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/usr/include/boost/multiprecision

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

Edit: /usr/include/boost/multiprecision/mpfi.hpp (76273B)

#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/detail/atomic.hpp>
#include <boost/multiprecision/mpfr.hpp>
#include <boost/multiprecision/logged_adaptor.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/functional/hash_fwd.hpp>
#include <mpfi.h>
#include <cmath>
#include <algorithm>

#ifndef BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION
#define BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION 20
#endif

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
{
#ifdef BOOST_HAS_LONG_LONG
   typedef mpl::list<long, boost::long_long_type>           signed_types;
   typedef mpl::list<unsigned long, boost::ulong_long_type> unsigned_types;
#else
   typedef mpl::list<long>          signed_types;
   typedef mpl::list<unsigned long> unsigned_types;
#endif
   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 : (unsigned)get_default_precision()));
      mpfi_set_ui(m_data, 0u);
   }
   mpfi_float_imp(unsigned prec)
   {
      mpfi_init2(m_data, prec);
      mpfi_set_ui(m_data, 0u);
   }

mpfi_float_imp(const mpfi_float_imp& o)
   {
      mpfi_init2(m_data, mpfi_get_prec(o.data()));
      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, mpfi_get_prec(o.data()));
      if (mpfi_get_prec(o.data()) != mpfi_get_prec(data()))
      {
         mpfi_float_imp t(mpfi_get_prec(o.data()));
         t = o;
         t.swap(*this);
      }
      else
      {
         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 BOOST_HAS_LONG_LONG
#ifdef _MPFR_H_HAVE_INTMAX_T
   mpfi_float_imp& operator=(boost::ulong_long_type i)
   {
      if (m_data[0].left._mpfr_d == 0)
         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)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=(boost::long_long_type i)
   {
      if (m_data[0].left._mpfr_d == 0)
         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)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=(boost::ulong_long_type i)
   {
      if (m_data[0].left._mpfr_d == 0)
         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
      boost::ulong_long_type mask  = ((((1uLL << (std::numeric_limits<unsigned long>::digits - 1)) - 1) << 1) | 1u);
      unsigned               shift = 0;
      mpfi_t                 t;
      mpfi_init2(t, (std::max)(static_cast<unsigned long>(std::numeric_limits<boost::ulong_long_type>::digits), static_cast<unsigned long>(multiprecision::detail::digits10_2_2(digits10))));
      mpfi_set_ui(m_data, 0);
      while (i)
      {
         mpfi_set_ui(t, static_cast<unsigned long>(i & mask));
         if (shift)
            mpfi_mul_2exp(t, t, shift);
         mpfi_add(m_data, m_data, t);
         shift += std::numeric_limits<unsigned long>::digits;
         i >>= std::numeric_limits<unsigned long>::digits;
      }
      mpfi_clear(t);
      return *this;
   }
   mpfi_float_imp& operator=(boost::long_long_type i)
   {
      if (m_data[0].left._mpfr_d == 0)
         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
      bool neg = i < 0;
      *this    = boost::multiprecision::detail::unsigned_abs(i);
      if (neg)
         mpfi_neg(m_data, m_data);
      return *this;
   }
#endif
#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 : (unsigned)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 : (unsigned)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 : (unsigned)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 : (unsigned)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)
   {
      using default_ops::eval_fpclassify;

if (m_data[0].left._mpfr_d == 0)
         mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)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();

if (eval_fpclassify(a) == (int)FP_NAN)
         {
            mpfi_set_fr(this->data(), a.data());
         }
         else if (eval_fpclassify(b) == (int)FP_NAN)
         {
            mpfi_set_fr(this->data(), b.data());
         }
         else
         {
            if (a.compare(b) > 0)
            {
               BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
            }
            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 boost::multiprecision::detail::precision_type& get_default_precision() BOOST_NOEXCEPT
   {
      static boost::multiprecision::detail::precision_type val(BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION);
      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 <unsigned D1, unsigned D2, mpfr_allocation_type AllocationType>
void assign_components(mpfi_float_backend<D1>& result, const mpfr_float_backend<D2, AllocationType>& a, const mpfr_float_backend<D2, AllocationType>& b);

template <unsigned Digits10, class V>
typename enable_if_c<boost::is_constructible<number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on>, V>::value || boost::is_convertible<V, const char*>::value>::type
assign_components(mpfi_float_backend<Digits10>& result, const V& a, const V& b);

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>(multiprecision::detail::digits10_2_2(digits10))
   {
      mpfi_set(this->m_data, o.data());
   }
   template <class V>
   mpfi_float_backend(const V& a, const V& b, unsigned digits10)
       : detail::mpfi_float_imp<0>(multiprecision::detail::digits10_2_2(digits10))
   {
      assign_components(*this, a, b);
   }

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_float_backend t(*this, digits10);
      this->swap(t);
   }
};

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(), boost::multiprecision::detail::unsigned_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(), boost::multiprecision::detail::unsigned_abs(i));
}
template <unsigned digits10>
inline void eval_multiply(mpfi_float_backend<digits10>& result, long i)
{
   mpfi_mul_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_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(), boost::multiprecision::detail::unsigned_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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(), boost::multiprecision::detail::unsigned_abs(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(boost::ulong_long_type* 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(boost::long_long_type* 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)
{
   using default_ops::eval_fpclassify;
   if (eval_fpclassify(a) == (int)FP_NAN)
   {
      mpfi_set_fr(result.data(), a.data());
   }
   else if (eval_fpclassify(b) == (int)FP_NAN)
   {
      mpfi_set_fr(result.data(), b.data());
   }
   else
   {
      if (a.compare(b) > 0)
      {
         BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
      }
      mpfi_interv_fr(result.data(), a.data(), b.data());
   }
}

template <unsigned Digits10, class V>
inline typename enable_if_c<boost::is_constructible<number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on>, V>::value || boost::is_convertible<V, const char*>::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;
#ifndef BOOST_NO_EXCEPTIONS
      try
      {
#endif
         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;
         }
#ifndef BOOST_NO_EXCEPTIONS
      }
      catch (const std::exception&)
      {
         // conversion failed, just fall through, value is not an integer.
      }
#endif
      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_exp2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
   mpfi_exp2(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());
}

template <unsigned Digits10>
inline void eval_log2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
   mpfi_log2(result.data(), arg.data());
}

template <unsigned Digits10>
inline std::size_t hash_value(const mpfi_float_backend<Digits10>& val)
{
   std::size_t result = 0;
   std::size_t len    = val.left_data()[0]._mpfr_prec / mp_bits_per_limb;
   if (val.left_data()[0]._mpfr_prec % mp_bits_per_limb)
      ++len;
   for (std::size_t i = 0; i < len; ++i)
      boost::hash_combine(result, val.left_data()[0]._mpfr_d[i]);
   boost::hash_combine(result, val.left_data()[0]._mpfr_exp);
   boost::hash_combine(result, val.left_data()[0]._mpfr_sign);

len = val.right_data()[0]._mpfr_prec / mp_bits_per_limb;
   if (val.right_data()[0]._mpfr_prec % mp_bits_per_limb)
      ++len;
   for (std::size_t i = 0; i < len; ++i)
      boost::hash_combine(result, val.right_data()[0]._mpfr_d[i]);
   boost::hash_combine(result, val.right_data()[0]._mpfr_exp);
   boost::hash_combine(result, val.right_data()[0]._mpfr_sign);
   return result;
}

template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const mpl::int_<number_kind_integer>& to_type, const mpl::int_<number_kind_floating_point>& from_type)
{
   using boost::multiprecision::detail::generic_interconvert;
   mpfr_float_backend<D> t;
   mpfi_mid(t.data(), from.data());
   generic_interconvert(to, t, to_type, from_type);
}

template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const mpl::int_<number_kind_rational>& to_type, const mpl::int_<number_kind_floating_point>& from_type)
{
   using boost::multiprecision::detail::generic_interconvert;
   mpfr_float_backend<D> t;
   mpfi_mid(t.data(), from.data());
   generic_interconvert(to, t, to_type, from_type);
}

template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const mpl::int_<number_kind_floating_point>& to_type, const mpl::int_<number_kind_floating_point>& from_type)
{
   using boost::multiprecision::detail::generic_interconvert;
   mpfr_float_backend<D> t;
   mpfi_mid(t.data(), from.data());
   generic_interconvert(to, t, to_type, from_type);
}

} // 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_
{};

} // namespace detail
#endif

namespace detail {
template <>
struct is_variable_precision<backends::mpfi_float_backend<0> > : public true_type
{};
} // namespace detail

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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(a, 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)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(a, 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;
};

//
// Overloaded special functions which call native mpfr routines:
//
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_asinh(result.backend().data(), arg.backend().data());
   return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_acosh(result.backend().data(), arg.backend().data());
   return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_atanh(result.backend().data(), arg.backend().data());
   return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_cbrt(result.backend().data(), arg.backend().data());
   return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_expm1(result.backend().data(), arg.backend().data());
   return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
   boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);

boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
   mpfi_log1p(result.backend().data(), arg.backend().data());
   return result;
}

} // namespace multiprecision

namespace math {

namespace tools {

template <>
inline int digits<boost::multiprecision::mpfi_float>()
#ifdef BOOST_MATH_NOEXCEPT
    BOOST_NOEXCEPT
#endif
{
   return multiprecision::detail::digits10_2_2(boost::multiprecision::mpfi_float::default_precision());
}
template <>
inline int digits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
#ifdef BOOST_MATH_NOEXCEPT
    BOOST_NOEXCEPT
#endif
{
   return multiprecision::detail::digits10_2_2(boost::multiprecision::mpfi_float::default_precision());
}

template <>
inline boost::multiprecision::mpfi_float
max_value<boost::multiprecision::mpfi_float>()
{
   boost::multiprecision::mpfi_float result(0.5);
   mpfi_mul_2exp(result.backend().data(), result.backend().data(), mpfr_get_emax());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline boost::multiprecision::mpfi_float
min_value<boost::multiprecision::mpfi_float>()
{
   boost::multiprecision::mpfi_float result(0.5);
   mpfi_div_2exp(result.backend().data(), result.backend().data(), -mpfr_get_emin());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off>
max_value<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
{
   boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> result(0.5);
   mpfi_mul_2exp(result.backend().data(), result.backend().data(), mpfr_get_emax());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off>
min_value<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
{
   boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> result(0.5);
   mpfi_div_2exp(result.backend().data(), result.backend().data(), -mpfr_get_emin());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

// mpfi gets used with logged_adaptor fairly often, so specialize for that use case as well:
typedef boost::multiprecision::number<boost::multiprecision::backends::logged_adaptor<boost::multiprecision::mpfi_float::backend_type>, boost::multiprecision::et_on>  logged_type1;
typedef boost::multiprecision::number<boost::multiprecision::backends::logged_adaptor<boost::multiprecision::mpfi_float::backend_type>, boost::multiprecision::et_off> logged_type2;

template <>
inline int digits<logged_type1>()
#ifdef BOOST_MATH_NOEXCEPT
    BOOST_NOEXCEPT
#endif
{
   return multiprecision::detail::digits10_2_2(logged_type1::default_precision());
}
template <>
inline int digits<logged_type2>()
#ifdef BOOST_MATH_NOEXCEPT
    BOOST_NOEXCEPT
#endif
{
   return multiprecision::detail::digits10_2_2(logged_type1::default_precision());
}

template <>
inline logged_type1
max_value<logged_type1>()
{
   logged_type1 result(0.5);
   mpfi_mul_2exp(result.backend().value().data(), result.backend().value().data(), mpfr_get_emax());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline logged_type1
min_value<logged_type1>()
{
   logged_type1 result(0.5);
   mpfi_div_2exp(result.backend().value().data(), result.backend().value().data(), -mpfr_get_emin());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline logged_type2
max_value<logged_type2>()
{
   logged_type2 result(0.5);
   mpfi_mul_2exp(result.backend().value().data(), result.backend().value().data(), mpfr_get_emax());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}

template <>
inline logged_type2
min_value<logged_type2>()
{
   logged_type2 result(0.5);
   mpfi_div_2exp(result.backend().value().data(), result.backend().value().data(), -mpfr_get_emin());
   //BOOST_ASSERT(mpfi_number_p(result.backend().data()));
   return result;
}
} // 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 const result_type& get(const boost::integral_constant<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;
   }
   static inline result_type get(const boost::integral_constant<int, 0>&)
   {
      result_type result;
      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 const result_type& get(const boost::integral_constant<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;
   }
   static inline result_type get(const boost::integral_constant<int, 0>&)
   {
      result_type result;
      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 boost::integral_constant<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;
   }
   static inline result_type get(const boost::integral_constant<int, 0>&)
   {
      result_type result;
      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 boost::integral_constant<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;
   }
   static inline result_type get(const boost::integral_constant<int, 0>&)
   {
      result_type result;
      mpfi_const_catalan(result.backend().data());
      return result;
   }
};

}} // namespace constants::detail

} // namespace math
} // namespace boost

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 + 3;
   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

/////////////////////////////////////////////////////////////////////////////// // 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 #include #include #include #include #include #include #include #include #include #include #include #include #ifndef BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION #define BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION 20 #endif namespace boost { namespace multiprecision { namespace backends { template struct mpfi_float_backend; } // namespace backends template struct number_category > : public mpl::int_ {}; 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 struct mpfi_float_imp; template struct mpfi_float_imp { #ifdef BOOST_HAS_LONG_LONG typedef mpl::list signed_types; typedef mpl::list unsigned_types; #else typedef mpl::list signed_types; typedef mpl::list unsigned_types; #endif typedef mpl::list float_types; typedef long exponent_type; mpfi_float_imp() { mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision())); mpfi_set_ui(m_data, 0u); } mpfi_float_imp(unsigned prec) { mpfi_init2(m_data, prec); mpfi_set_ui(m_data, 0u); } mpfi_float_imp(const mpfi_float_imp& o) { mpfi_init2(m_data, mpfi_get_prec(o.data())); 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, mpfi_get_prec(o.data())); if (mpfi_get_prec(o.data()) != mpfi_get_prec(data())) { mpfi_float_imp t(mpfi_get_prec(o.data())); t = o; t.swap(*this); } else { 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 BOOST_HAS_LONG_LONG #ifdef _MPFR_H_HAVE_INTMAX_T mpfi_float_imp& operator=(boost::ulong_long_type i) { if (m_data[0].left._mpfr_d == 0) mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)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=(boost::long_long_type i) { if (m_data[0].left._mpfr_d == 0) mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)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=(boost::ulong_long_type i) { if (m_data[0].left._mpfr_d == 0) mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision())); boost::ulong_long_type mask = ((((1uLL << (std::numeric_limits::digits - 1)) - 1) << 1) | 1u); unsigned shift = 0; mpfi_t t; mpfi_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(multiprecision::detail::digits10_2_2(digits10)))); mpfi_set_ui(m_data, 0); while (i) { mpfi_set_ui(t, static_cast(i & mask)); if (shift) mpfi_mul_2exp(t, t, shift); mpfi_add(m_data, m_data, t); shift += std::numeric_limits::digits; i >>= std::numeric_limits::digits; } mpfi_clear(t); return *this; } mpfi_float_imp& operator=(boost::long_long_type i) { if (m_data[0].left._mpfr_d == 0) mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision())); bool neg = i < 0; *this = boost::multiprecision::detail::unsigned_abs(i); if (neg) mpfi_neg(m_data, m_data); return *this; } #endif #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 : (unsigned)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 : (unsigned)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 : (unsigned)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 : (unsigned)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) { using default_ops::eval_fpclassify; if (m_data[0].left._mpfr_d == 0) mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision())); if (s && (*s == '{')) { mpfr_float_backend 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(); if (eval_fpclassify(a) == (int)FP_NAN) { mpfi_set_fr(this->data(), a.data()); } else if (eval_fpclassify(b) == (int)FP_NAN) { mpfi_set_fr(this->data(), b.data()); } else { if (a.compare(b) > 0) { BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end).")); } 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 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 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 boost::multiprecision::detail::precision_type& get_default_precision() BOOST_NOEXCEPT { static boost::multiprecision::detail::precision_type val(BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION); return val; } }; } // namespace detail template struct mpfi_float_backend : public detail::mpfi_float_imp { mpfi_float_backend() : detail::mpfi_float_imp() {} mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp(o) {} #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES mpfi_float_backend(mpfi_float_backend&& o) : detail::mpfi_float_imp(static_cast&&>(o)) {} #endif template mpfi_float_backend(const mpfi_float_backend& val, typename enable_if_c::type* = 0) : detail::mpfi_float_imp() { mpfi_set(this->m_data, val.data()); } template explicit mpfi_float_backend(const mpfi_float_backend& val, typename disable_if_c::type* = 0) : detail::mpfi_float_imp() { mpfi_set(this->m_data, val.data()); } mpfi_float_backend(const mpfi_t val) : detail::mpfi_float_imp() { mpfi_set(this->m_data, val); } mpfi_float_backend& operator=(const mpfi_float_backend& o) { *static_cast*>(this) = static_cast const&>(o); return *this; } template mpfi_float_backend(const mpfr_float_backend& val, typename enable_if_c::type* = 0) : detail::mpfi_float_imp() { mpfi_set_fr(this->m_data, val.data()); } template mpfi_float_backend& operator=(const mpfr_float_backend& val) { mpfi_set_fr(this->m_data, val.data()); return *this; } template explicit mpfi_float_backend(const mpfr_float_backend& val, typename disable_if_c::type* = 0) : detail::mpfi_float_imp() { 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*>(this) = static_cast&&>(o); return *this; } #endif template mpfi_float_backend& operator=(const V& v) { *static_cast*>(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 mpfi_float_backend& operator=(const mpfi_float_backend& val) { mpfi_set(this->m_data, val.data()); return *this; } }; template void assign_components(mpfi_float_backend& result, const mpfr_float_backend& a, const mpfr_float_backend& b); template typename enable_if_c, et_on>, V>::value || boost::is_convertible::value>::type assign_components(mpfi_float_backend& result, const V& a, const V& b); 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&&>(o)) {} #endif mpfi_float_backend(const mpfi_float_backend& o, unsigned digits10) : detail::mpfi_float_imp<0>(multiprecision::detail::digits10_2_2(digits10)) { mpfi_set(this->m_data, o.data()); } template mpfi_float_backend(const V& a, const V& b, unsigned digits10) : detail::mpfi_float_imp<0>(multiprecision::detail::digits10_2_2(digits10)) { assign_components(*this, a, b); } template mpfi_float_backend(const mpfi_float_backend& 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*>(this) = static_cast&&>(o); return *this; } #endif template mpfi_float_backend& operator=(const V& v) { *static_cast*>(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 mpfi_float_backend& operator=(const mpfi_float_backend& 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_float_backend t(*this, digits10); this->swap(t); } }; template inline typename enable_if, bool>::type eval_eq(const mpfi_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) == 0; } template inline typename enable_if, bool>::type eval_lt(const mpfi_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) < 0; } template inline typename enable_if, bool>::type eval_gt(const mpfi_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) > 0; } template inline void eval_add(mpfi_float_backend& result, const mpfi_float_backend& o) { mpfi_add(result.data(), result.data(), o.data()); } template inline void eval_subtract(mpfi_float_backend& result, const mpfi_float_backend& o) { mpfi_sub(result.data(), result.data(), o.data()); } template inline void eval_multiply(mpfi_float_backend& result, const mpfi_float_backend& o) { if ((void*)&result == (void*)&o) mpfi_sqr(result.data(), o.data()); else mpfi_mul(result.data(), result.data(), o.data()); } template inline void eval_divide(mpfi_float_backend& result, const mpfi_float_backend& o) { mpfi_div(result.data(), result.data(), o.data()); } template inline void eval_add(mpfi_float_backend& result, unsigned long i) { mpfi_add_ui(result.data(), result.data(), i); } template inline void eval_subtract(mpfi_float_backend& result, unsigned long i) { mpfi_sub_ui(result.data(), result.data(), i); } template inline void eval_multiply(mpfi_float_backend& result, unsigned long i) { mpfi_mul_ui(result.data(), result.data(), i); } template inline void eval_divide(mpfi_float_backend& result, unsigned long i) { mpfi_div_ui(result.data(), result.data(), i); } template inline void eval_add(mpfi_float_backend& result, long i) { if (i > 0) mpfi_add_ui(result.data(), result.data(), i); else mpfi_sub_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i)); } template inline void eval_subtract(mpfi_float_backend& result, long i) { if (i > 0) mpfi_sub_ui(result.data(), result.data(), i); else mpfi_add_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i)); } template inline void eval_multiply(mpfi_float_backend& result, long i) { mpfi_mul_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i)); if (i < 0) mpfi_neg(result.data(), result.data()); } template inline void eval_divide(mpfi_float_backend& result, long i) { mpfi_div_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i)); if (i < 0) mpfi_neg(result.data(), result.data()); } // // Specialised 3 arg versions of the basic operators: // template inline void eval_add(mpfi_float_backend& a, const mpfi_float_backend& x, const mpfi_float_backend& y) { mpfi_add(a.data(), x.data(), y.data()); } template inline void eval_add(mpfi_float_backend& a, const mpfi_float_backend& x, unsigned long y) { mpfi_add_ui(a.data(), x.data(), y); } template inline void eval_add(mpfi_float_backend& a, const mpfi_float_backend& x, long y) { if (y < 0) mpfi_sub_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y)); else mpfi_add_ui(a.data(), x.data(), y); } template inline void eval_add(mpfi_float_backend& a, unsigned long x, const mpfi_float_backend& y) { mpfi_add_ui(a.data(), y.data(), x); } template inline void eval_add(mpfi_float_backend& a, long x, const mpfi_float_backend& y) { if (x < 0) { mpfi_ui_sub(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data()); mpfi_neg(a.data(), a.data()); } else mpfi_add_ui(a.data(), y.data(), x); } template inline void eval_subtract(mpfi_float_backend& a, const mpfi_float_backend& x, const mpfi_float_backend& y) { mpfi_sub(a.data(), x.data(), y.data()); } template inline void eval_subtract(mpfi_float_backend& a, const mpfi_float_backend& x, unsigned long y) { mpfi_sub_ui(a.data(), x.data(), y); } template inline void eval_subtract(mpfi_float_backend& a, const mpfi_float_backend& x, long y) { if (y < 0) mpfi_add_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y)); else mpfi_sub_ui(a.data(), x.data(), y); } template inline void eval_subtract(mpfi_float_backend& a, unsigned long x, const mpfi_float_backend& y) { mpfi_ui_sub(a.data(), x, y.data()); } template inline void eval_subtract(mpfi_float_backend& a, long x, const mpfi_float_backend& y) { if (x < 0) { mpfi_add_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x)); mpfi_neg(a.data(), a.data()); } else mpfi_ui_sub(a.data(), x, y.data()); } template inline void eval_multiply(mpfi_float_backend& a, const mpfi_float_backend& x, const mpfi_float_backend& y) { if ((void*)&x == (void*)&y) mpfi_sqr(a.data(), x.data()); else mpfi_mul(a.data(), x.data(), y.data()); } template inline void eval_multiply(mpfi_float_backend& a, const mpfi_float_backend& x, unsigned long y) { mpfi_mul_ui(a.data(), x.data(), y); } template inline void eval_multiply(mpfi_float_backend& a, const mpfi_float_backend& x, long y) { if (y < 0) { mpfi_mul_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y)); a.negate(); } else mpfi_mul_ui(a.data(), x.data(), y); } template inline void eval_multiply(mpfi_float_backend& a, unsigned long x, const mpfi_float_backend& y) { mpfi_mul_ui(a.data(), y.data(), x); } template inline void eval_multiply(mpfi_float_backend& a, long x, const mpfi_float_backend& y) { if (x < 0) { mpfi_mul_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x)); mpfi_neg(a.data(), a.data()); } else mpfi_mul_ui(a.data(), y.data(), x); } template inline void eval_divide(mpfi_float_backend& a, const mpfi_float_backend& x, const mpfi_float_backend& y) { mpfi_div(a.data(), x.data(), y.data()); } template inline void eval_divide(mpfi_float_backend& a, const mpfi_float_backend& x, unsigned long y) { mpfi_div_ui(a.data(), x.data(), y); } template inline void eval_divide(mpfi_float_backend& a, const mpfi_float_backend& x, long y) { if (y < 0) { mpfi_div_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y)); a.negate(); } else mpfi_div_ui(a.data(), x.data(), y); } template inline void eval_divide(mpfi_float_backend& a, unsigned long x, const mpfi_float_backend& y) { mpfi_ui_div(a.data(), x, y.data()); } template inline void eval_divide(mpfi_float_backend& a, long x, const mpfi_float_backend& y) { if (x < 0) { mpfi_ui_div(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data()); mpfi_neg(a.data(), a.data()); } else mpfi_ui_div(a.data(), x, y.data()); } template inline bool eval_is_zero(const mpfi_float_backend& val) BOOST_NOEXCEPT { return 0 != mpfi_is_zero(val.data()); } template inline int eval_get_sign(const mpfi_float_backend& val) { return detail::mpfi_sgn(val.data()); } template inline void eval_convert_to(unsigned long* result, const mpfi_float_backend& val) { mpfr_float_backend t; mpfi_mid(t.data(), val.data()); eval_convert_to(result, t); } template inline void eval_convert_to(long* result, const mpfi_float_backend& val) { mpfr_float_backend t; mpfi_mid(t.data(), val.data()); eval_convert_to(result, t); } #ifdef _MPFR_H_HAVE_INTMAX_T template inline void eval_convert_to(boost::ulong_long_type* result, const mpfi_float_backend& val) { mpfr_float_backend t; mpfi_mid(t.data(), val.data()); eval_convert_to(result, t); } template inline void eval_convert_to(boost::long_long_type* result, const mpfi_float_backend& val) { mpfr_float_backend t; mpfi_mid(t.data(), val.data()); eval_convert_to(result, t); } #endif template inline void eval_convert_to(double* result, const mpfi_float_backend& val) BOOST_NOEXCEPT { *result = mpfi_get_d(val.data()); } template inline void eval_convert_to(long double* result, const mpfi_float_backend& val) BOOST_NOEXCEPT { mpfr_float_backend t; mpfi_mid(t.data(), val.data()); eval_convert_to(result, t); } template inline void assign_components(mpfi_float_backend& result, const mpfr_float_backend& a, const mpfr_float_backend& b) { using default_ops::eval_fpclassify; if (eval_fpclassify(a) == (int)FP_NAN) { mpfi_set_fr(result.data(), a.data()); } else if (eval_fpclassify(b) == (int)FP_NAN) { mpfi_set_fr(result.data(), b.data()); } else { if (a.compare(b) > 0) { BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end).")); } mpfi_interv_fr(result.data(), a.data(), b.data()); } } template inline typename enable_if_c, et_on>, V>::value || boost::is_convertible::value>::type assign_components(mpfi_float_backend& result, const V& a, const V& b) { number, et_on> x(a), y(b); assign_components(result, x.backend(), y.backend()); } // // Native non-member operations: // template inline void eval_sqrt(mpfi_float_backend& result, const mpfi_float_backend& val) { mpfi_sqrt(result.data(), val.data()); } template inline void eval_abs(mpfi_float_backend& result, const mpfi_float_backend& val) { mpfi_abs(result.data(), val.data()); } template inline void eval_fabs(mpfi_float_backend& result, const mpfi_float_backend& val) { mpfi_abs(result.data(), val.data()); } template inline void eval_ceil(mpfi_float_backend& result, const mpfi_float_backend& val) { mpfr_float_backend 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 inline void eval_floor(mpfi_float_backend& result, const mpfi_float_backend& val) { mpfr_float_backend 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 inline void eval_ldexp(mpfi_float_backend& result, const mpfi_float_backend& 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 inline void eval_frexp(mpfi_float_backend& result, const mpfi_float_backend& val, int* e) { mpfr_float_backend t, rt; mpfi_mid(t.data(), val.data()); eval_frexp(rt, t, e); eval_ldexp(result, val, -*e); } template inline void eval_frexp(mpfi_float_backend& result, const mpfi_float_backend& val, long* e) { mpfr_float_backend t, rt; mpfi_mid(t.data(), val.data()); eval_frexp(rt, t, e); eval_ldexp(result, val, -*e); } template inline int eval_fpclassify(const mpfi_float_backend& 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 inline void eval_pow(mpfi_float_backend& result, const mpfi_float_backend& b, const mpfi_float_backend& e) { typedef typename boost::multiprecision::detail::canonical >::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 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 >::type an; #ifndef BOOST_NO_EXCEPTIONS try { #endif using default_ops::eval_convert_to; eval_convert_to(&an, e); if (e.compare(an) == 0) { mpfi_float_backend pb(b); pb.negate(); eval_pow(result, pb, e); if (an & 1u) result.negate(); return; } #ifndef BOOST_NO_EXCEPTIONS } catch (const std::exception&) { // conversion failed, just fall through, value is not an integer. } #endif result = std::numeric_limits, 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 inline void eval_exp(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_exp(result.data(), arg.data()); } template inline void eval_exp2(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_exp2(result.data(), arg.data()); } template inline void eval_log(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_log(result.data(), arg.data()); } template inline void eval_log10(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_log10(result.data(), arg.data()); } template inline void eval_sin(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_sin(result.data(), arg.data()); } template inline void eval_cos(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_cos(result.data(), arg.data()); } template inline void eval_tan(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_tan(result.data(), arg.data()); } template inline void eval_asin(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_asin(result.data(), arg.data()); } template inline void eval_acos(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_acos(result.data(), arg.data()); } template inline void eval_atan(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_atan(result.data(), arg.data()); } template inline void eval_atan2(mpfi_float_backend& result, const mpfi_float_backend& arg1, const mpfi_float_backend& arg2) { mpfi_atan2(result.data(), arg1.data(), arg2.data()); } template inline void eval_sinh(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_sinh(result.data(), arg.data()); } template inline void eval_cosh(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_cosh(result.data(), arg.data()); } template inline void eval_tanh(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_tanh(result.data(), arg.data()); } template inline void eval_log2(mpfi_float_backend& result, const mpfi_float_backend& arg) { mpfi_log2(result.data(), arg.data()); } template inline std::size_t hash_value(const mpfi_float_backend& val) { std::size_t result = 0; std::size_t len = val.left_data()[0]._mpfr_prec / mp_bits_per_limb; if (val.left_data()[0]._mpfr_prec % mp_bits_per_limb) ++len; for (std::size_t i = 0; i < len; ++i) boost::hash_combine(result, val.left_data()[0]._mpfr_d[i]); boost::hash_combine(result, val.left_data()[0]._mpfr_exp); boost::hash_combine(result, val.left_data()[0]._mpfr_sign); len = val.right_data()[0]._mpfr_prec / mp_bits_per_limb; if (val.right_data()[0]._mpfr_prec % mp_bits_per_limb) ++len; for (std::size_t i = 0; i < len; ++i) boost::hash_combine(result, val.right_data()[0]._mpfr_d[i]); boost::hash_combine(result, val.right_data()[0]._mpfr_exp); boost::hash_combine(result, val.right_data()[0]._mpfr_sign); return result; } template void generic_interconvert(To& to, const mpfi_float_backend& from, const mpl::int_& to_type, const mpl::int_& from_type) { using boost::multiprecision::detail::generic_interconvert; mpfr_float_backend t; mpfi_mid(t.data(), from.data()); generic_interconvert(to, t, to_type, from_type); } template void generic_interconvert(To& to, const mpfi_float_backend& from, const mpl::int_& to_type, const mpl::int_& from_type) { using boost::multiprecision::detail::generic_interconvert; mpfr_float_backend t; mpfi_mid(t.data(), from.data()); generic_interconvert(to, t, to_type, from_type); } template void generic_interconvert(To& to, const mpfi_float_backend& from, const mpl::int_& to_type, const mpl::int_& from_type) { using boost::multiprecision::detail::generic_interconvert; mpfr_float_backend t; mpfi_mid(t.data(), from.data()); generic_interconvert(to, t, to_type, from_type); } } // namespace backends #ifdef BOOST_NO_SFINAE_EXPR namespace detail { template struct is_explicitly_convertible, backends::mpfi_float_backend > : public mpl::true_ {}; } // namespace detail #endif namespace detail { template <> struct is_variable_precision > : public true_type {}; } // namespace detail template <> struct number_category >::type> : public mpl::int_ {}; template struct is_interval_number > : public mpl::true_ {}; using boost::multiprecision::backends::mpfi_float_backend; typedef number > mpfi_float_50; typedef number > mpfi_float_100; typedef number > mpfi_float_500; typedef number > mpfi_float_1000; typedef number > mpfi_float; // // Special interval specific functions: // template inline number, ExpressionTemplates> lower(const number, ExpressionTemplates>& val) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(val); number > result; mpfr_set(result.backend().data(), val.backend().left_data(), GMP_RNDN); return result; } template inline number, ExpressionTemplates> upper(const number, ExpressionTemplates>& val) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(val); number > result; mpfr_set(result.backend().data(), val.backend().right_data(), GMP_RNDN); return result; } template inline number, ExpressionTemplates> median(const number, ExpressionTemplates>& val) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(val); number > result; mpfi_mid(result.backend().data(), val.backend().data()); return result; } template inline number, ExpressionTemplates> width(const number, ExpressionTemplates>& val) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(val); number > result; mpfi_diam_abs(result.backend().data(), val.backend().data()); return result; } template inline number, ExpressionTemplates> intersect(const number, ExpressionTemplates>& a, const number, ExpressionTemplates>& b) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(a, b); number, ExpressionTemplates> result; mpfi_intersect(result.backend().data(), a.backend().data(), b.backend().data()); return result; } template inline number, ExpressionTemplates> hull(const number, ExpressionTemplates>& a, const number, ExpressionTemplates>& b) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(a, b); number, ExpressionTemplates> result; mpfi_union(result.backend().data(), a.backend().data(), b.backend().data()); return result; } template inline bool overlap(const number, ExpressionTemplates>& a, const number, ExpressionTemplates>& b) { return (lower(a) <= lower(b) && lower(b) <= upper(a)) || (lower(b) <= lower(a) && lower(a) <= upper(b)); } template inline bool in(const number, ExpressionTemplates1>& a, const number, ExpressionTemplates2>& b) { return mpfi_is_inside_fr(a.backend().data(), b.backend().data()) != 0; } template inline bool zero_in(const number, ExpressionTemplates>& a) { return mpfi_has_zero(a.backend().data()) != 0; } template inline bool subset(const number, ExpressionTemplates>& a, const number, ExpressionTemplates>& b) { return mpfi_is_inside(a.backend().data(), b.backend().data()) != 0; } template inline bool proper_subset(const number, ExpressionTemplates>& a, const number, ExpressionTemplates>& b) { return mpfi_is_strictly_inside(a.backend().data(), b.backend().data()) != 0; } template inline bool empty(const number, ExpressionTemplates>& a) { return mpfi_is_empty(a.backend().data()) != 0; } template inline bool singleton(const number, ExpressionTemplates>& a) { return mpfr_cmp(a.backend().left_data(), a.backend().right_data()) == 0; } template struct component_type, ExpressionTemplates> > { typedef number, ExpressionTemplates> type; }; // // Overloaded special functions which call native mpfr routines: // template inline boost::multiprecision::number, ExpressionTemplates> asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number, ExpressionTemplates>& arg) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(arg); boost::multiprecision::number, ExpressionTemplates> result; mpfi_asinh(result.backend().data(), arg.backend().data()); return result; } template inline boost::multiprecision::number, ExpressionTemplates> acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number, ExpressionTemplates>& arg) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(arg); boost::multiprecision::number, ExpressionTemplates> result; mpfi_acosh(result.backend().data(), arg.backend().data()); return result; } template inline boost::multiprecision::number, ExpressionTemplates> atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number, ExpressionTemplates>& arg) { boost::multiprecision::detail::scoped_default_precision, ExpressionTemplates> > precision_guard(arg); boost::multiprecision::number, ExpressionTemplates> result; mpfi_atanh(result.backend().data(), arg.backend().data()); return result; } template inline boost::multiprecision::number