
-      return ((fpclass == mp_finite) && (data[0u] == 0u));
-   }
-   bool isone  (void) const;
-   bool isint  (void) const;
-   bool isneg  (void) const { return neg; }
-
-   // Operators pre-increment and pre-decrement
-   cpp_float& operator++(void)
-   {
-      return *this += one();
-   }
-   cpp_float& operator--(void)
-   {
-      return *this -= one();
-   }
-
-   std::string str(unsigned digits, bool scientific)const;
-
-   int compare(const cpp_float& v)const;
-   template <class V>
-   int compare(const V& v)const
-   {
-      cpp_float<Digits10> t;
-      t = v;
-      return compare(t);
-   }
-
-   void swap(cpp_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            (void) const;
-   long double        extract_long_double       (void) const;
-   signed long long   extract_signed_long_long  (void) const;
-   unsigned long long extract_unsigned_long_long(void) const;
-   void               extract_parts             (double& mantissa, boost::int64_t& exponent) const;
-   cpp_float           extract_integer_part      (void) const;
-   void precision(const boost::int32_t prec_digits)
-   {
-      if(prec_digits >= cpp_float_digits10)
-      {
-         prec_elem = mp_elem_number;
-      }
-      else
-      {
-         const boost::int32_t elems = static_cast<boost::int32_t>(  static_cast<boost::int32_t>( (prec_digits + (mp_elem_digits10 / 2)) / mp_elem_digits10)
-            + static_cast<boost::int32_t>(((prec_digits %  mp_elem_digits10) != 0) ? 1 : 0));
-
-         prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2)));
-      }
-   }
-   static cpp_float pow2(long long i);
-   long long order()const
-   {
-      const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast<boost::uint32_t>(0u)));
-      //
-      // Binary search to find the order of the leading term:
-      //
-      boost::uint32_t 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<boost::int64_t>(0)
-         : static_cast<boost::int64_t>(exp + prefix));
-   }
-
-private:
-   static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); }
-   static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(cpp_float::mp_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);
-
-   int cmp_data(const array_type& vd) const;
-
-   static void mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p);
-   static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
-   static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
-
-   bool rd_string(const char* const s);
-};
-
-template <unsigned Digits10>
-typename cpp_float<Digits10>::initializer cpp_float<Digits10>::init;
-
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::mp_radix;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits10_setting;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits10_limit;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits10;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits10_extra;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_max_digits10;
-template <unsigned Digits10>
-const boost::int64_t cpp_float<Digits10>::cpp_float_max_exp;
-template <unsigned Digits10>
-const boost::int64_t cpp_float<Digits10>::cpp_float_min_exp;
-template <unsigned Digits10>
-const boost::int64_t cpp_float<Digits10>::cpp_float_max_exp10;
-template <unsigned Digits10>
-const boost::int64_t cpp_float<Digits10>::cpp_float_min_exp10;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::mp_elem_digits10;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::cpp_float_digits10_num_base;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::mp_elem_number;
-template <unsigned Digits10>
-const boost::int32_t cpp_float<Digits10>::mp_elem_mask;
-
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::operator+=(const cpp_float<Digits10>& v)
-{
-   if(isnan())
-   {
-      return *this;
-   }
-
-   if(isinf())
-   {
-      if(v.isinf() && (isneg() != v.isneg()))
-      {
-         *this = nan();
-      }
-      return *this;
-   }
-
-   if(iszero())
-   {
-      return operator=(v);
-   }
-
-   // Get the offset for the add/sub operation.
-   static const boost::int64_t max_delta_exp = static_cast<boost::int64_t>((mp_elem_number - 1) * mp_elem_digits10);
-
-   const boost::int64_t ofs_exp = static_cast<boost::int64_t>(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::iterator       p_u    =   data.begin();
-   typename array_type::const_iterator p_v    = v.data.begin();
-   bool                       b_copy = false;
-   const boost::int32_t       ofs    = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / mp_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<boost::int32_t>(0))
-      {
-         std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs));
-         std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u));
-         p_v = n_data.begin();
-      }
-      else
-      {
-         std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs));
-         std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u));
-         p_u = n_data.begin();
-         b_copy = true;
-      }
-
-      // Addition algorithm
-      boost::uint32_t carry = static_cast<boost::uint32_t>(0u);
-
-      for(boost::int32_t j = static_cast<boost::int32_t>(mp_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--)
-      {
-         boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry);
-         carry    = t / static_cast<boost::uint32_t>(mp_elem_mask);
-         p_u[j]   = static_cast<boost::uint32_t>(t - static_cast<boost::uint32_t>(carry * static_cast<boost::uint32_t>(mp_elem_mask)));
-      }
-
-      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<boost::uint32_t>(0u))
-      {
-         std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end());
-         data[0] = carry;
-         exp += static_cast<boost::int64_t>(mp_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<boost::int32_t>(0))
-         || (   (ofs == static_cast<boost::int32_t>(0))
-         && (cmp_data(v.data) > static_cast<boost::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.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs));
-         std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u));
-         p_v = n_data.begin();
-      }
-      else
-      {
-         if(ofs != static_cast<boost::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.begin(), data.end() - static_cast<size_t>(-ofs), data.end());
-            std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::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.begin();
-         p_v    = data.begin();
-         b_copy = true;
-      }
-
-      boost::int32_t j;
-
-      // Subtraction algorithm
-      boost::int32_t borrow = static_cast<boost::int32_t>(0);
-
-      for(j = static_cast<boost::int32_t>(mp_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--)
-      {
-         boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>(  static_cast<boost::int32_t>(p_u[j])
-            - static_cast<boost::int32_t>(p_v[j])) - borrow);
-
-         // Underflow? Borrow?
-         if(t < static_cast<boost::int32_t>(0))
-         {
-            // Yes, underflow and borrow
-            t     += static_cast<boost::int32_t>(mp_elem_mask);
-            borrow = static_cast<boost::int32_t>(1);
-         }
-         else
-         {
-            borrow = static_cast<boost::int32_t>(0);
-         }
-
-         p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(mp_elem_mask));
-      }
-
-      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<boost::int64_t>(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::size_t>(sj), data.end(), data.begin());
-            std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u));
-
-            exp -= static_cast<boost::int64_t>(sj * static_cast<std::size_t>(mp_elem_digits10));
-         }
-      }
-   }
-
-   // Check for underflow.
-   if(iszero()) 
-   { 
-      return *this = zero();
-   }
-
-   bool overflow = exp >= cpp_float_max_exp;
-   if(exp == cpp_float_max_exp)
-   {
-      // Check to see if we really truely have an overflow or not...
-      if(isneg())
-      {
-         cpp_float t(*this);
-         t.negate();
-         overflow = t.compare((max)()) > 0;
-      }
-      else
-      {
-         overflow = compare((max)()) > 0;
-      }
-   }
-
-   // Check for overflow.
-   if(overflow)
-   {
-      const bool b_result_is_neg = neg;
-
-      *this = inf();
-      if(b_result_is_neg)
-         negate();
-   }
-
-   return *this;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::operator-=(const cpp_float<Digits10>& v)
-{
-   // Use *this - v = -(-*this + v).
-   negate();
-   *this += v;
-   negate();
-   return *this;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::operator*=(const cpp_float<Digits10>& 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 overflow or underflow.
-   const bool u_exp_is_neg =   (exp < static_cast<boost::int64_t>(0));
-   const bool v_exp_is_neg = (v.exp < static_cast<boost::int64_t>(0));
-
-   if(u_exp_is_neg == v_exp_is_neg)
-   {
-      // Get the unsigned base-10 exponents of *this and v and...
-      const boost::int64_t u_exp = ((!u_exp_is_neg) ?   exp : static_cast<boost::int64_t>(  -exp));
-      const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast<boost::int64_t>(-v.exp));
-
-      // Check the range of the upcoming multiplication.
-      const bool b_result_is_out_of_range = (v_exp >= static_cast<boost::int64_t>(cpp_float_max_exp10 - u_exp));
-
-      if(b_result_is_out_of_range)
-      {
-         if(u_exp_is_neg)
-         {
-            *this = zero();
-         }
-         else
-         {
-            *this = inf();
-            if(b_result_is_neg)
-               negate();
-         }
-         return *this;
-      }
-   }
-
-   // Set the exponent of the result.
-   exp += v.exp;
-
-   boost::array<boost::uint32_t, static_cast<std::size_t>(mp_elem_number + static_cast<boost::int32_t>(1))> w = {{ 0u }};
-
-   mul_loop_uv(data.data(), v.data.data(), w.data(), (std::min)(prec_elem, v.prec_elem));
-
-   // Copy the multiplication data into the result.
-   // Shift the result and adjust the exponent if necessary.
-   if(w[static_cast<std::size_t>(0u)] != static_cast<boost::uint32_t>(0u))
-   {
-      exp += static_cast<boost::int64_t>(mp_elem_digits10);
-
-      std::copy(w.begin(), w.end() - 1u, data.begin());
-   }
-   else
-   {
-      std::copy(w.begin() + 1u, w.end(), data.begin());
-   }
-
-   // Set the sign of the result.
-   neg = b_result_is_neg;
-
-   return *this;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::operator/=(const cpp_float<Digits10>& v)
-{
-   const bool u_and_v_are_finite_and_identical = (   isfinite()
-      && (fpclass == v.fpclass)
-      && (exp     == v.exp)
-      && (cmp_data(v.data) == static_cast<boost::int32_t>(0)));
-
-   if(u_and_v_are_finite_and_identical)
-   {
-      *this = one();
-      if(neg != v.neg)
-         negate();
-      return *this;
-   }
-   else
-   {
-      if(iszero())
-      {
-         if(v.isnan() || v.iszero())
-         {
-            return *this = v;
-         }
-         return *this;
-      }
-      cpp_float t(v);
-      t.calculate_inv();
-      return operator*=(t);
-   }
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::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<boost::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>(mp_elem_mask))
-   {
-      neg = b_neg;
-      cpp_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 boost::uint32_t nn = static_cast<boost::uint32_t>(n);
-   const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem);
-
-   // Handle the carry and adjust the exponent.
-   if(carry != static_cast<boost::uint32_t>(0u))
-   {
-      exp += static_cast<boost::int64_t>(mp_elem_digits10);
-
-      // Shift the result of the multiplication one element to the right.
-      std::copy_backward(data.begin(),
-         data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
-         data.begin() + static_cast<std::size_t>(prec_elem));
-
-      data.front() = static_cast<boost::uint32_t>(carry);
-   }
-
-   bool overflow = exp >= cpp_float_max_exp;
-   if(exp == cpp_float_max_exp)
-   {
-      // Check to see if we really truely have an overflow or not...
-      if(isneg())
-      {
-         cpp_float t(*this);
-         t.negate();
-         overflow = t.compare((max)()) > 0;
-      }
-      else
-      {
-         overflow = compare((max)()) > 0;
-      }
-   }
-
-   if(overflow)
-   {
-      *this = inf();
-      if(b_neg)
-         negate();
-      return *this;
-   }
-
-   // Set the sign.
-   neg = b_neg;
-
-   return *this;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::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>(mp_elem_mask))
-   {
-      neg = b_neg;
-      cpp_float t;
-      t = n;
-      return operator/=(t);
-   }
-
-   const boost::uint32_t nn = static_cast<boost::uint32_t>(n);
-
-   if(nn > static_cast<boost::uint32_t>(1u))
-   {
-      // Do the division loop.
-      const boost::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<boost::uint32_t>(0u))
-      {
-         // Adjust the exponent
-         exp -= static_cast<boost::int64_t>(mp_elem_digits10);
-
-         // Shift result of the division one element to the left.
-         std::copy(data.begin() + static_cast<std::size_t>(1u),
-            data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
-            data.begin());
-
-         data[prec_elem - static_cast<boost::int32_t>(1)] = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(prev * static_cast<boost::uint64_t>(mp_elem_mask)) / nn);
-      }
-   }
-
-   // Check for underflow.
-   if(iszero()) 
-   {
-      return *this = zero();
-   }
-
-   // Set the sign of the result.
-   neg = b_neg;
-
-   return *this; 
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::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_float<Digits10> x(*this);
-
-   // Generate the initial estimate using division.
-   // Extract the mantissa and exponent for a "manual"
-   // computation of the estimate.
-   double dd;
-   boost::int64_t  ne;
-   x.extract_parts(dd, ne);
-
-   // Do the inverse estimate using double precision estimates of mantissa and exponent.
-   operator=(cpp_float<Digits10>(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.
-
-   static const boost::int32_t double_digits10_minus_one = std::numeric_limits<double>::digits10 - 1;
-
-   for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast<boost::int32_t>(2))
-   {
-      // Adjust precision of the terms.
-      precision(static_cast<boost::int32_t>(digits * static_cast<boost::int32_t>(2)));
-      x.precision(static_cast<boost::int32_t>(digits * static_cast<boost::int32_t>(2)));
-
-      // Next iteration.
-      cpp_float t(*this);
-      t *= x;
-      t -= two();
-      t.negate();
-      *this *= t;
-   }
-
-   neg = b_neg;
-
-   prec_elem = mp_elem_number;
-
-   return *this;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::calculate_sqrt(void)
-{
-   // Compute the square root of *this.
-
-   if(isneg() || (!isfinite()))
-   {
-      *this = nan();
-      return *this;
-   }
-
-   if(iszero() || isone())
-   {
-      return *this;
-   }
-
-   // Save the original *this.
-   cpp_float<Digits10> x(*this);
-
-   // Generate the initial estimate using division.
-   // Extract the mantissa and exponent for a "manual"
-   // computation of the estimate.
-   double dd;
-   boost::int64_t  ne;
-   extract_parts(dd, ne);
-
-   // Force the exponent to be an even multiple of two.
-   if((ne % static_cast<boost::int64_t>(2)) != static_cast<boost::int64_t>(0))
-   {
-      ++ne;
-      dd /= 10.0;
-   }
-
-   // Setup the iteration.
-   // Estimate the square root using simple manipulations.
-   const double sqd = std::sqrt(dd);
-
-   *this = cpp_float<Digits10>(sqd, static_cast<boost::int64_t>(ne / static_cast<boost::int64_t>(2)));
-
-   // Estimate 1.0 / (2.0 * x0) using simple manipulations.
-   cpp_float<Digits10> vi(0.5 / sqd, static_cast<boost::int64_t>(-ne / static_cast<boost::int64_t>(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 references:
-   // http://www.jjj.de/pibook/pibook.html
-   // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846
-
-   static const boost::uint32_t double_digits10_minus_one = static_cast<boost::int32_t>(static_cast<boost::int32_t>(Digits10) - static_cast<boost::int32_t>(1));
-
-   for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= 2u)
-   {
-      // Adjust precision of the terms.
-      precision(digits * 2);
-      vi.precision(digits * 2);
-
-      // Next iteration of vi
-      cpp_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 = mp_elem_number;
-
-   return *this;
-}
-
-template <unsigned Digits10>
-int cpp_float<Digits10>::cmp_data(const array_type& vd) const
-{
-   // Compare the data of *this with those of v.
-   //         Return +1 for *this > v
-   //                 0 for *this = v
-   //                -1 for *this < v
-
-   const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin());
-
-   const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end()));
-
-   if(is_equal)
-   {
-      return 0;
-   }
-   else
-   {
-      return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1);
-   }
-}
-
-template <unsigned Digits10>
-int cpp_float<Digits10>::compare(const cpp_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_cmp_exp = ((exp < v.exp) ? 1 : -1);
-
-         return (neg ? val_cmp_exp : -val_cmp_exp);
-      }
-      else
-      {
-         // The signs are the same and the exponents are the same.
-         // Compare the data.
-         const int val_cmp_data = cmp_data(v.data);
-
-         return ((!neg) ? val_cmp_data : -val_cmp_data);
-      }
-   }
-}
-
-template <unsigned Digits10>
-bool cpp_float<Digits10>::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<boost::uint32_t>(1u)) && (exp == static_cast<boost::int64_t>(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<boost::uint32_t>(mp_elem_mask - 1)) && (exp == static_cast<boost::int64_t>(-mp_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>
-bool cpp_float<Digits10>::isint() const
-{
-   if(fpclass != mp_finite) { return false; }
-
-   if(iszero()) { return true; }
-
-   if(exp < static_cast<boost::int64_t>(0)) { return false; } // |*this| < 1.
-
-   const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / mp_elem_digits10) + 1u;
-
-   if(offset_decimal_part >= static_cast<typename array_type::size_type>(mp_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() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate);
-
-   return (it_non_zero == data.end());
-}
-
-template <unsigned Digits10>
-void cpp_float<Digits10>::extract_parts(double& mantissa, boost::int64_t& exponent) const
-{
-   // Extract the approximate parts mantissa and base-10 exponent from the input cpp_float<Digits10> value x.
-
-   // Extracts the mantissa and exponent.
-   exponent = exp;
-
-   boost::uint32_t p10  = static_cast<boost::uint32_t>(1u);
-   boost::uint32_t test = data[0u];
-
-   for(;;)
-   {
-      test /= static_cast<boost::uint32_t>(10u);
-
-      if(test == static_cast<boost::uint32_t>(0u))
-      {
-         break;
-      }
-
-      p10 *= static_cast<boost::uint32_t>(10u);
-      ++exponent;
-   }
-
-   mantissa =     static_cast<double>(data[0])
-      +  (static_cast<double>(data[1]) / static_cast<double>(mp_elem_mask))
-      + ((static_cast<double>(data[2]) / static_cast<double>(mp_elem_mask)) / static_cast<double>(mp_elem_mask));
-
-   mantissa /= static_cast<double>(p10);
-
-   if(neg) { mantissa = -mantissa; }
-}
-
-template <unsigned Digits10>
-double cpp_float<Digits10>::extract_double(void) const
-{
-   // Returns the double conversion of a cpp_float<Digits10>.
-
-   // Check for non-normal cpp_float<Digits10>.
-   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_float<Digits10> xx(*this);
-   if(xx.isneg())
-      xx.negate();
-
-   // Check for zero cpp_float<Digits10>.
-   if(iszero() || (xx.compare(double_min()) < 0))
-   {
-      return 0.0;
-   }
-
-   // Check if cpp_float<Digits10> 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 << str(std::numeric_limits<double>::digits10 + (2 + 1), true);
-
-   double d;
-   ss >> d;
-
-   return d;
-}
-
-template <unsigned Digits10>
-long double cpp_float<Digits10>::extract_long_double(void) const
-{
-   // Returns the long double conversion of a cpp_float<Digits10>.
-
-   // Check for non-normal cpp_float<Digits10>.
-   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_float<Digits10> xx(*this);
-   if(xx.isneg())
-      xx.negate();
-
-   // Check for zero cpp_float<Digits10>.
-   if(iszero() || (xx.compare(long_double_min()) < 0))
-   {
-      return static_cast<long double>(0.0);
-   }
-
-   // Check if cpp_float<Digits10> 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 << str(std::numeric_limits<long double>::digits10 + (2 + 1), true);
-
-   long double ld;
-   ss >> ld;
-
-   return ld;
-}
-
-template <unsigned Digits10>
-signed long long cpp_float<Digits10>::extract_signed_long_long(void) const
-{
-   // Extracts a signed long long from *this.
-   // If (x > maximum of signed long long) or (x < minimum of signed long long),
-   // then the maximum or minimum of signed long long is returned accordingly.
-
-   if(exp < static_cast<boost::int64_t>(0))
-   {
-      return static_cast<signed long long>(0);
-   }
-
-   const bool b_neg = isneg();
-
-   unsigned long long val;
-
-   if((!b_neg) && (compare(long_long_max()) > 0))
-   {
-      return (std::numeric_limits<signed long long>::max)();
-   }
-   else if(b_neg &&  (compare(long_long_min()) < 0))
-   {
-      return (std::numeric_limits<signed long long>::min)();
-   }
-   else
-   {
-      // Extract the data into an unsigned long long value.
-      cpp_float<Digits10> xn(extract_integer_part());
-      if(xn.isneg())
-         xn.negate();
-
-      val = static_cast<unsigned long long>(xn.data[0]);
-
-      const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / mp_elem_digits10), static_cast<boost::int32_t>(mp_elem_number - static_cast<boost::int32_t>(1)));
-
-      for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
-      {
-         val *= static_cast<unsigned long long>(mp_elem_mask);
-         val += static_cast<unsigned long long>(xn.data[i]);
-      }
-   }
-
-   return ((!b_neg) ? static_cast<signed long long>(val) : static_cast<signed long long>(-static_cast<signed long long>(val)));
-}
-
-template <unsigned Digits10>
-unsigned long long cpp_float<Digits10>::extract_unsigned_long_long(void) 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 signed long long extracted value is returned.
-
-   if(isneg())
-   {
-      return static_cast<unsigned long long>(extract_signed_long_long());
-   }
-
-   if(exp < static_cast<boost::int64_t>(0))
-   {
-      return static_cast<unsigned long long>(0u);
-   }
-
-   const cpp_float<Digits10> 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 boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / mp_elem_digits10), static_cast<boost::int32_t>(mp_elem_number - static_cast<boost::int32_t>(1)));
-
-      for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
-      {
-         val *= static_cast<unsigned long long>(mp_elem_mask);
-         val += static_cast<unsigned long long>(xn.data[i]);
-      }
-   }
-
-   return val;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10> cpp_float<Digits10>::extract_integer_part(void) const
-{
-   // Compute the signed integer part of x.
-
-   if(!isfinite())
-   {
-      return *this;
-   }
-
-   if(exp < static_cast<boost::int64_t>(0))
-   {
-      // The absolute value of the number is smaller than 1.
-      // Thus the integer part is zero.
-      return zero();
-   }
-   else if(exp >= Digits10 - 1)
-   {
-      // The number is too large to resolve the integer part.
-      // Thus it is already a pure integer part.
-      return *this;
-   }
-
-   // Make a local copy.
-   cpp_float<Digits10> x = *this;
-
-   // Clear out the decimal portion
-   const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(mp_elem_digits10)) + 1u;
-   const size_t last_clear  =  static_cast<size_t>(mp_elem_number);
-
-   std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u));
-
-   return x;
-}
-
-template <unsigned Digits10>
-std::string cpp_float<Digits10>::str(std::size_t number_of_digits, bool scientific) const
-{
-   std::string str;
-   boost::int64_t my_exp = order();
-   if(number_of_digits == 0)
-      number_of_digits = (std::numeric_limits<std::size_t>::max)();
-   // Determine the number of elements needed to provide the requested digits from cpp_float<Digits10>.
-   const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>((number_of_digits / static_cast<std::size_t>(mp_elem_digits10)) + 2u),
-      static_cast<std::size_t>(mp_elem_number));
-
-   // Extract the remaining digits from cpp_float<Digits10> after the decimal point.
-   str = boost::lexical_cast<std::string>(data[0]);
-
-   // Extract all of the digits from cpp_float<Digits10>, beginning with the first data element.
-   for(std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++)
-   {
-      std::stringstream ss;
-
-      ss << std::setw(static_cast<std::streamsize>(mp_elem_digits10))
-         << std::setfill(static_cast<char>('0'))
-         << data[i];
-
-      str += ss.str();
-   }
-
-   // Cut the output to the size of the precision.
-   if(str.length() > number_of_digits)
-   {
-      // Get the digit after the last needed digit for rounding
-      const boost::uint32_t round = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str.at(number_of_digits)) - static_cast<boost::uint32_t>('0'));
-
-      // Truncate the string
-      str = str.substr(static_cast<std::size_t>(0u), number_of_digits);
-
-      if(round >= static_cast<boost::uint32_t>(5u))
-      {
-         std::size_t ix = static_cast<std::size_t>(str.length() - 1u);
-
-         // Every trailing 9 must be rounded up
-         while(ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9)))
-         {
-            str.at(ix) = static_cast<char>('0');
-            --ix;
-         }
-
-         if(!ix)
-         {
-            // There were nothing but trailing nines.
-            if(static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>(0x30)) == static_cast<boost::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];
-         }
-      }
-   }
-   //
-   // Suppress trailing zeros:
-   //
-   std::string::iterator pos = str.end();
-   while(pos != str.begin() && *--pos == '0'){}
-   if(pos != str.end())
-      ++pos;
-   str.erase(pos, str.end());
-   if(str.empty())
-      str = '0';
-   if(!scientific && (str.size() < 20) && (my_exp >= 0) && (my_exp < 20))
-   {
-      if(1 + my_exp > str.size())
-      {
-         // Just pad out the end with zeros:
-         str.append(static_cast<std::string::size_type>(1 + my_exp - str.size()), '0');
-      }
-      else if(my_exp + 1 != str.size())
-      {
-         // Insert the decimal point:
-         str.insert(static_cast<std::string::size_type>(my_exp + 1), 1, '.');
-      }
-   }
-   else
-   {
-      // Scientific format:
-      str.insert(1, 1, '.');
-      if(str.size() == 2)
-         str.append(1, '0');
-      str.append(1, 'e');
-      str.append(boost::lexical_cast<std::string>(my_exp));
-   }
-   if(isneg())
-      str.insert(0, 1, '-');
-   return str;
-}
-
-template <unsigned Digits10>
-bool cpp_float<Digits10>::rd_string(const char* const s)
-{
-   std::string str(s);
-
-   // Get a possible exponent and remove it.
-   exp = static_cast<boost::int64_t>(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.
-      exp = boost::lexical_cast<boost::int64_t>(static_cast<const char* const>(str.c_str() + (pos + 1u)));
-      str = str.substr(static_cast<std::size_t>(0u), pos);
-   }
-
-   // Get a possible +/- sign and remove it.
-   neg = false;
-
-   if((pos = str.find(static_cast<char>('-'))) != std::string::npos)
-   {
-      neg = true;
-      str.erase(pos, static_cast<std::size_t>(1u));
-   }
-
-   if((pos = str.find(static_cast<char>('+'))) != std::string::npos)
-   {
-      str.erase(pos, static_cast<std::size_t>(1u));
-   }
-
-   // Remove 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_float<Digits10> input form
-   // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an
-   // even multiple of mp_elem_digits10 which are possibly zero padded
-   // on the right-end, and n is a signed 32-bit integer which is an
-   // even multiple of mp_elem_digits10.
-
-   // Find a possible decimal point.
-   pos = str.find(static_cast<char>('.'));
-
-   if(pos != std::string::npos)
-   {
-      // 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 != str.rbegin())
-      {
-         const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero);
-         str.erase(str.begin() + 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 = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero);
-         }
-
-         // Bring one single digit into the mantissa and adjust exponent accordingly.
-         str.erase(str.begin(), it_non_zero);
-         str.insert(static_cast<std::size_t>(1u), ".");
-         exp -= static_cast<boost::int64_t>(delta_exp + 1u);
-      }
-   }
-   else
-   {
-      // Input string has no decimal point: Append decimal point.
-      str.append(".");
-   }
-
-   // Shift the decimal point such that the exponent is an even multiple of mp_elem_digits10.
-   std::size_t n_shift   = static_cast<std::size_t>(0u);
-   const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<boost::int64_t>(mp_elem_digits10));
-
-   if((exp % static_cast<boost::int64_t>(mp_elem_digits10)) != static_cast<boost::int64_t>(0))
-   {
-      n_shift = ((exp < static_cast<boost::int64_t>(0))
-         ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(mp_elem_digits10))
-         : static_cast<std::size_t>(n_exp_rem));
-   }
-
-   // Make sure that there are enough digits for the decimal point shift.
-   pos = str.find(static_cast<char>('.'));
-
-   std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u);
-
-   if((str.length() - pos_plus_one) < n_shift)
-   {
-      const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one));
-
-      str.append(std::string(sz, static_cast<char>('0')));
-   }
-
-   // Do the decimal point shift.
-   if(n_shift != static_cast<std::size_t>(0u))
-   {
-      str.insert(static_cast<std::size_t>(pos_plus_one + n_shift), ".");
-
-      str.erase(pos, static_cast<std::size_t>(1u));
-
-      exp -= static_cast<boost::int64_t>(n_shift);
-   }
-
-   // Cut the size of the mantissa to <= mp_elem_digits10.
-   pos          = str.find(static_cast<char>('.'));
-   pos_plus_one = static_cast<std::size_t>(pos + 1u);
-
-   if(pos > static_cast<std::size_t>(mp_elem_digits10))
-   {
-      const boost::int32_t n_pos         = static_cast<boost::int32_t>(pos);
-      const boost::int32_t n_rem_is_zero = ((static_cast<boost::int32_t>(n_pos % mp_elem_digits10) == static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(1) : static_cast<boost::int32_t>(0));
-      const boost::int32_t n             = static_cast<boost::int32_t>(static_cast<boost::int32_t>(n_pos / mp_elem_digits10) - n_rem_is_zero);
-
-      str.insert(static_cast<std::size_t>(static_cast<boost::int32_t>(n_pos - static_cast<boost::int32_t>(n * mp_elem_digits10))), ".");
-
-      str.erase(pos_plus_one, static_cast<std::size_t>(1u));
-
-      exp += static_cast<boost::int64_t>(static_cast<boost::int64_t>(n) * static_cast<boost::int64_t>(mp_elem_digits10));
-   }
-
-   // Pad the decimal part such that its value is an even
-   // multiple of mp_elem_digits10.
-   pos          = str.find(static_cast<char>('.'));
-   pos_plus_one = static_cast<std::size_t>(pos + 1u);
-
-   const boost::int32_t n_dec = static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.length() - 1u) - static_cast<boost::int32_t>(pos));
-   const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % mp_elem_digits10);
-   boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(mp_elem_digits10 - n_rem)
-      : static_cast<boost::int32_t>(0));
-
-   if(n_cnt != static_cast<boost::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>((mp_elem_number - 1) * mp_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 + max_dec));
-   }
-
-   // Now the input string has the standard cpp_float<Digits10> input form.
-   // (See the comment above.)
-
-   // Set all the data elements to 0.
-   std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
-
-   // Extract the data.
-
-   // First get the digits to the left of the decimal point...
-   data[0u] = boost::lexical_cast<boost::uint32_t>(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 = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(mp_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()
-         + pos_plus_one
-         + (i * static_cast<std::string::size_type>(mp_elem_digits10));
-
-      data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(mp_elem_digits10)));
-   }
-
-   // Check for overflow...
-   if(exp > cpp_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_float_min_exp10)
-   {
-      if(exp == cpp_float_min_exp10)
-      {
-         // Check for identity with the minimum value.
-         cpp_float<Digits10> test = *this;
-
-         test.exp = static_cast<boost::int64_t>(0);
-
-         if(test.isone())
-         {
-            *this = zero();
-         }
-      }
-      else
-      {
-         *this = zero();
-      }
-   }
-
-   return true;
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>::cpp_float(const double mantissa, const boost::int64_t exponent) 
- : data     (),
-   exp      (static_cast<boost::int64_t>(0)),
-   neg      (false),
-   fpclass  (mp_finite),
-   prec_elem(mp_elem_number)
-{
-   // Create an cpp_float<Digits10> from mantissa and exponent.
-   // This ctor 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<boost::uint32_t>(0u));
-      return;
-   }
-
-   const bool b_neg = (mantissa < 0.0);
-
-   double d = ((!b_neg) ? mantissa : -mantissa);
-   boost::int64_t  e = exponent;
-
-   while(d > 10.0) { d /= 10.0; ++e; }
-   while(d <  1.0) { d *= 10.0; --e; }
-
-   boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(mp_elem_digits10));
-
-   while(static_cast<boost::int32_t>(shift-- % mp_elem_digits10) != static_cast<boost::int32_t>(0))
-   {
-      d *= 10.0;
-      --e;
-   }
-
-   exp = e;
-   neg = b_neg;
-
-   std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
-
-   static const boost::int32_t digit_ratio = static_cast<boost::int32_t>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / static_cast<boost::int32_t>(mp_elem_digits10));
-   static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2));
-
-   for(boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++)
-   {
-      boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d));
-      data[i]  = static_cast<boost::uint32_t>(n);
-      d       -= static_cast<double>(n);
-      d       *= static_cast<double>(mp_elem_mask);
-   }
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10>& cpp_float<Digits10>::operator = (long double 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.
-   using std::frexp;
-   using std::ldexp;
-   using std::floor;
-
-   if (a == 0) {
-      return *this = zero();
-   }
-
-   if (a == 1) {
-      return *this = one();
-   }
-
-   if((boost::math::isinf)(a))
-   {
-      return *this = inf();
-   }
-   if((boost::math::isnan)(a))
-      return *this = nan();
-
-   int e;
-   long double f, term;
-   *this = zero();
-
-   f = frexp(a, &e);
-
-   static const int shift = std::numeric_limits<int>::digits - 1;
-
-   while(f)
-   {
-      // extract int sized bits from f:
-      f = ldexp(f, shift);
-      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>
-void cpp_float<Digits10>::from_unsigned_long_long(const unsigned long long u)
-{
-   std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
-
-   exp = static_cast<boost::int64_t>(0);
-   neg = false;
-   fpclass = mp_finite;
-   prec_elem = mp_elem_number;
-
-   std::size_t i =static_cast<std::size_t>(0u);
-
-   unsigned long long uu = u;
-
-   boost::uint32_t temp[(std::numeric_limits<unsigned long long>::digits10 / static_cast<int>(mp_elem_digits10)) + 3] = { static_cast<boost::uint32_t>(0u) };
-
-   while(uu != static_cast<unsigned long long>(0u))
-   {
-      temp[i] = static_cast<boost::uint32_t>(uu % static_cast<unsigned long long>(mp_elem_mask));
-      uu = static_cast<unsigned long long>(uu / static_cast<unsigned long long>(mp_elem_mask));
-      ++i;
-   }
-
-   if(i > static_cast<std::size_t>(1u))
-   {
-      exp += static_cast<boost::int64_t>((i - 1u) * static_cast<std::size_t>(mp_elem_digits10));
-   }
-
-   std::reverse(temp, temp + i);
-   std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(mp_elem_number)), data.begin());
-}
-
-template <unsigned Digits10>
-void cpp_float<Digits10>::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p)
-{
-   boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
-
-   for(boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--)
-   {
-      boost::uint64_t sum = carry;
-
-      for(boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--)
-      {
-         sum += static_cast<boost::uint64_t>(u[i] * static_cast<boost::uint64_t>(v[j - i]));
-      }
-
-      w[j + 1] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(mp_elem_mask));
-      carry    = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(mp_elem_mask));
-   }
-
-   w[0u] = static_cast<boost::uint32_t>(carry);
-}
-
-template <unsigned Digits10>
-boost::uint32_t cpp_float<Digits10>::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p)
-{
-   boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
-
-   // Multiplication loop.
-   for(boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--)
-   {
-      const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n)));
-      carry          = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(mp_elem_mask));
-      u[j]           = static_cast<boost::uint32_t>(t - static_cast<boost::uint64_t>(static_cast<boost::uint32_t>(mp_elem_mask) * static_cast<boost::uint64_t>(carry)));
-   }
-
-   return static_cast<boost::uint32_t>(carry);
-}
-
-template <unsigned Digits10>
-boost::uint32_t cpp_float<Digits10>::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p)
-{
-   boost::uint64_t prev = static_cast<boost::uint64_t>(0u);
-
-   for(boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++)
-   {
-      const boost::uint64_t t = static_cast<boost::uint64_t>(u[j] + static_cast<boost::uint64_t>(prev * static_cast<boost::uint32_t>(mp_elem_mask)));
-      u[j]           = static_cast<boost::uint32_t>(t / n);
-      prev           = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j])));
-   }
-
-   return static_cast<boost::uint32_t>(prev);
-}
-
-template <unsigned Digits10>
-cpp_float<Digits10> cpp_float<Digits10>::pow2(const boost::int64_t p)
-{
-   // Create a static const table of p^2 for -128 < p < +128.
-   // Note: The size of this table must be odd-numbered and
-   // symmetric about 0.
-   init.do_nothing();
-   static const boost::array<cpp_float<Digits10>, 255u> p2_data =
-   {{
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-         cpp_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"),
-         cpp_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"),
-         cpp_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"),
-         cpp_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"),
-         cpp_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"),
-         cpp_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"),
-         cpp_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"),
-         cpp_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"),
-         cpp_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"),
-         cpp_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"),
-         cpp_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"),
-         cpp_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"),
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-         cpp_float(static_cast<unsigned long long>(64)),
-         cpp_float(static_cast<unsigned long long>(128)),
-         cpp_float(static_cast<unsigned long long>(256)),
-         cpp_float(static_cast<unsigned long long>(512)),
-         cpp_float(static_cast<unsigned long long>(1024)),
-         cpp_float(static_cast<unsigned long long>(2048)),
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-         cpp_float(static_cast<boost::uint64_t>(1uL << 22u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 23u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 24u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 25u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 26u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 27u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 28u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 29u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 30u)),
-         cpp_float(static_cast<boost::uint64_t>(1uL << 31u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 32u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 33u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 34u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 35u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 36u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 37u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 38u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 39u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 40u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 41u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 42u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 43u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 44u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 45u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 46u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 47u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 48u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 49u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 50u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 51u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 52u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 53u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 54u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 55u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 56u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 57u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 58u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 59u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 60u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 61u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 62u)),
-         cpp_float(static_cast<boost::uint64_t>(1uLL << 63u)),
-         cpp_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
-         cpp_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
-         cpp_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
-         cpp_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
-         cpp_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
-         cpp_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
-         cpp_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
-         cpp_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
-         cpp_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
-         cpp_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
-         cpp_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
-         cpp_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
-         cpp_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
-         cpp_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
-         cpp_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
-         cpp_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
-         cpp_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
-         cpp_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
-         cpp_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
-         cpp_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
-         cpp_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"),
-         cpp_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"),
-         cpp_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"),
-         cpp_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"),
-         cpp_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"),
-         cpp_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"),
-         cpp_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"),
-         cpp_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"),
-         cpp_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"),
-         cpp_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"),
-         cpp_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"),
-         cpp_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"),
-         cpp_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"),
-         cpp_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"),
-         cpp_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"),
-         cpp_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"),
-         cpp_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"),
-         cpp_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"),
-         cpp_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"),
-         cpp_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"),
-         cpp_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"),
-         cpp_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"),
-         cpp_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"),
-         cpp_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"),
-         cpp_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"),
-         cpp_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"),
-         cpp_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"),
-         cpp_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"),
-         cpp_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"),
-         cpp_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"),
-         cpp_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"),
-         cpp_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"),
-         cpp_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"),
-         cpp_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"),
-         cpp_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"),
-         cpp_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"),
-         cpp_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"),
-         cpp_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"),
-         cpp_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"),
-         cpp_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"),
-         cpp_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"),
-         cpp_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"),
-         cpp_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"),
-         cpp_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38")
-   }};
-
-   if((p > static_cast<boost::int64_t>(-128)) && (p < static_cast<boost::int64_t>(+128)))
-   {
-      return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))];
-   }
-
-   // Compute and return 2^p.
-   if(p < static_cast<boost::int64_t>(0))
-   {
-      return pow2(static_cast<boost::int64_t>(-p)).calculate_inv();
-   }
-   else if(p < static_cast<boost::int64_t>(std::numeric_limits<boost::uint64_t>::digits))
-   {
-      const boost::uint64_t p2 = static_cast<boost::uint64_t>(static_cast<boost::uint64_t>(1uLL) << p);
-      return cpp_float(p2);
-   }
-   else
-   {
-      cpp_float<Digits10> t;
-      default_ops::detail::pow_imp(t, two(), p, mpl::true_());
-      return t;
-   }
-}
-
-
-template <unsigned Digits10>
-inline void add(cpp_float<Digits10>& result, const cpp_float<Digits10>& o)
-{
-   result += o;
-}
-template <unsigned Digits10>
-inline void subtract(cpp_float<Digits10>& result, const cpp_float<Digits10>& o)
-{
-   result -= o;
-}
-template <unsigned Digits10>
-inline void multiply(cpp_float<Digits10>& result, const cpp_float<Digits10>& o)
-{
-   result *= o;
-}
-template <unsigned Digits10>
-inline void divide(cpp_float<Digits10>& result, const cpp_float<Digits10>& o)
-{
-   result /= o;
-}
-
-template <unsigned Digits10>
-inline void add(cpp_float<Digits10>& result, const unsigned long long& o)
-{
-   result.add_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void subtract(cpp_float<Digits10>& result, const unsigned long long& o)
-{
-   result.sub_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void multiply(cpp_float<Digits10>& result, const unsigned long long& o)
-{
-   result.mul_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void divide(cpp_float<Digits10>& result, const unsigned long long& o)
-{
-   result.div_unsigned_long_long(o);
-}
-
-template <unsigned Digits10>
-inline void add(cpp_float<Digits10>& result, long long o)
-{
-   if(o < 0)
-      result.sub_unsigned_long_long(-o);
-   else
-      result.add_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void subtract(cpp_float<Digits10>& result, long long o)
-{
-   if(o < 0)
-      result.add_unsigned_long_long(-o);
-   else
-      result.sub_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void multiply(cpp_float<Digits10>& result, long long o)
-{
-   if(o < 0)
-   {
-      result.mul_unsigned_long_long(-o);
-      result.negate();
-   }
-   else
-      result.mul_unsigned_long_long(o);
-}
-template <unsigned Digits10>
-inline void divide(cpp_float<Digits10>& result, long long o)
-{
-   if(o < 0)
-   {
-      result.div_unsigned_long_long(-o);
-      result.negate();
-   }
-   else
-      result.div_unsigned_long_long(o);
-}
-
-template <unsigned Digits10>
-inline void convert_to(unsigned long long* result, const cpp_float<Digits10>& val)
-{
-   *result = val.extract_unsigned_long_long();
-}
-template <unsigned Digits10>
-inline void convert_to(long long* result, const cpp_float<Digits10>& val)
-{
-   *result = val.extract_signed_long_long();
-}
-template <unsigned Digits10>
-inline void convert_to(long double* result, cpp_float<Digits10>& val)
-{
-   *result = val.extract_long_double();
-}
-
-//
-// Non member function support:
-//
-template <unsigned Digits10>
-inline int eval_fpclassify(const cpp_float<Digits10>& 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>
-inline void eval_abs(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   result = x;
-   if(x.isneg())
-      result.negate();
-}
-
-template <unsigned Digits10>
-inline void eval_fabs(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   result = x;
-   if(x.isneg())
-      result.negate();
-}
-
-template <unsigned Digits10>
-inline void eval_sqrt(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   result = x;
-   result.calculate_sqrt();
-}
-
-template <unsigned Digits10>
-inline void eval_floor(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   result = x;
-   if(!x.isfinite() || x.isint()) 
-   { 
-      return; 
-   }
-
-   if(x.isneg())
-      result -= cpp_float<Digits10>::one();
-   result = result.extract_integer_part();
-}
-
-template <unsigned Digits10>
-inline void eval_ceil(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   result = x;
-   if(!x.isfinite() || x.isint()) 
-   { 
-      return; 
-   }
-
-   if(!x.isneg())
-      result += cpp_float<Digits10>::one();
-   result = result.extract_integer_part();
-}
-
-template <unsigned Digits10>
-inline void eval_trunc(cpp_float<Digits10>& result, const cpp_float<Digits10>& x)
-{
-   if(!x.isfinite()) 
-   { 
-      result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number<cpp_float<Digits10> >(x), 0, boost::math::policies::policy<>()).backend();
-      return;
-   }
-   else if(x.isint())
-   {
-      result = x;
-      return;
-   }
-   result = x.extract_integer_part();
-}
-
-template <unsigned Digits10>
-inline void eval_ldexp(cpp_float<Digits10>& result, const cpp_float<Digits10>& x, long long e)
-{
-   result = x;
-   result *= cpp_float<Digits10>::pow2(e);
-}
-
-template <unsigned Digits10>
-inline void eval_frexp(cpp_float<Digits10>& result, const cpp_float<Digits10>& x, long long* e)
-{
-   result = x;
-   if(result.isneg())
-      result.negate();
-
-   long long t = result.order();
-
-   if(std::abs(t) > (std::numeric_limits<long long>::max)() / 3)
-      throw std::runtime_error("Exponent is too large to be represented as a power of 2.");
-   t *= 3;
-
-   result *= cpp_float<Digits10>::pow2(-t);
-
-   while(result.compare(cpp_float<Digits10>::one()) >= 0)
-   {
-      result /= cpp_float<Digits10>::two();
-      ++t;
-   }
-   while(result.compare(cpp_float<Digits10>::half()) < 0)
-   {
-      result *= cpp_float<Digits10>::two();
-      --t;
-   }
-   *e = t;
-   if(x.isneg())
-      result.negate();
-}
-
-template <unsigned Digits10>
-inline void eval_frexp(cpp_float<Digits10>& result, const cpp_float<Digits10>& x, int* e)
-{
-   long long t;
-   eval_frexp(result, x, &t);
-   if(t > (std::numeric_limits<int>::max)())
-      throw std::runtime_error("Exponent is outside the range of an int");
-   *e = static_cast<int>(t);
-}
-
-typedef mp_number<cpp_float<50> > cpp_float_50;
-typedef mp_number<cpp_float<100> > cpp_float_100;
-
-}}
-
-namespace std
-{
-   template <unsigned Digits10> 
-   class numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > >
-   {
-   public:
-      static const bool                    is_specialized    = true;
-      static const bool                    is_signed         = true;
-      static const bool                    is_integer        = false;
-      static const bool                    is_exact          = false;
-      static const bool                    is_bounded        = true;
-      static const bool                    is_modulo         = false;
-      static const bool                    is_iec559         = false;
-      static const int                     digits            = static_cast<int>(((Digits10 + 1) * 1000L) / 301L);
-      static const int                     digits10          = boost::multiprecision::cpp_float<Digits10>::cpp_float_digits10;
-      static const int                     max_digits10      = boost::multiprecision::cpp_float<Digits10>::cpp_float_max_digits10;
-      static const boost::int64_t          min_exponent      = boost::multiprecision::cpp_float<Digits10>::cpp_float_min_exp;      // Type differs from int.
-      static const boost::int64_t          min_exponent10    = boost::multiprecision::cpp_float<Digits10>::cpp_float_min_exp10;    // Type differs from int.
-      static const boost::int64_t          max_exponent      = boost::multiprecision::cpp_float<Digits10>::cpp_float_max_exp;      // Type differs from int.
-      static const boost::int64_t          max_exponent10    = boost::multiprecision::cpp_float<Digits10>::cpp_float_max_exp10;    // Type differs from int.
-      static const int                     radix             = boost::multiprecision::cpp_float<Digits10>::mp_radix;
-      static const std::float_round_style  round_style       = std::round_to_nearest;
-      static const bool                    has_infinity      = true;
-      static const bool                    has_quiet_NaN     = true;
-      static const bool                    has_signaling_NaN = false;
-      static const std::float_denorm_style has_denorm        = std::denorm_absent;
-      static const bool                    has_denorm_loss   = false;
-      static const bool                    traps             = false;
-      static const bool                    tinyness_before   = false;
-
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > (min)        (void) throw() { return (boost::multiprecision::cpp_float<Digits10>::min)(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > (max)        (void) throw() { return (boost::multiprecision::cpp_float<Digits10>::max)(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > lowest       (void) throw() { return boost::multiprecision::cpp_float<Digits10>::zero(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > epsilon      (void) throw() { return boost::multiprecision::cpp_float<Digits10>::eps(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > round_error  (void) throw() { return 0.5L; }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > infinity     (void) throw() { return boost::multiprecision::cpp_float<Digits10>::inf(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > quiet_NaN    (void) throw() { return boost::multiprecision::cpp_float<Digits10>::nan(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > signaling_NaN(void) throw() { return boost::multiprecision::cpp_float<Digits10>::zero(); }
-      static const boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> > denorm_min   (void) throw() { return boost::multiprecision::cpp_float<Digits10>::zero(); }
-   };
-}
-
-namespace boost{ namespace math{
-
-namespace policies{
-
-template <unsigned Digits10, class Policy>
-struct precision< boost::multiprecision::mp_number<boost::multiprecision::cpp_float<Digits10> >, Policy>
-{
-   typedef typename Policy::precision_type precision_type;
-   typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2;
-   typedef typename mpl::if_c<
-      ((digits_2::value <= precision_type::value) 
-      || (Policy::precision_type::value <= 0)),
-      // Default case, full precision for RealType:
-      digits_2,
-      // User customised precision:
-      precision_type
-   >::type type;
-};
-
-} // namespace policies
-
-}} // namespaces boost::math
-
-
-#endif
-