Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: //  Copyright 2011 John Maddock. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_BN_MPFI_HPP
Chris@16: #define BOOST_MATH_BN_MPFI_HPP
Chris@16: 
Chris@16: #include <boost/multiprecision/number.hpp>
Chris@16: #include <boost/math/special_functions/fpclassify.hpp>
Chris@16: #include <boost/cstdint.hpp>
Chris@16: #include <boost/multiprecision/detail/big_lanczos.hpp>
Chris@16: #include <boost/multiprecision/detail/digits.hpp>
Chris@16: #include <boost/multiprecision/mpfr.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: #include <mpfi.h>
Chris@16: #include <cmath>
Chris@16: #include <algorithm>
Chris@16: 
Chris@16: namespace boost{
Chris@16: namespace multiprecision{
Chris@16: namespace backends{
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: struct mpfi_float_backend;
Chris@16: 
Chris@16: } // namespace backends
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: struct number_category<backends::mpfi_float_backend<digits10> > : public mpl::int_<number_kind_floating_point>{};
Chris@16: 
Chris@16: struct interval_error : public std::runtime_error
Chris@16: {
Chris@16:    interval_error(const std::string& s) : std::runtime_error(s) {}
Chris@16: };
Chris@16: 
Chris@16: namespace backends{
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: inline int mpfi_sgn(mpfi_srcptr p)
Chris@16: {
Chris@16:    if(mpfi_is_zero(p))
Chris@16:       return 0;
Chris@16:    if(mpfi_is_strictly_pos(p))
Chris@16:       return 1;
Chris@16:    if(mpfi_is_strictly_neg(p))
Chris@16:       return -1;
Chris@16:    BOOST_THROW_EXCEPTION(interval_error("Sign of interval is ambiguous."));
Chris@16: }
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: struct mpfi_float_imp;
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: struct mpfi_float_imp
Chris@16: {
Chris@16:    typedef mpl::list<long, long long>                     signed_types;
Chris@16:    typedef mpl::list<unsigned long, unsigned long long>   unsigned_types;
Chris@16:    typedef mpl::list<double, long double>                 float_types;
Chris@16:    typedef long                                           exponent_type;
Chris@16: 
Chris@16:    mpfi_float_imp()
Chris@16:    {
Chris@16:       mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:    }
Chris@16:    mpfi_float_imp(unsigned prec)
Chris@16:    {
Chris@16:       mpfi_init2(m_data, prec);
Chris@16:    }
Chris@16: 
Chris@16:    mpfi_float_imp(const mpfi_float_imp& o)
Chris@16:    {
Chris@16:       mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       if(o.m_data[0].left._mpfr_d)
Chris@16:          mpfi_set(m_data, o.m_data);
Chris@16:    }
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_imp(mpfi_float_imp&& o) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       m_data[0] = o.m_data[0];
Chris@16:       o.m_data[0].left._mpfr_d = 0;
Chris@16:    }
Chris@16: #endif
Chris@16:    mpfi_float_imp& operator = (const mpfi_float_imp& o)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       if(o.m_data[0].left._mpfr_d)
Chris@16:          mpfi_set(m_data, o.m_data);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_imp& operator = (mpfi_float_imp&& o) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       mpfi_swap(m_data, o.m_data);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #endif
Chris@16: #ifdef _MPFR_H_HAVE_INTMAX_T
Chris@16:    mpfi_float_imp& operator = (unsigned long long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfr_set_uj(left_data(), i, GMP_RNDD);
Chris@16:       mpfr_set_uj(right_data(), i, GMP_RNDU);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (long long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfr_set_sj(left_data(), i, GMP_RNDD);
Chris@16:       mpfr_set_sj(right_data(), i, GMP_RNDU);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #else
Chris@16:    mpfi_float_imp& operator = (unsigned long long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       unsigned long long mask = ((1uLL << std::numeric_limits<unsigned>::digits) - 1);
Chris@16:       unsigned shift = 0;
Chris@16:       mpfi_t t;
Chris@16:       mpfi_init2(t, (std::max)(static_cast<unsigned>(std::numeric_limits<unsigned long long>::digits), static_cast<unsigned>(multiprecision::detail::digits10_2_2(digits10))));
Chris@16:       mpfi_set_ui(m_data, 0);
Chris@16:       while(i)
Chris@16:       {
Chris@16:          mpfi_set_ui(t, static_cast<unsigned>(i & mask));
Chris@16:          if(shift)
Chris@16:             mpfi_mul_2exp(t, t, shift);
Chris@16:          mpfi_add(m_data, m_data, t);
Chris@16:          shift += std::numeric_limits<unsigned>::digits;
Chris@16:          i >>= std::numeric_limits<unsigned>::digits;
Chris@16:       }
Chris@16:       mpfi_clear(t);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (long long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       bool neg = i < 0;
Chris@101:       *this = boost::multiprecision::detail::unsigned_abs(i);
Chris@16:       if(neg)
Chris@16:          mpfi_neg(m_data, m_data);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #endif
Chris@16:    mpfi_float_imp& operator = (unsigned long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfi_set_ui(m_data, i);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (long i)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfi_set_si(m_data, i);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (double d)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfi_set_d(m_data, d);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (long double a)
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16:       mpfr_set_ld(left_data(), a, GMP_RNDD);
Chris@16:       mpfr_set_ld(right_data(), a, GMP_RNDU);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_imp& operator = (const char* s)
Chris@16:    {
Chris@101:       using default_ops::eval_fpclassify;
Chris@101:    
Chris@16:       if(m_data[0].left._mpfr_d == 0)
Chris@16:          mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision()));
Chris@16: 
Chris@16:       if(s && (*s == '{'))
Chris@16:       {
Chris@16:          mpfr_float_backend<digits10> a, b;
Chris@16:          std::string part;
Chris@16:          const char* p = ++s;
Chris@16:          while(*p && (*p != ',') && (*p != '}'))
Chris@16:             ++p;
Chris@16:          part.assign(s + 1, p);
Chris@16:          a = part.c_str();
Chris@16:          s = p;
Chris@16:          if(*p && (*p != '}'))
Chris@16:          {
Chris@16:             ++p;
Chris@16:             while(*p && (*p != ',') && (*p != '}'))
Chris@16:                ++p;
Chris@16:             part.assign(s + 1, p);
Chris@16:          }
Chris@16:          else
Chris@16:             part.erase();
Chris@16:          b = part.c_str();
Chris@16: 
Chris@101:          if(eval_fpclassify(a) == (int)FP_NAN)
Chris@101:          {
Chris@101:             mpfi_set_fr(this->data(), a.data());
Chris@101:          }
Chris@101:          else if(eval_fpclassify(b) == (int)FP_NAN)
Chris@101:          {
Chris@101:             mpfi_set_fr(this->data(), b.data());
Chris@101:          }
Chris@101:          else
Chris@101:          {
Chris@101:             if(a.compare(b) > 0)
Chris@101:             {
Chris@101:                BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
Chris@101:             }
Chris@101:             mpfi_interv_fr(m_data, a.data(), b.data());
Chris@101:          }
Chris@16:       }
Chris@16:       else if(mpfi_set_str(m_data, s, 10) != 0)
Chris@16:       {
Chris@16:          BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number.")));
Chris@16:       }
Chris@16:       return *this;
Chris@16:    }
Chris@16:    void swap(mpfi_float_imp& o) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       mpfi_swap(m_data, o.m_data);
Chris@16:    }
Chris@16:    std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16: 
Chris@16:       mpfr_float_backend<digits10> a, b;
Chris@16: 
Chris@16:       mpfi_get_left(a.data(), m_data);
Chris@16:       mpfi_get_right(b.data(), m_data);
Chris@16: 
Chris@16:       if(a.compare(b) == 0)
Chris@16:          return a.str(digits, f);
Chris@16: 
Chris@16:       return "{" + a.str(digits, f) + "," + b.str(digits, f) + "}";
Chris@16:    }
Chris@16:    ~mpfi_float_imp() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       if(m_data[0].left._mpfr_d)
Chris@16:          mpfi_clear(m_data);
Chris@16:    }
Chris@16:    void negate() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       mpfi_neg(m_data, m_data);
Chris@16:    }
Chris@16:    int compare(const mpfi_float_imp& o)const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d && o.m_data[0].left._mpfr_d);
Chris@16:       if(mpfr_cmp(right_data(), o.left_data()) < 0)
Chris@16:          return -1;
Chris@16:       if(mpfr_cmp(left_data(), o.right_data()) > 0)
Chris@16:          return 1;
Chris@16:       if((mpfr_cmp(left_data(), o.left_data()) == 0) && (mpfr_cmp(right_data(), o.right_data()) == 0))
Chris@16:          return 0;
Chris@16:       BOOST_THROW_EXCEPTION(interval_error("Ambiguous comparison between two values."));
Chris@16:       return 0;
Chris@16:    }
Chris@16:    template <class V>
Chris@16:    int compare(V v)const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       mpfi_float_imp d;
Chris@16:       d = v;
Chris@16:       return compare(d);
Chris@16:    }
Chris@16:    mpfi_t& data() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return m_data;
Chris@16:    }
Chris@16:    const mpfi_t& data()const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return m_data;
Chris@16:    }
Chris@16:    mpfr_ptr left_data() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return &(m_data[0].left);
Chris@16:    }
Chris@16:    mpfr_srcptr left_data()const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return &(m_data[0].left);
Chris@16:    }
Chris@16:    mpfr_ptr right_data() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return &(m_data[0].right);
Chris@16:    }
Chris@16:    mpfr_srcptr right_data()const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       BOOST_ASSERT(m_data[0].left._mpfr_d);
Chris@16:       return &(m_data[0].right);
Chris@16:    }
Chris@16: protected:
Chris@16:    mpfi_t m_data;
Chris@16:    static unsigned& get_default_precision() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       static unsigned val = 50;
Chris@16:       return val;
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: struct mpfi_float_backend : public detail::mpfi_float_imp<digits10>
Chris@16: {
Chris@16:    mpfi_float_backend() : detail::mpfi_float_imp<digits10>() {}
Chris@16:    mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<digits10>(o) {}
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_backend(mpfi_float_backend&& o) : detail::mpfi_float_imp<digits10>(static_cast<detail::mpfi_float_imp<digits10>&&>(o)) {}
Chris@16: #endif
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend(const mpfi_float_backend<D>& val, typename enable_if_c<D <= digits10>::type* = 0)
Chris@16:        : detail::mpfi_float_imp<digits10>()
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val.data());
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    explicit mpfi_float_backend(const mpfi_float_backend<D>& val, typename disable_if_c<D <= digits10>::type* = 0)
Chris@16:        : detail::mpfi_float_imp<digits10>()
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val.data());
Chris@16:    }
Chris@16:    mpfi_float_backend(const mpfi_t val)
Chris@16:        : detail::mpfi_float_imp<digits10>()
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val);
Chris@16:    }
Chris@16:    mpfi_float_backend& operator=(const mpfi_float_backend& o)
Chris@16:    {
Chris@16:       *static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10> const&>(o);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend(const mpfr_float_backend<D>& val, typename enable_if_c<D <= digits10>::type* = 0)
Chris@16:        : detail::mpfi_float_imp<digits10>()
Chris@16:    {
Chris@16:       mpfi_set_fr(this->m_data, val.data());
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend& operator=(const mpfr_float_backend<D>& val)
Chris@16:    {
Chris@16:       mpfi_set_fr(this->m_data, val.data());
Chris@16:       return *this;
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    explicit mpfi_float_backend(const mpfr_float_backend<D>& val, typename disable_if_c<D <= digits10>::type* = 0)
Chris@16:        : detail::mpfi_float_imp<digits10>()
Chris@16:    {
Chris@16:       mpfi_set_fr(this->m_data, val.data());
Chris@16:    }
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_backend& operator=(mpfi_float_backend&& o) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       *static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10>&&>(o);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #endif
Chris@16:    template <class V>
Chris@16:    mpfi_float_backend& operator=(const V& v)
Chris@16:    {
Chris@16:       *static_cast<detail::mpfi_float_imp<digits10>*>(this) = v;
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_backend& operator=(const mpfi_t val)
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    // We don't change our precision here, this is a fixed precision type:
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val.data());
Chris@16:       return *this;
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: template <>
Chris@16: struct mpfi_float_backend<0> : public detail::mpfi_float_imp<0>
Chris@16: {
Chris@16:    mpfi_float_backend() : detail::mpfi_float_imp<0>() {}
Chris@16:    mpfi_float_backend(const mpfi_t val)
Chris@16:       : detail::mpfi_float_imp<0>(mpfi_get_prec(val))
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val);
Chris@16:    }
Chris@16:    mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<0>(o) {}
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_backend(mpfi_float_backend&& o) BOOST_NOEXCEPT : detail::mpfi_float_imp<0>(static_cast<detail::mpfi_float_imp<0>&&>(o)) {}
Chris@16: #endif
Chris@16:    mpfi_float_backend(const mpfi_float_backend& o, unsigned digits10)
Chris@16:       : detail::mpfi_float_imp<0>(digits10)
Chris@16:    {
Chris@16:       *this = o;
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend(const mpfi_float_backend<D>& val)
Chris@16:       : detail::mpfi_float_imp<0>(mpfi_get_prec(val.data()))
Chris@16:    {
Chris@16:       mpfi_set(this->m_data, val.data());
Chris@16:    }
Chris@16:    mpfi_float_backend& operator=(const mpfi_float_backend& o)
Chris@16:    {
Chris@16:       mpfi_set_prec(this->m_data, mpfi_get_prec(o.data()));
Chris@16:       mpfi_set(this->m_data, o.data());
Chris@16:       return *this;
Chris@16:    }
Chris@16: #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Chris@16:    mpfi_float_backend& operator=(mpfi_float_backend&& o) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       *static_cast<detail::mpfi_float_imp<0>*>(this) = static_cast<detail::mpfi_float_imp<0> &&>(o);
Chris@16:       return *this;
Chris@16:    }
Chris@16: #endif
Chris@16:    template <class V>
Chris@16:    mpfi_float_backend& operator=(const V& v)
Chris@16:    {
Chris@16:       *static_cast<detail::mpfi_float_imp<0>*>(this) = v;
Chris@16:       return *this;
Chris@16:    }
Chris@16:    mpfi_float_backend& operator=(const mpfi_t val)
Chris@16:    {
Chris@16:       mpfi_set_prec(this->m_data, mpfi_get_prec(val));
Chris@16:       mpfi_set(this->m_data, val);
Chris@16:       return *this;
Chris@16:    }
Chris@16:    template <unsigned D>
Chris@16:    mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
Chris@16:    {
Chris@16:       mpfi_set_prec(this->m_data, mpfi_get_prec(val.data()));
Chris@16:       mpfi_set(this->m_data, val.data());
Chris@16:       return *this;
Chris@16:    }
Chris@16:    static unsigned default_precision() BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       return get_default_precision();
Chris@16:    }
Chris@16:    static void default_precision(unsigned v) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       get_default_precision() = v;
Chris@16:    }
Chris@16:    unsigned precision()const BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       return multiprecision::detail::digits2_2_10(mpfi_get_prec(this->m_data));
Chris@16:    }
Chris@16:    void precision(unsigned digits10) BOOST_NOEXCEPT
Chris@16:    {
Chris@16:       mpfi_set_prec(this->m_data, multiprecision::detail::digits2_2_10((digits10)));
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: template <unsigned digits10, class T>
Chris@16: inline typename enable_if<is_arithmetic<T>, bool>::type eval_eq(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return a.compare(b) == 0;
Chris@16: }
Chris@16: template <unsigned digits10, class T>
Chris@16: inline typename enable_if<is_arithmetic<T>, bool>::type eval_lt(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return a.compare(b) < 0;
Chris@16: }
Chris@16: template <unsigned digits10, class T>
Chris@16: inline typename enable_if<is_arithmetic<T>, bool>::type eval_gt(const mpfi_float_backend<digits10>& a, const T& b) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return a.compare(b) > 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
Chris@16: {
Chris@16:    mpfi_add(result.data(), result.data(), o.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
Chris@16: {
Chris@16:    mpfi_sub(result.data(), result.data(), o.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
Chris@16: {
Chris@16:    if((void*)&result == (void*)&o)
Chris@16:       mpfi_sqr(result.data(), o.data());
Chris@16:    else
Chris@16:       mpfi_mul(result.data(), result.data(), o.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
Chris@16: {
Chris@16:    mpfi_div(result.data(), result.data(), o.data());
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_add(mpfi_float_backend<digits10>& result, unsigned long i)
Chris@16: {
Chris@16:    mpfi_add_ui(result.data(), result.data(), i);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_subtract(mpfi_float_backend<digits10>& result, unsigned long i)
Chris@16: {
Chris@16:    mpfi_sub_ui(result.data(), result.data(), i);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_multiply(mpfi_float_backend<digits10>& result, unsigned long i)
Chris@16: {
Chris@16:    mpfi_mul_ui(result.data(), result.data(), i);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_divide(mpfi_float_backend<digits10>& result, unsigned long i)
Chris@16: {
Chris@16:    mpfi_div_ui(result.data(), result.data(), i);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_add(mpfi_float_backend<digits10>& result, long i)
Chris@16: {
Chris@16:    if(i > 0)
Chris@16:       mpfi_add_ui(result.data(), result.data(), i);
Chris@16:    else
Chris@101:       mpfi_sub_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_subtract(mpfi_float_backend<digits10>& result, long i)
Chris@16: {
Chris@16:    if(i > 0)
Chris@16:       mpfi_sub_ui(result.data(), result.data(), i);
Chris@16:    else
Chris@101:       mpfi_add_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_multiply(mpfi_float_backend<digits10>& result, long i)
Chris@16: {
Chris@101:    mpfi_mul_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
Chris@16:    if(i < 0)
Chris@16:       mpfi_neg(result.data(), result.data());
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_divide(mpfi_float_backend<digits10>& result, long i)
Chris@16: {
Chris@101:    mpfi_div_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
Chris@16:    if(i < 0)
Chris@16:       mpfi_neg(result.data(), result.data());
Chris@16: }
Chris@16: //
Chris@16: // Specialised 3 arg versions of the basic operators:
Chris@16: //
Chris@16: template <unsigned D1, unsigned D2, unsigned D3>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
Chris@16: {
Chris@16:    mpfi_add(a.data(), x.data(), y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
Chris@16: {
Chris@16:    mpfi_add_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
Chris@16: {
Chris@16:    if(y < 0)
Chris@101:       mpfi_sub_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
Chris@16:    else
Chris@16:       mpfi_add_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    mpfi_add_ui(a.data(), y.data(), x);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_add(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    if(x < 0)
Chris@16:    {
Chris@101:       mpfi_ui_sub(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
Chris@16:       mpfi_neg(a.data(), a.data());
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_add_ui(a.data(), y.data(), x);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2, unsigned D3>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
Chris@16: {
Chris@16:    mpfi_sub(a.data(), x.data(), y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
Chris@16: {
Chris@16:    mpfi_sub_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
Chris@16: {
Chris@16:    if(y < 0)
Chris@101:       mpfi_add_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
Chris@16:    else
Chris@16:       mpfi_sub_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    mpfi_ui_sub(a.data(), x, y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_subtract(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    if(x < 0)
Chris@16:    {
Chris@101:       mpfi_add_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
Chris@16:       mpfi_neg(a.data(), a.data());
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_ui_sub(a.data(), x, y.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned D1, unsigned D2, unsigned D3>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
Chris@16: {
Chris@16:    if((void*)&x == (void*)&y)
Chris@16:       mpfi_sqr(a.data(), x.data());
Chris@16:    else
Chris@16:       mpfi_mul(a.data(), x.data(), y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
Chris@16: {
Chris@16:    mpfi_mul_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
Chris@16: {
Chris@16:    if(y < 0)
Chris@16:    {
Chris@101:       mpfi_mul_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
Chris@16:       a.negate();
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_mul_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    mpfi_mul_ui(a.data(), y.data(), x);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_multiply(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    if(x < 0)
Chris@16:    {
Chris@101:       mpfi_mul_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
Chris@16:       mpfi_neg(a.data(), a.data());
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_mul_ui(a.data(), y.data(), x);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned D1, unsigned D2, unsigned D3>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
Chris@16: {
Chris@16:    mpfi_div(a.data(), x.data(), y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
Chris@16: {
Chris@16:    mpfi_div_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
Chris@16: {
Chris@16:    if(y < 0)
Chris@16:    {
Chris@101:       mpfi_div_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
Chris@16:       a.negate();
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_div_ui(a.data(), x.data(), y);
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    mpfi_ui_div(a.data(), x, y.data());
Chris@16: }
Chris@16: template <unsigned D1, unsigned D2>
Chris@16: inline void eval_divide(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
Chris@16: {
Chris@16:    if(x < 0)
Chris@16:    {
Chris@101:       mpfi_ui_div(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
Chris@16:       mpfi_neg(a.data(), a.data());
Chris@16:    }
Chris@16:    else
Chris@16:       mpfi_ui_div(a.data(), x, y.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: inline bool eval_is_zero(const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return 0 != mpfi_is_zero(val.data());
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline int eval_get_sign(const mpfi_float_backend<digits10>& val)
Chris@16: {
Chris@16:    return detail::mpfi_sgn(val.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(unsigned long* result, const mpfi_float_backend<digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<digits10> t;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_convert_to(result, t);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(long* result, const mpfi_float_backend<digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<digits10> t;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_convert_to(result, t);
Chris@16: }
Chris@16: #ifdef _MPFR_H_HAVE_INTMAX_T
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(unsigned long long* result, const mpfi_float_backend<digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<digits10> t;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_convert_to(result, t);
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(long long* result, const mpfi_float_backend<digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<digits10> t;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_convert_to(result, t);
Chris@16: }
Chris@16: #endif
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(double* result, const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    *result = mpfi_get_d(val.data());
Chris@16: }
Chris@16: template <unsigned digits10>
Chris@16: inline void eval_convert_to(long double* result, const mpfi_float_backend<digits10>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    mpfr_float_backend<digits10> t;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_convert_to(result, t);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned D1, unsigned D2, mpfr_allocation_type AllocationType>
Chris@16: inline void assign_components(mpfi_float_backend<D1>& result, const mpfr_float_backend<D2, AllocationType>& a, const mpfr_float_backend<D2, AllocationType>& b)
Chris@16: {
Chris@101:    using default_ops::eval_fpclassify;
Chris@101:    if(eval_fpclassify(a) == (int)FP_NAN)
Chris@101:    {
Chris@101:       mpfi_set_fr(result.data(), a.data());
Chris@101:    }
Chris@101:    else if(eval_fpclassify(b) == (int)FP_NAN)
Chris@101:    {
Chris@101:       mpfi_set_fr(result.data(), b.data());
Chris@101:    }
Chris@101:    else
Chris@101:    {
Chris@101:       if(a.compare(b) > 0)
Chris@101:       {
Chris@101:          BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
Chris@101:       }
Chris@101:       mpfi_interv_fr(result.data(), a.data(), b.data());
Chris@101:    }
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, class V>
Chris@16: inline typename enable_if_c<is_convertible<V, number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on> >::value >::type 
Chris@16:    assign_components(mpfi_float_backend<Digits10>& result, const V& a, const V& b)
Chris@16: {
Chris@16:    number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on> x(a), y(b);
Chris@16:    assign_components(result, x.backend(), y.backend());
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Native non-member operations:
Chris@16: //
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_sqrt(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
Chris@16: {
Chris@16:    mpfi_sqrt(result.data(), val.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_abs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
Chris@16: {
Chris@16:    mpfi_abs(result.data(), val.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_fabs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
Chris@16: {
Chris@16:    mpfi_abs(result.data(), val.data());
Chris@16: }
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_ceil(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<Digits10> a, b;
Chris@16:    mpfr_set(a.data(), val.left_data(), GMP_RNDN);
Chris@16:    mpfr_set(b.data(), val.right_data(), GMP_RNDN);
Chris@16:    eval_ceil(a, a);
Chris@16:    eval_ceil(b, b);
Chris@16:    if(a.compare(b) != 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(interval_error("Attempt to take the ceil of a value that straddles an integer boundary."));
Chris@16:    }
Chris@16:    mpfi_set_fr(result.data(), a.data());
Chris@16: }
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_floor(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
Chris@16: {
Chris@16:    mpfr_float_backend<Digits10> a, b;
Chris@16:    mpfr_set(a.data(), val.left_data(), GMP_RNDN);
Chris@16:    mpfr_set(b.data(), val.right_data(), GMP_RNDN);
Chris@16:    eval_floor(a, a);
Chris@16:    eval_floor(b, b);
Chris@16:    if(a.compare(b) != 0)
Chris@16:    {
Chris@16:       BOOST_THROW_EXCEPTION(interval_error("Attempt to take the floor of a value that straddles an integer boundary."));
Chris@16:    }
Chris@16:    mpfi_set_fr(result.data(), a.data());
Chris@16: }
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_ldexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long e)
Chris@16: {
Chris@16:    if(e > 0)
Chris@16:       mpfi_mul_2exp(result.data(), val.data(), e);
Chris@16:    else if(e < 0)
Chris@16:       mpfi_div_2exp(result.data(), val.data(), -e);
Chris@16:    else
Chris@16:       result = val;
Chris@16: }
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, int* e)
Chris@16: {
Chris@16:    mpfr_float_backend<Digits10> t, rt;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_frexp(rt, t, e);
Chris@16:    eval_ldexp(result, val, -*e);
Chris@16: }
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long* e)
Chris@16: {
Chris@16:    mpfr_float_backend<Digits10> t, rt;
Chris@16:    mpfi_mid(t.data(), val.data());
Chris@16:    eval_frexp(rt, t, e);
Chris@16:    eval_ldexp(result, val, -*e);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline int eval_fpclassify(const mpfi_float_backend<Digits10>& val) BOOST_NOEXCEPT
Chris@16: {
Chris@16:    return mpfi_inf_p(val.data()) ? FP_INFINITE : mpfi_nan_p(val.data()) ? FP_NAN : mpfi_is_zero(val.data()) ? FP_ZERO : FP_NORMAL;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_pow(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& b, const mpfi_float_backend<Digits10>& e)
Chris@16: {
Chris@16:    typedef typename boost::multiprecision::detail::canonical<unsigned, mpfi_float_backend<Digits10> >::type ui_type;
Chris@16:    using default_ops::eval_get_sign;
Chris@16:    int s = eval_get_sign(b);
Chris@16:    if(s == 0)
Chris@16:    {
Chris@16:       if(eval_get_sign(e) == 0)
Chris@16:       {
Chris@16:          result = ui_type(1);
Chris@16:       }
Chris@16:       else
Chris@16:       {
Chris@16:          result = ui_type(0);
Chris@16:       }
Chris@16:       return;
Chris@16:    }
Chris@16:    if(s < 0)
Chris@16:    {
Chris@16:       if(eval_get_sign(e) < 0)
Chris@16:       {
Chris@16:          mpfi_float_backend<Digits10> t1, t2;
Chris@16:          t1 = e;
Chris@16:          t1.negate();
Chris@16:          eval_pow(t2, b, t1);
Chris@16:          t1 = ui_type(1);
Chris@16:          eval_divide(result, t1, t2);
Chris@16:          return;
Chris@16:       }
Chris@16:       typename boost::multiprecision::detail::canonical<boost::uintmax_t, mpfi_float_backend<Digits10> >::type an;
Chris@16:       try
Chris@16:       {
Chris@16:          using default_ops::eval_convert_to;
Chris@16:          eval_convert_to(&an, e);
Chris@16:          if(e.compare(an) == 0)
Chris@16:          {
Chris@16:             mpfi_float_backend<Digits10> pb(b);
Chris@16:             pb.negate();
Chris@16:             eval_pow(result, pb, e);
Chris@16:             if(an & 1u)
Chris@16:                result.negate();
Chris@16:             return;
Chris@16:          }
Chris@16:       }
Chris@16:       catch(const std::exception&)
Chris@16:       {
Chris@16:          // conversion failed, just fall through, value is not an integer.
Chris@16:       }
Chris@16:       result = std::numeric_limits<number<mpfi_float_backend<Digits10>, et_on> >::quiet_NaN().backend();
Chris@16:       return;
Chris@16:    }
Chris@16:    mpfi_log(result.data(), b.data());
Chris@16:    mpfi_mul(result.data(), result.data(), e.data());
Chris@16:    mpfi_exp(result.data(), result.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_exp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_exp(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_log(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_log(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_log10(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_log10(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_sin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_sin(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_cos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_cos(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_tan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_tan(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_asin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_asin(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_acos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_acos(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_atan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_atan(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_atan2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg1, const mpfi_float_backend<Digits10>& arg2)
Chris@16: {
Chris@16:    mpfi_atan2(result.data(), arg1.data(), arg2.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_sinh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_sinh(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_cosh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_cosh(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10>
Chris@16: inline void eval_tanh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
Chris@16: {
Chris@16:    mpfi_tanh(result.data(), arg.data());
Chris@16: }
Chris@16: 
Chris@16: } // namespace backends
Chris@16: 
Chris@16: #ifdef BOOST_NO_SFINAE_EXPR
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: template<unsigned D1, unsigned D2>
Chris@16: struct is_explicitly_convertible<backends::mpfi_float_backend<D1>, backends::mpfi_float_backend<D2> > : public mpl::true_ {};
Chris@16: 
Chris@16: }
Chris@16: 
Chris@16: #endif
Chris@16: 
Chris@16: template<>
Chris@16: struct number_category<detail::canonical<mpfi_t, backends::mpfi_float_backend<0> >::type> : public mpl::int_<number_kind_floating_point>{};
Chris@16: template <unsigned Digits10>
Chris@16: struct is_interval_number<backends::mpfi_float_backend<Digits10> > : public mpl::true_ {};
Chris@16: 
Chris@16: using boost::multiprecision::backends::mpfi_float_backend;
Chris@16: 
Chris@16: typedef number<mpfi_float_backend<50> >    mpfi_float_50;
Chris@16: typedef number<mpfi_float_backend<100> >   mpfi_float_100;
Chris@16: typedef number<mpfi_float_backend<500> >   mpfi_float_500;
Chris@16: typedef number<mpfi_float_backend<1000> >  mpfi_float_1000;
Chris@16: typedef number<mpfi_float_backend<0> >     mpfi_float;
Chris@16: 
Chris@16: //
Chris@16: // Special interval specific functions:
Chris@16: //
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> lower(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
Chris@16: {
Chris@16:    number<mpfr_float_backend<Digits10> > result;
Chris@16:    mpfr_set(result.backend().data(), val.backend().left_data(), GMP_RNDN);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> upper(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
Chris@16: {
Chris@16:    number<mpfr_float_backend<Digits10> > result;
Chris@16:    mpfr_set(result.backend().data(), val.backend().right_data(), GMP_RNDN);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> median(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
Chris@16: {
Chris@16:    number<mpfr_float_backend<Digits10> > result;
Chris@16:    mpfi_mid(result.backend().data(), val.backend().data());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> width(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
Chris@16: {
Chris@16:    number<mpfr_float_backend<Digits10> > result;
Chris@16:    mpfi_diam_abs(result.backend().data(), val.backend().data());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> intersect(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
Chris@16: {
Chris@16:    number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
Chris@16:    mpfi_intersect(result.backend().data(), a.backend().data(), b.backend().data());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> hull(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
Chris@16: {
Chris@16:    number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
Chris@16:    mpfi_union(result.backend().data(), a.backend().data(), b.backend().data());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool overlap(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
Chris@16: {
Chris@16:   return (lower(a) <= lower(b) && lower(b) <= upper(a)) ||
Chris@16:          (lower(b) <= lower(a) && lower(a) <= upper(b));
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates1, expression_template_option ExpressionTemplates2>
Chris@16: inline bool in(const number<mpfr_float_backend<Digits10>, ExpressionTemplates1>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates2>&  b)
Chris@16: {
Chris@16:   return mpfi_is_inside_fr(a.backend().data(), b.backend().data()) != 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool zero_in(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
Chris@16: {
Chris@16:   return mpfi_has_zero(a.backend().data()) != 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
Chris@16: {
Chris@16:   return mpfi_is_inside(a.backend().data(), b.backend().data()) != 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool proper_subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b)
Chris@16: {
Chris@16:   return mpfi_is_strictly_inside(a.backend().data(), b.backend().data()) != 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool empty(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
Chris@16: {
Chris@16:   return mpfi_is_empty(a.backend().data()) != 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: inline bool singleton(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  a)
Chris@16: {
Chris@16:   return mpfr_cmp(a.backend().left_data(), a.backend().right_data()) == 0;
Chris@16: }
Chris@16: 
Chris@16: template <unsigned Digits10, expression_template_option ExpressionTemplates>
Chris@16: struct component_type<number<mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef number<mpfr_float_backend<Digits10>, ExpressionTemplates> type;
Chris@16: };
Chris@16: 
Chris@16: } // namespace multiprecision
Chris@16: 
Chris@16: namespace math{
Chris@16: 
Chris@16: namespace tools{
Chris@16: 
Chris@16: template <>
Chris@16: inline int digits<boost::multiprecision::mpfi_float>()
Chris@16: {
Chris@16:    return boost::multiprecision::backends::detail::get_default_precision();
Chris@16: }
Chris@16: template <>
Chris@16: inline int digits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
Chris@16: {
Chris@16:    return boost::multiprecision::backends::detail::get_default_precision();
Chris@16: }
Chris@16: 
Chris@16: } // namespace tools
Chris@16: 
Chris@16: namespace constants{ namespace detail{
Chris@16: 
Chris@16: template <class T> struct constant_pi;
Chris@16: template <class T> struct constant_ln_two;
Chris@16: template <class T> struct constant_euler;
Chris@16: template <class T> struct constant_catalan;
Chris@16: 
Chris@16: //
Chris@16: // Initializer: ensure all our constants are initialized prior to the first call of main:
Chris@16: //
Chris@16: template <class T>
Chris@16: struct mpfi_initializer
Chris@16: {
Chris@16:    struct init
Chris@16:    {
Chris@16:       init()
Chris@16:       {
Chris@16:          boost::math::constants::pi<T>();
Chris@16:          boost::math::constants::ln_two<T>();
Chris@16:          boost::math::constants::euler<T>();
Chris@16:          boost::math::constants::catalan<T>();
Chris@16:       }
Chris@16:       void force_instantiate()const{}
Chris@16:    };
Chris@16:    static const init initializer;
Chris@16:    static void force_instantiate()
Chris@16:    {
Chris@16:       initializer.force_instantiate();
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: template <class T>
Chris@16: const typename mpfi_initializer<T>::init mpfi_initializer<T>::initializer;
Chris@16: 
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct constant_pi<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
Chris@16:    template<int N>
Chris@16:    static inline result_type const& get(const mpl::int_<N>&)
Chris@16:    {
Chris@16:       mpfi_initializer<result_type>::force_instantiate();
Chris@16:       static result_type result;
Chris@16:       static bool has_init = false;
Chris@16:       if(!has_init)
Chris@16:       {
Chris@16:          has_init = true;
Chris@16:          mpfi_const_pi(result.backend().data());
Chris@16:       }
Chris@16:       return result;
Chris@16:    }
Chris@16: };
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct constant_ln_two<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
Chris@16:    template<int N>
Chris@16:    static inline result_type const& get(const mpl::int_<N>&)
Chris@16:    {
Chris@16:       mpfi_initializer<result_type>::force_instantiate();
Chris@16:       static result_type result;
Chris@16:       static bool has_init = false;
Chris@16:       if(!has_init)
Chris@16:       {
Chris@16:          has_init = true;
Chris@16:          mpfi_const_log2(result.backend().data());
Chris@16:       }
Chris@16:       return result;
Chris@16:    }
Chris@16: };
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct constant_euler<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
Chris@16:    template<int N>
Chris@16:    static inline result_type const& get(const mpl::int_<N>&)
Chris@16:    {
Chris@16:       mpfi_initializer<result_type>::force_instantiate();
Chris@16:       static result_type result;
Chris@16:       static bool has_init = false;
Chris@16:       if(!has_init)
Chris@16:       {
Chris@16:          has_init = true;
Chris@16:          mpfi_const_euler(result.backend().data());
Chris@16:       }
Chris@16:       return result;
Chris@16:    }
Chris@16: };
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct constant_catalan<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result_type;
Chris@16:    template<int N>
Chris@16:    static inline result_type const& get(const mpl::int_<N>&)
Chris@16:    {
Chris@16:       mpfi_initializer<result_type>::force_instantiate();
Chris@16:       static result_type result;
Chris@16:       static bool has_init = false;
Chris@16:       if(!has_init)
Chris@16:       {
Chris@16:          has_init = true;
Chris@16:          mpfi_const_catalan(result.backend().data());
Chris@16:       }
Chris@16:       return result;
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: }} // namespaces
Chris@16: 
Chris@16: }}  // namespaces
Chris@16: 
Chris@16: namespace std{
Chris@16: 
Chris@16: //
Chris@16: // numeric_limits [partial] specializations for the types declared in this header:
Chris@16: //
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: class numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> number_type;
Chris@16: public:
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_specialized = true;
Chris@16:    static number_type (min)()
Chris@16:    {
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          value.first = true;
Chris@16:          value.second = 0.5;
Chris@16:          mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin());
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    static number_type (max)()
Chris@16:    {
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          value.first = true;
Chris@16:          value.second = 0.5;
Chris@16:          mpfi_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax());
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    BOOST_STATIC_CONSTEXPR number_type lowest()
Chris@16:    {
Chris@16:       return -(max)();
Chris@16:    }
Chris@16:    BOOST_STATIC_CONSTEXPR int digits = static_cast<int>((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301 ? 2 : 1));
Chris@16:    BOOST_STATIC_CONSTEXPR int digits10 = Digits10;
Chris@16:    // Is this really correct???
Chris@16:    BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_signed = true;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_integer = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_exact = false;
Chris@16:    BOOST_STATIC_CONSTEXPR int radix = 2;
Chris@16:    static number_type epsilon()
Chris@16:    {
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          value.first = true;
Chris@16:          value.second = 1;
Chris@16:          mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits<number_type>::digits - 1);
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    // What value should this be????
Chris@16:    static number_type round_error()
Chris@16:    {
Chris@16:       // returns epsilon/2
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          value.first = true;
Chris@16:          value.second = 1;
Chris@16:          mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), 1);
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    BOOST_STATIC_CONSTEXPR long min_exponent = MPFR_EMIN_DEFAULT;
Chris@16:    BOOST_STATIC_CONSTEXPR long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L;
Chris@16:    BOOST_STATIC_CONSTEXPR long max_exponent = MPFR_EMAX_DEFAULT;
Chris@16:    BOOST_STATIC_CONSTEXPR long max_exponent10 = (MPFR_EMAX_DEFAULT / 1000) * 301L;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_infinity = true;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
Chris@16:    BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
Chris@16:    static number_type infinity()
Chris@16:    {
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          boost::multiprecision::mpfr_float_backend<Digits10> t;
Chris@16:          mpfr_set_inf(t.data(), 1);
Chris@16:          value.first = true;
Chris@16:          mpfi_set_fr(value.second.backend().data(), t.data());
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    static number_type quiet_NaN()
Chris@16:    {
Chris@16:       initializer.do_nothing();
Chris@16:       static std::pair<bool, number_type> value;
Chris@16:       if(!value.first)
Chris@16:       {
Chris@16:          boost::multiprecision::mpfr_float_backend<Digits10> t;
Chris@16:          mpfr_set_nan(t.data());
Chris@16:          value.first = true;
Chris@16:          mpfi_set_fr(value.second.backend().data(), t.data());
Chris@16:       }
Chris@16:       return value.second;
Chris@16:    }
Chris@16:    BOOST_STATIC_CONSTEXPR number_type signaling_NaN()
Chris@16:    {
Chris@16:       return number_type(0);
Chris@16:    }
Chris@16:    BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); }
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_bounded = true;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_modulo = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool traps = true;
Chris@16:    BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
Chris@16:    BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;
Chris@16: 
Chris@16: private:
Chris@16:    struct data_initializer
Chris@16:    {
Chris@16:       data_initializer()
Chris@16:       {
Chris@16:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::epsilon();
Chris@16:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::round_error();
Chris@16:          (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::min)();
Chris@16:          (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::max)();
Chris@16:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::infinity();
Chris@16:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<digits10> > >::quiet_NaN();
Chris@16:       }
Chris@16:       void do_nothing()const{}
Chris@16:    };
Chris@16:    static const data_initializer initializer;
Chris@16: };
Chris@16: 
Chris@16: template<unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: 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;
Chris@16: 
Chris@16: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
Chris@16: 
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits10;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_digits10;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_signed;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_integer;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_exact;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::radix;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent10;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent10;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_infinity;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_quiet_NaN;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_signaling_NaN;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm_loss;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_iec559;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_bounded;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_modulo;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::traps;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::tinyness_before;
Chris@16: template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::round_style;
Chris@16: 
Chris@16: #endif
Chris@16: 
Chris@16: 
Chris@16: template<boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: class numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >
Chris@16: {
Chris@16:    typedef boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> number_type;
Chris@16: public:
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_specialized = false;
Chris@16:    static number_type (min)() { return number_type(0); }
Chris@16:    static number_type (max)() { return number_type(0); }
Chris@16:    static number_type lowest() { return number_type(0); }
Chris@16:    BOOST_STATIC_CONSTEXPR int digits = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR int digits10 = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR int max_digits10 = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_signed = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_integer = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_exact = false;
Chris@16:    BOOST_STATIC_CONSTEXPR int radix = 0;
Chris@16:    static number_type epsilon() { return number_type(0); }
Chris@16:    static number_type round_error() { return number_type(0); }
Chris@16:    BOOST_STATIC_CONSTEXPR int min_exponent = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR int max_exponent = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_infinity = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
Chris@16:    BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
Chris@16:    BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
Chris@16:    static number_type infinity() { return number_type(0); }
Chris@16:    static number_type quiet_NaN() { return number_type(0); }
Chris@16:    static number_type signaling_NaN() { return number_type(0); }
Chris@16:    static number_type denorm_min() { return number_type(0); }
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_bounded = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool is_modulo = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool traps = false;
Chris@16:    BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
Chris@16:    BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
Chris@16: };
Chris@16: 
Chris@16: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
Chris@16: 
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::digits;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::digits10;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_digits10;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_signed;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_integer;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_exact;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::radix;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent10;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent10;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_infinity;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_quiet_NaN;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_signaling_NaN;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm_loss;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_iec559;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_bounded;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_modulo;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::traps;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::tinyness_before;
Chris@16: template <boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::round_style;
Chris@16: 
Chris@16: #endif
Chris@16: } // namespace std
Chris@16: #endif