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Diffstat (limited to 'boost/multiprecision/cpp_bin_float.hpp')
| -rw-r--r-- | boost/multiprecision/cpp_bin_float.hpp | 1598 |
1 files changed, 1598 insertions, 0 deletions
diff --git a/boost/multiprecision/cpp_bin_float.hpp b/boost/multiprecision/cpp_bin_float.hpp new file mode 100644 index 0000000000..cc2454c243 --- /dev/null +++ b/boost/multiprecision/cpp_bin_float.hpp @@ -0,0 +1,1598 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_CPP_BIN_FLOAT_HPP +#define BOOST_MATH_CPP_BIN_FLOAT_HPP + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/integer.hpp> +#include <boost/math/special_functions/trunc.hpp> +#include <boost/multiprecision/detail/float_string_cvt.hpp> + +namespace boost{ namespace multiprecision{ namespace backends{ + +enum digit_base_type +{ + digit_base_2 = 2, + digit_base_10 = 10 +}; + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4522) // multiple assignment operators specified +#endif + +namespace detail{ + +template <class U> +inline typename enable_if_c<is_unsigned<U>::value, bool>::type is_negative(U) { return false; } +template <class S> +inline typename disable_if_c<is_unsigned<S>::value, bool>::type is_negative(S s) { return s < 0; } + +} + +template <unsigned Digits, digit_base_type DigitBase = digit_base_10, class Allocator = void, class Exponent = int, Exponent MinExponent = 0, Exponent MaxExponent = 0> +class cpp_bin_float +{ +public: + static const unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + ((Digits * 1000uL) % 301 ? 2u : 1u); + 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; + 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; + + typedef typename rep_type::signed_types signed_types; + typedef typename rep_type::unsigned_types unsigned_types; + typedef boost::mpl::list<double, long double> float_types; + typedef Exponent exponent_type; + + static const exponent_type max_exponent_limit = boost::integer_traits<exponent_type>::const_max - 2 * static_cast<exponent_type>(bit_count); + static const exponent_type min_exponent_limit = boost::integer_traits<exponent_type>::const_min + 2 * static_cast<exponent_type>(bit_count); + + BOOST_STATIC_ASSERT_MSG(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!"); + BOOST_STATIC_ASSERT_MSG(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!"); + BOOST_STATIC_ASSERT_MSG(MinExponent <= 0, "Template parameter MinExponent can not be positive!"); + BOOST_STATIC_ASSERT_MSG(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!"); + + static const exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent; + static const exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent; + + static const exponent_type exponent_zero = max_exponent + 1; + static const exponent_type exponent_infinity = max_exponent + 2; + static const exponent_type exponent_nan = max_exponent + 3; + +private: + + rep_type m_data; + exponent_type m_exponent; + bool m_sign; +public: + cpp_bin_float() : m_data(), m_exponent(exponent_nan), m_sign(false) {} + + cpp_bin_float(const cpp_bin_float &o) + : m_data(o.m_data), m_exponent(o.m_exponent), m_sign(o.m_sign) {} + + template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE> + 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) + : m_exponent(o.exponent()), m_sign(o.sign()) + { + typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits()); + this->sign() = o.sign(); + this->exponent() = o.exponent() + (int)bit_count - (int)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count; + copy_and_round(*this, b); + } + + template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE> + 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) + : m_exponent(o.exponent()), m_sign(o.sign()) + { + typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits()); + this->sign() = o.sign(); + this->exponent() = o.exponent() - (int)(cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count - bit_count); + copy_and_round(*this, b); + } + + template <class Float> + cpp_bin_float(const Float& f, + typename boost::enable_if_c< + (number_category<Float>::value == number_kind_floating_point) + && (std::numeric_limits<Float>::digits <= (int)bit_count) + && (std::numeric_limits<Float>::radix == 2) + >::type const* = 0) + : m_data(), m_exponent(0), m_sign(false) + { + this->assign_float(f); + } + + cpp_bin_float& operator=(const cpp_bin_float &o) + { + m_data = o.m_data; + m_exponent = o.m_exponent; + m_sign = o.m_sign; + return *this; + } + + template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE> + cpp_bin_float& operator=(const cpp_bin_float<D, B, A, E, MinE, MaxE> &o) + { + typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(o.bits()); + this->exponent() = o.exponent() + (int)bit_count - (int)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count; + this->sign() = o.sign(); + copy_and_round(*this, b); + return *this; + } + + template <class Float> + typename boost::enable_if_c< + (number_category<Float>::value == number_kind_floating_point) + && (std::numeric_limits<Float>::digits <= (int)bit_count) + && (std::numeric_limits<Float>::radix == 2), cpp_bin_float&>::type operator=(const Float& f) + { + return assign_float(f); + } + + template <class Float> + typename boost::enable_if_c<is_floating_point<Float>::value, cpp_bin_float&>::type assign_float(Float f) + { + BOOST_MATH_STD_USING + using default_ops::eval_add; + + switch((boost::math::fpclassify)(f)) + { + case FP_ZERO: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_zero; + return *this; + case FP_NAN: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_nan; + return *this; + case FP_INFINITE: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_infinity; + return *this; + } + if(f < 0) + { + *this = -f; + this->negate(); + return *this; + } + + typedef typename mpl::front<unsigned_types>::type ui_type; + m_data = static_cast<ui_type>(0u); + m_sign = false; + m_exponent = 0; + + static const int bits = sizeof(int) * CHAR_BIT - 1; + int e; + f = frexp(f, &e); + while(f) + { + f = ldexp(f, bits); + e -= bits; + int ipart = itrunc(f); + f -= ipart; + m_exponent += bits; + eval_add(*this, ipart); + } + m_exponent += static_cast<Exponent>(e); + return *this; + } + + template <class Float> + typename boost::enable_if_c< + (number_category<Float>::value == number_kind_floating_point) + && !is_floating_point<Float>::value + /*&& (std::numeric_limits<number<Float> >::radix == 2)*/, + cpp_bin_float&>::type assign_float(Float f) + { + BOOST_MATH_STD_USING + using default_ops::eval_add; + using default_ops::eval_get_sign; + using default_ops::eval_convert_to; + using default_ops::eval_subtract; + + typedef typename boost::multiprecision::detail::canonical<int, Float>::type f_int_type; + typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type; + + switch(eval_fpclassify(f)) + { + case FP_ZERO: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_zero; + return *this; + case FP_NAN: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_nan; + return *this; + case FP_INFINITE: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_infinity; + return *this; + } + if(eval_get_sign(f) < 0) + { + f.negate(); + *this = f; + this->negate(); + return *this; + } + + typedef typename mpl::front<unsigned_types>::type ui_type; + m_data = static_cast<ui_type>(0u); + m_sign = false; + m_exponent = 0; + + static const int bits = sizeof(int) * CHAR_BIT - 1; + int e; + eval_frexp(f, f, &e); + while(eval_get_sign(f) != 0) + { + eval_ldexp(f, f, bits); + e -= bits; + int ipart; + eval_convert_to(&ipart, f); + eval_subtract(f, static_cast<f_int_type>(ipart)); + m_exponent += bits; + eval_add(*this, static_cast<bf_int_type>(ipart)); + } + m_exponent += e; + if(m_exponent > max_exponent) + m_exponent = exponent_infinity; + if(m_exponent < min_exponent) + { + m_data = limb_type(0u); + m_exponent = exponent_zero; + m_sign = false; + } + else if(eval_get_sign(m_data) == 0) + { + m_exponent = exponent_zero; + m_sign = false; + } + return *this; + } + + template <class I> + typename boost::enable_if<is_integral<I>, cpp_bin_float&>::type operator=(const I& i) + { + using default_ops::eval_bit_test; + if(!i) + { + m_data = static_cast<limb_type>(0); + m_exponent = exponent_zero; + m_sign = false; + } + else + { + typedef typename make_unsigned<I>::type ui_type; + ui_type fi = static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(i)); + typedef typename boost::multiprecision::detail::canonical<ui_type, rep_type>::type ar_type; + m_data = static_cast<ar_type>(fi); + unsigned shift = msb(fi); + if(shift >= bit_count) + { + m_exponent = static_cast<Exponent>(shift); + m_data = static_cast<ar_type>(fi >> (shift + 1 - bit_count)); + } + else + { + m_exponent = static_cast<Exponent>(shift); + eval_left_shift(m_data, bit_count - shift - 1); + } + BOOST_ASSERT(eval_bit_test(m_data, bit_count-1)); + m_sign = detail::is_negative(i); + } + return *this; + } + + cpp_bin_float& operator=(const char *s); + + void swap(cpp_bin_float &o) BOOST_NOEXCEPT + { + m_data.swap(o.m_data); + std::swap(m_exponent, o.m_exponent); + std::swap(m_sign, o.m_sign); + } + + std::string str(std::streamsize dig, std::ios_base::fmtflags f) const; + + void negate() + { + if((m_exponent != exponent_zero) && (m_exponent != exponent_nan)) + m_sign = !m_sign; + } + + int compare(const cpp_bin_float &o) const BOOST_NOEXCEPT + { + if(m_sign != o.m_sign) + return m_sign ? -1 : 1; + int result; + if(m_exponent == exponent_nan) + return -1; + else if(m_exponent != o.m_exponent) + { + if(m_exponent == exponent_zero) + result = -1; + else if(o.m_exponent == exponent_zero) + result = 1; + else + result = m_exponent > o.m_exponent ? 1 : -1; + } + else + result = m_data.compare(o.m_data); + if(m_sign) + result = -result; + return result; + } + template <class A> + int compare(const A& o) const BOOST_NOEXCEPT + { + cpp_bin_float b; + b = o; + return compare(b); + } + + rep_type& bits() { return m_data; } + const rep_type& bits()const { return m_data; } + exponent_type& exponent() { return m_exponent; } + const exponent_type& exponent()const { return m_exponent; } + bool& sign() { return m_sign; } + const bool& sign()const { return m_sign; } + void check_invariants() + { + using default_ops::eval_bit_test; + using default_ops::eval_is_zero; + if((m_exponent <= max_exponent) && (m_exponent >= min_exponent)) + { + BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1)); + } + else + { + BOOST_ASSERT(m_exponent > max_exponent); + BOOST_ASSERT(m_exponent <= exponent_nan); + BOOST_ASSERT(eval_is_zero(m_data)); + } + } + template<class Archive> + void serialize(Archive & ar, const unsigned int /*version*/) + { + ar & m_data; + ar & m_exponent; + ar & m_sign; + } +}; + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class Int> +inline void copy_and_round(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, Int &arg) +{ + // Precondition: exponent of res must have been set before this function is called + // 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. + using default_ops::eval_msb; + using default_ops::eval_lsb; + using default_ops::eval_left_shift; + using default_ops::eval_bit_test; + using default_ops::eval_right_shift; + using default_ops::eval_increment; + using default_ops::eval_get_sign; + + // cancellation may have resulted in arg being all zeros: + if(eval_get_sign(arg) == 0) + { + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero; + res.sign() = false; + res.bits() = static_cast<limb_type>(0u); + return; + } + int msb = eval_msb(arg); + if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) > msb + 1) + { + // Must have had cancellation in subtraction, shift left and copy: + res.bits() = arg; + eval_left_shift(res.bits(), cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1); + res.exponent() -= static_cast<Exponent>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1); + } + else if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) < msb + 1) + { + // We have more cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count than we need, so round as required, + // first get the rounding bit: + bool roundup = eval_bit_test(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count); + // Then check for a tie: + if(roundup && (msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count == eval_lsb(arg))) + { + // Ties round towards even: + if(!eval_bit_test(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1)) + roundup = false; + } + // Shift off the cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count we don't need: + eval_right_shift(arg, msb - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1); + res.exponent() += static_cast<Exponent>(msb - (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1); + if(roundup) + { + eval_increment(arg); + if(eval_bit_test(arg, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)) + { + // This happens very very rairly: + eval_right_shift(arg, 1u); + ++res.exponent(); + } + } + res.bits() = arg; + } + else + { + res.bits() = arg; + } + BOOST_ASSERT((eval_msb(res.bits()) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)); + + if(res.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) + { + // Overflow: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity; + res.bits() = static_cast<limb_type>(0u); + } + else if(res.exponent() < cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent) + { + // Underflow: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero; + res.bits() = static_cast<limb_type>(0u); + res.sign() = false; + } +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_add; + using default_ops::eval_bit_test; + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + res = b; + if(res.sign()) + res.negate(); + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan) + res = b; + else + res = a; + return; // result is still infinite. + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = a; + return; // result is still a NaN. + } + switch(b.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = b; + if(res.sign()) + res.negate(); + return; // result is infinite. + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = b; + return; // result is a NaN. + } + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent(); + bool s = a.sign(); + if(e_diff >= 0) + { + dt = a.bits(); + if(e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + eval_left_shift(dt, e_diff); + res.exponent() = a.exponent() - e_diff; + eval_add(dt, b.bits()); + } + else + res.exponent() = a.exponent(); + } + else + { + dt= b.bits(); + if(-e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + eval_left_shift(dt, -e_diff); + res.exponent() = b.exponent() + e_diff; + eval_add(dt, a.bits()); + } + else + res.exponent() = b.exponent(); + } + + copy_and_round(res, dt); + res.check_invariants(); + if(res.sign() != s) + res.negate(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_subtract; + using default_ops::eval_bit_test; + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan) + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + else + { + res = b; + if(!res.sign()) + res.negate(); + } + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + 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)) + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + else + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = a; + return; // result is still a NaN. + } + switch(b.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan; + res.sign() = false; + res.bits() = static_cast<limb_type>(0u); + return; // result is a NaN. + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = b; + return; // result is still a NaN. + } + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent(); + bool s = a.sign(); + if((e_diff > 0) || ((e_diff == 0) && a.bits().compare(b.bits()) >= 0)) + { + dt = a.bits(); + if(e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + eval_left_shift(dt, e_diff); + res.exponent() = a.exponent() - e_diff; + eval_subtract(dt, b.bits()); + } + else + res.exponent() = a.exponent(); + } + else + { + dt = b.bits(); + if(-e_diff < (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + eval_left_shift(dt, -e_diff); + res.exponent() = b.exponent() + e_diff; + eval_subtract(dt, a.bits()); + } + else + res.exponent() = b.exponent(); + s = !s; + } + + copy_and_round(res, dt); + if(res.sign() != s) + res.negate(); + res.check_invariants(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + if(a.sign() == b.sign()) + do_eval_add(res, a, b); + else + do_eval_subtract(res, a, b); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + return eval_add(res, res, a); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + if(a.sign() != b.sign()) + do_eval_add(res, a, b); + else + do_eval_subtract(res, a, b); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + return eval_subtract(res, res, a); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_bit_test; + using default_ops::eval_multiply; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + if(b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan) + res = b; + else + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + switch(b.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + break; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = b; + break; + default: + res = a; + break; + } + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = a; + return; + } + if(b.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) + { + res = b; + return; + } + if((a.exponent() > 0) && (b.exponent() > 0)) + { + if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent + 2 - a.exponent() < b.exponent()) + { + // We will certainly overflow: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity; + res.sign() = a.sign() != b.sign(); + res.bits() = static_cast<limb_type>(0u); + return; + } + } + if((a.exponent() < 0) && (b.exponent() < 0)) + { + if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - 2 - a.exponent() > b.exponent()) + { + // We will certainly underflow: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero; + res.sign() = false; + res.bits() = static_cast<limb_type>(0u); + return; + } + } + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt; + eval_multiply(dt, a.bits(), b.bits()); + res.exponent() = a.exponent() + b.exponent() - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1; + copy_and_round(res, dt); + res.check_invariants(); + res.sign() = a.sign() != b.sign(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + eval_multiply(res, res, a); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U> +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) +{ + using default_ops::eval_bit_test; + using default_ops::eval_multiply; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + if(b == 0) + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + else + res = a; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = a; + return; + } + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt; + typedef typename boost::multiprecision::detail::canonical<U, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::type canon_ui_type; + eval_multiply(dt, a.bits(), static_cast<canon_ui_type>(b)); + res.exponent() = a.exponent(); + copy_and_round(res, dt); + res.check_invariants(); + res.sign() = a.sign(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U> +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) +{ + eval_multiply(res, res, b); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S> +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) +{ + typedef typename make_unsigned<S>::type ui_type; + eval_multiply(res, a, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(b))); + if(b < 0) + res.negate(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S> +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) +{ + eval_multiply(res, res, b); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_subtract; + using default_ops::eval_qr; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_increment; + + // + // Special cases first: + // + switch(u.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + switch(v.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + switch(v.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + switch(v.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + { + bool s = u.sign() != v.sign(); + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend(); + res.sign() = s; + return; + } + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero; + res.bits() = limb_type(0); + res.sign() = false; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + + // We can scale u and v so that both are integers, then perform integer + // division to obtain quotient q and remainder r, such that: + // + // q * v + r = u + // + // and hense: + // + // q + r/v = u/v + // + // From this, assuming q has cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + // bits we only need to determine whether + // r/v is less than, equal to, or greater than 0.5 to determine rounding - + // this we can do with a shift and comparison. + // + // We can set the exponent and sign of the result up front: + // + res.exponent() = u.exponent() - v.exponent() - 1; + res.sign() = u.sign() != v.sign(); + // + // Now get the quotient and remainder: + // + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), t2(v.bits()), q, r; + eval_left_shift(t, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count); + eval_qr(t, t2, q, r); + // + // 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 + // bits in q. + // + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + if(eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)) + { + // + // OK we have cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1 bits, + // so we already have rounding info, + // we just need to changes things if the last bit is 1 and either the + // remainder is non-zero (ie we do not have a tie) or the quotient would + // be odd if it were shifted to the correct number of bits (ie a tiebreak). + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)); + if((q.limbs()[0] & 1u) && (eval_get_sign(r) || (q.limbs()[0] & 2u))) + { + eval_increment(q); + } + } + else + { + // + // We have exactly "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" bits in q. + // Get rounding info, which we can get by comparing 2r with v. + // We want to call copy_and_round to handle rounding and general cleanup, + // so we'll left shift q and add some fake digits on the end to represent + // how we'll be rounding. + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)); + static const unsigned lshift = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits ? 2 : limb_bits; + eval_left_shift(q, lshift); + res.exponent() -= lshift; + eval_left_shift(r, 1u); + int c = r.compare(v.bits()); + if(c == 0) + q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1); + else if(c > 0) + q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u); + } + copy_and_round(res, q); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + eval_divide(res, res, arg); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U> +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) +{ + using default_ops::eval_subtract; + using default_ops::eval_qr; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_increment; + + // + // Special cases first: + // + switch(u.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + if(v == 0) + { + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = u; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + if(v == 0) + { + bool s = u.sign(); + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend(); + res.sign() = s; + return; + } + + // We can scale u and v so that both are integers, then perform integer + // division to obtain quotient q and remainder r, such that: + // + // q * v + r = u + // + // and hense: + // + // q + r/v = u/v + // + // 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 + // r/v is less than, equal to, or greater than 0.5 to determine rounding - + // this we can do with a shift and comparison. + // + // We can set the exponent and sign of the result up front: + // + int gb = msb(v); + res.exponent() = u.exponent() - static_cast<Exponent>(gb) - static_cast<Exponent>(1); + res.sign() = u.sign(); + // + // Now get the quotient and remainder: + // + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), q, r; + eval_left_shift(t, gb + 1); + eval_qr(t, number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v), q, r); + // + // 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. + // + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + if(eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)) + { + // + // 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, + // we just need to changes things if the last bit is 1 and the + // remainder is non-zero (ie we do not have a tie). + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)); + if((q.limbs()[0] & 1u) && eval_get_sign(r)) + { + eval_increment(q); + } + } + else + { + // + // 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. + // Get rounding info, which we can get by comparing 2r with v. + // We want to call copy_and_round to handle rounding and general cleanup, + // 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 + // how we'll be rounding. + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)); + static const unsigned lshift = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits ? 2 : limb_bits; + eval_left_shift(q, lshift); + res.exponent() -= lshift; + eval_left_shift(r, 1u); + int c = r.compare(number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v)); + if(c == 0) + q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1); + else if(c > 0) + q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u); + } + copy_and_round(res, q); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U> +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) +{ + eval_divide(res, res, v); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S> +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) +{ + typedef typename make_unsigned<S>::type ui_type; + eval_divide(res, u, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(v))); + if(v < 0) + res.negate(); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S> +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) +{ + eval_divide(res, res, v); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline int eval_get_sign(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero ? 0 : arg.sign() ? -1 : 1; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline bool eval_is_zero(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + return (a.exponent() == b.exponent()) + && (a.sign() == b.sign()) + && (a.bits().compare(b.bits()) == 0) + && (a.exponent() != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline void eval_convert_to(long long *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + *res = 0; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + *res = (std::numeric_limits<long long>::max)(); + if(arg.sign()) + *res = -*res; + return; + } + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits()); + 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 - 1 - arg.exponent(); + if(shift > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1) + { + *res = 0; + return; + } + if(arg.sign() && (arg.compare((std::numeric_limits<long long>::min)()) <= 0)) + { + *res = (std::numeric_limits<long long>::min)(); + return; + } + else if(!arg.sign() && (arg.compare((std::numeric_limits<long long>::max)()) >= 0)) + { + *res = (std::numeric_limits<long long>::max)(); + return; + } + eval_right_shift(man, shift); + eval_convert_to(res, man); + if(arg.sign()) + { + *res = -*res; + } +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline void eval_convert_to(unsigned long long *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + *res = 0; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + *res = (std::numeric_limits<unsigned long long>::max)(); + return; + } + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits()); + 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 - 1 - arg.exponent(); + if(shift > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1) + { + *res = 0; + return; + } + else if(shift < 0) + { + // TODO: what if we have fewer cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count than a long long? + *res = (std::numeric_limits<long long>::max)(); + return; + } + eval_right_shift(man, shift); + eval_convert_to(res, man); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline void eval_convert_to(long double *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + *res = 0; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + *res = std::numeric_limits<long double>::quiet_NaN(); + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + *res = (std::numeric_limits<long double>::infinity)(); + if(arg.sign()) + *res = -*res; + return; + } + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e = arg.exponent(); + e -= cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1; + *res = std::ldexp(static_cast<long double>(*arg.bits().limbs()), e); + for(unsigned i = 1; i < arg.bits().size(); ++i) + { + e += sizeof(*arg.bits().limbs()) * CHAR_BIT; + *res += std::ldexp(static_cast<long double>(arg.bits().limbs()[i]), e); + } + if(arg.sign()) + *res = -*res; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + *e = 0; + res = arg; + return; + } + res = arg; + *e = arg.exponent() + 1; + res.exponent() = -1; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I> +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) +{ + Exponent e; + eval_frexp(res, arg, &e); + if((e > (std::numeric_limits<I>::max)()) || (e < (std::numeric_limits<I>::min)())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent was outside of the range of the argument type to frexp.")); + } + *pe = static_cast<I>(e); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = arg; + return; + } + if((e > 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent - e < arg.exponent())) + { + // Overflow: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend(); + res.sign() = arg.sign(); + } + else if((e < 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - e > arg.exponent())) + { + // Underflow: + res = limb_type(0); + } + else + { + res = arg; + res.exponent() += e; + } +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I> +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) +{ + typedef typename make_signed<I>::type si_type; + if(e > static_cast<I>((std::numeric_limits<si_type>::max)())) + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend(); + else + eval_ldexp(res, arg, static_cast<si_type>(e)); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I> +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) +{ + if((e > (std::numeric_limits<Exponent>::max)()) || (e < (std::numeric_limits<Exponent>::min)())) + { + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend(); + if(e < 0) + res.negate(); + } + else + eval_ldexp(res, arg, static_cast<Exponent>(e)); +} + +/* +* Sign manipulation +*/ + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + res = arg; + res.sign() = false; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + res = arg; + res.sign() = false; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +inline int eval_fpclassify(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + return FP_ZERO; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + return FP_INFINITE; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + return FP_NAN; + } + return FP_NORMAL; +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_integer_sqrt; + using default_ops::eval_bit_test; + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + res = arg; + return; + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + if(arg.sign()) + { + res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend(); + return; + } + + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(arg.bits()), r, s; + 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); + eval_integer_sqrt(s, r, t); + + if(!eval_bit_test(s, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)) + { + // We have exactly the right number of cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in the result, round as required: + if(s.compare(r) < 0) + { + eval_increment(s); + } + } + typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type ae = arg.exponent(); + res.exponent() = ae / 2; + if((ae & 1) && (ae < 0)) + --res.exponent(); + copy_and_round(res, s); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = arg; + return; + } + 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; + if((arg.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0)) + { + // Either arg is already an integer, or a special value: + res = arg; + return; + } + if(shift >= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + res = static_cast<signed_limb_type>(arg.sign() ? -1 : 0); + return; + } + bool fractional = (int)eval_lsb(arg.bits()) < shift; + res = arg; + eval_right_shift(res.bits(), shift); + if(fractional && res.sign()) + { + eval_increment(res.bits()); + if(eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift) + { + // Must have extended result by one bit in the increment: + --shift; + ++res.exponent(); + } + } + eval_left_shift(res.bits(), shift); +} + +template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +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) +{ + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan: + case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity: + res = arg; + return; + } + 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; + if((arg.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0)) + { + // Either arg is already an integer, or a special value: + res = arg; + return; + } + if(shift >= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) + { + res = static_cast<signed_limb_type>(arg.sign() ? 0 : 1); + return; + } + bool fractional = (int)eval_lsb(arg.bits()) < shift; + res = arg; + eval_right_shift(res.bits(), shift); + if(fractional && !res.sign()) + { + eval_increment(res.bits()); + if(eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift) + { + // Must have extended result by one bit in the increment: + --shift; + ++res.exponent(); + } + } + eval_left_shift(res.bits(), shift); +} + +} // namespace backends + +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +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> +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_ {}; + +} +#endif + + +using backends::cpp_bin_float; +using backends::digit_base_2; +using backends::digit_base_10; + +template<unsigned Digits, backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator> +struct number_category<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > : public boost::mpl::int_<boost::multiprecision::number_kind_floating_point>{}; + +template<unsigned Digits, backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE> +struct expression_template_default<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > +{ + static const expression_template_option value = is_void<Allocator>::value ? et_off : et_on; +}; + +typedef number<backends::cpp_bin_float<50> > cpp_bin_float_50; +typedef number<backends::cpp_bin_float<100> > cpp_bin_float_100; + +typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single; +typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double; +typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended; +typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad; + +}} // namespaces + +#include <boost/multiprecision/cpp_bin_float/io.hpp> +#include <boost/multiprecision/cpp_bin_float/transcendental.hpp> + +namespace std{ + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + static number_type (min)() + { + initializer.do_nothing(); + static std::pair<bool, number_type> value; + if(!value.first) + { + value.first = true; + value.second = 1u; + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent; + } + return value.second; + } + static number_type (max)() + { + initializer.do_nothing(); + static std::pair<bool, number_type> value; + if(!value.first) + { + value.first = true; + eval_complement(value.second.backend().bits(), value.second.backend().bits()); + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent; + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count; + BOOST_STATIC_CONSTEXPR int digits10 = digits * 301 / 1000; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + static number_type epsilon() + { + initializer.do_nothing(); + static std::pair<bool, number_type> value; + if(!value.first) + { + value.first = true; + value.second = 1; + value.second = ldexp(value.second, 1 - (int)digits); + } + return value.second; + } + // What value should this be???? + static number_type round_error() + { + // returns 0.5 + initializer.do_nothing(); + static std::pair<bool, number_type> value; + if(!value.first) + { + value.first = true; + value.second = 1; + value.second = ldexp(value.second, -1); + } + return value.second; + } + 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; + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent10 = (min_exponent / 1000) * 301L; + 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; + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent10 = (max_exponent / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + static number_type infinity() + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair<bool, number_type> value; + if(!value.first) + { + value.first = true; + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity; + } + return value.second; + } + static number_type quiet_NaN() + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() + { + return number_type(0); + } + BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::epsilon(); + std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::round_error(); + (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::min)(); + (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::max)(); + std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity(); + std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits10; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_digits10; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_signed; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_integer; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_exact; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::radix; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_infinity; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_iec559; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_bounded; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_modulo; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::traps; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::tinyness_before; +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates> +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; + +#endif + +} // namespace std + +#endif |