comparison DEPENDENCIES/generic/include/boost/multiprecision/mpfi.hpp @ 16:2665513ce2d3

Add boost headers

+///////////////////////////////////////////////////////////////////////////////
+//  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_BN_MPFI_HPP
+#define BOOST_MATH_BN_MPFI_HPP
+
+#include <boost/multiprecision/number.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/cstdint.hpp>
+#include <boost/multiprecision/detail/big_lanczos.hpp>
+#include <boost/multiprecision/detail/digits.hpp>
+#include <boost/multiprecision/mpfr.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <mpfi.h>
+#include <cmath>
+#include <algorithm>
+
+namespace boost{
+namespace multiprecision{
+namespace backends{
+
+template <unsigned digits10>
+struct mpfi_float_backend;
+
+} // namespace backends
+
+template <unsigned digits10>
+struct number_category<backends::mpfi_float_backend<digits10> > : public mpl::int_<number_kind_floating_point>{};
+
+struct interval_error : public std::runtime_error
+{
+   interval_error(const std::string& s) : std::runtime_error(s) {}
+};
+
+namespace backends{
+
+namespace detail{
+
+inline int mpfi_sgn(mpfi_srcptr p)
+{
+   if(mpfi_is_zero(p))
+      return 0;
+   if(mpfi_is_strictly_pos(p))
+      return 1;
+   if(mpfi_is_strictly_neg(p))
+      return -1;
+   BOOST_THROW_EXCEPTION(interval_error("Sign of interval is ambiguous."));
+}
+
+template <unsigned digits10>
+struct mpfi_float_imp;
+
+template <unsigned digits10>
+struct mpfi_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;
+
+   mpfi_float_imp()
+   {
+      mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+   }
+   mpfi_float_imp(unsigned prec)
+   {
+      mpfi_init2(m_data, prec);
+   }
+
+   mpfi_float_imp(const mpfi_float_imp& o)
+   {
+      mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      if(o.m_data[0].left._mpfr_d)
+         mpfi_set(m_data, o.m_data);
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_imp(mpfi_float_imp&& o) BOOST_NOEXCEPT
+   {
+      m_data[0] = o.m_data[0];
+      o.m_data[0].left._mpfr_d = 0;
+   }
+#endif
+   mpfi_float_imp& operator = (const mpfi_float_imp& o)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      if(o.m_data[0].left._mpfr_d)
+         mpfi_set(m_data, o.m_data);
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_imp& operator = (mpfi_float_imp&& o) BOOST_NOEXCEPT
+   {
+      mpfi_swap(m_data, o.m_data);
+      return *this;
+   }
+#endif
+#ifdef _MPFR_H_HAVE_INTMAX_T
+   mpfi_float_imp& operator = (unsigned long long i)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfr_set_uj(left_data(), i, GMP_RNDD);
+      mpfr_set_uj(right_data(), i, GMP_RNDU);
+      return *this;
+   }
+   mpfi_float_imp& operator = (long long i)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfr_set_sj(left_data(), i, GMP_RNDD);
+      mpfr_set_sj(right_data(), i, GMP_RNDU);
+      return *this;
+   }
+#else
+   mpfi_float_imp& operator = (unsigned long long i)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_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;
+      mpfi_t t;
+      mpfi_init2(t, (std::max)(static_cast<unsigned>(std::numeric_limits<unsigned long long>::digits), static_cast<unsigned>(multiprecision::detail::digits10_2_2(digits10))));
+      mpfi_set_ui(m_data, 0);
+      while(i)
+      {
+         mpfi_set_ui(t, static_cast<unsigned>(i & mask));
+         if(shift)
+            mpfi_mul_2exp(t, t, shift);
+         mpfi_add(m_data, m_data, t);
+         shift += std::numeric_limits<unsigned>::digits;
+         i >>= std::numeric_limits<unsigned>::digits;
+      }
+      mpfi_clear(t);
+      return *this;
+   }
+   mpfi_float_imp& operator = (long long i)
+   {
+      BOOST_MP_USING_ABS
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      bool neg = i < 0;
+      *this = static_cast<unsigned long long>(abs(i));
+      if(neg)
+         mpfi_neg(m_data, m_data);
+      return *this;
+   }
+#endif
+   mpfi_float_imp& operator = (unsigned long i)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfi_set_ui(m_data, i);
+      return *this;
+   }
+   mpfi_float_imp& operator = (long i)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfi_set_si(m_data, i);
+      return *this;
+   }
+   mpfi_float_imp& operator = (double d)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfi_set_d(m_data, d);
+      return *this;
+   }
+   mpfi_float_imp& operator = (long double a)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+      mpfr_set_ld(left_data(), a, GMP_RNDD);
+      mpfr_set_ld(right_data(), a, GMP_RNDU);
+      return *this;
+   }
+   mpfi_float_imp& operator = (const char* s)
+   {
+      if(m_data[0].left._mpfr_d == 0)
+         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
+
+      if(s && (*s == '{'))
+      {
+         mpfr_float_backend<digits10> a, b;
+         std::string part;
+         const char* p = ++s;
+         while(*p && (*p != ',') && (*p != '}'))
+            ++p;
+         part.assign(s + 1, p);
+         a = part.c_str();
+         s = p;
+         if(*p && (*p != '}'))
+         {
+            ++p;
+            while(*p && (*p != ',') && (*p != '}'))
+               ++p;
+            part.assign(s + 1, p);
+         }
+         else
+            part.erase();
+         b = part.c_str();
+
+         mpfi_interv_fr(m_data, a.data(), b.data());
+      }
+      else if(mpfi_set_str(m_data, s, 10) != 0)
+      {
+         BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number.")));
+      }
+      return *this;
+   }
+   void swap(mpfi_float_imp& o) BOOST_NOEXCEPT
+   {
+      mpfi_swap(m_data, o.m_data);
+   }
+   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+
+      mpfr_float_backend<digits10> a, b;
+
+      mpfi_get_left(a.data(), m_data);
+      mpfi_get_right(b.data(), m_data);
+
+      if(a.compare(b) == 0)
+         return a.str(digits, f);
+
+      return "{" + a.str(digits, f) + "," + b.str(digits, f) + "}";
+   }
+   ~mpfi_float_imp() BOOST_NOEXCEPT
+   {
+      if(m_data[0].left._mpfr_d)
+         mpfi_clear(m_data);
+   }
+   void negate() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      mpfi_neg(m_data, m_data);
+   }
+   int compare(const mpfi_float_imp& o)const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d && o.m_data[0].left._mpfr_d);
+      if(mpfr_cmp(right_data(), o.left_data()) < 0)
+         return -1;
+      if(mpfr_cmp(left_data(), o.right_data()) > 0)
+         return 1;
+      if((mpfr_cmp(left_data(), o.left_data()) == 0) && (mpfr_cmp(right_data(), o.right_data()) == 0))
+         return 0;
+      BOOST_THROW_EXCEPTION(interval_error("Ambiguous comparison between two values."));
+      return 0;
+   }
+   template <class V>
+   int compare(V v)const BOOST_NOEXCEPT
+   {
+      mpfi_float_imp d;
+      d = v;
+      return compare(d);
+   }
+   mpfi_t& data() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return m_data;
+   }
+   const mpfi_t& data()const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return m_data;
+   }
+   mpfr_ptr left_data() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return &(m_data[0].left);
+   }
+   mpfr_srcptr left_data()const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return &(m_data[0].left);
+   }
+   mpfr_ptr right_data() BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return &(m_data[0].right);
+   }
+   mpfr_srcptr right_data()const BOOST_NOEXCEPT
+   {
+      BOOST_ASSERT(m_data[0].left._mpfr_d);
+      return &(m_data[0].right);
+   }
+protected:
+   mpfi_t m_data;
+   static unsigned& get_default_precision() BOOST_NOEXCEPT
+   {
+      static unsigned val = 50;
+      return val;
+   }
+};
+
+} // namespace detail
+
+template <unsigned digits10>
+struct mpfi_float_backend : public detail::mpfi_float_imp<digits10>
+{
+   mpfi_float_backend() : detail::mpfi_float_imp<digits10>() {}
+   mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<digits10>(o) {}
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_backend(mpfi_float_backend&& o) : detail::mpfi_float_imp<digits10>(static_cast<detail::mpfi_float_imp<digits10>&&>(o)) {}
+#endif
+   template <unsigned D>
+   mpfi_float_backend(const mpfi_float_backend<D>& val, typename enable_if_c<D <= digits10>::type* = 0)
+       : detail::mpfi_float_imp<digits10>()
+   {
+      mpfi_set(this->m_data, val.data());
+   }
+   template <unsigned D>
+   explicit mpfi_float_backend(const mpfi_float_backend<D>& val, typename disable_if_c<D <= digits10>::type* = 0)
+       : detail::mpfi_float_imp<digits10>()
+   {
+      mpfi_set(this->m_data, val.data());
+   }
+   mpfi_float_backend(const mpfi_t val)
+       : detail::mpfi_float_imp<digits10>()
+   {
+      mpfi_set(this->m_data, val);
+   }
+   mpfi_float_backend& operator=(const mpfi_float_backend& o)
+   {
+      *static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10> const&>(o);
+      return *this;
+   }
+   template <unsigned D>
+   mpfi_float_backend(const mpfr_float_backend<D>& val, typename enable_if_c<D <= digits10>::type* = 0)
+       : detail::mpfi_float_imp<digits10>()
+   {
+      mpfi_set_fr(this->m_data, val.data());
+   }
+   template <unsigned D>
+   mpfi_float_backend& operator=(const mpfr_float_backend<D>& val)
+   {
+      mpfi_set_fr(this->m_data, val.data());
+      return *this;
+   }
+   template <unsigned D>
+   explicit mpfi_float_backend(const mpfr_float_backend<D>& val, typename disable_if_c<D <= digits10>::type* = 0)
+       : detail::mpfi_float_imp<digits10>()
+   {
+      mpfi_set_fr(this->m_data, val.data());
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_backend& operator=(mpfi_float_backend&& o) BOOST_NOEXCEPT
+   {
+      *static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10>&&>(o);
+      return *this;
+   }
+#endif
+   template <class V>
+   mpfi_float_backend& operator=(const V& v)
+   {
+      *static_cast<detail::mpfi_float_imp<digits10>*>(this) = v;
+      return *this;
+   }
+   mpfi_float_backend& operator=(const mpfi_t val)
+   {
+      mpfi_set(this->m_data, val);
+      return *this;
+   }
+   // We don't change our precision here, this is a fixed precision type:
+   template <unsigned D>
+   mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
+   {
+      mpfi_set(this->m_data, val.data());
+      return *this;
+   }
+};
+
+template <>
+struct mpfi_float_backend<0> : public detail::mpfi_float_imp<0>
+{
+   mpfi_float_backend() : detail::mpfi_float_imp<0>() {}
+   mpfi_float_backend(const mpfi_t val)
+      : detail::mpfi_float_imp<0>(mpfi_get_prec(val))
+   {
+      mpfi_set(this->m_data, val);
+   }
+   mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<0>(o) {}
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_backend(mpfi_float_backend&& o) BOOST_NOEXCEPT : detail::mpfi_float_imp<0>(static_cast<detail::mpfi_float_imp<0>&&>(o)) {}
+#endif
+   mpfi_float_backend(const mpfi_float_backend& o, unsigned digits10)
+      : detail::mpfi_float_imp<0>(digits10)
+   {
+      *this = o;
+   }
+   template <unsigned D>
+   mpfi_float_backend(const mpfi_float_backend<D>& val)
+      : detail::mpfi_float_imp<0>(mpfi_get_prec(val.data()))
+   {
+      mpfi_set(this->m_data, val.data());
+   }
+   mpfi_float_backend& operator=(const mpfi_float_backend& o)
+   {
+      mpfi_set_prec(this->m_data, mpfi_get_prec(o.data()));
+      mpfi_set(this->m_data, o.data());
+      return *this;
+   }
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   mpfi_float_backend& operator=(mpfi_float_backend&& o) BOOST_NOEXCEPT
+   {
+      *static_cast<detail::mpfi_float_imp<0>*>(this) = static_cast<detail::mpfi_float_imp<0> &&>(o);
+      return *this;
+   }
+#endif
+   template <class V>
+   mpfi_float_backend& operator=(const V& v)
+   {
+      *static_cast<detail::mpfi_float_imp<0>*>(this) = v;
+      return *this;
+   }
+   mpfi_float_backend& operator=(const mpfi_t val)
+   {
+      mpfi_set_prec(this->m_data, mpfi_get_prec(val));
+      mpfi_set(this->m_data, val);
+      return *this;
+   }
+   template <unsigned D>
+   mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
+   {
+      mpfi_set_prec(this->m_data, mpfi_get_prec(val.data()));
+      mpfi_set(this->m_data, val.data());
+      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(mpfi_get_prec(this->m_data));
+   }
+   void precision(unsigned digits10) BOOST_NOEXCEPT
+   {
+      mpfi_set_prec(this->m_data, multiprecision::detail::digits2_2_10((digits10)));
+   }
+};
+
+template <unsigned digits10, class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_eq(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) == 0;
+}
+template <unsigned digits10, class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_lt(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) < 0;
+}
+template <unsigned digits10, class T>
+inline typename enable_if<is_arithmetic<T>, bool>::type eval_gt(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
+{
+   return a.compare(b) > 0;
+}
+
+template <unsigned D1, unsigned D2>
+inline void eval_add(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
+{
+   mpfi_add(result.data(), result.data(), o.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
+{
+   mpfi_sub(result.data(), result.data(), o.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
+{
+   if((void*)&result == (void*)&o)
+      mpfi_sqr(result.data(), o.data());
+   else
+      mpfi_mul(result.data(), result.data(), o.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
+{
+   mpfi_div(result.data(), result.data(), o.data());
+}
+template <unsigned digits10>
+inline void eval_add(mpfi_float_backend<digits10>& result, unsigned long i)
+{
+   mpfi_add_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_subtract(mpfi_float_backend<digits10>& result, unsigned long i)
+{
+   mpfi_sub_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_multiply(mpfi_float_backend<digits10>& result, unsigned long i)
+{
+   mpfi_mul_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_divide(mpfi_float_backend<digits10>& result, unsigned long i)
+{
+   mpfi_div_ui(result.data(), result.data(), i);
+}
+template <unsigned digits10>
+inline void eval_add(mpfi_float_backend<digits10>& result, long i)
+{
+   if(i > 0)
+      mpfi_add_ui(result.data(), result.data(), i);
+   else
+      mpfi_sub_ui(result.data(), result.data(), std::abs(i));
+}
+template <unsigned digits10>
+inline void eval_subtract(mpfi_float_backend<digits10>& result, long i)
+{
+   if(i > 0)
+      mpfi_sub_ui(result.data(), result.data(), i);
+   else
+      mpfi_add_ui(result.data(), result.data(), std::abs(i));
+}
+template <unsigned digits10>
+inline void eval_multiply(mpfi_float_backend<digits10>& result, long i)
+{
+   mpfi_mul_ui(result.data(), result.data(), std::abs(i));
+   if(i < 0)
+      mpfi_neg(result.data(), result.data());
+}
+template <unsigned digits10>
+inline void eval_divide(mpfi_float_backend<digits10>& result, long i)
+{
+   mpfi_div_ui(result.data(), result.data(), std::abs(i));
+   if(i < 0)
+      mpfi_neg(result.data(), result.data());
+}
+//
+// Specialised 3 arg versions of the basic operators:
+//
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
+{
+   mpfi_add(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
+{
+   mpfi_add_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
+{
+   if(y < 0)
+      mpfi_sub_ui(a.data(), x.data(), -y);
+   else
+      mpfi_add_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
+{
+   mpfi_add_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_add(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
+{
+   if(x < 0)
+   {
+      mpfi_ui_sub(a.data(), -x, y.data());
+      mpfi_neg(a.data(), a.data());
+   }
+   else
+      mpfi_add_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
+{
+   mpfi_sub(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
+{
+   mpfi_sub_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
+{
+   if(y < 0)
+      mpfi_add_ui(a.data(), x.data(), -y);
+   else
+      mpfi_sub_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
+{
+   mpfi_ui_sub(a.data(), x, y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_subtract(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
+{
+   if(x < 0)
+   {
+      mpfi_add_ui(a.data(), y.data(), -x);
+      mpfi_neg(a.data(), a.data());
+   }
+   else
+      mpfi_ui_sub(a.data(), x, y.data());
+}
+
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
+{
+   if((void*)&x == (void*)&y)
+      mpfi_sqr(a.data(), x.data());
+   else
+      mpfi_mul(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
+{
+   mpfi_mul_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
+{
+   if(y < 0)
+   {
+      mpfi_mul_ui(a.data(), x.data(), -y);
+      a.negate();
+   }
+   else
+      mpfi_mul_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
+{
+   mpfi_mul_ui(a.data(), y.data(), x);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_multiply(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
+{
+   if(x < 0)
+   {
+      mpfi_mul_ui(a.data(), y.data(), -x);
+      mpfi_neg(a.data(), a.data());
+   }
+   else
+      mpfi_mul_ui(a.data(), y.data(), x);
+}
+
+template <unsigned D1, unsigned D2, unsigned D3>
+inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
+{
+   mpfi_div(a.data(), x.data(), y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
+{
+   mpfi_div_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
+{
+   if(y < 0)
+   {
+      mpfi_div_ui(a.data(), x.data(), -y);
+      a.negate();
+   }
+   else
+      mpfi_div_ui(a.data(), x.data(), y);
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
+{
+   mpfi_ui_div(a.data(), x, y.data());
+}
+template <unsigned D1, unsigned D2>
+inline void eval_divide(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
+{
+   if(x < 0)
+   {
+      mpfi_ui_div(a.data(), -x, y.data());
+      mpfi_neg(a.data(), a.data());
+   }
+   else
+      mpfi_ui_div(a.data(), x, y.data());
+}
+
+template <unsigned digits10>
+inline bool eval_is_zero(const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
+{
+   return 0 != mpfi_is_zero(val.data());
+}
+template <unsigned digits10>
+inline int eval_get_sign(const mpfi_float_backend<digits10>& val)
+{
+   return detail::mpfi_sgn(val.data());
+}
+
+template <unsigned digits10>
+inline void eval_convert_to(unsigned long* result, const mpfi_float_backend<digits10>& val)
+{
+   mpfr_float_backend<digits10> t;
+   mpfi_mid(t.data(), val.data());
+   eval_convert_to(result, t);
+}
+template <unsigned digits10>
+inline void eval_convert_to(long* result, const mpfi_float_backend<digits10>& val)
+{
+   mpfr_float_backend<digits10> t;
+   mpfi_mid(t.data(), val.data());
+   eval_convert_to(result, t);
+}
+#ifdef _MPFR_H_HAVE_INTMAX_T
+template <unsigned digits10>
+inline void eval_convert_to(unsigned long long* result, const mpfi_float_backend<digits10>& val)
+{
+   mpfr_float_backend<digits10> t;
+   mpfi_mid(t.data(), val.data());
+   eval_convert_to(result, t);
+}
+template <unsigned digits10>
+inline void eval_convert_to(long long* result, const mpfi_float_backend<digits10>& val)
+{
+   mpfr_float_backend<digits10> t;
+   mpfi_mid(t.data(), val.data());
+   eval_convert_to(result, t);
+}
+#endif
+template <unsigned digits10>
+inline void eval_convert_to(double* result, const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
+{
+   *result = mpfi_get_d(val.data());
+}
+template <unsigned digits10>
+inline void eval_convert_to(long double* result, const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
+{
+   mpfr_float_backend<digits10> t;
+   mpfi_mid(t.data(), val.data());
+   eval_convert_to(result, t);
+}
+
+template <unsigned D1, unsigned D2, mpfr_allocation_type AllocationType>
+inline void assign_components(mpfi_float_backend<D1>& result, const mpfr_float_backend<D2, AllocationType>& a, const mpfr_float_backend<D2, AllocationType>& b)
+{
+   mpfi_interv_fr(result.data(), a.data(), b.data());
+}
+
+template <unsigned Digits10, class V>
+inline typename enable_if_c<is_convertible<V, number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on> >::value >::type 
+   assign_components(mpfi_float_backend<Digits10>& result, const V& a, const V& b)
+{
+   number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on> x(a), y(b);
+   assign_components(result, x.backend(), y.backend());
+}
+
+//
+// Native non-member operations:
+//
+template <unsigned Digits10>
+inline void eval_sqrt(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
+{
+   mpfi_sqrt(result.data(), val.data());
+}
+
+template <unsigned Digits10>
+inline void eval_abs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
+{
+   mpfi_abs(result.data(), val.data());
+}
+
+template <unsigned Digits10>
+inline void eval_fabs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
+{
+   mpfi_abs(result.data(), val.data());
+}
+template <unsigned Digits10>
+inline void eval_ceil(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
+{
+   mpfr_float_backend<Digits10> a, b;
+   mpfr_set(a.data(), val.left_data(), GMP_RNDN);
+   mpfr_set(b.data(), val.right_data(), GMP_RNDN);
+   eval_ceil(a, a);
+   eval_ceil(b, b);
+   if(a.compare(b) != 0)
+   {
+      BOOST_THROW_EXCEPTION(interval_error("Attempt to take the ceil of a value that straddles an integer boundary."));
+   }
+   mpfi_set_fr(result.data(), a.data());
+}
+template <unsigned Digits10>
+inline void eval_floor(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
+{
+   mpfr_float_backend<Digits10> a, b;
+   mpfr_set(a.data(), val.left_data(), GMP_RNDN);
+   mpfr_set(b.data(), val.right_data(), GMP_RNDN);
+   eval_floor(a, a);
+   eval_floor(b, b);
+   if(a.compare(b) != 0)
+   {
+      BOOST_THROW_EXCEPTION(interval_error("Attempt to take the floor of a value that straddles an integer boundary."));
+   }
+   mpfi_set_fr(result.data(), a.data());
+}
+template <unsigned Digits10>
+inline void eval_ldexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long e)
+{
+   if(e > 0)
+      mpfi_mul_2exp(result.data(), val.data(), e);
+   else if(e < 0)
+      mpfi_div_2exp(result.data(), val.data(), -e);
+   else
+      result = val;
+}
+template <unsigned Digits10>
+inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, int* e)
+{
+   mpfr_float_backend<Digits10> t, rt;
+   mpfi_mid(t.data(), val.data());
+   eval_frexp(rt, t, e);
+   eval_ldexp(result, val, -*e);
+}
+template <unsigned Digits10>
+inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long* e)
+{
+   mpfr_float_backend<Digits10> t, rt;
+   mpfi_mid(t.data(), val.data());
+   eval_frexp(rt, t, e);
+   eval_ldexp(result, val, -*e);
+}
+
+template <unsigned Digits10>
+inline int eval_fpclassify(const mpfi_float_backend<Digits10>& val) BOOST_NOEXCEPT
+{
+   return mpfi_inf_p(val.data()) ? FP_INFINITE : mpfi_nan_p(val.data()) ? FP_NAN : mpfi_is_zero(val.data()) ? FP_ZERO : FP_NORMAL;
+}
+
+template <unsigned Digits10>
+inline void eval_pow(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& b, const mpfi_float_backend<Digits10>& e)
+{
+   typedef typename boost::multiprecision::detail::canonical<unsigned, mpfi_float_backend<Digits10> >::type ui_type;
+   using default_ops::eval_get_sign;
+   int s = eval_get_sign(b);
+   if(s == 0)
+   {
+      if(eval_get_sign(e) == 0)
+      {
+         result = ui_type(1);
+      }
+      else
+      {
+         result = ui_type(0);
+      }
+      return;
+   }
+   if(s < 0)
+   {
+      if(eval_get_sign(e) < 0)
+      {
+         mpfi_float_backend<Digits10> t1, t2;
+         t1 = e;
+         t1.negate();
+         eval_pow(t2, b, t1);
+         t1 = ui_type(1);
+         eval_divide(result, t1, t2);
+         return;
+      }
+      typename boost::multiprecision::detail::canonical<boost::uintmax_t, mpfi_float_backend<Digits10> >::type an;
+      try
+      {
+         using default_ops::eval_convert_to;
+         eval_convert_to(&an, e);
+         if(e.compare(an) == 0)
+         {
+            mpfi_float_backend<Digits10> pb(b);
+            pb.negate();
+            eval_pow(result, pb, e);
+            if(an & 1u)
+               result.negate();
+            return;
+         }
+      }
+      catch(const std::exception&)
+      {
+         // conversion failed, just fall through, value is not an integer.
+      }
+      result = std::numeric_limits<number<mpfi_float_backend<Digits10>, et_on> >::quiet_NaN().backend();
+      return;
+   }
+   mpfi_log(result.data(), b.data());
+   mpfi_mul(result.data(), result.data(), e.data());
+   mpfi_exp(result.data(), result.data());
+}
+
+template <unsigned Digits10>
+inline void eval_exp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_exp(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_log(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_log(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_log10(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_log10(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_sin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_sin(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_cos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_cos(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_tan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_tan(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_asin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_asin(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_acos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_acos(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_atan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_atan(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_atan2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg1, const mpfi_float_backend<Digits10>& arg2)
+{
+   mpfi_atan2(result.data(), arg1.data(), arg2.data());
+}
+
+template <unsigned Digits10>
+inline void eval_sinh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_sinh(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_cosh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_cosh(result.data(), arg.data());
+}
+
+template <unsigned Digits10>
+inline void eval_tanh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
+{
+   mpfi_tanh(result.data(), arg.data());
+}
+
+} // namespace backends
+
+#ifdef BOOST_NO_SFINAE_EXPR
+
+namespace detail{
+
+template<unsigned D1, unsigned D2>
+struct is_explicitly_convertible<backends::mpfi_float_backend<D1>, backends::mpfi_float_backend<D2> > : public mpl::true_ {};
+
+}
+
+#endif
+
+template<>
+struct number_category<detail::canonical<mpfi_t, backends::mpfi_float_backend<0> >::type> : public mpl::int_<number_kind_floating_point>{};
+template <unsigned Digits10>
+struct is_interval_number<backends::mpfi_float_backend<Digits10> > : public mpl::true_ {};
+
+using boost::multiprecision::backends::mpfi_float_backend;
+
+typedef number<mpfi_float_backend<50> >    mpfi_float_50;
+typedef number<mpfi_float_backend<100> >   mpfi_float_100;
+typedef number<mpfi_float_backend<500> >   mpfi_float_500;
+typedef number<mpfi_float_backend<1000> >  mpfi_float_1000;
+typedef number<mpfi_float_backend<0> >     mpfi_float;
+
+//
+// Special interval specific functions:
+//
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> lower(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
+{
+   number<mpfr_float_backend<Digits10> > result;
+   mpfr_set(result.backend().data(), val.backend().left_data(), GMP_RNDN);
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> upper(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
+{
+   number<mpfr_float_backend<Digits10> > result;
+   mpfr_set(result.backend().data(), val.backend().right_data(), GMP_RNDN);
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> median(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
+{
+   number<mpfr_float_backend<Digits10> > result;
+   mpfi_mid(result.backend().data(), val.backend().data());
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> width(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
+{
+   number<mpfr_float_backend<Digits10> > result;
+   mpfi_diam_abs(result.backend().data(), val.backend().data());
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> intersect(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
+{
+   number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
+   mpfi_intersect(result.backend().data(), a.backend().data(), b.backend().data());
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> hull(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
+{
+   number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
+   mpfi_union(result.backend().data(), a.backend().data(), b.backend().data());
+   return result;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool overlap(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
+{
+  return (lower(a) <= lower(b) && lower(b) <= upper(a)) ||
+         (lower(b) <= lower(a) && lower(a) <= upper(b));
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates1, expression_template_option ExpressionTemplates2>
+inline bool in(const number<mpfr_float_backend<Digits10>, ExpressionTemplates1>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates2>&  b)
+{
+  return mpfi_is_inside_fr(a.backend().data(), b.backend().data()) != 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool zero_in(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
+{
+  return mpfi_has_zero(a.backend().data()) != 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
+{
+  return mpfi_is_inside(a.backend().data(), b.backend().data()) != 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool proper_subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
+{
+  return mpfi_is_strictly_inside(a.backend().data(), b.backend().data()) != 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool empty(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
+{
+  return mpfi_is_empty(a.backend().data()) != 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+inline bool singleton(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
+{
+  return mpfr_cmp(a.backend().left_data(), a.backend().right_data()) == 0;
+}
+
+template <unsigned Digits10, expression_template_option ExpressionTemplates>
+struct component_type<number<mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef number<mpfr_float_backend<Digits10>, ExpressionTemplates> type;
+};
+
+} // namespace multiprecision
+
+namespace math{
+
+namespace tools{
+
+template <>
+inline int digits<boost::multiprecision::mpfi_float>()
+{
+   return boost::multiprecision::backends::detail::get_default_precision();
+}
+template <>
+inline int digits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
+{
+   return boost::multiprecision::backends::detail::get_default_precision();
+}
+
+} // namespace tools
+
+namespace constants{ namespace detail{
+
+template <class T> struct constant_pi;
+template <class T> struct constant_ln_two;
+template <class T> struct constant_euler;
+template <class T> struct constant_catalan;
+
+//
+// Initializer: ensure all our constants are initialized prior to the first call of main:
+//
+template <class T>
+struct mpfi_initializer
+{
+   struct init
+   {
+      init()
+      {
+         boost::math::constants::pi<T>();
+         boost::math::constants::ln_two<T>();
+         boost::math::constants::euler<T>();
+         boost::math::constants::catalan<T>();
+      }
+      void force_instantiate()const{}
+   };
+   static const init initializer;
+   static void force_instantiate()
+   {
+      initializer.force_instantiate();
+   }
+};
+
+template <class T>
+const typename mpfi_initializer<T>::init mpfi_initializer<T>::initializer;
+
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+struct constant_pi<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
+   template<int N>
+   static inline result_type const& get(const mpl::int_<N>&)
+   {
+      mpfi_initializer<result_type>::force_instantiate();
+      static result_type result;
+      static bool has_init = false;
+      if(!has_init)
+      {
+         has_init = true;
+         mpfi_const_pi(result.backend().data());
+      }
+      return result;
+   }
+};
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+struct constant_ln_two<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
+   template<int N>
+   static inline result_type const& get(const mpl::int_<N>&)
+   {
+      mpfi_initializer<result_type>::force_instantiate();
+      static result_type result;
+      static bool has_init = false;
+      if(!has_init)
+      {
+         has_init = true;
+         mpfi_const_log2(result.backend().data());
+      }
+      return result;
+   }
+};
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+struct constant_euler<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
+   template<int N>
+   static inline result_type const& get(const mpl::int_<N>&)
+   {
+      mpfi_initializer<result_type>::force_instantiate();
+      static result_type result;
+      static bool has_init = false;
+      if(!has_init)
+      {
+         has_init = true;
+         mpfi_const_euler(result.backend().data());
+      }
+      return result;
+   }
+};
+template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+struct constant_catalan<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
+   template<int N>
+   static inline result_type const& get(const mpl::int_<N>&)
+   {
+      mpfi_initializer<result_type>::force_instantiate();
+      static result_type result;
+      static bool has_init = false;
+      if(!has_init)
+      {
+         has_init = true;
+         mpfi_const_catalan(result.backend().data());
+      }
+      return result;
+   }
+};
+
+}} // namespaces
+
+}}  // 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::mpfi_float_backend<Digits10>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   static number_type (min)()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         value.first = true;
+         value.second = 0.5;
+         mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin());
+      }
+      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 = 0.5;
+         mpfi_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax());
+      }
+      return value.second;
+   }
+   BOOST_STATIC_CONSTEXPR number_type lowest()
+   {
+      return -(max)();
+   }
+   BOOST_STATIC_CONSTEXPR int digits = static_cast<int>((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301 ? 2 : 1));
+   BOOST_STATIC_CONSTEXPR int digits10 = Digits10;
+   // Is this really correct???
+   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 = 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;
+         mpfi_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;
+         mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), 1);
+      }
+      return value.second;
+   }
+   BOOST_STATIC_CONSTEXPR long min_exponent = MPFR_EMIN_DEFAULT;
+   BOOST_STATIC_CONSTEXPR long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR long max_exponent = MPFR_EMAX_DEFAULT;
+   BOOST_STATIC_CONSTEXPR long max_exponent10 = (MPFR_EMAX_DEFAULT / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = true;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
+   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()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         boost::multiprecision::mpfr_float_backend<Digits10> t;
+         mpfr_set_inf(t.data(), 1);
+         value.first = true;
+         mpfi_set_fr(value.second.backend().data(), t.data());
+      }
+      return value.second;
+   }
+   static number_type quiet_NaN()
+   {
+      initializer.do_nothing();
+      static std::pair<bool, number_type> value;
+      if(!value.first)
+      {
+         boost::multiprecision::mpfr_float_backend<Digits10> t;
+         mpfr_set_nan(t.data());
+         value.first = true;
+         mpfi_set_fr(value.second.backend().data(), t.data());
+      }
+      return value.second;
+   }
+   BOOST_STATIC_CONSTEXPR number_type signaling_NaN()
+   {
+      return number_type(0);
+   }
+   BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); }
+   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_to_nearest;
+
+private:
+   struct data_initializer
+   {
+      data_initializer()
+      {
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::epsilon();
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::round_error();
+         (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::min)();
+         (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::max)();
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::infinity();
+         std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::quiet_NaN();
+      }
+      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::mpfi_float_backend<Digits10>, ExpressionTemplates> >::data_initializer numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::initializer;
+
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits10;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_digits10;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_signed;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_integer;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_exact;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::radix;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent10;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent10;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_infinity;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_quiet_NaN;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_signaling_NaN;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm_loss;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_iec559;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_bounded;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_modulo;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::traps;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::tinyness_before;
+template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::round_style;
+
+#endif
+
+
+template<boost::multiprecision::expression_template_option ExpressionTemplates>
+class numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = false;
+   static number_type (min)() { return number_type(0); }
+   static number_type (max)() { return number_type(0); }
+   static number_type lowest() { return number_type(0); }
+   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(0); }
+   static number_type round_error() { return number_type(0); }
+   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(0); }
+   static number_type quiet_NaN() { return number_type(0); }
+   static number_type signaling_NaN() { return number_type(0); }
+   static number_type denorm_min() { return number_type(0); }
+   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::mpfi_float_backend<0>, ExpressionTemplates> >::digits;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_digits10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_signed;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_integer;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_exact;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::radix;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent10;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_infinity;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_quiet_NaN;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<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::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm_loss;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_iec559;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_bounded;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_modulo;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::traps;
+template <boost::multiprecision::expression_template_option ExpressionTemplates>
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<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::mpfi_float_backend<0>, ExpressionTemplates> >::round_style;
+
+#endif
+} // namespace std
+#endif