Imported Upstream version 1.57.0upstream/1.57.0

1 files changed, 2625 insertions, 0 deletions

diff --git a/boost/multiprecision/gmp.hpp b/boost/multiprecision/gmp.hpp
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+++ b/boost/multiprecision/gmp.hpp
@@ -0,0 +1,2625 @@
+///////////////////////////////////////////////////////////////////////////////
+//  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)
+
+#ifndef BOOST_MATH_ER_GMP_BACKEND_HPP
+#define BOOST_MATH_ER_GMP_BACKEND_HPP
+
+#include <boost/multiprecision/number.hpp>
+#include <boost/multiprecision/detail/integer_ops.hpp>
+#include <boost/multiprecision/detail/big_lanczos.hpp>
+#include <boost/multiprecision/detail/digits.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/cstdint.hpp>
+#ifdef BOOST_MSVC
+#  pragma warning(push)
+#  pragma warning(disable:4127)
+#endif
+#include <gmp.h>
+#ifdef BOOST_MSVC
+#  pragma warning(pop)
+#endif
+#include <cmath>
+#include <limits>
+#include <climits>
+
+namespace boost{
+namespace multiprecision{
+namespace backends{
+
+#ifdef BOOST_MSVC
+// warning C4127: conditional expression is constant
+#pragma warning(push)
+#pragma warning(disable:4127)
+#endif
+
+template <unsigned digits10>
+struct gmp_float;
+struct gmp_int;
+struct gmp_rational;
+
+} // namespace backends
+
+template<>
+struct number_category<backends::gmp_int> : public mpl::int_<number_kind_integer>{};
+template<>
+struct number_category<backends::gmp_rational> : public mpl::int_<number_kind_rational>{};
+template <unsigned digits10>
+struct number_category<backends::gmp_float<digits10> > : public mpl::int_<number_kind_floating_point>{};
+
+namespace backends{
+//
+// Within this file, the only functions we mark as noexcept are those that manipulate
+// (but don't create) an mpf_t.  All other types may allocate at pretty much any time
+// via a user-supplied allocator, and therefore throw.
+//
+namespace detail{
+
+template <unsigned digits10>
+struct gmp_float_imp
+{
+   typedef mpl::list<long, long long>                 signed_types;
+   typedef mpl::list<unsigned long, unsigned long long>   unsigned_types;
+   typedef mpl::list<double, long double>            float_types;
+   typedef long                                      exponent_type;
+
+   gmp_float_imp() BOOST_NOEXCEPT {}
+
+   gmp_float_imp(const gmp_float_imp& o)
+   {
+      //
+      // We have to do an init followed by a set here, otherwise *this may be at
+      // a lower precision than o: seems like mpf_init_set copies just enough bits
+      // to get the right value, but if it's then used in further calculations
+      // things go badly wrong!!
+      //
+      mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      if(o.m_data[0]._mp_d)
+         mpf_set(m_data, o.m_data);
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float_imp(gmp_float_imp&& o) BOOST_NOEXCEPT
+   {
+      m_data[0] = o.m_data[0];
+      o.m_data[0]._mp_d = 0;
+   }
+#endif
+   gmp_float_imp& operator = (const gmp_float_imp& o)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      if(o.m_data[0]._mp_d)
+         mpf_set(m_data, o.m_data);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float_imp& operator = (gmp_float_imp&& o) BOOST_NOEXCEPT
+   {
+      mpf_swap(m_data, o.m_data);
+      return *this;
+   }
+#endif
+   gmp_float_imp& operator = (unsigned long long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      unsigned long long mask = ((1uLL << std::numeric_limits<unsigned>::digits) - 1);
+      unsigned shift = 0;
+      mpf_t t;
+      mpf_init2(t, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpf_set_ui(m_data, 0);
+      while(i)
+      {
+         mpf_set_ui(t, static_cast<unsigned>(i & mask));
+         if(shift)
+            mpf_mul_2exp(t, t, shift);
+         mpf_add(m_data, m_data, t);
+         shift += std::numeric_limits<unsigned>::digits;
+         i >>= std::numeric_limits<unsigned>::digits;
+      }
+      mpf_clear(t);
+      return *this;
+   }
+   gmp_float_imp& operator = (long long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      bool neg = i < 0;
+      *this = static_cast<unsigned long long>(boost::multiprecision::detail::unsigned_abs(i));
+      if(neg)
+         mpf_neg(m_data, m_data);
+      return *this;
+   }
+   gmp_float_imp& operator = (unsigned long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpf_set_ui(m_data, i);
+      return *this;
+   }
+   gmp_float_imp& operator = (long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpf_set_si(m_data, i);
+      return *this;
+   }
+   gmp_float_imp& operator = (double d)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpf_set_d(m_data, d);
+      return *this;
+   }
+   gmp_float_imp& operator = (long double a)
+   {
+      using std::frexp;
+      using std::ldexp;
+      using std::floor;
+
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+
+      if (a == 0) {
+         mpf_set_si(m_data, 0);
+         return *this;
+      }
+
+      if (a == 1) {
+         mpf_set_si(m_data, 1);
+         return *this;
+      }
+
+      BOOST_ASSERT(!(boost::math::isinf)(a));
+      BOOST_ASSERT(!(boost::math::isnan)(a));
+
+      int e;
+      long double f, term;
+      mpf_set_ui(m_data, 0u);
+
+      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;
+         mpf_mul_2exp(m_data, m_data, shift);
+         if(term > 0)
+            mpf_add_ui(m_data, m_data, static_cast<unsigned>(term));
+         else
+            mpf_sub_ui(m_data, m_data, static_cast<unsigned>(-term));
+         f -= term;
+      }
+      if(e > 0)
+         mpf_mul_2exp(m_data, m_data, e);
+      else if(e < 0)
+         mpf_div_2exp(m_data, m_data, -e);
+      return *this;
+   }
+   gmp_float_imp& operator = (const char* s)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      if(0 != mpf_set_str(m_data, s, 10))
+         BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid floating point number.")));
+      return *this;
+   }
+   void swap(gmp_float_imp& o) BOOST_NOEXCEPT
+   {
+      mpf_swap(m_data, o.m_data);
+   }
+   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+
+      bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific;
+      bool fixed      = (f & std::ios_base::fixed) == std::ios_base::fixed;
+      std::streamsize org_digits(digits);
+
+      if(scientific && digits)
+         ++digits;
+
+      std::string result;
+      mp_exp_t e;
+      void *(*alloc_func_ptr) (size_t);
+      void *(*realloc_func_ptr) (void *, size_t, size_t);
+      void (*free_func_ptr) (void *, size_t);
+      mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr);
+
+      if(mpf_sgn(m_data) == 0)
+      {
+         e = 0;
+         result = "0";
+         if(fixed && digits)
+            ++digits;
+      }
+      else
+      {
+         char* ps = mpf_get_str (0, &e, 10, static_cast<std::size_t>(digits), m_data);
+         --e;  // To match with what our formatter expects.
+         if(fixed && e != -1)
+         {
+            // Oops we actually need a different number of digits to what we asked for:
+            (*free_func_ptr)((void*)ps, std::strlen(ps) + 1);
+            digits += e + 1;
+            if(digits == 0)
+            {
+               // We need to get *all* the digits and then possibly round up,
+               // we end up with either "0" or "1" as the result.
+               ps = mpf_get_str (0, &e, 10, 0, m_data);
+               --e;
+               unsigned offset = *ps == '-' ? 1 : 0;
+               if(ps[offset] > '5')
+               {
+                  ++e;
+                  ps[offset] = '1';
+                  ps[offset + 1] = 0;
+               }
+               else if(ps[offset] == '5')
+               {
+                  unsigned i = offset + 1;
+                  bool round_up = false;
+                  while(ps[i] != 0)
+                  {
+                     if(ps[i] != '0')
+                     {
+                        round_up = true;
+                        break;
+                     }
+                  }
+                  if(round_up)
+                  {
+                     ++e;
+                     ps[offset] = '1';
+                     ps[offset + 1] = 0;
+                  }
+                  else
+                  {
+                     ps[offset] = '0';
+                     ps[offset + 1] = 0;
+                  }
+               }
+               else
+               {
+                  ps[offset] = '0';
+                  ps[offset + 1] = 0;
+               }
+            }
+            else if(digits > 0)
+            {
+               ps = mpf_get_str (0, &e, 10, static_cast<std::size_t>(digits), m_data);
+               --e;  // To match with what our formatter expects.
+            }
+            else
+            {
+               ps = mpf_get_str (0, &e, 10, 1, m_data);
+               --e;
+               unsigned offset = *ps == '-' ? 1 : 0;
+               ps[offset] = '0';
+               ps[offset + 1] = 0;
+            }
+         }
+         result = ps;
+         (*free_func_ptr)((void*)ps, std::strlen(ps) + 1);
+      }
+      boost::multiprecision::detail::format_float_string(result, e, org_digits, f, mpf_sgn(m_data) == 0);
+      return result;
+   }
+   ~gmp_float_imp() BOOST_NOEXCEPT
+   {
+      if(m_data[0]._mp_d)
+         mpf_clear(m_data);
+   }
+   void negate() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      mpf_neg(m_data, m_data);
+   }
+   int compare(const gmp_float<digits10>& o)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d && o.m_data[0]._mp_d);
+      return mpf_cmp(m_data, o.m_data);
+   }
+   int compare(long i)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return mpf_cmp_si(m_data, i);
+   }
+   int compare(unsigned long i)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return mpf_cmp_ui(m_data, i);
+   }
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(V v)const
+   {
+      gmp_float<digits10> d;
+      d = v;
+      return compare(d);
+   }
+   mpf_t& data() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return m_data;
+   }
+   const mpf_t& data()const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return m_data;
+   }
+protected:
+   mpf_t m_data;
+   static unsigned& get_default_precision() BOOST_NOEXCEPT
+   {
+      static unsigned val = 50;
+      return val;
+   }
+};
+
+} // namespace detail
+
+struct gmp_int;
+struct gmp_rational;
+
+template <unsigned digits10>
+struct gmp_float : public detail::gmp_float_imp<digits10>
+{
+   gmp_float()
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+   }
+   gmp_float(const gmp_float& o) : detail::gmp_float_imp<digits10>(o) {}
+   template <unsigned D>
+   gmp_float(const gmp_float<D>& o, typename enable_if_c<D <= digits10>::type* = 0);
+   template <unsigned D>
+   explicit gmp_float(const gmp_float<D>& o, typename disable_if_c<D <= digits10>::type* = 0);
+   gmp_float(const gmp_int& o);
+   gmp_float(const gmp_rational& o);
+   gmp_float(const mpf_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set(this->m_data, val);
+   }
+   gmp_float(const mpz_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set_z(this->m_data, val);
+   }
+   gmp_float(const mpq_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set_q(this->m_data, val);
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float(gmp_float&& o) BOOST_NOEXCEPT : detail::gmp_float_imp<digits10>(static_cast<detail::gmp_float_imp<digits10>&&>(o)) {}
+#endif
+   gmp_float& operator=(const gmp_float& o)
+   {
+      *static_cast<detail::gmp_float_imp<digits10>*>(this) = static_cast<detail::gmp_float_imp<digits10> const&>(o);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float& operator=(gmp_float&& o) BOOST_NOEXCEPT
+   {
+      *static_cast<detail::gmp_float_imp<digits10>*>(this) = static_cast<detail::gmp_float_imp<digits10>&&>(o);
+      return *this;
+   }
+#endif
+   template <unsigned D>
+   gmp_float& operator=(const gmp_float<D>& o);
+   gmp_float& operator=(const gmp_int& o);
+   gmp_float& operator=(const gmp_rational& o);
+   gmp_float& operator=(const mpf_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set(this->m_data, val);
+      return *this;
+   }
+   gmp_float& operator=(const mpz_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set_z(this->m_data, val);
+      return *this;
+   }
+   gmp_float& operator=(const mpq_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set_q(this->m_data, val);
+      return *this;
+   }
+   template <class V>
+   gmp_float& operator=(const V& v)
+   {
+      *static_cast<detail::gmp_float_imp<digits10>*>(this) = v;
+      return *this;
+   }
+};
+
+template <>
+struct gmp_float<0> : public detail::gmp_float_imp<0>
+{
+   gmp_float()
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+   }
+   gmp_float(const mpf_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set(this->m_data, val);
+   }
+   gmp_float(const mpz_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set_z(this->m_data, val);
+   }
+   gmp_float(const mpq_t val)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set_q(this->m_data, val);
+   }
+   gmp_float(const gmp_float& o) : detail::gmp_float_imp<0>(o) {}
+   template <unsigned D>
+   gmp_float(const gmp_float<D>& o)
+   {
+      mpf_init2(this->m_data, mpf_get_prec(o.data()));
+      mpf_set(this->m_data, o.data());
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float(gmp_float&& o) BOOST_NOEXCEPT : detail::gmp_float_imp<0>(static_cast<detail::gmp_float_imp<0>&&>(o)) {}
+#endif
+   gmp_float(const gmp_int& o);
+   gmp_float(const gmp_rational& o);
+   gmp_float(const gmp_float& o, unsigned digits10)
+   {
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+      mpf_set(this->m_data, o.data());
+   }
+
+   gmp_float& operator=(const gmp_float& o)
+   {
+      *static_cast<detail::gmp_float_imp<0>*>(this) = static_cast<detail::gmp_float_imp<0> const&>(o);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_float& operator=(gmp_float&& o) BOOST_NOEXCEPT
+   {
+      *static_cast<detail::gmp_float_imp<0>*>(this) = static_cast<detail::gmp_float_imp<0> &&>(o);
+      return *this;
+   }
+#endif
+   template <unsigned D>
+   gmp_float& operator=(const gmp_float<D>& o)
+   {
+      if(this->m_data[0]._mp_d == 0)
+      {
+         mpf_init2(this->m_data, mpf_get_prec(o.data()));
+      }
+      else
+      {
+         mpf_set_prec(this->m_data, mpf_get_prec(o.data()));
+      }
+      mpf_set(this->m_data, o.data());
+      return *this;
+   }
+   gmp_float& operator=(const gmp_int& o);
+   gmp_float& operator=(const gmp_rational& o);
+   gmp_float& operator=(const mpf_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set(this->m_data, val);
+      return *this;
+   }
+   gmp_float& operator=(const mpz_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set_z(this->m_data, val);
+      return *this;
+   }
+   gmp_float& operator=(const mpq_t val)
+   {
+      if(this->m_data[0]._mp_d == 0)
+         mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+      mpf_set_q(this->m_data, val);
+      return *this;
+   }
+   template <class V>
+   gmp_float& operator=(const V& v)
+   {
+      *static_cast<detail::gmp_float_imp<0>*>(this) = v;
+      return *this;
+   }
+   static unsigned default_precision() BOOST_NOEXCEPT
+   {
+      return get_default_precision();
+   }
+   static void default_precision(unsigned v) BOOST_NOEXCEPT
+   {
+      get_default_precision() = v;
+   }
+   unsigned precision()const BOOST_NOEXCEPT
+   {
+      return multiprecision::detail::digits2_2_10(mpf_get_prec(this->m_data));
+   }
+   void precision(unsigned digits10) BOOST_NOEXCEPT
+   {
+      mpf_set_prec(this->m_data, multiprecision::detail::digits10_2_2(digits10));
+   }
+};
+
+template <unsigned digits10, class T>
+inline typename enable_if_c<is_arithmetic<T>::value, bool>::type eval_eq(const gmp_float<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) == 0;
+}
+template <unsigned digits10, class T>
+inline typename enable_if_c<is_arithmetic<T>::value, bool>::type eval_lt(const gmp_float<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) < 0;
+}
+template <unsigned digits10, class T>
+inline typename enable_if_c<is_arithmetic<T>::value, bool>::type eval_gt(const gmp_float<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) > 0;
+}
+
+template <unsigned D1, unsigned D2>
+inline void eval_add(gmp_float<D1>& result, const gmp_float<D2>& o)
+{
+   mpf_add(result.data(), result.data(), o.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(gmp_float<D1>& result, const gmp_float<D2>& o)
+{
+   mpf_sub(result.data(), result.data(), o.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(gmp_float<D1>& result, const gmp_float<D2>& o)
+{
+   mpf_mul(result.data(), result.data(), o.data());
+}
+template <unsigned digits10>
+inline bool eval_is_zero(const gmp_float<digits10>& val) BOOST_NOEXCEPT
+{
+   return mpf_sgn(val.data()) == 0;
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(gmp_float<D1>& result, const gmp_float<D2>& o)
+{
+   if(eval_is_zero(o))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_div(result.data(), result.data(), o.data());
+}
+template <unsigned digits10>
+inline void eval_add(gmp_float<digits10>& result, unsigned long i)
+{
+   mpf_add_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_subtract(gmp_float<digits10>& result, unsigned long i)
+{
+   mpf_sub_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_multiply(gmp_float<digits10>& result, unsigned long i)
+{
+   mpf_mul_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_divide(gmp_float<digits10>& result, unsigned long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_div_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_add(gmp_float<digits10>& result, long i)
+{
+   if(i > 0)
+      mpf_add_ui(result.data(), result.data(), i);
+   else
+      mpf_sub_ui(result.data(), result.data(), std::abs(i));
+}
+template <unsigned digits10>
+inline void eval_subtract(gmp_float<digits10>& result, long i)
+{
+   if(i > 0)
+      mpf_sub_ui(result.data(), result.data(), i);
+   else
+      mpf_add_ui(result.data(), result.data(), std::abs(i));
+}
+template <unsigned digits10>
+inline void eval_multiply(gmp_float<digits10>& result, long i)
+{
+   mpf_mul_ui(result.data(), result.data(), std::abs(i));
+   if(i < 0)
+      mpf_neg(result.data(), result.data());
+}
+template <unsigned digits10>
+inline void eval_divide(gmp_float<digits10>& result, long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_div_ui(result.data(), result.data(), std::abs(i));
+   if(i < 0)
+      mpf_neg(result.data(), result.data());
+}
+//
+// Specialised 3 arg versions of the basic operators:
+//
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_add(gmp_float<D1>& a, const gmp_float<D2>& x, const gmp_float<D3>& y)
+{
+   mpf_add(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(gmp_float<D1>& a, const gmp_float<D2>& x, unsigned long y)
+{
+   mpf_add_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(gmp_float<D1>& a, const gmp_float<D2>& x, long y)
+{
+   if(y < 0)
+      mpf_sub_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
+   else
+      mpf_add_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(gmp_float<D1>& a, unsigned long x, const gmp_float<D2>& y)
+{
+   mpf_add_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(gmp_float<D1>& a, long x, const gmp_float<D2>& y)
+{
+   if(x < 0)
+   {
+      mpf_ui_sub(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
+      mpf_neg(a.data(), a.data());
+   }
+   else
+      mpf_add_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_subtract(gmp_float<D1>& a, const gmp_float<D2>& x, const gmp_float<D3>& y)
+{
+   mpf_sub(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(gmp_float<D1>& a, const gmp_float<D2>& x, unsigned long y)
+{
+   mpf_sub_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(gmp_float<D1>& a, const gmp_float<D2>& x, long y)
+{
+   if(y < 0)
+      mpf_add_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
+   else
+      mpf_sub_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(gmp_float<D1>& a, unsigned long x, const gmp_float<D2>& y)
+{
+   mpf_ui_sub(a.data(), x, y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(gmp_float<D1>& a, long x, const gmp_float<D2>& y)
+{
+   if(x < 0)
+   {
+      mpf_add_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
+      mpf_neg(a.data(), a.data());
+   }
+   else
+      mpf_ui_sub(a.data(), x, y.data());
+}
+
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_multiply(gmp_float<D1>& a, const gmp_float<D2>& x, const gmp_float<D3>& y)
+{
+   mpf_mul(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(gmp_float<D1>& a, const gmp_float<D2>& x, unsigned long y)
+{
+   mpf_mul_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(gmp_float<D1>& a, const gmp_float<D2>& x, long y)
+{
+   if(y < 0)
+   {
+      mpf_mul_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
+      a.negate();
+   }
+   else
+      mpf_mul_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(gmp_float<D1>& a, unsigned long x, const gmp_float<D2>& y)
+{
+   mpf_mul_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(gmp_float<D1>& a, long x, const gmp_float<D2>& y)
+{
+   if(x < 0)
+   {
+      mpf_mul_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
+      mpf_neg(a.data(), a.data());
+   }
+   else
+      mpf_mul_ui(a.data(), y.data(), x);
+}
+
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_divide(gmp_float<D1>& a, const gmp_float<D2>& x, const gmp_float<D3>& y)
+{
+   if(eval_is_zero(y))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_div(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(gmp_float<D1>& a, const gmp_float<D2>& x, unsigned long y)
+{
+   if(y == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_div_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(gmp_float<D1>& a, const gmp_float<D2>& x, long y)
+{
+   if(y == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   if(y < 0)
+   {
+      mpf_div_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
+      a.negate();
+   }
+   else
+      mpf_div_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(gmp_float<D1>& a, unsigned long x, const gmp_float<D2>& y)
+{
+   if(eval_is_zero(y))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpf_ui_div(a.data(), x, y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(gmp_float<D1>& a, long x, const gmp_float<D2>& y)
+{
+   if(eval_is_zero(y))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   if(x < 0)
+   {
+      mpf_ui_div(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
+      mpf_neg(a.data(), a.data());
+   }
+   else
+      mpf_ui_div(a.data(), x, y.data());
+}
+
+template <unsigned digits10>
+inline int eval_get_sign(const gmp_float<digits10>& val) BOOST_NOEXCEPT
+{
+   return mpf_sgn(val.data());
+}
+
+template <unsigned digits10>
+inline void eval_convert_to(unsigned long* result, const gmp_float<digits10>& val) BOOST_NOEXCEPT
+{
+   if(0 == mpf_fits_ulong_p(val.data()))
+      *result = (std::numeric_limits<unsigned long>::max)();
+   else
+      *result = mpf_get_ui(val.data());
+}
+template <unsigned digits10>
+inline void eval_convert_to(long* result, const gmp_float<digits10>& val) BOOST_NOEXCEPT
+{
+   if(0 == mpf_fits_slong_p(val.data()))
+   {
+      *result = (std::numeric_limits<unsigned long>::max)();
+      *result *= mpf_sgn(val.data());
+   }
+   else
+      *result = mpf_get_si(val.data());
+}
+template <unsigned digits10>
+inline void eval_convert_to(double* result, const gmp_float<digits10>& val) BOOST_NOEXCEPT
+{
+   *result = mpf_get_d(val.data());
+}
+#ifdef BOOST_HAS_LONG_LONG
+template <unsigned digits10>
+inline void eval_convert_to(long long* result, const gmp_float<digits10>& val)
+{
+   gmp_float<digits10> t(val);
+   if(eval_get_sign(t) < 0)
+      t.negate();
+
+   long digits = std::numeric_limits<long long>::digits - std::numeric_limits<long>::digits;
+
+   if(digits > 0)
+      mpf_div_2exp(t.data(), t.data(), digits);
+
+   if(!mpf_fits_slong_p(t.data()))
+   {
+      if(eval_get_sign(val) < 0)
+         *result = (std::numeric_limits<long long>::min)();
+      else
+         *result = (std::numeric_limits<long long>::max)();
+      return;
+   };
+
+   *result = mpf_get_si(t.data());
+   while(digits > 0)
+   {
+      *result <<= digits;
+      digits -= std::numeric_limits<unsigned long>::digits;
+      mpf_mul_2exp(t.data(), t.data(), digits >= 0 ? std::numeric_limits<unsigned long>::digits : std::numeric_limits<unsigned long>::digits + digits);
+      unsigned long l = mpf_get_ui(t.data());
+      if(digits < 0)
+         l >>= -digits;
+      *result |= l;
+   }
+   if(eval_get_sign(val) < 0)
+      *result = -*result;
+}
+template <unsigned digits10>
+inline void eval_convert_to(unsigned long long* result, const gmp_float<digits10>& val)
+{
+   gmp_float<digits10> t(val);
+
+   long digits = std::numeric_limits<long long>::digits - std::numeric_limits<long>::digits;
+
+   if(digits > 0)
+      mpf_div_2exp(t.data(), t.data(), digits);
+
+   if(!mpf_fits_ulong_p(t.data()))
+   {
+      *result = (std::numeric_limits<long long>::max)();
+      return;
+   }
+
+   *result = mpf_get_ui(t.data());
+   while(digits > 0)
+   {
+      *result <<= digits;
+      digits -= std::numeric_limits<unsigned long>::digits;
+      mpf_mul_2exp(t.data(), t.data(), digits >= 0 ? std::numeric_limits<unsigned long>::digits : std::numeric_limits<unsigned long>::digits + digits);
+      unsigned long l = mpf_get_ui(t.data());
+      if(digits < 0)
+         l >>= -digits;
+      *result |= l;
+   }
+}
+#endif
+
+//
+// Native non-member operations:
+//
+template <unsigned Digits10>
+inline void eval_sqrt(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_sqrt(result.data(), val.data());
+}
+
+template <unsigned Digits10>
+inline void eval_abs(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_abs(result.data(), val.data());
+}
+
+template <unsigned Digits10>
+inline void eval_fabs(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_abs(result.data(), val.data());
+}
+template <unsigned Digits10>
+inline void eval_ceil(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_ceil(result.data(), val.data());
+}
+template <unsigned Digits10>
+inline void eval_floor(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_floor(result.data(), val.data());
+}
+template <unsigned Digits10>
+inline void eval_trunc(gmp_float<Digits10>& result, const gmp_float<Digits10>& val)
+{
+   mpf_trunc(result.data(), val.data());
+}
+template <unsigned Digits10>
+inline void eval_ldexp(gmp_float<Digits10>& result, const gmp_float<Digits10>& val, long e)
+{
+   if(e > 0)
+      mpf_mul_2exp(result.data(), val.data(), e);
+   else if(e < 0)
+      mpf_div_2exp(result.data(), val.data(), -e);
+   else
+      result = val;
+}
+template <unsigned Digits10>
+inline void eval_frexp(gmp_float<Digits10>& result, const gmp_float<Digits10>& val, int* e)
+{
+   long v;
+   mpf_get_d_2exp(&v, val.data());
+   *e = v;
+   eval_ldexp(result, val, -v);
+}
+template <unsigned Digits10>
+inline void eval_frexp(gmp_float<Digits10>& result, const gmp_float<Digits10>& val, long* e)
+{
+   mpf_get_d_2exp(e, val.data());
+   eval_ldexp(result, val, -*e);
+}
+
+struct gmp_int
+{
+   typedef mpl::list<long, long long>                     signed_types;
+   typedef mpl::list<unsigned long, unsigned long long>   unsigned_types;
+   typedef mpl::list<double, long double>                 float_types;
+
+   gmp_int()
+   {
+      mpz_init(this->m_data);
+   }
+   gmp_int(const gmp_int& o)
+   {
+      if(o.m_data[0]._mp_d)
+         mpz_init_set(m_data, o.m_data);
+      else
+         mpz_init(this->m_data);
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_int(gmp_int&& o) BOOST_NOEXCEPT
+   {
+      m_data[0] = o.m_data[0];
+      o.m_data[0]._mp_d = 0;
+   }
+#endif
+   explicit gmp_int(const mpf_t val)
+   {
+      mpz_init(this->m_data);
+      mpz_set_f(this->m_data, val);
+   }
+   gmp_int(const mpz_t val)
+   {
+      mpz_init_set(this->m_data, val);
+   }
+   explicit gmp_int(const mpq_t val)
+   {
+      mpz_init(this->m_data);
+      mpz_set_q(this->m_data, val);
+   }
+   template <unsigned Digits10>
+   explicit gmp_int(const gmp_float<Digits10>& o)
+   {
+      mpz_init(this->m_data);
+      mpz_set_f(this->m_data, o.data());
+   }
+   explicit gmp_int(const gmp_rational& o);
+   gmp_int& operator = (const gmp_int& o)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set(m_data, o.m_data);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_int& operator = (gmp_int&& o) BOOST_NOEXCEPT
+   {
+      mpz_swap(m_data, o.m_data);
+      return *this;
+   }
+#endif
+   gmp_int& operator = (unsigned long long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      unsigned long long mask = ((1uLL << std::numeric_limits<unsigned>::digits) - 1);
+      unsigned shift = 0;
+      mpz_t t;
+      mpz_set_ui(m_data, 0);
+      mpz_init_set_ui(t, 0);
+      while(i)
+      {
+         mpz_set_ui(t, static_cast<unsigned>(i & mask));
+         if(shift)
+            mpz_mul_2exp(t, t, shift);
+         mpz_add(m_data, m_data, t);
+         shift += std::numeric_limits<unsigned>::digits;
+         i >>= std::numeric_limits<unsigned>::digits;
+      }
+      mpz_clear(t);
+      return *this;
+   }
+   gmp_int& operator = (long long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      bool neg = i < 0;
+      *this = boost::multiprecision::detail::unsigned_abs(i);
+      if(neg)
+         mpz_neg(m_data, m_data);
+      return *this;
+   }
+   gmp_int& operator = (unsigned long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_ui(m_data, i);
+      return *this;
+   }
+   gmp_int& operator = (long i)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_si(m_data, i);
+      return *this;
+   }
+   gmp_int& operator = (double d)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_d(m_data, d);
+      return *this;
+   }
+   gmp_int& operator = (long double a)
+   {
+      using std::frexp;
+      using std::ldexp;
+      using std::floor;
+
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+
+      if (a == 0) {
+         mpz_set_si(m_data, 0);
+         return *this;
+      }
+
+      if (a == 1) {
+         mpz_set_si(m_data, 1);
+         return *this;
+      }
+
+      BOOST_ASSERT(!(boost::math::isinf)(a));
+      BOOST_ASSERT(!(boost::math::isnan)(a));
+
+      int e;
+      long double f, term;
+      mpz_set_ui(m_data, 0u);
+
+      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;
+         mpz_mul_2exp(m_data, m_data, shift);
+         if(term > 0)
+            mpz_add_ui(m_data, m_data, static_cast<unsigned>(term));
+         else
+            mpz_sub_ui(m_data, m_data, static_cast<unsigned>(-term));
+         f -= term;
+      }
+      if(e > 0)
+         mpz_mul_2exp(m_data, m_data, e);
+      else if(e < 0)
+         mpz_div_2exp(m_data, m_data, -e);
+      return *this;
+   }
+   gmp_int& operator = (const char* s)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      std::size_t n = s ? std::strlen(s) : 0;
+      int radix = 10;
+      if(n && (*s == '0'))
+      {
+         if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
+         {
+            radix = 16;
+            s +=2;
+            n -= 2;
+         }
+         else
+         {
+            radix = 8;
+            n -= 1;
+         }
+      }
+      if(n)
+      {
+         if(0 != mpz_set_str(m_data, s, radix))
+            BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid integer.")));
+      }
+      else
+         mpz_set_ui(m_data, 0);
+      return *this;
+   }
+   gmp_int& operator=(const mpf_t val)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_f(this->m_data, val);
+      return *this;
+   }
+   gmp_int& operator=(const mpz_t val)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set(this->m_data, val);
+      return *this;
+   }
+   gmp_int& operator=(const mpq_t val)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_q(this->m_data, val);
+      return *this;
+   }
+   template <unsigned Digits10>
+   gmp_int& operator=(const gmp_float<Digits10>& o)
+   {
+      if(m_data[0]._mp_d == 0)
+         mpz_init(this->m_data);
+      mpz_set_f(this->m_data, o.data());
+      return *this;
+   }
+   gmp_int& operator=(const gmp_rational& o);
+   void swap(gmp_int& o)
+   {
+      mpz_swap(m_data, o.m_data);
+   }
+   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+
+      int base = 10;
+      if((f & std::ios_base::oct) == std::ios_base::oct)
+         base = 8;
+      else if((f & std::ios_base::hex) == std::ios_base::hex)
+         base = 16;
+      //
+      // sanity check, bases 8 and 16 are only available for positive numbers:
+      //
+      if((base != 10) && (mpz_sgn(m_data) < 0))
+         BOOST_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers"));
+      void *(*alloc_func_ptr) (size_t);
+      void *(*realloc_func_ptr) (void *, size_t, size_t);
+      void (*free_func_ptr) (void *, size_t);
+      const char* ps = mpz_get_str (0, base, m_data);
+      std::string s = ps;
+      mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr);
+      (*free_func_ptr)((void*)ps, std::strlen(ps) + 1);
+
+      if((base != 10) && (f & std::ios_base::showbase))
+      {
+         int pos = s[0] == '-' ? 1 : 0;
+         const char* pp = base == 8 ? "0" : "0x";
+         s.insert(pos, pp);
+      }
+      if((f & std::ios_base::showpos) && (s[0] != '-'))
+         s.insert(0, 1, '+');
+
+      return s;
+   }
+   ~gmp_int() BOOST_NOEXCEPT
+   {
+      if(m_data[0]._mp_d)
+         mpz_clear(m_data);
+   }
+   void negate() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      mpz_neg(m_data, m_data);
+   }
+   int compare(const gmp_int& o)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d && o.m_data[0]._mp_d);
+      return mpz_cmp(m_data, o.m_data);
+   }
+   int compare(long i)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return mpz_cmp_si(m_data, i);
+   }
+   int compare(unsigned long i)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return mpz_cmp_ui(m_data, i);
+   }
+   template <class V>
+   int compare(V v)const
+   {
+      gmp_int d;
+      d = v;
+      return compare(d);
+   }
+   mpz_t& data() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return m_data;
+   }
+   const mpz_t& data()const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0]._mp_d);
+      return m_data;
+   }
+protected:
+   mpz_t m_data;
+};
+
+template <class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_eq(const gmp_int& a, const T& b)
+{
+   return a.compare(b) == 0;
+}
+template <class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_lt(const gmp_int& a, const T& b)
+{
+   return a.compare(b) < 0;
+}
+template <class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_gt(const gmp_int& a, const T& b)
+{
+   return a.compare(b) > 0;
+}
+
+inline bool eval_is_zero(const gmp_int& val)
+{
+   return mpz_sgn(val.data()) == 0;
+}
+inline void eval_add(gmp_int& t, const gmp_int& o)
+{
+   mpz_add(t.data(), t.data(), o.data());
+}
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, const gmp_int& b)
+{
+   mpz_addmul(t.data(), a.data(), b.data());
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, const gmp_int& b)
+{
+   mpz_submul(t.data(), a.data(), b.data());
+}
+inline void eval_subtract(gmp_int& t, const gmp_int& o)
+{
+   mpz_sub(t.data(), t.data(), o.data());
+}
+inline void eval_multiply(gmp_int& t, const gmp_int& o)
+{
+   mpz_mul(t.data(), t.data(), o.data());
+}
+inline void eval_divide(gmp_int& t, const gmp_int& o)
+{
+   if(eval_is_zero(o))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q(t.data(), t.data(), o.data());
+}
+inline void eval_modulus(gmp_int& t, const gmp_int& o)
+{
+   mpz_tdiv_r(t.data(), t.data(), o.data());
+}
+inline void eval_add(gmp_int& t, unsigned long i)
+{
+   mpz_add_ui(t.data(), t.data(), i);
+}
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, unsigned long i)
+{
+   mpz_addmul_ui(t.data(), a.data(), i);
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, unsigned long i)
+{
+   mpz_submul_ui(t.data(), a.data(), i);
+}
+inline void eval_subtract(gmp_int& t, unsigned long i)
+{
+   mpz_sub_ui(t.data(), t.data(), i);
+}
+inline void eval_multiply(gmp_int& t, unsigned long i)
+{
+   mpz_mul_ui(t.data(), t.data(), i);
+}
+inline void eval_modulus(gmp_int& t, unsigned long i)
+{
+   mpz_tdiv_r_ui(t.data(), t.data(), i);
+}
+inline void eval_divide(gmp_int& t, unsigned long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q_ui(t.data(), t.data(), i);
+}
+inline void eval_add(gmp_int& t, long i)
+{
+   if(i > 0)
+      mpz_add_ui(t.data(), t.data(), i);
+   else
+      mpz_sub_ui(t.data(), t.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, long i)
+{
+   if(i > 0)
+      mpz_addmul_ui(t.data(), a.data(), i);
+   else
+      mpz_submul_ui(t.data(), a.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, long i)
+{
+   if(i > 0)
+      mpz_submul_ui(t.data(), a.data(), i);
+   else
+      mpz_addmul_ui(t.data(), a.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_subtract(gmp_int& t, long i)
+{
+   if(i > 0)
+      mpz_sub_ui(t.data(), t.data(), i);
+   else
+      mpz_add_ui(t.data(), t.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_multiply(gmp_int& t, long i)
+{
+   mpz_mul_ui(t.data(), t.data(), std::abs(i));
+   if(i < 0)
+      mpz_neg(t.data(), t.data());
+}
+inline void eval_modulus(gmp_int& t, long i)
+{
+   mpz_tdiv_r_ui(t.data(), t.data(), std::abs(i));
+}
+inline void eval_divide(gmp_int& t, long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q_ui(t.data(), t.data(), std::abs(i));
+   if(i < 0)
+      mpz_neg(t.data(), t.data());
+}
+template <class UI>
+inline void eval_left_shift(gmp_int& t, UI i)
+{
+   mpz_mul_2exp(t.data(), t.data(), static_cast<unsigned long>(i));
+}
+template <class UI>
+inline void eval_right_shift(gmp_int& t, UI i)
+{
+   mpz_fdiv_q_2exp(t.data(), t.data(), static_cast<unsigned long>(i));
+}
+template <class UI>
+inline void eval_left_shift(gmp_int& t, const gmp_int& v, UI i)
+{
+   mpz_mul_2exp(t.data(), v.data(), static_cast<unsigned long>(i));
+}
+template <class UI>
+inline void eval_right_shift(gmp_int& t, const gmp_int& v, UI i)
+{
+   mpz_fdiv_q_2exp(t.data(), v.data(), static_cast<unsigned long>(i));
+}
+
+inline void eval_bitwise_and(gmp_int& result, const gmp_int& v)
+{
+   mpz_and(result.data(), result.data(), v.data());
+}
+
+inline void eval_bitwise_or(gmp_int& result, const gmp_int& v)
+{
+   mpz_ior(result.data(), result.data(), v.data());
+}
+
+inline void eval_bitwise_xor(gmp_int& result, const gmp_int& v)
+{
+   mpz_xor(result.data(), result.data(), v.data());
+}
+
+inline void eval_add(gmp_int& t, const gmp_int& p, const gmp_int& o)
+{
+   mpz_add(t.data(), p.data(), o.data());
+}
+inline void eval_subtract(gmp_int& t, const gmp_int& p, const gmp_int& o)
+{
+   mpz_sub(t.data(), p.data(), o.data());
+}
+inline void eval_multiply(gmp_int& t, const gmp_int& p, const gmp_int& o)
+{
+   mpz_mul(t.data(), p.data(), o.data());
+}
+inline void eval_divide(gmp_int& t, const gmp_int& p, const gmp_int& o)
+{
+   if(eval_is_zero(o))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q(t.data(), p.data(), o.data());
+}
+inline void eval_modulus(gmp_int& t, const gmp_int& p, const gmp_int& o)
+{
+   mpz_tdiv_r(t.data(), p.data(), o.data());
+}
+inline void eval_add(gmp_int& t, const gmp_int& p, unsigned long i)
+{
+   mpz_add_ui(t.data(), p.data(), i);
+}
+inline void eval_subtract(gmp_int& t, const gmp_int& p, unsigned long i)
+{
+   mpz_sub_ui(t.data(), p.data(), i);
+}
+inline void eval_multiply(gmp_int& t, const gmp_int& p, unsigned long i)
+{
+   mpz_mul_ui(t.data(), p.data(), i);
+}
+inline void eval_modulus(gmp_int& t, const gmp_int& p, unsigned long i)
+{
+   mpz_tdiv_r_ui(t.data(), p.data(), i);
+}
+inline void eval_divide(gmp_int& t, const gmp_int& p, unsigned long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q_ui(t.data(), p.data(), i);
+}
+inline void eval_add(gmp_int& t, const gmp_int& p, long i)
+{
+   if(i > 0)
+      mpz_add_ui(t.data(), p.data(), i);
+   else
+      mpz_sub_ui(t.data(), p.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_subtract(gmp_int& t, const gmp_int& p, long i)
+{
+   if(i > 0)
+      mpz_sub_ui(t.data(), p.data(), i);
+   else
+      mpz_add_ui(t.data(), p.data(), boost::multiprecision::detail::unsigned_abs(i));
+}
+inline void eval_multiply(gmp_int& t, const gmp_int& p, long i)
+{
+   mpz_mul_ui(t.data(), p.data(), std::abs(i));
+   if(i < 0)
+      mpz_neg(t.data(), t.data());
+}
+inline void eval_modulus(gmp_int& t, const gmp_int& p, long i)
+{
+   mpz_tdiv_r_ui(t.data(), p.data(), std::abs(i));
+}
+inline void eval_divide(gmp_int& t, const gmp_int& p, long i)
+{
+   if(i == 0)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpz_tdiv_q_ui(t.data(), p.data(), std::abs(i));
+   if(i < 0)
+      mpz_neg(t.data(), t.data());
+}
+
+inline void eval_bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v)
+{
+   mpz_and(result.data(), u.data(), v.data());
+}
+
+inline void eval_bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v)
+{
+   mpz_ior(result.data(), u.data(), v.data());
+}
+
+inline void eval_bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v)
+{
+   mpz_xor(result.data(), u.data(), v.data());
+}
+
+inline void eval_complement(gmp_int& result, const gmp_int& u)
+{
+   mpz_com(result.data(), u.data());
+}
+
+inline int eval_get_sign(const gmp_int& val)
+{
+   return mpz_sgn(val.data());
+}
+inline void eval_convert_to(unsigned long* result, const gmp_int& val)
+{
+   if(0 == mpz_fits_ulong_p(val.data()))
+   {
+      *result = (std::numeric_limits<unsigned long>::max)();
+   }
+   else
+      *result = mpz_get_ui(val.data());
+}
+inline void eval_convert_to(long* result, const gmp_int& val)
+{
+   if(0 == mpz_fits_slong_p(val.data()))
+   {
+      *result = (std::numeric_limits<unsigned long>::max)();
+      *result *= mpz_sgn(val.data());
+   }
+   else
+      *result = mpz_get_si(val.data());
+}
+inline void eval_convert_to(double* result, const gmp_int& val)
+{
+   *result = mpz_get_d(val.data());
+}
+
+inline void eval_abs(gmp_int& result, const gmp_int& val)
+{
+   mpz_abs(result.data(), val.data());
+}
+
+inline void eval_gcd(gmp_int& result, const gmp_int& a, const gmp_int& b)
+{
+   mpz_gcd(result.data(), a.data(), b.data());
+}
+inline void eval_lcm(gmp_int& result, const gmp_int& a, const gmp_int& b)
+{
+   mpz_lcm(result.data(), a.data(), b.data());
+}
+template <class I>
+inline typename enable_if_c<(is_unsigned<I>::value && (sizeof(I) <= sizeof(unsigned long)))>::type eval_gcd(gmp_int& result, const gmp_int& a, const I b)
+{
+   mpz_gcd_ui(result.data(), a.data(), b);
+}
+template <class I>
+inline typename enable_if_c<(is_unsigned<I>::value && (sizeof(I) <= sizeof(unsigned long)))>::type eval_lcm(gmp_int& result, const gmp_int& a, const I b)
+{
+   mpz_lcm_ui(result.data(), a.data(), b);
+}
+template <class I>
+inline typename enable_if_c<(is_signed<I>::value && (sizeof(I) <= sizeof(long)))>::type eval_gcd(gmp_int& result, const gmp_int& a, const I b)
+{
+   mpz_gcd_ui(result.data(), a.data(), std::abs(b));
+}
+template <class I>
+inline typename enable_if_c<is_signed<I>::value && ((sizeof(I) <= sizeof(long)))>::type eval_lcm(gmp_int& result, const gmp_int& a, const I b)
+{
+   mpz_lcm_ui(result.data(), a.data(), std::abs(b));
+}
+
+inline void eval_integer_sqrt(gmp_int& s, gmp_int& r, const gmp_int& x)
+{
+   mpz_sqrtrem(s.data(), r.data(), x.data());
+}
+
+inline unsigned eval_lsb(const gmp_int& val)
+{
+   int c = eval_get_sign(val);
+   if(c == 0)
+   {
+      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
+   }
+   if(c < 0)
+   {
+      BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
+   }
+   return mpz_scan1(val.data(), 0);
+}
+
+inline unsigned eval_msb(const gmp_int& val)
+{
+   int c = eval_get_sign(val);
+   if(c == 0)
+   {
+      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
+   }
+   if(c < 0)
+   {
+      BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
+   }
+   return mpz_sizeinbase(val.data(), 2) - 1;
+}
+
+inline bool eval_bit_test(const gmp_int& val, unsigned index)
+{
+   return mpz_tstbit(val.data(), index) ? true : false;
+}
+
+inline void eval_bit_set(gmp_int& val, unsigned index)
+{
+   mpz_setbit(val.data(), index);
+}
+
+inline void eval_bit_unset(gmp_int& val, unsigned index)
+{
+   mpz_clrbit(val.data(), index);
+}
+
+inline void eval_bit_flip(gmp_int& val, unsigned index)
+{
+   mpz_combit(val.data(), index);
+}
+
+inline void eval_qr(const gmp_int& x, const gmp_int& y,
+   gmp_int& q, gmp_int& r)
+{
+   mpz_tdiv_qr(q.data(), r.data(), x.data(), y.data());
+}
+
+template <class Integer>
+inline typename enable_if<is_unsigned<Integer>, Integer>::type eval_integer_modulus(const gmp_int& x, Integer val)
+{
+   if((sizeof(Integer) <= sizeof(long)) || (val <= (std::numeric_limits<unsigned long>::max)()))
+   {
+      return mpz_tdiv_ui(x.data(), val);
+   }
+   else
+   {
+      return default_ops::eval_integer_modulus(x, val);
+   }
+}
+template <class Integer>
+inline typename enable_if<is_signed<Integer>, Integer>::type eval_integer_modulus(const gmp_int& x, Integer val)
+{
+   typedef typename make_unsigned<Integer>::type unsigned_type;
+   return eval_integer_modulus(x, static_cast<unsigned_type>(std::abs(val)));
+}
+inline void eval_powm(gmp_int& result, const gmp_int& base, const gmp_int& p, const gmp_int& m)
+{
+   if(eval_get_sign(p) < 0)
+   {
+      BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
+   }
+   mpz_powm(result.data(), base.data(), p.data(), m.data());
+}
+
+template <class Integer>
+inline typename enable_if<
+   mpl::and_<
+      is_unsigned<Integer>,
+      mpl::bool_<sizeof(Integer) <= sizeof(unsigned long)>
+   >
+>::type eval_powm(gmp_int& result, const gmp_int& base, Integer p, const gmp_int& m)
+{
+   mpz_powm_ui(result.data(), base.data(), p, m.data());
+}
+template <class Integer>
+inline typename enable_if<
+   mpl::and_<
+      is_signed<Integer>,
+      mpl::bool_<sizeof(Integer) <= sizeof(unsigned long)>
+   >
+>::type eval_powm(gmp_int& result, const gmp_int& base, Integer p, const gmp_int& m)
+{
+   if(p < 0)
+   {
+      BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
+   }
+   mpz_powm_ui(result.data(), base.data(), p, m.data());
+}
+
+struct gmp_rational;
+void eval_add(gmp_rational& t, const gmp_rational& o);
+
+struct gmp_rational
+{
+   typedef mpl::list<long, long long>                 signed_types;
+   typedef mpl::list<unsigned long, unsigned long long>   unsigned_types;
+   typedef mpl::list<double, long double>            float_types;
+
+   gmp_rational()
+   {
+      mpq_init(this->m_data);
+   }
+   gmp_rational(const gmp_rational& o)
+   {
+      mpq_init(m_data);
+      if(o.m_data[0]._mp_num._mp_d)
+         mpq_set(m_data, o.m_data);
+   }
+   gmp_rational(const gmp_int& o)
+   {
+      mpq_init(m_data);
+      mpq_set_z(m_data, o.data());
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_rational(gmp_rational&& o) BOOST_NOEXCEPT
+   {
+      m_data[0] = o.m_data[0];
+      o.m_data[0]._mp_num._mp_d = 0;
+      o.m_data[0]._mp_den._mp_d = 0;
+   }
+#endif
+   gmp_rational(const mpq_t o)
+   {
+      mpq_init(m_data);
+      mpq_set(m_data, o);
+   }
+   gmp_rational(const mpz_t o)
+   {
+      mpq_init(m_data);
+      mpq_set_z(m_data, o);
+   }
+   gmp_rational& operator = (const gmp_rational& o)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set(m_data, o.m_data);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   gmp_rational& operator = (gmp_rational&& o) BOOST_NOEXCEPT
+   {
+      mpq_swap(m_data, o.m_data);
+      return *this;
+   }
+#endif
+   gmp_rational& operator = (unsigned long long i)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      unsigned long long mask = ((1uLL << std::numeric_limits<unsigned>::digits) - 1);
+      unsigned shift = 0;
+      mpq_t t;
+      mpq_set_ui(m_data, 0, 1);
+      mpq_init(t);
+      while(i)
+      {
+         mpq_set_ui(t, static_cast<unsigned>(i & mask), 1);
+         if(shift)
+            mpq_mul_2exp(t, t, shift);
+         mpq_add(m_data, m_data, t);
+         shift += std::numeric_limits<unsigned>::digits;
+         i >>= std::numeric_limits<unsigned>::digits;
+      }
+      mpq_clear(t);
+      return *this;
+   }
+   gmp_rational& operator = (long long i)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      bool neg = i < 0;
+      *this = boost::multiprecision::detail::unsigned_abs(i);
+      if(neg)
+         mpq_neg(m_data, m_data);
+      return *this;
+   }
+   gmp_rational& operator = (unsigned long i)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set_ui(m_data, i, 1);
+      return *this;
+   }
+   gmp_rational& operator = (long i)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set_si(m_data, i, 1);
+      return *this;
+   }
+   gmp_rational& operator = (double d)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set_d(m_data, d);
+      return *this;
+   }
+   gmp_rational& operator = (long double a)
+   {
+      using std::frexp;
+      using std::ldexp;
+      using std::floor;
+      using default_ops::eval_add;
+      using default_ops::eval_subtract;
+
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+
+      if (a == 0) {
+         mpq_set_si(m_data, 0, 1);
+         return *this;
+      }
+
+      if (a == 1) {
+         mpq_set_si(m_data, 1, 1);
+         return *this;
+      }
+
+      BOOST_ASSERT(!(boost::math::isinf)(a));
+      BOOST_ASSERT(!(boost::math::isnan)(a));
+
+      int e;
+      long double f, term;
+      mpq_set_ui(m_data, 0, 1);
+      mpq_set_ui(m_data, 0u, 1);
+      gmp_rational t;
+
+      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;
+         mpq_mul_2exp(m_data, m_data, shift);
+         t = static_cast<long>(term);
+         eval_add(*this, t);
+         f -= term;
+      }
+      if(e > 0)
+         mpq_mul_2exp(m_data, m_data, e);
+      else if(e < 0)
+         mpq_div_2exp(m_data, m_data, -e);
+      return *this;
+   }
+   gmp_rational& operator = (const char* s)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      if(0 != mpq_set_str(m_data, s, 10))
+         BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid rational number.")));
+      return *this;
+   }
+   gmp_rational& operator=(const gmp_int& o)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set_z(m_data, o.data());
+      return *this;
+   }
+   gmp_rational& operator=(const mpq_t o)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set(m_data, o);
+      return *this;
+   }
+   gmp_rational& operator=(const mpz_t o)
+   {
+      if(m_data[0]._mp_den._mp_d == 0)
+         mpq_init(m_data);
+      mpq_set_z(m_data, o);
+      return *this;
+   }
+   void swap(gmp_rational& o)
+   {
+      mpq_swap(m_data, o.m_data);
+   }
+   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags /*f*/)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      // TODO make a better job of this including handling of f!!
+      void *(*alloc_func_ptr) (size_t);
+      void *(*realloc_func_ptr) (void *, size_t, size_t);
+      void (*free_func_ptr) (void *, size_t);
+      const char* ps = mpq_get_str (0, 10, m_data);
+      std::string s = ps;
+      mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr);
+      (*free_func_ptr)((void*)ps, std::strlen(ps) + 1);
+      return s;
+   }
+   ~gmp_rational()
+   {
+      if(m_data[0]._mp_num._mp_d || m_data[0]._mp_den._mp_d)
+         mpq_clear(m_data);
+   }
+   void negate()
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      mpq_neg(m_data, m_data);
+   }
+   int compare(const gmp_rational& o)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d && o.m_data[0]._mp_num._mp_d);
+      return mpq_cmp(m_data, o.m_data);
+   }
+   template <class V>
+   int compare(V v)const
+   {
+      gmp_rational d;
+      d = v;
+      return compare(d);
+   }
+   int compare(unsigned long v)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      return mpq_cmp_ui(m_data, v, 1);
+   }
+   int compare(long v)const
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      return mpq_cmp_si(m_data, v, 1);
+   }
+   mpq_t& data()
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      return m_data;
+   }
+   const mpq_t& data()const
+   {
+      BOOST_ASSERT(m_data[0]._mp_num._mp_d);
+      return m_data;
+   }
+protected:
+   mpq_t m_data;
+};
+
+inline bool eval_is_zero(const gmp_rational& val)
+{
+   return mpq_sgn(val.data()) == 0;
+}
+template <class T>
+inline bool eval_eq(gmp_rational& a, const T& b)
+{
+   return a.compare(b) == 0;
+}
+template <class T>
+inline bool eval_lt(gmp_rational& a, const T& b)
+{
+   return a.compare(b) < 0;
+}
+template <class T>
+inline bool eval_gt(gmp_rational& a, const T& b)
+{
+   return a.compare(b) > 0;
+}
+
+inline void eval_add(gmp_rational& t, const gmp_rational& o)
+{
+   mpq_add(t.data(), t.data(), o.data());
+}
+inline void eval_subtract(gmp_rational& t, const gmp_rational& o)
+{
+   mpq_sub(t.data(), t.data(), o.data());
+}
+inline void eval_multiply(gmp_rational& t, const gmp_rational& o)
+{
+   mpq_mul(t.data(), t.data(), o.data());
+}
+inline void eval_divide(gmp_rational& t, const gmp_rational& o)
+{
+   if(eval_is_zero(o))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpq_div(t.data(), t.data(), o.data());
+}
+inline void eval_add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o)
+{
+   mpq_add(t.data(), p.data(), o.data());
+}
+inline void eval_subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o)
+{
+   mpq_sub(t.data(), p.data(), o.data());
+}
+inline void eval_multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o)
+{
+   mpq_mul(t.data(), p.data(), o.data());
+}
+inline void eval_divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o)
+{
+   if(eval_is_zero(o))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   mpq_div(t.data(), p.data(), o.data());
+}
+
+inline int eval_get_sign(const gmp_rational& val)
+{
+   return mpq_sgn(val.data());
+}
+inline void eval_convert_to(double* result, const gmp_rational& val)
+{
+   //
+   // This does not round correctly:
+   //
+   //*result = mpq_get_d(val.data());
+   //
+   // This does:
+   //
+   boost::multiprecision::detail::generic_convert_rational_to_float(*result, val);
+}
+
+inline void eval_convert_to(long* result, const gmp_rational& val)
+{
+   double r;
+   eval_convert_to(&r, val);
+   *result = static_cast<long>(r);
+}
+
+inline void eval_convert_to(unsigned long* result, const gmp_rational& val)
+{
+   double r;
+   eval_convert_to(&r, val);
+   *result = static_cast<long>(r);
+}
+
+inline void eval_abs(gmp_rational& result, const gmp_rational& val)
+{
+   mpq_abs(result.data(), val.data());
+}
+
+inline void assign_components(gmp_rational& result, unsigned long v1, unsigned long v2)
+{
+   mpq_set_ui(result.data(), v1, v2);
+   mpq_canonicalize(result.data());
+}
+inline void assign_components(gmp_rational& result, long v1, long v2)
+{
+   mpq_set_si(result.data(), v1, v2);
+   mpq_canonicalize(result.data());
+}
+inline void assign_components(gmp_rational& result, gmp_int const& v1, gmp_int const& v2)
+{
+   mpz_set(mpq_numref(result.data()), v1.data());
+   mpz_set(mpq_denref(result.data()), v2.data());
+   mpq_canonicalize(result.data());
+}
+
+//
+// Some member functions that are dependent upon previous code go here:
+//
+template <unsigned Digits10>
+template <unsigned D>
+inline gmp_float<Digits10>::gmp_float(const gmp_float<D>& o, typename enable_if_c<D <= Digits10>::type*)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set(this->m_data, o.data());
+}
+template <unsigned Digits10>
+template <unsigned D>
+inline gmp_float<Digits10>::gmp_float(const gmp_float<D>& o, typename disable_if_c<D <= Digits10>::type*)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set(this->m_data, o.data());
+}
+template <unsigned Digits10>
+inline gmp_float<Digits10>::gmp_float(const gmp_int& o)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set_z(this->data(), o.data());
+}
+template <unsigned Digits10>
+inline gmp_float<Digits10>::gmp_float(const gmp_rational& o)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set_q(this->data(), o.data());
+}
+template <unsigned Digits10>
+template <unsigned D>
+inline gmp_float<Digits10>& gmp_float<Digits10>::operator=(const gmp_float<D>& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set(this->m_data, o.data());
+   return *this;
+}
+template <unsigned Digits10>
+inline gmp_float<Digits10>& gmp_float<Digits10>::operator=(const gmp_int& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set_z(this->data(), o.data());
+   return *this;
+}
+template <unsigned Digits10>
+inline gmp_float<Digits10>& gmp_float<Digits10>::operator=(const gmp_rational& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision()));
+   mpf_set_q(this->data(), o.data());
+   return *this;
+}
+inline gmp_float<0>::gmp_float(const gmp_int& o)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+   mpf_set_z(this->data(), o.data());
+}
+inline gmp_float<0>::gmp_float(const gmp_rational& o)
+{
+   mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision()));
+   mpf_set_q(this->data(), o.data());
+}
+inline gmp_float<0>& gmp_float<0>::operator=(const gmp_int& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(this->get_default_precision()));
+   mpf_set_z(this->data(), o.data());
+   return *this;
+}
+inline gmp_float<0>& gmp_float<0>::operator=(const gmp_rational& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(this->get_default_precision()));
+   mpf_set_q(this->data(), o.data());
+   return *this;
+}
+inline gmp_int::gmp_int(const gmp_rational& o)
+{
+   mpz_init(this->m_data);
+   mpz_set_q(this->m_data, o.data());
+}
+inline gmp_int& gmp_int::operator=(const gmp_rational& o)
+{
+   if(this->m_data[0]._mp_d == 0)
+      mpz_init(this->m_data);
+   mpz_set_q(this->m_data, o.data());
+   return *this;
+}
+
+} //namespace backends
+
+using boost::multiprecision::backends::gmp_int;
+using boost::multiprecision::backends::gmp_rational;
+using boost::multiprecision::backends::gmp_float;
+
+template <>
+struct component_type<number<gmp_rational> >
+{
+   typedef number<gmp_int> type;
+};
+
+template <expression_template_option ET>
+inline number<gmp_int, ET> numerator(const number<gmp_rational, ET>& val)
+{
+   number<gmp_int, ET> result;
+   mpz_set(result.backend().data(), (mpq_numref(val.backend().data())));
+   return result;
+}
+template <expression_template_option ET>
+inline number<gmp_int, ET> denominator(const number<gmp_rational, ET>& val)
+{
+   number<gmp_int, ET> result;
+   mpz_set(result.backend().data(), (mpq_denref(val.backend().data())));
+   return result;
+}
+
+#ifdef BOOST_NO_SFINAE_EXPR
+
+namespace detail{
+
+template<>
+struct is_explicitly_convertible<canonical<mpf_t, gmp_int>::type, gmp_int> : public mpl::true_ {};
+template<>
+struct is_explicitly_convertible<canonical<mpq_t, gmp_int>::type, gmp_int> : public mpl::true_ {};
+template<unsigned Digits10>
+struct is_explicitly_convertible<gmp_float<Digits10>, gmp_int> : public mpl::true_ {};
+template<>
+struct is_explicitly_convertible<gmp_rational, gmp_int> : public mpl::true_ {};
+template<unsigned D1, unsigned D2>
+struct is_explicitly_convertible<gmp_float<D1>, gmp_float<D2> > : public mpl::true_ {};
+
+}
+
+#endif
+
+template<>
+struct number_category<detail::canonical<mpz_t, gmp_int>::type> : public mpl::int_<number_kind_integer>{};
+template<>
+struct number_category<detail::canonical<mpq_t, gmp_rational>::type> : public mpl::int_<number_kind_rational>{};
+template<>
+struct number_category<detail::canonical<mpf_t, gmp_float<0> >::type> : public mpl::int_<number_kind_floating_point>{};
+
+
+typedef number<gmp_float<50> >    mpf_float_50;
+typedef number<gmp_float<100> >   mpf_float_100;
+typedef number<gmp_float<500> >   mpf_float_500;
+typedef number<gmp_float<1000> >  mpf_float_1000;
+typedef number<gmp_float<0> >     mpf_float;
+typedef number<gmp_int >         mpz_int;
+typedef number<gmp_rational >    mpq_rational;
+
+}}  // namespaces
+
+namespace std{
+
+//
+// numeric_limits [partial] specializations for the types declared in this header:
+//
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+class numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::gmp_float<Digits10>, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   //
+   // min and max values chosen so as to not cause segfaults when calling
+   // mpf_get_str on 64-bit Linux builds.  Possibly we could use larger
+   // exponent values elsewhere.
+   //
+   static number_type (min)()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         value.first = true;
+         value.second = 1;
+         mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), (std::numeric_limits<mp_exp_t>::max)() / 64 + 1);
+      }
+      return value.second;
+   }
+   static number_type (max)()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         value.first = true;
+         value.second = 1;
+         mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), (std::numeric_limits<mp_exp_t>::max)() / 64 + 1);
+      }
+      return value.second;
+   }
+   BOOST_STATIC_CONSTEXPR number_type lowest()
+   {
+      return -(max)();
+   }
+   BOOST_STATIC_CONSTEXPR int digits = static_cast<int>((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301L ? 2 : 1));
+   BOOST_STATIC_CONSTEXPR int digits10 = Digits10;
+   // Have to allow for a possible extra limb inside the gmp data structure:
+   BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2 + ((GMP_LIMB_BITS * 301L) / 1000L);
+   BOOST_STATIC_CONSTEXPR bool is_signed = true;
+   BOOST_STATIC_CONSTEXPR bool is_integer = false;
+   BOOST_STATIC_CONSTEXPR bool is_exact = false;
+   BOOST_STATIC_CONSTEXPR int radix = 2;
+   static number_type epsilon()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         value.first = true;
+         value.second = 1;
+         mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits<number_type>::digits - 1);
+      }
+      return value.second;
+   }
+   // What value should this be????
+   static number_type round_error()
+   {
+      // returns epsilon/2
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         value.first = true;
+         value.second = 1;
+      }
+      return value.second;
+   }
+   BOOST_STATIC_CONSTEXPR long min_exponent = LONG_MIN;
+   BOOST_STATIC_CONSTEXPR long min_exponent10 = (LONG_MIN / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR long max_exponent = LONG_MAX;
+   BOOST_STATIC_CONSTEXPR long max_exponent10 = (LONG_MAX / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   BOOST_STATIC_CONSTEXPR number_type infinity() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type quiet_NaN() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type signaling_NaN() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = true;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
+   BOOST_STATIC_CONSTEXPR bool traps = true;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_indeterminate;
+
+private:
+   struct data_initializer
+   {
+      data_initializer()
+      {
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<digits10> > >::epsilon();
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<digits10> > >::round_error();
+         (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<digits10> > >::min)();
+         (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<digits10> > >::max)();
+      }
+      void do_nothing()const{}
+   };
+   static const data_initializer initializer;
+};
+
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+const typename numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<Digits10>, ExpressionTemplates> >::data_initializer numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<Digits10>, ExpressionTemplates> >::initializer;
+
+template<boost::multiprecision::expression_template_option ExpressionTemplates>
+class numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = false;
+   static number_type (min)() { return number_type(); }
+   static number_type (max)() { return number_type(); }
+   static number_type lowest() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR int digits = 0;
+   BOOST_STATIC_CONSTEXPR int digits10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_digits10 = 0;
+   BOOST_STATIC_CONSTEXPR bool is_signed = false;
+   BOOST_STATIC_CONSTEXPR bool is_integer = false;
+   BOOST_STATIC_CONSTEXPR bool is_exact = false;
+   BOOST_STATIC_CONSTEXPR int radix = 0;
+   static number_type epsilon() { return number_type(); }
+   static number_type round_error() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   static number_type infinity() { return number_type(); }
+   static number_type quiet_NaN() { return number_type(); }
+   static number_type signaling_NaN() { return number_type(); }
+   static number_type denorm_min() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
+   BOOST_STATIC_CONSTEXPR bool traps = false;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_indeterminate;
+};
+
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::digits;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::max_digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_signed;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_integer;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_exact;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::radix;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::min_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::min_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::max_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::max_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::has_infinity;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::has_quiet_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::has_signaling_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::has_denorm;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::has_denorm_loss;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_iec559;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_bounded;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::is_modulo;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::traps;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::tinyness_before;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<0>, ExpressionTemplates> >::round_style;
+
+#endif
+
+template<boost::multiprecision::expression_template_option ExpressionTemplates>
+class numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   //
+   // Largest and smallest numbers are bounded only by available memory, set
+   // to zero:
+   //
+   static number_type (min)()
+   {
+      return number_type();
+   }
+   static number_type (max)()
+   {
+      return number_type();
+   }
+   static number_type lowest() { return (min)(); }
+   BOOST_STATIC_CONSTEXPR int digits = INT_MAX;
+   BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
+   BOOST_STATIC_CONSTEXPR bool is_signed = true;
+   BOOST_STATIC_CONSTEXPR bool is_integer = true;
+   BOOST_STATIC_CONSTEXPR bool is_exact = true;
+   BOOST_STATIC_CONSTEXPR int radix = 2;
+   static number_type epsilon() { return number_type(); }
+   static number_type round_error() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   static number_type infinity() { return number_type(); }
+   static number_type quiet_NaN() { return number_type(); }
+   static number_type signaling_NaN() { return number_type(); }
+   static number_type denorm_min() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
+   BOOST_STATIC_CONSTEXPR bool traps = false;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
+};
+
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::digits;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::max_digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_signed;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_integer;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_exact;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::radix;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::min_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::min_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::max_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::max_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::has_infinity;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::has_quiet_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::has_signaling_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::has_denorm;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::has_denorm_loss;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_iec559;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_bounded;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::is_modulo;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::traps;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::tinyness_before;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_int, ExpressionTemplates> >::round_style;
+
+#endif
+
+template<boost::multiprecision::expression_template_option ExpressionTemplates>
+class numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   //
+   // Largest and smallest numbers are bounded only by available memory, set
+   // to zero:
+   //
+   static number_type (min)()
+   {
+      return number_type();
+   }
+   static number_type (max)()
+   {
+      return number_type();
+   }
+   static number_type lowest() { return (min)(); }
+   // Digits are unbounded, use zero for now:
+   BOOST_STATIC_CONSTEXPR int digits = INT_MAX;
+   BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
+   BOOST_STATIC_CONSTEXPR bool is_signed = true;
+   BOOST_STATIC_CONSTEXPR bool is_integer = false;
+   BOOST_STATIC_CONSTEXPR bool is_exact = true;
+   BOOST_STATIC_CONSTEXPR int radix = 2;
+   static number_type epsilon() { return number_type(); }
+   static number_type round_error() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   static number_type infinity() { return number_type(); }
+   static number_type quiet_NaN() { return number_type(); }
+   static number_type signaling_NaN() { return number_type(); }
+   static number_type denorm_min() { return number_type(); }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
+   BOOST_STATIC_CONSTEXPR bool traps = false;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
+};
+
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::digits;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::max_digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_signed;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_integer;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_exact;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::radix;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::min_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::min_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::max_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::max_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::has_infinity;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::has_quiet_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::has_signaling_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::has_denorm;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::has_denorm_loss;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_iec559;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_bounded;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::is_modulo;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::traps;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::tinyness_before;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_rational, ExpressionTemplates> >::round_style;
+
+#endif
+
+#ifdef BOOST_MSVC
+#pragma warning(pop)
+#endif
+
+} // namespace std
+
+#endif