1786 lines
85 KiB
Plaintext
1786 lines
85 KiB
Plaintext
///////////////////////////////////////////////////////////////
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// Copyright 2013 John Maddock. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
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#ifndef BOOST_MATH_CPP_BIN_FLOAT_HPP
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#define BOOST_MATH_CPP_BIN_FLOAT_HPP
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#include <boost/multiprecision/cpp_int.hpp>
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#include <boost/multiprecision/integer.hpp>
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#include <boost/math/special_functions/trunc.hpp>
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#include <boost/multiprecision/detail/float_string_cvt.hpp>
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//
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// Some includes we need from Boost.Math, since we rely on that library to provide these functions:
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//
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#include <boost/math/special_functions/asinh.hpp>
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#include <boost/math/special_functions/acosh.hpp>
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#include <boost/math/special_functions/atanh.hpp>
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#include <boost/math/special_functions/cbrt.hpp>
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#include <boost/math/special_functions/expm1.hpp>
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#include <boost/math/special_functions/gamma.hpp>
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namespace boost{ namespace multiprecision{ namespace backends{
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enum digit_base_type
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{
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digit_base_2 = 2,
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digit_base_10 = 10
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};
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4522 6326) // multiple assignment operators specified, comparison of two constants
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#endif
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namespace detail{
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template <class U>
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inline typename enable_if_c<is_unsigned<U>::value, bool>::type is_negative(U) { return false; }
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template <class S>
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inline typename disable_if_c<is_unsigned<S>::value, bool>::type is_negative(S s) { return s < 0; }
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}
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template <unsigned Digits, digit_base_type DigitBase = digit_base_10, class Allocator = void, class Exponent = int, Exponent MinExponent = 0, Exponent MaxExponent = 0>
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class cpp_bin_float
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{
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public:
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static const unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + (((Digits * 1000uL) % 301) ? 2u : 1u);
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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;
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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;
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typedef typename rep_type::signed_types signed_types;
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typedef typename rep_type::unsigned_types unsigned_types;
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typedef boost::mpl::list<float, double, long double> float_types;
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typedef Exponent exponent_type;
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static const exponent_type max_exponent_limit = boost::integer_traits<exponent_type>::const_max - 2 * static_cast<exponent_type>(bit_count);
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static const exponent_type min_exponent_limit = boost::integer_traits<exponent_type>::const_min + 2 * static_cast<exponent_type>(bit_count);
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BOOST_STATIC_ASSERT_MSG(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!");
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BOOST_STATIC_ASSERT_MSG(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!");
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BOOST_STATIC_ASSERT_MSG(MinExponent <= 0, "Template parameter MinExponent can not be positive!");
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BOOST_STATIC_ASSERT_MSG(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!");
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static const exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent;
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static const exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent;
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static const exponent_type exponent_zero = max_exponent + 1;
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static const exponent_type exponent_infinity = max_exponent + 2;
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static const exponent_type exponent_nan = max_exponent + 3;
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private:
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rep_type m_data;
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exponent_type m_exponent;
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bool m_sign;
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public:
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cpp_bin_float() BOOST_MP_NOEXCEPT_IF(noexcept(rep_type())) : m_data(), m_exponent(exponent_zero), m_sign(false) {}
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cpp_bin_float(const cpp_bin_float &o) BOOST_MP_NOEXCEPT_IF(noexcept(rep_type(std::declval<const rep_type&>())))
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: m_data(o.m_data), m_exponent(o.m_exponent), m_sign(o.m_sign) {}
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template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
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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)
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{
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*this = o;
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}
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template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
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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)
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: m_exponent(o.exponent()), m_sign(o.sign())
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{
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*this = o;
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}
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template <class Float>
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cpp_bin_float(const Float& f,
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typename boost::enable_if_c<
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(number_category<Float>::value == number_kind_floating_point)
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&& (std::numeric_limits<Float>::digits <= (int)bit_count)
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&& (std::numeric_limits<Float>::radix == 2)
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>::type const* = 0)
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: m_data(), m_exponent(0), m_sign(false)
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{
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this->assign_float(f);
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}
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template <class Float>
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explicit cpp_bin_float(const Float& f,
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typename boost::enable_if_c<
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(number_category<Float>::value == number_kind_floating_point)
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&& (std::numeric_limits<Float>::digits > (int)bit_count)
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&& (std::numeric_limits<Float>::radix == 2)
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>::type const* = 0)
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: m_data(), m_exponent(0), m_sign(false)
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{
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this->assign_float(f);
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}
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cpp_bin_float& operator=(const cpp_bin_float &o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<rep_type&>() = std::declval<const rep_type&>()))
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{
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m_data = o.m_data;
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m_exponent = o.m_exponent;
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m_sign = o.m_sign;
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return *this;
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}
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template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
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cpp_bin_float& operator=(const cpp_bin_float<D, B, A, E, MinE, MaxE> &f)
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{
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switch(eval_fpclassify(f))
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{
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case FP_ZERO:
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m_data = limb_type(0);
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m_sign = f.sign();
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m_exponent = exponent_zero;
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break;
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case FP_NAN:
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m_data = limb_type(0);
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m_sign = false;
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m_exponent = exponent_nan;
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break;;
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case FP_INFINITE:
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m_data = limb_type(0);
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m_sign = f.sign();
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m_exponent = exponent_infinity;
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break;
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default:
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typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(f.bits());
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this->exponent() = f.exponent() + (int)bit_count - (int)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count;
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this->sign() = f.sign();
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copy_and_round(*this, b);
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}
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return *this;
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}
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template <class Float>
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typename boost::enable_if_c<
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(number_category<Float>::value == number_kind_floating_point)
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//&& (std::numeric_limits<Float>::digits <= (int)bit_count)
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&& (std::numeric_limits<Float>::radix == 2), cpp_bin_float&>::type operator=(const Float& f)
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{
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return assign_float(f);
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}
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template <class Float>
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typename boost::enable_if_c<is_floating_point<Float>::value, cpp_bin_float&>::type assign_float(Float f)
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{
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BOOST_MATH_STD_USING
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using default_ops::eval_add;
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typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;
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switch((boost::math::fpclassify)(f))
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{
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case FP_ZERO:
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m_data = limb_type(0);
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m_sign = ((boost::math::signbit)(f) > 0);
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m_exponent = exponent_zero;
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return *this;
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case FP_NAN:
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m_data = limb_type(0);
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m_sign = false;
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m_exponent = exponent_nan;
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return *this;
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case FP_INFINITE:
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m_data = limb_type(0);
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m_sign = (f < 0);
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m_exponent = exponent_infinity;
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return *this;
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}
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if(f < 0)
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{
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*this = -f;
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this->negate();
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return *this;
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}
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typedef typename mpl::front<unsigned_types>::type ui_type;
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m_data = static_cast<ui_type>(0u);
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m_sign = false;
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m_exponent = 0;
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static const int bits = sizeof(int) * CHAR_BIT - 1;
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int e;
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f = frexp(f, &e);
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while(f)
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{
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f = ldexp(f, bits);
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e -= bits;
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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int ipart = itrunc(f);
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#else
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int ipart = static_cast<int>(f);
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#endif
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f -= ipart;
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m_exponent += bits;
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cpp_bin_float t;
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t = static_cast<bf_int_type>(ipart);
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eval_add(*this, t);
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}
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m_exponent += static_cast<Exponent>(e);
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return *this;
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}
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template <class Float>
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typename boost::enable_if_c<
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(number_category<Float>::value == number_kind_floating_point)
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&& !boost::is_floating_point<Float>::value
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/*&& (std::numeric_limits<number<Float> >::radix == 2)*/,
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cpp_bin_float&>::type assign_float(Float f)
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{
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BOOST_MATH_STD_USING
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using default_ops::eval_add;
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using default_ops::eval_get_sign;
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using default_ops::eval_convert_to;
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using default_ops::eval_subtract;
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typedef typename boost::multiprecision::detail::canonical<int, Float>::type f_int_type;
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typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;
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switch(eval_fpclassify(f))
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{
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case FP_ZERO:
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m_data = limb_type(0);
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m_sign = ((boost::math::signbit)(f) > 0);
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m_exponent = exponent_zero;
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return *this;
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case FP_NAN:
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m_data = limb_type(0);
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m_sign = false;
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m_exponent = exponent_nan;
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return *this;
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case FP_INFINITE:
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m_data = limb_type(0);
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m_sign = (f < 0);
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m_exponent = exponent_infinity;
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return *this;
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}
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if(eval_get_sign(f) < 0)
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{
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f.negate();
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*this = f;
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this->negate();
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return *this;
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}
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typedef typename mpl::front<unsigned_types>::type ui_type;
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m_data = static_cast<ui_type>(0u);
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m_sign = false;
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m_exponent = 0;
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static const int bits = sizeof(int) * CHAR_BIT - 1;
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int e;
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eval_frexp(f, f, &e);
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while(eval_get_sign(f) != 0)
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{
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eval_ldexp(f, f, bits);
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e -= bits;
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int ipart;
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eval_convert_to(&ipart, f);
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eval_subtract(f, static_cast<f_int_type>(ipart));
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m_exponent += bits;
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eval_add(*this, static_cast<bf_int_type>(ipart));
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}
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m_exponent += e;
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if(m_exponent > max_exponent)
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m_exponent = exponent_infinity;
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if(m_exponent < min_exponent)
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{
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m_data = limb_type(0u);
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m_exponent = exponent_zero;
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m_sign = ((boost::math::signbit)(f) > 0);
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}
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else if(eval_get_sign(m_data) == 0)
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{
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m_exponent = exponent_zero;
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m_sign = ((boost::math::signbit)(f) > 0);
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}
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return *this;
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}
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template <class I>
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typename boost::enable_if<is_integral<I>, cpp_bin_float&>::type operator=(const I& i)
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{
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using default_ops::eval_bit_test;
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if(!i)
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{
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m_data = static_cast<limb_type>(0);
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m_exponent = exponent_zero;
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m_sign = false;
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}
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else
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{
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typedef typename make_unsigned<I>::type ui_type;
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ui_type fi = static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(i));
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typedef typename boost::multiprecision::detail::canonical<ui_type, rep_type>::type ar_type;
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m_data = static_cast<ar_type>(fi);
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unsigned shift = msb(fi);
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if(shift >= bit_count)
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{
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m_exponent = static_cast<Exponent>(shift);
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m_data = static_cast<ar_type>(fi >> (shift + 1 - bit_count));
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}
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else
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{
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m_exponent = static_cast<Exponent>(shift);
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eval_left_shift(m_data, bit_count - shift - 1);
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}
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BOOST_ASSERT(eval_bit_test(m_data, bit_count-1));
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m_sign = detail::is_negative(i);
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}
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return *this;
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}
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cpp_bin_float& operator=(const char *s);
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void swap(cpp_bin_float &o) BOOST_NOEXCEPT
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{
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m_data.swap(o.m_data);
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std::swap(m_exponent, o.m_exponent);
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std::swap(m_sign, o.m_sign);
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}
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std::string str(std::streamsize dig, std::ios_base::fmtflags f) const;
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void negate()
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{
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if(m_exponent != exponent_nan)
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m_sign = !m_sign;
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}
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int compare(const cpp_bin_float &o) const BOOST_NOEXCEPT
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{
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if(m_sign != o.m_sign)
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return (m_exponent == exponent_zero) && (m_exponent == o.m_exponent) ? 0 : m_sign ? -1 : 1;
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int result;
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if(m_exponent == exponent_nan)
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return -1;
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else if(m_exponent != o.m_exponent)
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{
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if(m_exponent == exponent_zero)
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result = -1;
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else if(o.m_exponent == exponent_zero)
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result = 1;
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else
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result = m_exponent > o.m_exponent ? 1 : -1;
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}
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else
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result = m_data.compare(o.m_data);
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if(m_sign)
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result = -result;
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return result;
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}
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template <class A>
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int compare(const A& o) const BOOST_NOEXCEPT
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{
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cpp_bin_float b;
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b = o;
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return compare(b);
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}
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rep_type& bits() { return m_data; }
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const rep_type& bits()const { return m_data; }
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exponent_type& exponent() { return m_exponent; }
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const exponent_type& exponent()const { return m_exponent; }
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bool& sign() { return m_sign; }
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const bool& sign()const { return m_sign; }
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void check_invariants()
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{
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using default_ops::eval_bit_test;
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using default_ops::eval_is_zero;
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if((m_exponent <= max_exponent) && (m_exponent >= min_exponent))
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{
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BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1));
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}
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else
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{
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BOOST_ASSERT(m_exponent > max_exponent);
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BOOST_ASSERT(m_exponent <= exponent_nan);
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BOOST_ASSERT(eval_is_zero(m_data));
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}
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}
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template<class Archive>
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void serialize(Archive & ar, const unsigned int /*version*/)
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{
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ar & m_data;
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ar & m_exponent;
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ar & m_sign;
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}
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};
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class Int>
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inline void copy_and_round(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, Int &arg)
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{
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// Precondition: exponent of res must have been set before this function is called
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// 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.
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using default_ops::eval_msb;
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using default_ops::eval_lsb;
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using default_ops::eval_left_shift;
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using default_ops::eval_bit_test;
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using default_ops::eval_right_shift;
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using default_ops::eval_increment;
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using default_ops::eval_get_sign;
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// cancellation may have resulted in arg being all zeros:
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if(eval_get_sign(arg) == 0)
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{
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res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
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res.sign() = false;
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res.bits() = static_cast<limb_type>(0u);
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return;
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}
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int msb = eval_msb(arg);
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if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) > msb + 1)
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{
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// Must have had cancellation in subtraction, shift left and copy:
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res.bits() = arg;
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eval_left_shift(res.bits(), cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1);
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res.exponent() -= static_cast<Exponent>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - msb - 1);
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}
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else if(static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) < msb + 1)
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{
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// We have more cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count than we need, so round as required,
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// first get the rounding bit:
|
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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);
|
|
}
|
|
}
|
|
|
|
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)
|
|
{
|
|
if(a.exponent() < b.exponent())
|
|
{
|
|
bool s = a.sign();
|
|
do_eval_add(res, b, a);
|
|
if(res.sign() != s)
|
|
res.negate();
|
|
return;
|
|
}
|
|
|
|
using default_ops::eval_add;
|
|
using default_ops::eval_bit_test;
|
|
|
|
typedef typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type exponent_type;
|
|
|
|
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:
|
|
{
|
|
bool s = a.sign();
|
|
res = b;
|
|
res.sign() = s;
|
|
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.
|
|
}
|
|
|
|
BOOST_STATIC_ASSERT(boost::integer_traits<exponent_type>::const_max - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent);
|
|
|
|
bool s = a.sign();
|
|
dt = a.bits();
|
|
if(a.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + b.exponent())
|
|
{
|
|
res.exponent() = a.exponent();
|
|
}
|
|
else
|
|
{
|
|
exponent_type e_diff = a.exponent() - b.exponent();
|
|
BOOST_ASSERT(e_diff >= 0);
|
|
eval_left_shift(dt, e_diff);
|
|
res.exponent() = a.exponent() - e_diff;
|
|
eval_add(dt, b.bits());
|
|
}
|
|
|
|
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
|
|
{
|
|
bool s = a.sign();
|
|
res = b;
|
|
if(res.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
|
|
res.sign() = false;
|
|
else if(res.sign() == s)
|
|
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_infinity;
|
|
res.sign() = !a.sign();
|
|
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.
|
|
}
|
|
|
|
bool s = a.sign();
|
|
if((a.exponent() > b.exponent()) || ((a.exponent() == b.exponent()) && a.bits().compare(b.bits()) >= 0))
|
|
{
|
|
dt = a.bits();
|
|
if(a.exponent() <= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + b.exponent())
|
|
{
|
|
typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
|
|
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(b.exponent() <= a.exponent() + (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
|
|
{
|
|
typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
|
|
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.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
|
|
res.sign() = false;
|
|
else 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 if(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
|
|
{
|
|
bool s = a.sign() != b.sign();
|
|
res = a;
|
|
res.sign() = s;
|
|
}
|
|
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:
|
|
bool s = a.sign() != b.sign();
|
|
res = a;
|
|
res.sign() = s;
|
|
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)
|
|
{
|
|
bool s = a.sign() != b.sign();
|
|
res = b;
|
|
res.sign() = s;
|
|
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:
|
|
bool s = a.sign() != b.sign();
|
|
res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
|
|
res.sign() = s;
|
|
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() = a.sign() != b.sign();
|
|
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:
|
|
{
|
|
bool s = a.sign();
|
|
res = a;
|
|
res.sign() = s;
|
|
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)
|
|
{
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(push)
|
|
#pragma warning(disable:6326) // comparison of two constants
|
|
#endif
|
|
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;
|
|
}
|
|
bool s = u.sign() != v.sign();
|
|
res = u;
|
|
res.sign() = s;
|
|
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;
|
|
}
|
|
bool s = u.sign() != v.sign();
|
|
res = u;
|
|
res.sign() = s;
|
|
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() = u.sign() != v.sign();
|
|
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:
|
|
//
|
|
if((v.exponent() < 0) && (u.exponent() > 0))
|
|
{
|
|
// Check for overflow:
|
|
if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent + v.exponent() < u.exponent() - 1)
|
|
{
|
|
res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
|
|
res.sign() = u.sign() != v.sign();
|
|
res.bits() = static_cast<limb_type>(0u);
|
|
return;
|
|
}
|
|
}
|
|
else if((v.exponent() > 0) && (u.exponent() < 0))
|
|
{
|
|
// Check for underflow:
|
|
if(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent + v.exponent() > u.exponent())
|
|
{
|
|
// We will certainly underflow:
|
|
res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
|
|
res.sign() = u.sign() != v.sign();
|
|
res.bits() = static_cast<limb_type>(0u);
|
|
return;
|
|
}
|
|
}
|
|
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);
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(pop)
|
|
#endif
|
|
}
|
|
|
|
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)
|
|
{
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(push)
|
|
#pragma warning(disable:6326) // comparison of two constants
|
|
#endif
|
|
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;
|
|
}
|
|
bool s = u.sign() != (v < 0);
|
|
res = u;
|
|
res.sign() = s;
|
|
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);
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(pop)
|
|
#endif
|
|
}
|
|
|
|
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)
|
|
{
|
|
if(a.exponent() == b.exponent())
|
|
{
|
|
if(a.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
|
|
return true;
|
|
return (a.sign() == b.sign())
|
|
&& (a.bits().compare(b.bits()) == 0)
|
|
&& (a.exponent() != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan);
|
|
}
|
|
return false;
|
|
}
|
|
|
|
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
|
|
inline void eval_convert_to(boost::long_long_type *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<boost::long_long_type>::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<boost::long_long_type>::min)()) <= 0))
|
|
{
|
|
*res = (std::numeric_limits<boost::long_long_type>::min)();
|
|
return;
|
|
}
|
|
else if(!arg.sign() && (arg.compare((std::numeric_limits<boost::long_long_type>::max)()) >= 0))
|
|
{
|
|
*res = (std::numeric_limits<boost::long_long_type>::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(boost::ulong_long_type *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<boost::ulong_long_type>::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 boost::long_long_type?
|
|
*res = (std::numeric_limits<boost::long_long_type>::max)();
|
|
return;
|
|
}
|
|
eval_right_shift(man, shift);
|
|
eval_convert_to(res, man);
|
|
}
|
|
|
|
template <class Float, unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
|
|
inline typename boost::enable_if_c<boost::is_float<Float>::value>::type eval_convert_to(Float *res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &original_arg)
|
|
{
|
|
//
|
|
// Perform rounding first, then afterwards extract the digits:
|
|
//
|
|
typedef cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, void, Exponent, MinE, MaxE> conv_type;
|
|
typedef typename common_type<typename conv_type::exponent_type, int>::type common_exp_type;
|
|
conv_type arg(original_arg);
|
|
switch(arg.exponent())
|
|
{
|
|
case conv_type::exponent_zero:
|
|
*res = 0;
|
|
if(arg.sign())
|
|
*res = -*res;
|
|
return;
|
|
case conv_type::exponent_nan:
|
|
*res = std::numeric_limits<Float>::quiet_NaN();
|
|
return;
|
|
case conv_type::exponent_infinity:
|
|
*res = (std::numeric_limits<Float>::infinity)();
|
|
if(arg.sign())
|
|
*res = -*res;
|
|
return;
|
|
}
|
|
common_exp_type e = arg.exponent();
|
|
static const common_exp_type min_exp_limit = std::numeric_limits<Float>::min_exponent
|
|
- (common_exp_type)cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, void, Exponent, MinE, MaxE>::bit_count - std::numeric_limits<Float>::digits - 2;
|
|
e -= cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, void, Exponent, MinE, MaxE>::bit_count - 1;
|
|
if(e < min_exp_limit)
|
|
{
|
|
*res = 0;
|
|
return;
|
|
}
|
|
if(e > std::numeric_limits<Float>::max_exponent)
|
|
{
|
|
*res = std::numeric_limits<Float>::has_infinity ? std::numeric_limits<Float>::infinity() : (std::numeric_limits<Float>::max)();
|
|
return;
|
|
}
|
|
|
|
*res = std::ldexp(static_cast<Float>(*arg.bits().limbs()), static_cast<int>(e));
|
|
for(unsigned i = 1; i < arg.bits().size(); ++i)
|
|
{
|
|
e += sizeof(*arg.bits().limbs()) * CHAR_BIT;
|
|
*res += std::ldexp(static_cast<Float>(arg.bits().limbs()[i]), static_cast<int>(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:
|
|
if(arg.sign())
|
|
res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
|
|
else
|
|
res = arg;
|
|
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)
|
|
{
|
|
bool s = arg.sign(); // takes care of signed zeros
|
|
res = static_cast<signed_limb_type>(arg.sign() ? 0 : 1);
|
|
res.sign() = s;
|
|
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 D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2>
|
|
inline std::size_t hash_value(const cpp_bin_float<D1, B1, A1, E1, M1, M2>& val)
|
|
{
|
|
std::size_t result = hash_value(val.bits());
|
|
boost::hash_combine(result, val.exponent());
|
|
boost::hash_combine(result, val.sign());
|
|
return result;
|
|
}
|
|
|
|
|
|
} // namespace backends
|
|
|
|
#ifdef BOOST_NO_SFINAE_EXPR
|
|
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namespace detail{
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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>
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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_ {};
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template<class FloatT, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
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struct is_explicitly_convertible<FloatT, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public boost::is_floating_point<FloatT> {};
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}
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#endif
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template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
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inline int signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>& arg)
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{
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return arg.backend().sign();
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}
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template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
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inline boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>
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copysign BOOST_PREVENT_MACRO_SUBSTITUTION(
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const boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>& a,
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const boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>& b)
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{
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boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> res(a);
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res.backend().sign() = b.backend().sign();
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return res;
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}
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using backends::cpp_bin_float;
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using backends::digit_base_2;
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using backends::digit_base_10;
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template<unsigned Digits, backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator>
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struct number_category<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > : public boost::mpl::int_<boost::multiprecision::number_kind_floating_point>{};
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template<unsigned Digits, backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
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struct expression_template_default<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >
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{
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static const expression_template_option value = is_void<Allocator>::value ? et_off : et_on;
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};
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typedef number<backends::cpp_bin_float<50> > cpp_bin_float_50;
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typedef number<backends::cpp_bin_float<100> > cpp_bin_float_100;
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typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single;
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typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double;
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typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended;
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typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad;
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} // namespace multiprecision
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namespace math {
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using boost::multiprecision::signbit;
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using boost::multiprecision::copysign;
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} // namespace math
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} // namespace boost
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#include <boost/multiprecision/cpp_bin_float/io.hpp>
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#include <boost/multiprecision/cpp_bin_float/transcendental.hpp>
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namespace std{
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//
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// numeric_limits [partial] specializations for the types declared in this header:
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//
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template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >
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{
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typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> number_type;
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public:
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BOOST_STATIC_CONSTEXPR bool is_specialized = true;
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static number_type (min)()
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{
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initializer.do_nothing();
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static std::pair<bool, number_type> value;
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if(!value.first)
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{
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value.first = true;
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value.second = 1u;
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value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent;
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}
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return value.second;
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}
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static number_type (max)()
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{
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initializer.do_nothing();
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static std::pair<bool, number_type> value;
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if(!value.first)
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{
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value.first = true;
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eval_complement(value.second.backend().bits(), value.second.backend().bits());
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value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent;
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}
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return value.second;
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}
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BOOST_STATIC_CONSTEXPR number_type lowest()
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{
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return -(max)();
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}
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BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count;
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BOOST_STATIC_CONSTEXPR int digits10 = (digits - 1) * 301 / 1000;
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// Is this really correct???
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BOOST_STATIC_CONSTEXPR int max_digits10 = (digits * 301 / 1000) + 3;
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BOOST_STATIC_CONSTEXPR bool is_signed = true;
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BOOST_STATIC_CONSTEXPR bool is_integer = false;
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BOOST_STATIC_CONSTEXPR bool is_exact = false;
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BOOST_STATIC_CONSTEXPR int radix = 2;
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static number_type epsilon()
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{
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initializer.do_nothing();
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static std::pair<bool, number_type> value;
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if(!value.first)
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{
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value.first = true;
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value.second = 1;
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value.second = ldexp(value.second, 1 - (int)digits);
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}
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return value.second;
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}
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// What value should this be????
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static number_type round_error()
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{
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// returns 0.5
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initializer.do_nothing();
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static std::pair<bool, number_type> value;
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if(!value.first)
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{
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value.first = true;
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value.second = 1;
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value.second = ldexp(value.second, -1);
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}
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return value.second;
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}
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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;
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BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent10 = (min_exponent / 1000) * 301L;
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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;
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BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent10 = (max_exponent / 1000) * 301L;
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BOOST_STATIC_CONSTEXPR bool has_infinity = true;
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BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
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BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
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BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
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BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
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static number_type infinity()
|
|
{
|
|
initializer.do_nothing();
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|
static std::pair<bool, number_type> value;
|
|
if(!value.first)
|
|
{
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|
value.first = true;
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value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
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}
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return value.second;
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}
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static number_type quiet_NaN()
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|
{
|
|
initializer.do_nothing();
|
|
static std::pair<bool, number_type> value;
|
|
if(!value.first)
|
|
{
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|
value.first = true;
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value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan;
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}
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return value.second;
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}
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BOOST_STATIC_CONSTEXPR number_type signaling_NaN()
|
|
{
|
|
return number_type(0);
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|
}
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BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); }
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BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
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BOOST_STATIC_CONSTEXPR bool is_bounded = true;
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|
BOOST_STATIC_CONSTEXPR bool is_modulo = false;
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|
BOOST_STATIC_CONSTEXPR bool traps = true;
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BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
|
|
BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;
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|
private:
|
|
struct data_initializer
|
|
{
|
|
data_initializer()
|
|
{
|
|
std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::epsilon();
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|
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)();
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|
(std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::max)();
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|
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();
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|
}
|
|
void do_nothing()const{}
|
|
};
|
|
static const data_initializer initializer;
|
|
};
|
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|
template<unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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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;
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|
|
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
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template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits;
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|
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;
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|
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_digits10;
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template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_signed;
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template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
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BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_integer;
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|
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;
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|
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;
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|
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>
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|
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
|