Chris@102: ///////////////////////////////////////////////////////////////
Chris@102: //  Copyright 2013 John Maddock. Distributed under the Boost
Chris@102: //  Software License, Version 1.0. (See accompanying file
Chris@102: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
Chris@102: 
Chris@102: #ifndef BOOST_MATH_CPP_BIN_FLOAT_HPP
Chris@102: #define BOOST_MATH_CPP_BIN_FLOAT_HPP
Chris@102: 
Chris@102: #include <boost/multiprecision/cpp_int.hpp>
Chris@102: #include <boost/multiprecision/integer.hpp>
Chris@102: #include <boost/math/special_functions/trunc.hpp>
Chris@102: #include <boost/multiprecision/detail/float_string_cvt.hpp>
Chris@102: 
Chris@102: namespace boost{ namespace multiprecision{ namespace backends{
Chris@102: 
Chris@102: enum digit_base_type
Chris@102: {
Chris@102:    digit_base_2 = 2, 
Chris@102:    digit_base_10 = 10
Chris@102: };
Chris@102: 
Chris@102: #ifdef BOOST_MSVC
Chris@102: #pragma warning(push)
Chris@102: #pragma warning(disable:4522)  // multiple assignment operators specified
Chris@102: #endif
Chris@102: 
Chris@102: namespace detail{
Chris@102: 
Chris@102: template <class U>
Chris@102: inline typename enable_if_c<is_unsigned<U>::value, bool>::type is_negative(U) { return false; }
Chris@102: template <class S>
Chris@102: inline typename disable_if_c<is_unsigned<S>::value, bool>::type is_negative(S s) { return s < 0; }
Chris@102: 
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase = digit_base_10, class Allocator = void, class Exponent = int, Exponent MinExponent = 0, Exponent MaxExponent = 0>
Chris@102: class cpp_bin_float
Chris@102: {
Chris@102: public:
Chris@102:    static const unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + ((Digits * 1000uL) % 301 ? 2u : 1u);
Chris@102:    typedef cpp_int_backend<is_void<Allocator>::value ? bit_count : 0, bit_count, is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> rep_type;
Chris@102:    typedef cpp_int_backend<is_void<Allocator>::value ? 2 * bit_count : 0, 2 * bit_count, is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> double_rep_type;
Chris@102: 
Chris@102:    typedef typename rep_type::signed_types                        signed_types;
Chris@102:    typedef typename rep_type::unsigned_types                      unsigned_types;
Chris@102:    typedef boost::mpl::list<double, long double>                  float_types;
Chris@102:    typedef Exponent                                               exponent_type;
Chris@102: 
Chris@102:    static const exponent_type max_exponent_limit = boost::integer_traits<exponent_type>::const_max - 2 * static_cast<exponent_type>(bit_count);
Chris@102:    static const exponent_type min_exponent_limit = boost::integer_traits<exponent_type>::const_min + 2 * static_cast<exponent_type>(bit_count);
Chris@102: 
Chris@102:    BOOST_STATIC_ASSERT_MSG(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!");
Chris@102:    BOOST_STATIC_ASSERT_MSG(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!");
Chris@102:    BOOST_STATIC_ASSERT_MSG(MinExponent <= 0, "Template parameter MinExponent can not be positive!");
Chris@102:    BOOST_STATIC_ASSERT_MSG(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!");
Chris@102: 
Chris@102:    static const exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent;
Chris@102:    static const exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent;
Chris@102: 
Chris@102:    static const exponent_type exponent_zero = max_exponent + 1;
Chris@102:    static const exponent_type exponent_infinity = max_exponent + 2;
Chris@102:    static const exponent_type exponent_nan = max_exponent + 3;
Chris@102: 
Chris@102: private:
Chris@102: 
Chris@102:    rep_type m_data;
Chris@102:    exponent_type m_exponent;
Chris@102:    bool m_sign;
Chris@102: public:
Chris@102:    cpp_bin_float() BOOST_NOEXCEPT_IF(noexcept(rep_type())) : m_data(), m_exponent(exponent_nan), m_sign(false) {}
Chris@102: 
Chris@102:    cpp_bin_float(const cpp_bin_float &o) BOOST_NOEXCEPT_IF(noexcept(rep_type(std::declval<const rep_type&>())))
Chris@102:       : m_data(o.m_data), m_exponent(o.m_exponent), m_sign(o.m_sign) {}
Chris@102: 
Chris@102:    template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
Chris@102:    cpp_bin_float(const cpp_bin_float<D, B, A, E, MinE, MaxE> &o, typename boost::enable_if_c<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = 0)
Chris@102:       : m_exponent(o.exponent()), m_sign(o.sign()) 
Chris@102:    {
Chris@102:       typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits());
Chris@102:       this->sign() = o.sign();
Chris@102:       this->exponent() = o.exponent() + (int)bit_count - (int)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count;
Chris@102:       copy_and_round(*this, b);
Chris@102:    }
Chris@102: 
Chris@102:    template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
Chris@102:    explicit cpp_bin_float(const cpp_bin_float<D, B, A, E, MinE, MaxE> &o, typename boost::disable_if_c<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = 0)
Chris@102:       : m_exponent(o.exponent()), m_sign(o.sign()) 
Chris@102:    {
Chris@102:       typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits());
Chris@102:       this->sign() = o.sign();
Chris@102:       this->exponent() = o.exponent() - (int)(cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count - bit_count);
Chris@102:       copy_and_round(*this, b);
Chris@102:    }
Chris@102: 
Chris@102:    template <class Float>
Chris@102:    cpp_bin_float(const Float& f, 
Chris@102:       typename boost::enable_if_c<
Chris@102:          (number_category<Float>::value == number_kind_floating_point)
Chris@102:          && (std::numeric_limits<Float>::digits <= (int)bit_count)
Chris@102:          && (std::numeric_limits<Float>::radix == 2)
Chris@102:       >::type const* = 0)
Chris@102:       : m_data(), m_exponent(0), m_sign(false)
Chris@102:    {
Chris@102:       this->assign_float(f);
Chris@102:    }
Chris@102: 
Chris@102:    cpp_bin_float& operator=(const cpp_bin_float &o) BOOST_NOEXCEPT_IF(noexcept(std::declval<rep_type&>() = std::declval<const rep_type&>()))
Chris@102:    {
Chris@102:       m_data = o.m_data;
Chris@102:       m_exponent = o.m_exponent;
Chris@102:       m_sign = o.m_sign;
Chris@102:       return *this;
Chris@102:    }
Chris@102: 
Chris@102:    template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
Chris@102:    cpp_bin_float& operator=(const cpp_bin_float<D, B, A, E, MinE, MaxE> &o)
Chris@102:    {
Chris@102:       typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits());
Chris@102:       this->exponent() = o.exponent() + (int)bit_count - (int)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count;
Chris@102:       this->sign() = o.sign();
Chris@102:       copy_and_round(*this, b);
Chris@102:       return *this;
Chris@102:    }
Chris@102: 
Chris@102:    template <class Float>
Chris@102:    typename boost::enable_if_c<
Chris@102:       (number_category<Float>::value == number_kind_floating_point)
Chris@102:       && (std::numeric_limits<Float>::digits <= (int)bit_count)
Chris@102:       && (std::numeric_limits<Float>::radix == 2), cpp_bin_float&>::type operator=(const Float& f)
Chris@102:    {
Chris@102:       return assign_float(f);
Chris@102:    }
Chris@102: 
Chris@102:    template <class Float>
Chris@102:    typename boost::enable_if_c<is_floating_point<Float>::value, cpp_bin_float&>::type assign_float(Float f)
Chris@102:    {
Chris@102:       BOOST_MATH_STD_USING
Chris@102:       using default_ops::eval_add;
Chris@102:       typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;
Chris@102: 
Chris@102:       switch((boost::math::fpclassify)(f))
Chris@102:       {
Chris@102:       case FP_ZERO:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_zero;
Chris@102:          return *this;
Chris@102:       case FP_NAN:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_nan;
Chris@102:          return *this;
Chris@102:       case FP_INFINITE:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_infinity;
Chris@102:          return *this;
Chris@102:       }
Chris@102:       if(f < 0)
Chris@102:       {
Chris@102:          *this = -f;
Chris@102:          this->negate();
Chris@102:          return *this;
Chris@102:       }
Chris@102: 
Chris@102:       typedef typename mpl::front<unsigned_types>::type ui_type;
Chris@102:       m_data = static_cast<ui_type>(0u);
Chris@102:       m_sign = false;
Chris@102:       m_exponent = 0;
Chris@102: 
Chris@102:       static const int bits = sizeof(int) * CHAR_BIT - 1;
Chris@102:       int e;
Chris@102:       f = frexp(f, &e);
Chris@102:       while(f)
Chris@102:       {
Chris@102:          f = ldexp(f, bits);
Chris@102:          e -= bits;
Chris@102: #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
Chris@102:          int ipart = itrunc(f);
Chris@102: #else
Chris@102:          int ipart = static_cast<int>(f);
Chris@102: #endif
Chris@102:          f -= ipart;
Chris@102:          m_exponent += bits;
Chris@102:          cpp_bin_float t;
Chris@102:          t = static_cast<bf_int_type>(ipart);
Chris@102:          eval_add(*this, t);
Chris@102:       }
Chris@102:       m_exponent += static_cast<Exponent>(e);
Chris@102:       return *this;
Chris@102:    }
Chris@102: 
Chris@102:    template <class Float>
Chris@102:    typename boost::enable_if_c<
Chris@102:       (number_category<Float>::value == number_kind_floating_point) 
Chris@102:          && !is_floating_point<Float>::value
Chris@102:          /*&& (std::numeric_limits<number<Float> >::radix == 2)*/, 
Chris@102:       cpp_bin_float&>::type assign_float(Float f)
Chris@102:    {
Chris@102:       BOOST_MATH_STD_USING
Chris@102:       using default_ops::eval_add;
Chris@102:       using default_ops::eval_get_sign;
Chris@102:       using default_ops::eval_convert_to;
Chris@102:       using default_ops::eval_subtract;
Chris@102: 
Chris@102:       typedef typename boost::multiprecision::detail::canonical<int, Float>::type f_int_type;
Chris@102:       typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;
Chris@102: 
Chris@102:       switch(eval_fpclassify(f))
Chris@102:       {
Chris@102:       case FP_ZERO:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_zero;
Chris@102:          return *this;
Chris@102:       case FP_NAN:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_nan;
Chris@102:          return *this;
Chris@102:       case FP_INFINITE:
Chris@102:          m_data = limb_type(0);
Chris@102:          m_sign = false;
Chris@102:          m_exponent = exponent_infinity;
Chris@102:          return *this;
Chris@102:       }
Chris@102:       if(eval_get_sign(f) < 0)
Chris@102:       {
Chris@102:          f.negate();
Chris@102:          *this = f;
Chris@102:          this->negate();
Chris@102:          return *this;
Chris@102:       }
Chris@102: 
Chris@102:       typedef typename mpl::front<unsigned_types>::type ui_type;
Chris@102:       m_data = static_cast<ui_type>(0u);
Chris@102:       m_sign = false;
Chris@102:       m_exponent = 0;
Chris@102: 
Chris@102:       static const int bits = sizeof(int) * CHAR_BIT - 1;
Chris@102:       int e;
Chris@102:       eval_frexp(f, f, &e);
Chris@102:       while(eval_get_sign(f) != 0)
Chris@102:       {
Chris@102:          eval_ldexp(f, f, bits);
Chris@102:          e -= bits;
Chris@102:          int ipart;
Chris@102:          eval_convert_to(&ipart, f);
Chris@102:          eval_subtract(f, static_cast<f_int_type>(ipart));
Chris@102:          m_exponent += bits;
Chris@102:          eval_add(*this, static_cast<bf_int_type>(ipart));
Chris@102:       }
Chris@102:       m_exponent += e;
Chris@102:       if(m_exponent > max_exponent)
Chris@102:          m_exponent = exponent_infinity;
Chris@102:       if(m_exponent < min_exponent)
Chris@102:       {
Chris@102:          m_data = limb_type(0u);
Chris@102:          m_exponent = exponent_zero;
Chris@102:          m_sign = false;
Chris@102:       }
Chris@102:       else if(eval_get_sign(m_data) == 0)
Chris@102:       {
Chris@102:          m_exponent = exponent_zero;
Chris@102:          m_sign = false;
Chris@102:       }
Chris@102:       return *this;
Chris@102:    }
Chris@102: 
Chris@102:    template <class I>
Chris@102:    typename boost::enable_if<is_integral<I>, cpp_bin_float&>::type operator=(const I& i)
Chris@102:    {
Chris@102:       using default_ops::eval_bit_test;
Chris@102:       if(!i)
Chris@102:       {
Chris@102:          m_data = static_cast<limb_type>(0);
Chris@102:          m_exponent = exponent_zero;
Chris@102:          m_sign = false;
Chris@102:       }
Chris@102:       else
Chris@102:       {
Chris@102:          typedef typename make_unsigned<I>::type ui_type;
Chris@102:          ui_type fi = static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(i));
Chris@102:          typedef typename boost::multiprecision::detail::canonical<ui_type, rep_type>::type ar_type;
Chris@102:          m_data = static_cast<ar_type>(fi);
Chris@102:          unsigned shift = msb(fi);
Chris@102:          if(shift >= bit_count)
Chris@102:          {
Chris@102:             m_exponent = static_cast<Exponent>(shift);
Chris@102:             m_data = static_cast<ar_type>(fi >> (shift + 1 - bit_count));
Chris@102:          }
Chris@102:          else
Chris@102:          {
Chris@102:             m_exponent = static_cast<Exponent>(shift);
Chris@102:             eval_left_shift(m_data, bit_count - shift - 1);
Chris@102:          }
Chris@102:          BOOST_ASSERT(eval_bit_test(m_data, bit_count-1));
Chris@102:          m_sign = detail::is_negative(i);
Chris@102:       }
Chris@102:       return *this;
Chris@102:    }
Chris@102: 
Chris@102:    cpp_bin_float& operator=(const char *s);
Chris@102: 
Chris@102:    void swap(cpp_bin_float &o) BOOST_NOEXCEPT
Chris@102:    {
Chris@102:       m_data.swap(o.m_data);
Chris@102:       std::swap(m_exponent, o.m_exponent);
Chris@102:       std::swap(m_sign, o.m_sign);
Chris@102:    }
Chris@102: 
Chris@102:    std::string str(std::streamsize dig, std::ios_base::fmtflags f) const;
Chris@102: 
Chris@102:    void negate()
Chris@102:    {
Chris@102:       if((m_exponent != exponent_zero) && (m_exponent != exponent_nan))
Chris@102:          m_sign = !m_sign;
Chris@102:    }
Chris@102: 
Chris@102:    int compare(const cpp_bin_float &o) const BOOST_NOEXCEPT
Chris@102:    {
Chris@102:       if(m_sign != o.m_sign)
Chris@102:          return m_sign ? -1 : 1;
Chris@102:       int result;
Chris@102:       if(m_exponent == exponent_nan)
Chris@102:          return -1;
Chris@102:       else if(m_exponent != o.m_exponent)
Chris@102:       {
Chris@102:          if(m_exponent == exponent_zero)
Chris@102:             result = -1;
Chris@102:          else if(o.m_exponent == exponent_zero)
Chris@102:             result = 1;
Chris@102:          else 
Chris@102:             result = m_exponent > o.m_exponent ? 1 : -1;
Chris@102:       }
Chris@102:       else
Chris@102:          result = m_data.compare(o.m_data);
Chris@102:       if(m_sign)
Chris@102:          result = -result;
Chris@102:       return result;
Chris@102:    }
Chris@102:    template <class A>
Chris@102:    int compare(const A& o) const BOOST_NOEXCEPT
Chris@102:    {
Chris@102:       cpp_bin_float b;
Chris@102:       b = o;
Chris@102:       return compare(b);
Chris@102:    }
Chris@102: 
Chris@102:    rep_type& bits() { return m_data; }
Chris@102:    const rep_type& bits()const { return m_data; }
Chris@102:    exponent_type& exponent() { return m_exponent; }
Chris@102:    const exponent_type& exponent()const { return m_exponent; }
Chris@102:    bool& sign() { return m_sign; }
Chris@102:    const bool& sign()const { return m_sign; }
Chris@102:    void check_invariants()
Chris@102:    {
Chris@102:       using default_ops::eval_bit_test;
Chris@102:       using default_ops::eval_is_zero;
Chris@102:       if((m_exponent <= max_exponent) && (m_exponent >= min_exponent))
Chris@102:       {
Chris@102:          BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1));
Chris@102:       }
Chris@102:       else
Chris@102:       {
Chris@102:          BOOST_ASSERT(m_exponent > max_exponent);
Chris@102:          BOOST_ASSERT(m_exponent <= exponent_nan);
Chris@102:          BOOST_ASSERT(eval_is_zero(m_data));
Chris@102:       }
Chris@102:    }
Chris@102:    template<class Archive>
Chris@102:    void serialize(Archive & ar, const unsigned int /*version*/)
Chris@102:    {
Chris@102:       ar & m_data;
Chris@102:       ar & m_exponent;
Chris@102:       ar & m_sign;
Chris@102:    }
Chris@102: };
Chris@102: 
Chris@102: #ifdef BOOST_MSVC
Chris@102: #pragma warning(pop)
Chris@102: #endif
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class Int>
Chris@102: inline void copy_and_round(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, Int &arg)
Chris@102: {
Chris@102:    // Precondition: exponent of res must have been set before this function is called
Chris@102:    // as we may need to adjust it based on how many cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in arg are set.
Chris@102:    using default_ops::eval_msb;
Chris@102:    using default_ops::eval_lsb;
Chris@102:    using default_ops::eval_left_shift;
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_right_shift;
Chris@102:    using default_ops::eval_increment;
Chris@102:    using default_ops::eval_get_sign;
Chris@102: 
Chris@102:    // cancellation may have resulted in arg being all zeros:
Chris@102:    if(eval_get_sign(arg) == 0)
Chris@102:    {
Chris@102:       res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
Chris@102:       res.sign() = false;
Chris@102:       res.bits() = static_cast<limb_type>(0u);
Chris@102:       return;
Chris@102:    }
Chris@102:    int msb = eval_msb(arg);
Chris@102:    if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) > msb + 1)
Chris@102:    {
Chris@102:       // Must have had cancellation in subtraction, shift left and copy:
Chris@102:       res.bits() = arg;
Chris@102:       eval_left_shift(res.bits(), cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1);
Chris@102:       res.exponent() -= static_cast<Exponent>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1);
Chris@102:    }
Chris@102:    else if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) < msb + 1)
Chris@102:    {
Chris@102:       // We have more cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count than we need, so round as required, 
Chris@102:       // first get the rounding bit:
Chris@102:       bool roundup = eval_bit_test(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count);
Chris@102:       // Then check for a tie:
Chris@102:       if(roundup && (msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count == eval_lsb(arg)))
Chris@102:       {
Chris@102:          // Ties round towards even:
Chris@102:          if(!eval_bit_test(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1))
Chris@102:             roundup = false;
Chris@102:       }
Chris@102:       // Shift off the cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count we don't need:
Chris@102:       eval_right_shift(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1);
Chris@102:       res.exponent() += static_cast<Exponent>(msb - (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1);
Chris@102:       if(roundup)
Chris@102:       {
Chris@102:          eval_increment(arg);
Chris@102:          if(eval_bit_test(arg, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
Chris@102:          {
Chris@102:             // This happens very very rairly:
Chris@102:             eval_right_shift(arg, 1u);
Chris@102:             ++res.exponent();
Chris@102:          }
Chris@102:       }
Chris@102:       res.bits() = arg;
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       res.bits() = arg;
Chris@102:    }
Chris@102:    BOOST_ASSERT((eval_msb(res.bits()) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
Chris@102: 
Chris@102:    if(res.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
Chris@102:    {
Chris@102:       // Overflow:
Chris@102:       res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
Chris@102:       res.bits() = static_cast<limb_type>(0u);
Chris@102:    }
Chris@102:    else if(res.exponent() < cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent)
Chris@102:    {
Chris@102:       // Underflow:
Chris@102:       res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
Chris@102:       res.bits() = static_cast<limb_type>(0u);
Chris@102:       res.sign() = false;
Chris@102:    }
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void do_eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    using default_ops::eval_add;
Chris@102:    using default_ops::eval_bit_test;
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
Chris@102: 
Chris@102:    // Special cases first:
Chris@102:    switch(a.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       res = b;
Chris@102:       if(res.sign())
Chris@102:          res.negate();
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
Chris@102:          res = b;
Chris@102:       else
Chris@102:          res = a;
Chris@102:       return; // result is still infinite.
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = a;
Chris@102:       return; // result is still a NaN.
Chris@102:    }
Chris@102:    switch(b.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = b;
Chris@102:       if(res.sign())
Chris@102:          res.negate();
Chris@102:       return; // result is infinite.
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = b;
Chris@102:       return; // result is a NaN.
Chris@102:    }
Chris@102:    
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
Chris@102:    bool s = a.sign();
Chris@102:    if(e_diff >= 0)
Chris@102:    {
Chris@102:       dt = a.bits();
Chris@102:       if(e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:       {
Chris@102:          eval_left_shift(dt, e_diff);
Chris@102:          res.exponent() = a.exponent() - e_diff;
Chris@102:          eval_add(dt, b.bits());
Chris@102:       }
Chris@102:       else
Chris@102:          res.exponent() = a.exponent();
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       dt= b.bits();
Chris@102:       if(-e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:       {
Chris@102:          eval_left_shift(dt, -e_diff);
Chris@102:          res.exponent() = b.exponent() + e_diff;
Chris@102:          eval_add(dt, a.bits());
Chris@102:       }
Chris@102:       else
Chris@102:          res.exponent() = b.exponent();
Chris@102:    }
Chris@102:    
Chris@102:    copy_and_round(res, dt);
Chris@102:    res.check_invariants();
Chris@102:    if(res.sign() != s)
Chris@102:       res.negate();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void do_eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    using default_ops::eval_subtract;
Chris@102:    using default_ops::eval_bit_test;
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
Chris@102:    
Chris@102:    // Special cases first:
Chris@102:    switch(a.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       else
Chris@102:       {
Chris@102:          res = b;
Chris@102:          if(!res.sign())
Chris@102:             res.negate();
Chris@102:       }
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       if((b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan) || (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity))
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       else
Chris@102:          res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = a;
Chris@102:       return; // result is still a NaN.
Chris@102:    }
Chris@102:    switch(b.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan;
Chris@102:       res.sign() = false;
Chris@102:       res.bits() = static_cast<limb_type>(0u);
Chris@102:       return; // result is a NaN.
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = b;
Chris@102:       return; // result is still a NaN.
Chris@102:    }
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
Chris@102:    bool s = a.sign();
Chris@102:    if((e_diff > 0) || ((e_diff == 0) && a.bits().compare(b.bits()) >= 0))
Chris@102:    {
Chris@102:       dt = a.bits();
Chris@102:       if(e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:       {
Chris@102:          eval_left_shift(dt, e_diff);
Chris@102:          res.exponent() = a.exponent() - e_diff;
Chris@102:          eval_subtract(dt, b.bits());
Chris@102:       }
Chris@102:       else
Chris@102:          res.exponent() = a.exponent();
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       dt = b.bits();
Chris@102:       if(-e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:       {
Chris@102:          eval_left_shift(dt, -e_diff);
Chris@102:          res.exponent() = b.exponent() + e_diff;
Chris@102:          eval_subtract(dt, a.bits());
Chris@102:       }
Chris@102:       else
Chris@102:          res.exponent() = b.exponent();
Chris@102:       s = !s;
Chris@102:    }
Chris@102:    
Chris@102:    copy_and_round(res, dt);
Chris@102:    if(res.sign() != s)
Chris@102:       res.negate();
Chris@102:    res.check_invariants();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    if(a.sign() == b.sign())
Chris@102:       do_eval_add(res, a, b);
Chris@102:    else
Chris@102:       do_eval_subtract(res, a, b);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a)
Chris@102: {
Chris@102:    return eval_add(res, res, a);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    if(a.sign() != b.sign())
Chris@102:       do_eval_add(res, a, b);
Chris@102:    else
Chris@102:       do_eval_subtract(res, a, b);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a)
Chris@102: {
Chris@102:    return eval_subtract(res, res, a);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_multiply;
Chris@102: 
Chris@102:    // Special cases first:
Chris@102:    switch(a.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
Chris@102:          res = b;
Chris@102:       else
Chris@102:          res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       switch(b.exponent())
Chris@102:       {
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:          break;
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:          res = b;
Chris@102:          break;
Chris@102:       default:
Chris@102:          res = a;
Chris@102:          break;
Chris@102:       }
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = a;
Chris@102:       return;
Chris@102:    }
Chris@102:    if(b.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
Chris@102:    {
Chris@102:       res = b;
Chris@102:       return;
Chris@102:    }
Chris@102:    if((a.exponent() > 0) && (b.exponent() > 0))
Chris@102:    {
Chris@102:       if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent + 2 - a.exponent() < b.exponent())
Chris@102:       {
Chris@102:          // We will certainly overflow:
Chris@102:          res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
Chris@102:          res.sign() = a.sign() != b.sign();
Chris@102:          res.bits() = static_cast<limb_type>(0u);
Chris@102:          return;
Chris@102:       }
Chris@102:    }
Chris@102:    if((a.exponent() < 0) && (b.exponent() < 0))
Chris@102:    {
Chris@102:       if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - 2 - a.exponent() > b.exponent())
Chris@102:       {
Chris@102:          // We will certainly underflow:
Chris@102:          res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
Chris@102:          res.sign() = false;
Chris@102:          res.bits() = static_cast<limb_type>(0u);
Chris@102:          return;
Chris@102:       }
Chris@102:    }
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
Chris@102:    eval_multiply(dt, a.bits(), b.bits());
Chris@102:    res.exponent() = a.exponent() + b.exponent() - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1;
Chris@102:    copy_and_round(res, dt);
Chris@102:    res.check_invariants();
Chris@102:    res.sign() = a.sign() != b.sign();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a)
Chris@102: {
Chris@102:    eval_multiply(res, res, a);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
Chris@102: inline typename enable_if_c<is_unsigned<U>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const U &b)
Chris@102: {
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_multiply;
Chris@102: 
Chris@102:    // Special cases first:
Chris@102:    switch(a.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       if(b == 0)
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       else
Chris@102:          res = a;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = a;
Chris@102:       return;
Chris@102:    }
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
Chris@102:    typedef typename boost::multiprecision::detail::canonical<U, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::type canon_ui_type;
Chris@102:    eval_multiply(dt, a.bits(), static_cast<canon_ui_type>(b));
Chris@102:    res.exponent() = a.exponent();
Chris@102:    copy_and_round(res, dt);
Chris@102:    res.check_invariants();
Chris@102:    res.sign() = a.sign();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
Chris@102: inline typename enable_if_c<is_unsigned<U>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const U &b)
Chris@102: {
Chris@102:    eval_multiply(res, res, b);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
Chris@102: inline typename enable_if_c<is_signed<S>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, const S &b)
Chris@102: {
Chris@102:    typedef typename make_unsigned<S>::type ui_type;
Chris@102:    eval_multiply(res, a, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(b)));
Chris@102:    if(b < 0)
Chris@102:       res.negate();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
Chris@102: inline typename enable_if_c<is_signed<S>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const S &b)
Chris@102: {
Chris@102:    eval_multiply(res, res, b);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &u, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &v)
Chris@102: {
Chris@102:    using default_ops::eval_subtract;
Chris@102:    using default_ops::eval_qr;
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_get_sign;
Chris@102:    using default_ops::eval_increment;
Chris@102: 
Chris@102:    //
Chris@102:    // Special cases first:
Chris@102:    //
Chris@102:    switch(u.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       switch(v.exponent())
Chris@102:       {
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:          return;
Chris@102:       }
Chris@102:       res = u;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       switch(v.exponent())
Chris@102:       {
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:          return;
Chris@102:       }
Chris@102:       res = u;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       return;
Chris@102:    }
Chris@102:    switch(v.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       {
Chris@102:       bool s = u.sign() != v.sign();
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
Chris@102:       res.sign() = s;
Chris@102:       return;
Chris@102:       }
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
Chris@102:       res.bits() = limb_type(0);
Chris@102:       res.sign() = false;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       return;
Chris@102:    }
Chris@102: 
Chris@102:    // We can scale u and v so that both are integers, then perform integer
Chris@102:    // division to obtain quotient q and remainder r, such that:
Chris@102:    //
Chris@102:    // q * v + r = u
Chris@102:    //
Chris@102:    // and hense:
Chris@102:    //
Chris@102:    // q + r/v = u/v
Chris@102:    //
Chris@102:    // From this, assuming q has cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count 
Chris@102:    // bits we only need to determine whether
Chris@102:    // r/v is less than, equal to, or greater than 0.5 to determine rounding - 
Chris@102:    // this we can do with a shift and comparison.
Chris@102:    //
Chris@102:    // We can set the exponent and sign of the result up front:
Chris@102:    //
Chris@102:    res.exponent() = u.exponent() - v.exponent() - 1;
Chris@102:    res.sign() = u.sign() != v.sign();
Chris@102:    //
Chris@102:    // Now get the quotient and remainder:
Chris@102:    //
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), t2(v.bits()), q, r;
Chris@102:    eval_left_shift(t, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count);
Chris@102:    eval_qr(t, t2, q, r);
Chris@102:    //
Chris@102:    // We now have either "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" 
Chris@102:    // or "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1" significant 
Chris@102:    // bits in q.
Chris@102:    //
Chris@102:    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
Chris@102:    if(eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
Chris@102:    {
Chris@102:       //
Chris@102:       // OK we have cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1 bits, 
Chris@102:       // so we already have rounding info,
Chris@102:       // we just need to changes things if the last bit is 1 and either the
Chris@102:       // remainder is non-zero (ie we do not have a tie) or the quotient would
Chris@102:       // be odd if it were shifted to the correct number of bits (ie a tiebreak).
Chris@102:       //
Chris@102:       BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count));
Chris@102:       if((q.limbs()[0] & 1u) && (eval_get_sign(r) || (q.limbs()[0] & 2u)))
Chris@102:       {
Chris@102:          eval_increment(q);
Chris@102:       }
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       //
Chris@102:       // We have exactly "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" bits in q.
Chris@102:       // Get rounding info, which we can get by comparing 2r with v.
Chris@102:       // We want to call copy_and_round to handle rounding and general cleanup,
Chris@102:       // so we'll left shift q and add some fake digits on the end to represent
Chris@102:       // how we'll be rounding.
Chris@102:       //
Chris@102:       BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
Chris@102:       static const unsigned lshift = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits ? 2 : limb_bits;
Chris@102:       eval_left_shift(q, lshift);
Chris@102:       res.exponent() -= lshift;
Chris@102:       eval_left_shift(r, 1u);
Chris@102:       int c = r.compare(v.bits());
Chris@102:       if(c == 0)
Chris@102:          q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1);
Chris@102:       else if(c > 0)
Chris@102:          q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u);
Chris@102:    }
Chris@102:    copy_and_round(res, q);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    eval_divide(res, res, arg);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
Chris@102: inline typename enable_if_c<is_unsigned<U>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &u, const U &v)
Chris@102: {
Chris@102:    using default_ops::eval_subtract;
Chris@102:    using default_ops::eval_qr;
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_get_sign;
Chris@102:    using default_ops::eval_increment;
Chris@102: 
Chris@102:    //
Chris@102:    // Special cases first:
Chris@102:    //
Chris@102:    switch(u.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       if(v == 0)
Chris@102:       {
Chris@102:          res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:          return;
Chris@102:       }
Chris@102:       res = u;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = u;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       return;
Chris@102:    }
Chris@102:    if(v == 0)
Chris@102:    {
Chris@102:       bool s = u.sign();
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
Chris@102:       res.sign() = s;
Chris@102:       return;
Chris@102:    }
Chris@102: 
Chris@102:    // We can scale u and v so that both are integers, then perform integer
Chris@102:    // division to obtain quotient q and remainder r, such that:
Chris@102:    //
Chris@102:    // q * v + r = u
Chris@102:    //
Chris@102:    // and hense:
Chris@102:    //
Chris@102:    // q + r/v = u/v
Chris@102:    //
Chris@102:    // From this, assuming q has "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count, we only need to determine whether
Chris@102:    // r/v is less than, equal to, or greater than 0.5 to determine rounding - 
Chris@102:    // this we can do with a shift and comparison.
Chris@102:    //
Chris@102:    // We can set the exponent and sign of the result up front:
Chris@102:    //
Chris@102:    int gb = msb(v);
Chris@102:    res.exponent() = u.exponent() - static_cast<Exponent>(gb) - static_cast<Exponent>(1);
Chris@102:    res.sign() = u.sign();
Chris@102:    //
Chris@102:    // Now get the quotient and remainder:
Chris@102:    //
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), q, r;
Chris@102:    eval_left_shift(t, gb + 1);
Chris@102:    eval_qr(t, number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v), q, r);
Chris@102:    //
Chris@102:    // We now have either "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" or "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1" significant cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in q.
Chris@102:    //
Chris@102:    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
Chris@102:    if(eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
Chris@102:    {
Chris@102:       //
Chris@102:       // OK we have cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1 cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count, so we already have rounding info,
Chris@102:       // we just need to changes things if the last bit is 1 and the
Chris@102:       // remainder is non-zero (ie we do not have a tie).
Chris@102:       //
Chris@102:       BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count));
Chris@102:       if((q.limbs()[0] & 1u) && eval_get_sign(r))
Chris@102:       {
Chris@102:          eval_increment(q);
Chris@102:       }
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       //
Chris@102:       // We have exactly "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in q.
Chris@102:       // Get rounding info, which we can get by comparing 2r with v.
Chris@102:       // We want to call copy_and_round to handle rounding and general cleanup,
Chris@102:       // so we'll left shift q and add some fake cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count on the end to represent
Chris@102:       // how we'll be rounding.
Chris@102:       //
Chris@102:       BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
Chris@102:       static const unsigned lshift = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits ? 2 : limb_bits;
Chris@102:       eval_left_shift(q, lshift);
Chris@102:       res.exponent() -= lshift;
Chris@102:       eval_left_shift(r, 1u);
Chris@102:       int c = r.compare(number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v));
Chris@102:       if(c == 0)
Chris@102:          q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1);
Chris@102:       else if(c > 0)
Chris@102:          q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u);
Chris@102:    }
Chris@102:    copy_and_round(res, q);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
Chris@102: inline typename enable_if_c<is_unsigned<U>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const U &v)
Chris@102: {
Chris@102:    eval_divide(res, res, v);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
Chris@102: inline typename enable_if_c<is_signed<S>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &u, const S &v)
Chris@102: {
Chris@102:    typedef typename make_unsigned<S>::type ui_type;
Chris@102:    eval_divide(res, u, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(v)));
Chris@102:    if(v < 0)
Chris@102:       res.negate();
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
Chris@102: inline typename enable_if_c<is_signed<S>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const S &v)
Chris@102: {
Chris@102:    eval_divide(res, res, v);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline int eval_get_sign(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero ? 0 : arg.sign() ? -1 : 1;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline bool eval_is_zero(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline bool eval_eq(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &a, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &b)
Chris@102: {
Chris@102:    return (a.exponent() == b.exponent())
Chris@102:       && (a.sign() == b.sign())
Chris@102:       && (a.bits().compare(b.bits()) == 0)
Chris@102:       && (a.exponent() != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_convert_to(long long *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       *res = 0;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       *res = (std::numeric_limits<long long>::max)();
Chris@102:       if(arg.sign())
Chris@102:          *res = -*res;
Chris@102:       return;
Chris@102:    }
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits());
Chris@102:    typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift 
Chris@102:       = (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - arg.exponent();
Chris@102:    if(shift > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
Chris@102:    {
Chris@102:       *res = 0;
Chris@102:       return;
Chris@102:    }
Chris@102:    if(arg.sign() && (arg.compare((std::numeric_limits<long long>::min)()) <= 0))
Chris@102:    {
Chris@102:       *res = (std::numeric_limits<long long>::min)();
Chris@102:       return;
Chris@102:    }
Chris@102:    else if(!arg.sign() && (arg.compare((std::numeric_limits<long long>::max)()) >= 0))
Chris@102:    {
Chris@102:       *res = (std::numeric_limits<long long>::max)();
Chris@102:       return;
Chris@102:    }
Chris@102:    eval_right_shift(man, shift);
Chris@102:    eval_convert_to(res, man);
Chris@102:    if(arg.sign())
Chris@102:    {
Chris@102:       *res = -*res;
Chris@102:    }
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_convert_to(unsigned long long *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       *res = 0;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       *res = (std::numeric_limits<unsigned long long>::max)();
Chris@102:       return;
Chris@102:    }
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits());
Chris@102:    typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift 
Chris@102:       = (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - arg.exponent();
Chris@102:    if(shift > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
Chris@102:    {
Chris@102:       *res = 0;
Chris@102:       return;
Chris@102:    }
Chris@102:    else if(shift < 0)
Chris@102:    {
Chris@102:       // TODO: what if we have fewer cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count than a long long?
Chris@102:       *res = (std::numeric_limits<long long>::max)();
Chris@102:       return;
Chris@102:    }
Chris@102:    eval_right_shift(man, shift);
Chris@102:    eval_convert_to(res, man);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_convert_to(long double *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       *res = 0;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       *res = std::numeric_limits<long double>::quiet_NaN();
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       *res = (std::numeric_limits<long double>::infinity)();
Chris@102:       if(arg.sign())
Chris@102:          *res = -*res;
Chris@102:       return;
Chris@102:    }
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e = arg.exponent();
Chris@102:    e -= cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1;
Chris@102:    *res = std::ldexp(static_cast<long double>(*arg.bits().limbs()), e);
Chris@102:    for(unsigned i = 1; i < arg.bits().size(); ++i)
Chris@102:    {
Chris@102:       e += sizeof(*arg.bits().limbs()) * CHAR_BIT;
Chris@102:       *res += std::ldexp(static_cast<long double>(arg.bits().limbs()[i]), e);
Chris@102:    }
Chris@102:    if(arg.sign())
Chris@102:       *res = -*res;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_frexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg, Exponent *e)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       *e = 0;
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    res = arg;
Chris@102:    *e = arg.exponent() + 1;
Chris@102:    res.exponent() = -1;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
Chris@102: inline void eval_frexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg, I *pe)
Chris@102: {
Chris@102:    Exponent e;
Chris@102:    eval_frexp(res, arg, &e);
Chris@102:    if((e > (std::numeric_limits<I>::max)()) || (e < (std::numeric_limits<I>::min)()))
Chris@102:    {
Chris@102:       BOOST_THROW_EXCEPTION(std::runtime_error("Exponent was outside of the range of the argument type to frexp."));
Chris@102:    }
Chris@102:    *pe = static_cast<I>(e);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg, Exponent e)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    if((e > 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent - e < arg.exponent()))
Chris@102:    {
Chris@102:       // Overflow:
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
Chris@102:       res.sign() = arg.sign();
Chris@102:    }
Chris@102:    else if((e < 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - e > arg.exponent()))
Chris@102:    {
Chris@102:       // Underflow:
Chris@102:       res = limb_type(0);
Chris@102:    }
Chris@102:    else
Chris@102:    {
Chris@102:       res = arg;
Chris@102:       res.exponent() += e;
Chris@102:    }
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
Chris@102: inline typename enable_if_c<is_unsigned<I>::value>::type eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg, I e)
Chris@102: {
Chris@102:    typedef typename make_signed<I>::type si_type;
Chris@102:    if(e > static_cast<I>((std::numeric_limits<si_type>::max)()))
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
Chris@102:    else
Chris@102:       eval_ldexp(res, arg, static_cast<si_type>(e));
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
Chris@102: inline typename enable_if_c<is_signed<I>::value>::type eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg, I e)
Chris@102: {
Chris@102:    if((e > (std::numeric_limits<Exponent>::max)()) || (e < (std::numeric_limits<Exponent>::min)()))
Chris@102:    {
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
Chris@102:       if(e < 0)
Chris@102:          res.negate();
Chris@102:    }
Chris@102:    else
Chris@102:       eval_ldexp(res, arg, static_cast<Exponent>(e));
Chris@102: }
Chris@102: 
Chris@102: /*
Chris@102: * Sign manipulation
Chris@102: */
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_abs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    res = arg;
Chris@102:    res.sign() = false;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_fabs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    res = arg;
Chris@102:    res.sign() = false;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline int eval_fpclassify(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:       return FP_ZERO;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       return FP_INFINITE;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       return FP_NAN;
Chris@102:    }
Chris@102:    return FP_NORMAL;
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_sqrt(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    using default_ops::eval_integer_sqrt;
Chris@102:    using default_ops::eval_bit_test;
Chris@102:    using default_ops::eval_increment;
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       return;
Chris@102:    }
Chris@102:    if(arg.sign())
Chris@102:    {
Chris@102:       res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
Chris@102:       return;
Chris@102:    }
Chris@102: 
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(arg.bits()), r, s;
Chris@102:    eval_left_shift(t, arg.exponent() & 1 ? cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count : cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1);
Chris@102:    eval_integer_sqrt(s, r, t);
Chris@102: 
Chris@102:    if(!eval_bit_test(s, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
Chris@102:    {
Chris@102:       // We have exactly the right number of cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in the result, round as required:
Chris@102:       if(s.compare(r) < 0)
Chris@102:       {
Chris@102:          eval_increment(s);
Chris@102:       }
Chris@102:    }
Chris@102:    typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type ae = arg.exponent();
Chris@102:    res.exponent() = ae / 2;
Chris@102:    if((ae & 1) && (ae < 0))
Chris@102:       --res.exponent();
Chris@102:    copy_and_round(res, s);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_floor(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    using default_ops::eval_increment;
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift = 
Chris@102:       (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - arg.exponent() - 1;
Chris@102:    if((arg.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0))
Chris@102:    {
Chris@102:       // Either arg is already an integer, or a special value:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    if(shift >= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:    {
Chris@102:       res = static_cast<signed_limb_type>(arg.sign() ? -1 : 0);
Chris@102:       return;
Chris@102:    }
Chris@102:    bool fractional = (int)eval_lsb(arg.bits()) < shift;
Chris@102:    res = arg;
Chris@102:    eval_right_shift(res.bits(), shift);
Chris@102:    if(fractional && res.sign())
Chris@102:    {
Chris@102:       eval_increment(res.bits());
Chris@102:       if(eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift)
Chris@102:       {
Chris@102:          // Must have extended result by one bit in the increment:
Chris@102:          --shift;
Chris@102:          ++res.exponent();
Chris@102:       }
Chris@102:    }
Chris@102:    eval_left_shift(res.bits(), shift);
Chris@102: }
Chris@102: 
Chris@102: template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: inline void eval_ceil(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
Chris@102: {
Chris@102:    using default_ops::eval_increment;
Chris@102:    switch(arg.exponent())
Chris@102:    {
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
Chris@102:    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift = (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - arg.exponent() - 1;
Chris@102:    if((arg.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0))
Chris@102:    {
Chris@102:       // Either arg is already an integer, or a special value:
Chris@102:       res = arg;
Chris@102:       return;
Chris@102:    }
Chris@102:    if(shift >= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
Chris@102:    {
Chris@102:       res = static_cast<signed_limb_type>(arg.sign() ? 0 : 1);
Chris@102:       return;
Chris@102:    }
Chris@102:    bool fractional = (int)eval_lsb(arg.bits()) < shift;
Chris@102:    res = arg;
Chris@102:    eval_right_shift(res.bits(), shift);
Chris@102:    if(fractional && !res.sign())
Chris@102:    {
Chris@102:       eval_increment(res.bits());
Chris@102:       if(eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift)
Chris@102:       {
Chris@102:          // Must have extended result by one bit in the increment:
Chris@102:          --shift;
Chris@102:          ++res.exponent();
Chris@102:       }
Chris@102:    }
Chris@102:    eval_left_shift(res.bits(), shift);
Chris@102: }
Chris@102: 
Chris@102: } // namespace backends
Chris@102: 
Chris@102: #ifdef BOOST_NO_SFINAE_EXPR
Chris@102: 
Chris@102: namespace detail{
Chris@102: 
Chris@102: template<unsigned D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
Chris@102: struct is_explicitly_convertible<backends::cpp_bin_float<D1, B1, A1, E1, M1, M2>, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public mpl::true_ {};
Chris@102: 
Chris@102: }
Chris@102: #endif
Chris@102: 
Chris@102: 
Chris@102: using backends::cpp_bin_float;
Chris@102: using backends::digit_base_2;
Chris@102: using backends::digit_base_10;
Chris@102: 
Chris@102: template<unsigned Digits, backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator>
Chris@102: struct number_category<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > : public boost::mpl::int_<boost::multiprecision::number_kind_floating_point>{};
Chris@102: 
Chris@102: template<unsigned Digits, backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
Chris@102: struct expression_template_default<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >
Chris@102: {
Chris@102:    static const expression_template_option value = is_void<Allocator>::value ? et_off : et_on;
Chris@102: };
Chris@102: 
Chris@102: typedef number<backends::cpp_bin_float<50> > cpp_bin_float_50;
Chris@102: typedef number<backends::cpp_bin_float<100> > cpp_bin_float_100;
Chris@102: 
Chris@102: typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single;
Chris@102: typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double;
Chris@102: typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended;
Chris@102: typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad;
Chris@102: 
Chris@102: }} // namespaces
Chris@102: 
Chris@102: #include <boost/multiprecision/cpp_bin_float/io.hpp>
Chris@102: #include <boost/multiprecision/cpp_bin_float/transcendental.hpp>
Chris@102: 
Chris@102: namespace std{
Chris@102: 
Chris@102: //
Chris@102: // numeric_limits [partial] specializations for the types declared in this header:
Chris@102: //
Chris@102: template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >
Chris@102: {
Chris@102:    typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> number_type;
Chris@102: public:
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_specialized = true;
Chris@102:    static number_type (min)()
Chris@102:    {
Chris@102:       initializer.do_nothing();
Chris@102:       static std::pair<bool, number_type> value;
Chris@102:       if(!value.first)
Chris@102:       {
Chris@102:          value.first = true;
Chris@102:          value.second = 1u;
Chris@102:          value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent;
Chris@102:       }
Chris@102:       return value.second;
Chris@102:    }
Chris@102:    static number_type (max)()
Chris@102:    {
Chris@102:       initializer.do_nothing();
Chris@102:       static std::pair<bool, number_type> value;
Chris@102:       if(!value.first)
Chris@102:       {
Chris@102:          value.first = true;
Chris@102:          eval_complement(value.second.backend().bits(), value.second.backend().bits());
Chris@102:          value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent;
Chris@102:       }
Chris@102:       return value.second;
Chris@102:    }
Chris@102:    BOOST_STATIC_CONSTEXPR number_type lowest()
Chris@102:    {
Chris@102:       return -(max)();
Chris@102:    }
Chris@102:    BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count;
Chris@102:    BOOST_STATIC_CONSTEXPR int digits10 = digits * 301 / 1000;
Chris@102:    // Is this really correct???
Chris@102:    BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_signed = true;
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_integer = false;
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_exact = false;
Chris@102:    BOOST_STATIC_CONSTEXPR int radix = 2;
Chris@102:    static number_type epsilon()
Chris@102:    {
Chris@102:       initializer.do_nothing();
Chris@102:       static std::pair<bool, number_type> value;
Chris@102:       if(!value.first)
Chris@102:       {
Chris@102:          value.first = true;
Chris@102:          value.second = 1;
Chris@102:          value.second = ldexp(value.second, 1 - (int)digits);
Chris@102:       }
Chris@102:       return value.second;
Chris@102:    }
Chris@102:    // What value should this be????
Chris@102:    static number_type round_error()
Chris@102:    {
Chris@102:       // returns 0.5
Chris@102:       initializer.do_nothing();
Chris@102:       static std::pair<bool, number_type> value;
Chris@102:       if(!value.first)
Chris@102:       {
Chris@102:          value.first = true;
Chris@102:          value.second = 1;
Chris@102:          value.second = ldexp(value.second, -1);
Chris@102:       }
Chris@102:       return value.second;
Chris@102:    }
Chris@102:    BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent;
Chris@102:    BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent10 = (min_exponent / 1000) * 301L;
Chris@102:    BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent;
Chris@102:    BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent10 = (max_exponent / 1000) * 301L;
Chris@102:    BOOST_STATIC_CONSTEXPR bool has_infinity = true;
Chris@102:    BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
Chris@102:    BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
Chris@102:    BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
Chris@102:    BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
Chris@102:    static number_type infinity()
Chris@102:    {
Chris@102:       // returns epsilon/2
Chris@102:       initializer.do_nothing();
Chris@102:       static std::pair<bool, number_type> value;
Chris@102:       if(!value.first)
Chris@102:       {
Chris@102:          value.first = true;
Chris@102:          value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
Chris@102:       }
Chris@102:       return value.second;
Chris@102:    }
Chris@102:    static number_type quiet_NaN()
Chris@102:    {
Chris@102:       return number_type();
Chris@102:    }
Chris@102:    BOOST_STATIC_CONSTEXPR number_type signaling_NaN()
Chris@102:    {
Chris@102:       return number_type(0);
Chris@102:    }
Chris@102:    BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); }
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_bounded = true;
Chris@102:    BOOST_STATIC_CONSTEXPR bool is_modulo = false;
Chris@102:    BOOST_STATIC_CONSTEXPR bool traps = true;
Chris@102:    BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
Chris@102:    BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;
Chris@102: private:
Chris@102:    struct data_initializer
Chris@102:    {
Chris@102:       data_initializer()
Chris@102:       {
Chris@102:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::epsilon();
Chris@102:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::round_error();
Chris@102:          (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::min)();
Chris@102:          (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::max)();
Chris@102:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity();
Chris@102:          std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN();
Chris@102:       }
Chris@102:       void do_nothing()const{}
Chris@102:    };
Chris@102:    static const data_initializer initializer;
Chris@102: };
Chris@102: 
Chris@102: template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: const typename numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::data_initializer numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::initializer;
Chris@102: 
Chris@102: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
Chris@102: 
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits10;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_digits10;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_signed;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_integer;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_exact;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::radix;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::min_exponent;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::min_exponent10;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_exponent;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_exponent10;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_infinity;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_quiet_NaN;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_signaling_NaN;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_denorm;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_denorm_loss;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_iec559;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_bounded;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_modulo;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::traps;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::tinyness_before;
Chris@102: template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@102: BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::round_style;
Chris@102: 
Chris@102: #endif
Chris@102: 
Chris@102: } // namespace std
Chris@102: 
Chris@102: #endif