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soft_double.h
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///////////////////////////////////////////////////////////////////
// Copyright Christopher Kormanyos 2012 - 2025. //
// Distributed under the Boost Software License, //
// Version 1.0. (See accompanying file LICENSE_1_0.txt //
// or copy at http://www.boost.org/LICENSE_1_0.txt) //
///////////////////////////////////////////////////////////////////
// This work uses (significantly) modified parts of
// SoftFloat IEEE Floating-Point Arithmetic Package,
// Release 3e, by John R. Hauser.
// Full original SoftFloat 3e copyright information follows.
/*----------------------------------------------------------------------------
This C header file is part of the SoftFloat IEEE Floating-Point Arithmetic
Package, Release 3e, by John R. Hauser.
Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
University of California. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions, and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the University nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-----------------------------------------------------------------------------*/
#ifndef SOFT_DOUBLE_2020_10_27_H // NOLINT(llvm-header-guard)
#define SOFT_DOUBLE_2020_10_27_H
//#define SOFT_DOUBLE_DISABLE_IOSTREAM
#define SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS 0 // NOLINT(cppcoreguidelines-macro-usage)
#include <array>
#if defined(__has_include)
#if ((__has_include(<bit>) != 0) && (defined(__cpp_lib_bit_cast) && (__cpp_lib_bit_cast == 201806L)))
#include <bit>
#undef SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS
#define SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS 1 // NOLINT(cppcoreguidelines-macro-usage)
#endif
#endif
#include <cstddef>
#include <cstdint>
#if !defined(SOFT_DOUBLE_DISABLE_IOSTREAM)
#include <iomanip>
#endif
#include <limits>
#if !defined(SOFT_DOUBLE_DISABLE_IOSTREAM)
#include <sstream>
#endif
#include <type_traits>
#if (defined(__clang__) && (__clang_major__ <= 9))
#define SOFT_DOUBLE_NUM_LIMITS_CLASS_TYPE struct // NOLINT(cppcoreguidelines-macro-usage)
#else
#define SOFT_DOUBLE_NUM_LIMITS_CLASS_TYPE class // NOLINT(cppcoreguidelines-macro-usage)
#endif
#if defined(__clang__)
#if(__cplusplus >= 201703L)
#define SOFT_DOUBLE_NODISCARD [[nodiscard]] // NOLINT(cppcoreguidelines-macro-usage)
#else
#define SOFT_DOUBLE_NODISCARD // NOLINT(cppcoreguidelines-macro-usage)
#endif
#else
#if (defined(_MSC_VER) && (_MSC_VER < 1920))
#define SOFT_DOUBLE_NODISCARD
#else
#if (defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard))
#define SOFT_DOUBLE_NODISCARD [[nodiscard]]
#else
#define SOFT_DOUBLE_NODISCARD
#endif
#endif
#endif
#if(__cplusplus >= 201703L)
namespace math::softfloat {
#else
namespace math { namespace softfloat { // NOLINT(modernize-concat-nested-namespaces)
#endif
// Forward declaration the math::softfloat::soft_double class.
class soft_double;
#if(__cplusplus >= 201703L)
} // namespace math::softfloat
#else
} // namespace softfloat
} // namespace math
#endif
namespace std {
// Forward declaration of the specialization of numeric_limits for soft_double.
template<>
SOFT_DOUBLE_NUM_LIMITS_CLASS_TYPE numeric_limits<::math::softfloat::soft_double>;
} // namespace std
#if(__cplusplus >= 201703L)
namespace math::softfloat {
#else
namespace math { namespace softfloat { // NOLINT(modernize-concat-nested-namespaces)
#endif
namespace detail {
template<typename T>
constexpr auto my_max(T a, T b) noexcept -> T { return ((a > b) ? a : b); }
template<const int BitCount,
typename EnableType = void>
struct uint_type_helper
{
static_assert(((BitCount >= static_cast<int>(INT8_C(8))) && (BitCount <= static_cast<int>(INT8_C(64)))),
"Error: uint_type_helper is not intended to be used for this BitCount");
using exact_unsigned_type = std::uintmax_t;
};
template<const int BitCount> struct uint_type_helper<BitCount, typename std::enable_if< (BitCount <= static_cast<int>(INT8_C( 8)))>::type> { using exact_unsigned_type = std::uint8_t; };
template<const int BitCount> struct uint_type_helper<BitCount, typename std::enable_if<(BitCount >= static_cast<int>(INT8_C( 9))) && (BitCount <= static_cast<int>(INT8_C(16)))>::type> { using exact_unsigned_type = std::uint16_t; };
template<const int BitCount> struct uint_type_helper<BitCount, typename std::enable_if<(BitCount >= static_cast<int>(INT8_C(17))) && (BitCount <= static_cast<int>(INT8_C(32)))>::type> { using exact_unsigned_type = std::uint32_t; };
template<const int BitCount> struct uint_type_helper<BitCount, typename std::enable_if<(BitCount >= static_cast<int>(INT8_C(33))) && (BitCount <= static_cast<int>(INT8_C(64)))>::type> { using exact_unsigned_type = std::uint64_t; };
struct uint128_compound
{
explicit constexpr uint128_compound(std::uint64_t a = std::uint64_t(), // NOLINT(bugprone-easily-swappable-parameters)
std::uint64_t b = std::uint64_t()) noexcept
: v0(a),
v1(b) { }
std::uint64_t v0; // NOLINT(misc-non-private-member-variables-in-classes)
std::uint64_t v1; // NOLINT(misc-non-private-member-variables-in-classes)
};
template<typename UnsignedIntegralType>
constexpr auto negate(UnsignedIntegralType u) -> typename std::enable_if< std::is_integral<UnsignedIntegralType>::value
&& std::is_unsigned<UnsignedIntegralType>::value, UnsignedIntegralType>::type
{
return
static_cast<UnsignedIntegralType>
(
static_cast<UnsignedIntegralType>(~u)
+ static_cast<UnsignedIntegralType>(UINT8_C(1))
);
}
template<typename SignedIntegralType>
constexpr auto negate(SignedIntegralType n) -> typename std::enable_if< std::is_integral<SignedIntegralType>::value
&& std::is_signed <SignedIntegralType>::value, SignedIntegralType>::type
{
return static_cast<SignedIntegralType>(detail::negate(static_cast<unsigned long long>(n))); // NOLINT(google-runtime-int)
}
constexpr auto signF32UI(std::uint32_t a) -> bool { return (static_cast<std::uint_fast8_t>(a >> static_cast<unsigned>(UINT8_C(31))) != static_cast<std::uint_fast8_t>(UINT8_C(0))); }
constexpr auto expF32UI (std::uint32_t a) -> std::int16_t { return static_cast<std::int16_t>(static_cast<std::int16_t>(a >> static_cast<unsigned>(UINT8_C(23))) & static_cast<std::int16_t>(INT16_C(0xFF))); } // NOLINT(hicpp-signed-bitwise)
constexpr auto fracF32UI(std::uint32_t a) -> std::uint32_t { return static_cast<std::uint32_t>(a & static_cast<std::uint32_t>(UINT32_C(0x007FFFFF))); }
constexpr auto signF64UI(std::uint64_t a) -> bool { return (static_cast<std::uint_fast8_t>(a >> static_cast<unsigned>(UINT8_C(63))) != static_cast<std::uint_fast8_t>(UINT8_C(0))); }
constexpr auto expF64UI (std::uint64_t a) -> std::int16_t { return static_cast<std::int16_t>(static_cast<std::int16_t>(a >> static_cast<unsigned>(UINT8_C(52))) & static_cast<std::int16_t>(INT16_C(0x7FF))); } // NOLINT(hicpp-signed-bitwise)
constexpr auto fracF64UI(std::uint64_t a) -> std::uint64_t { return static_cast<std::uint64_t>(a & static_cast<std::uint64_t>(UINT64_C(0x000FFFFFFFFFFFFF))); }
template<typename IntegralTypeExp,
typename IntegralTypeSig>
constexpr auto packToF64UI(bool sign, IntegralTypeExp expA, IntegralTypeSig sig) -> std::uint64_t
{
using local_unsigned_sig_type =
typename detail::uint_type_helper<std::numeric_limits<IntegralTypeSig>::digits>::exact_unsigned_type;
using local_unsigned_exp_type =
typename detail::uint_type_helper<std::numeric_limits<IntegralTypeExp>::digits>::exact_unsigned_type;
return
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>(sign ? static_cast<std::uint64_t>(static_cast<std::uint64_t>(UINT8_C(1)) << static_cast<unsigned>(UINT8_C(63))) : static_cast<std::uint64_t>(UINT8_C(0)))
+ static_cast<std::uint64_t>(static_cast<std::uint64_t>(static_cast<local_unsigned_exp_type>(expA)) << static_cast<unsigned>(UINT8_C(52))) // NOLINT(clang-analyzer-core.UndefinedBinaryOperatorResult)
+ static_cast<std::uint64_t>(static_cast<local_unsigned_sig_type>(sig))
);
}
template<typename IntegralTypeExp,
typename IntegralTypeSig>
constexpr auto packToF32UI(bool sign, IntegralTypeExp expA, IntegralTypeSig sig) -> std::uint32_t
{
return
static_cast<std::uint32_t>
(
static_cast<std::uint32_t>(sign ? static_cast<std::uint32_t>(UINT8_C(1)) << static_cast<unsigned>(UINT8_C(31)) : static_cast<std::uint32_t>(UINT8_C(0)))
+ static_cast<std::uint32_t>(static_cast<std::uint32_t>(expA) << static_cast<unsigned>(UINT8_C(23)))
+ static_cast<std::uint32_t>(sig)
);
}
constexpr auto softfloat_shortShiftRightJam64(std::uint64_t a, std::uint_fast16_t dist) -> std::uint64_t
{
return
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>(a >> dist)
| static_cast<unsigned>
(
(static_cast<std::uint64_t>(a << static_cast<unsigned>(negate(dist) & static_cast<unsigned>(UINT8_C(63)))) != static_cast<std::uint64_t>(UINT8_C(0)))
? static_cast<unsigned>(UINT8_C(1))
: static_cast<unsigned>(UINT8_C(0))
)
);
}
constexpr auto softfloat_shiftRightJam64(std::uint64_t a, std::uint_fast16_t dist) -> std::uint64_t
{
return
static_cast<std::uint64_t>
(
(dist < static_cast<std::uint_fast16_t>(UINT8_C(63)))
? softfloat_shortShiftRightJam64(a, dist)
: static_cast<std::uint64_t>
(
(a != static_cast<std::uint64_t>(UINT8_C(0)))
? static_cast<unsigned>(UINT8_C(1))
: static_cast<unsigned>(UINT8_C(0))
)
);
}
constexpr auto softfloat_countLeadingZeros8_z_table(std::uint_fast8_t index) -> std::uint_fast8_t
{
// A constant table that translates an 8-bit unsigned integer (the array index)
// into the number of leading 0 bits before the most-significant 1 of that
// integer. For integer zero (index 0), the corresponding table element is 8.
return
static_cast<std::uint_fast8_t>
(
((index < static_cast<std::uint_fast8_t>(UINT8_C(0x1))) ? static_cast<std::uint_fast8_t>(UINT8_C(4))
: ((index < static_cast<std::uint_fast8_t>(UINT8_C(0x2))) ? static_cast<std::uint_fast8_t>(UINT8_C(3))
: ((index < static_cast<std::uint_fast8_t>(UINT8_C(0x4))) ? static_cast<std::uint_fast8_t>(UINT8_C(2))
: ((index < static_cast<std::uint_fast8_t>(UINT8_C(0x8))) ? static_cast<std::uint_fast8_t>(UINT8_C(1))
: static_cast<std::uint_fast8_t>(UINT8_C(0))))))
);
}
constexpr auto softfloat_countLeadingZeros8(std::uint8_t a) -> std::uint_fast8_t
{
return
static_cast<std::uint_fast8_t>
(
(a < static_cast<std::uint_fast8_t>(UINT8_C(0x10)))
? static_cast<std::uint_fast8_t>
(
static_cast<std::uint_fast8_t>(UINT8_C(4))
+ softfloat_countLeadingZeros8_z_table(static_cast<std::uint_fast8_t>(a & static_cast<std::uint8_t>(UINT8_C(0xF))))
)
: softfloat_countLeadingZeros8_z_table(static_cast<std::uint_fast8_t>(a >> static_cast<unsigned>(UINT8_C(4))))
);
}
constexpr auto softfloat_countLeadingZeros16(std::uint16_t a) -> std::uint_fast8_t
{
return
static_cast<std::uint_fast8_t>
(
(a < static_cast<std::uint16_t>(UINT16_C(0x100)))
? static_cast<std::uint_fast8_t>
(
static_cast<std::uint_fast8_t>(UINT8_C(8))
+ softfloat_countLeadingZeros8(static_cast<std::uint8_t>(a))
)
: softfloat_countLeadingZeros8(static_cast<std::uint8_t>(a >> static_cast<unsigned>(UINT8_C(8))))
);
}
constexpr auto softfloat_countLeadingZeros32(std::uint32_t a) -> std::uint_fast8_t
{
return
static_cast<std::uint_fast8_t>
(
(a < static_cast<std::uint32_t>(UINT32_C(0x10000)))
? static_cast<std::uint_fast8_t>
(
static_cast<std::uint_fast8_t>(UINT8_C(16))
+ softfloat_countLeadingZeros16(static_cast<std::uint16_t>(a))
)
: softfloat_countLeadingZeros16(static_cast<std::uint16_t>(a >> static_cast<unsigned>(UINT8_C(16))))
);
}
constexpr auto softfloat_countLeadingZeros64(std::uint64_t a) -> std::uint_fast8_t
{
return
static_cast<std::uint_fast8_t>
(
(a < static_cast<std::uint64_t>(UINT64_C(0x100000000)))
? static_cast<std::uint_fast8_t>
(
static_cast<unsigned>(UINT8_C(32))
+ softfloat_countLeadingZeros32(static_cast<std::uint32_t>(a))
)
: softfloat_countLeadingZeros32(static_cast<std::uint32_t>(a >> static_cast<unsigned>(UINT8_C(32))))
);
}
constexpr auto softfloat_approxRecip32_1(std::uint32_t a) -> std::uint32_t
{
// Returns an approximation to the reciprocal of the number represented by a,
// where a is interpreted as an unsigned fixed-point number with one integer
// bit and 31 fraction bits.
return
static_cast<std::uint32_t>
(
static_cast<std::uint64_t>(UINT64_C(0x7FFFFFFFFFFFFFFF))
/ a
);
}
constexpr auto softfloat_shiftRightJam64Extra(std::uint64_t a,
std::uint64_t extra,
std::uint32_t dist) -> uint128_compound
{
// Shifts the 128 bits formed by concatenating a and extra right by 64
// _plus_ the number of bits given in dist, which must not be zero. This
// shifted value is at most 64 nonzero bits and is returned in the v field
// of the struct uint64_extra result.
return
uint128_compound
{
static_cast<std::uint64_t>
(
(dist < static_cast<std::uint32_t>(UINT8_C(64)))
? static_cast<std::uint64_t>
( static_cast<std::uint64_t>
(
a << static_cast<unsigned>
(
static_cast<unsigned>(negate(dist)) & static_cast<std::uint32_t>(UINT8_C(63))
)
)
| static_cast<unsigned>
(
(extra != static_cast<std::uint64_t>(UINT8_C(0)))
? static_cast<unsigned>(UINT8_C(1))
: static_cast<unsigned>(UINT8_C(0))
)
)
:
static_cast<std::uint64_t>
(
(dist == static_cast<std::uint32_t>(UINT8_C(64)))
? a
: static_cast<std::uint64_t>
(
((a != static_cast<std::uint64_t>(UINT8_C(0))) || (extra != static_cast<std::uint64_t>(UINT8_C(0))))
? static_cast<unsigned>(UINT8_C(1))
: static_cast<unsigned>(UINT8_C(0))
)
)
),
static_cast<std::uint64_t>
(
(dist < static_cast<std::uint32_t>(UINT8_C(64)))
? static_cast<std::uint64_t>(a >> static_cast<unsigned>(dist))
: static_cast<std::uint64_t>(UINT8_C(0))
)
};
}
#if (defined(SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS) && (SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS == 0))
template<typename BuiltInFloatType,
typename ExactUnsignedIntegralType = typename uint_type_helper<std::numeric_limits<BuiltInFloatType>::digits>::exact_unsigned_type>
union uz_type
{
static_assert(( std::is_same<BuiltInFloatType, float>::value
|| std::is_same<BuiltInFloatType, double>::value),
"Error: This template is intended for either built-in float or double, but not for any other type(s)");
using float_type = BuiltInFloatType;
using unsigned_type = ExactUnsignedIntegralType;
const float_type my_f; // NOLINT(misc-non-private-member-variables-in-classes)
const unsigned_type my_u; // NOLINT(misc-non-private-member-variables-in-classes)
explicit constexpr uz_type(float_type f) noexcept : my_f(f) { }
explicit constexpr uz_type(unsigned_type u) noexcept : my_u(u) { }
SOFT_DOUBLE_NODISCARD constexpr auto get_f() const noexcept -> float_type { return my_f; }
SOFT_DOUBLE_NODISCARD constexpr auto get_u() const noexcept -> unsigned_type { return my_u; }
};
#elif (defined(SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS) && (SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS == 1))
template<typename BuiltInFloatType,
typename ExactUnsignedIntegralType = typename uint_type_helper<std::numeric_limits<BuiltInFloatType>::digits>::exact_unsigned_type>
struct uz_type
{
static_assert(( std::is_same<BuiltInFloatType, float>::value
|| std::is_same<BuiltInFloatType, double>::value),
"Error: This template is intended for either built-in float or double, but not for any other type(s)");
using float_type = BuiltInFloatType;
using unsigned_type = ExactUnsignedIntegralType;
const float_type my_f; // NOLINT(misc-non-private-member-variables-in-classes,cppcoreguidelines-avoid-const-or-ref-data-members)
explicit constexpr uz_type(float_type f) noexcept : my_f(f) { }
explicit constexpr uz_type(unsigned_type u) noexcept : my_f(std::bit_cast<float_type>(u)) { }
SOFT_DOUBLE_NODISCARD constexpr auto get_u() const noexcept -> unsigned_type { return std::bit_cast<unsigned_type>(my_f); }
SOFT_DOUBLE_NODISCARD constexpr auto get_f() const noexcept -> float_type { return my_f; }
};
#else
#error Configuration error regarding SOFT_DOUBLE_CONSTEXPR_BUILTIN_FLOATS
#endif
struct nothing { };
} // namespace detail
constexpr auto operator+(const soft_double& a, const soft_double& b) -> soft_double;
constexpr auto operator-(const soft_double& a, const soft_double& b) -> soft_double;
constexpr auto operator*(const soft_double& a, const soft_double& b) -> soft_double;
constexpr auto operator/(const soft_double& a, const soft_double& b) -> soft_double;
template<typename UnsignedIntegralType> constexpr auto operator+(const soft_double& u, UnsignedIntegralType n) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator-(const soft_double& u, UnsignedIntegralType n) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator*(const soft_double& u, UnsignedIntegralType n) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator/(const soft_double& u, UnsignedIntegralType n) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator+(UnsignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator-(UnsignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator*(UnsignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename UnsignedIntegralType> constexpr auto operator/(UnsignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator+(const soft_double& u, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator-(const soft_double& u, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator*(const soft_double& u, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator/(const soft_double& u, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator+(SignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator-(SignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator*(SignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
template<typename SignedIntegralType> constexpr auto operator/(SignedIntegralType n, const soft_double& u) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, soft_double>::type;
constexpr auto operator+(const soft_double& u, float f) -> soft_double;
constexpr auto operator-(const soft_double& u, float f) -> soft_double;
constexpr auto operator*(const soft_double& u, float f) -> soft_double;
constexpr auto operator/(const soft_double& u, float f) -> soft_double;
constexpr auto operator+(float f, const soft_double& u) -> soft_double;
constexpr auto operator-(float f, const soft_double& u) -> soft_double;
constexpr auto operator*(float f, const soft_double& u) -> soft_double;
constexpr auto operator/(float f, const soft_double& u) -> soft_double;
constexpr auto operator+(const soft_double& u, double f) -> soft_double;
constexpr auto operator-(const soft_double& u, double f) -> soft_double;
constexpr auto operator*(const soft_double& u, double f) -> soft_double;
constexpr auto operator/(const soft_double& u, double f) -> soft_double;
constexpr auto operator+(double f, const soft_double& u) -> soft_double;
constexpr auto operator-(double f, const soft_double& u) -> soft_double;
constexpr auto operator*(double f, const soft_double& u) -> soft_double;
constexpr auto operator/(double f, const soft_double& u) -> soft_double;
constexpr auto operator+(const soft_double& u, long double f) -> soft_double;
constexpr auto operator-(const soft_double& u, long double f) -> soft_double;
constexpr auto operator*(const soft_double& u, long double f) -> soft_double;
constexpr auto operator/(const soft_double& u, long double f) -> soft_double;
constexpr auto operator+(long double f, const soft_double& u) -> soft_double;
constexpr auto operator-(long double f, const soft_double& u) -> soft_double;
constexpr auto operator*(long double f, const soft_double& u) -> soft_double;
constexpr auto operator/(long double f, const soft_double& u) -> soft_double;
constexpr auto operator< (const soft_double& a, const soft_double& b) -> bool;
constexpr auto operator<=(const soft_double& a, const soft_double& b) -> bool;
constexpr auto operator==(const soft_double& a, const soft_double& b) -> bool;
constexpr auto operator!=(const soft_double& a, const soft_double& b) -> bool;
constexpr auto operator>=(const soft_double& a, const soft_double& b) -> bool;
constexpr auto operator> (const soft_double& a, const soft_double& b) -> bool;
template<typename UnsignedIntegralType> constexpr auto operator< (const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator<=(const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator==(const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator!=(const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator>=(const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator> (const soft_double& a, UnsignedIntegralType u) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator< (UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator<=(UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator==(UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator!=(UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator>=(UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename UnsignedIntegralType> constexpr auto operator> (UnsignedIntegralType u, const soft_double& a) -> typename std::enable_if<std::is_integral<UnsignedIntegralType>::value && std::is_unsigned<UnsignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator< (const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator<=(const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator==(const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator!=(const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator>=(const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator> (const soft_double& a, SignedIntegralType n) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator< (SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator<=(SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator==(SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator!=(SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator>=(SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
template<typename SignedIntegralType> constexpr auto operator> (SignedIntegralType n, const soft_double& a) -> typename std::enable_if<std::is_integral<SignedIntegralType>::value && std::is_signed<SignedIntegralType>::value, bool>::type;
constexpr auto operator< (const soft_double& a, float f) -> bool;
constexpr auto operator<=(const soft_double& a, float f) -> bool;
constexpr auto operator==(const soft_double& a, float f) -> bool;
constexpr auto operator!=(const soft_double& a, float f) -> bool;
constexpr auto operator>=(const soft_double& a, float f) -> bool;
constexpr auto operator> (const soft_double& a, float f) -> bool;
constexpr auto operator< (float f, const soft_double& a) -> bool;
constexpr auto operator<=(float f, const soft_double& a) -> bool;
constexpr auto operator==(float f, const soft_double& a) -> bool;
constexpr auto operator!=(float f, const soft_double& a) -> bool;
constexpr auto operator>=(float f, const soft_double& a) -> bool;
constexpr auto operator> (float f, const soft_double& a) -> bool;
constexpr auto operator< (const soft_double& a, double f) -> bool;
constexpr auto operator<=(const soft_double& a, double f) -> bool;
constexpr auto operator==(const soft_double& a, double f) -> bool;
constexpr auto operator!=(const soft_double& a, double f) -> bool;
constexpr auto operator>=(const soft_double& a, double f) -> bool;
constexpr auto operator> (const soft_double& a, double f) -> bool;
constexpr auto operator< (double f, const soft_double& a) -> bool;
constexpr auto operator<=(double f, const soft_double& a) -> bool;
constexpr auto operator==(double f, const soft_double& a) -> bool;
constexpr auto operator!=(double f, const soft_double& a) -> bool;
constexpr auto operator>=(double f, const soft_double& a) -> bool;
constexpr auto operator> (double f, const soft_double& a) -> bool;
constexpr auto operator< (const soft_double& a, long double f) -> bool;
constexpr auto operator<=(const soft_double& a, long double f) -> bool;
constexpr auto operator==(const soft_double& a, long double f) -> bool;
constexpr auto operator!=(const soft_double& a, long double f) -> bool;
constexpr auto operator>=(const soft_double& a, long double f) -> bool;
constexpr auto operator> (const soft_double& a, long double f) -> bool;
constexpr auto operator< (long double f, const soft_double& a) -> bool;
constexpr auto operator<=(long double f, const soft_double& a) -> bool;
constexpr auto operator==(long double f, const soft_double& a) -> bool;
constexpr auto operator!=(long double f, const soft_double& a) -> bool;
constexpr auto operator>=(long double f, const soft_double& a) -> bool;
constexpr auto operator> (long double f, const soft_double& a) -> bool;
#if !defined(SOFT_DOUBLE_DISABLE_IOSTREAM)
template<typename char_type, typename traits_type> auto operator<<(std::basic_ostream<char_type, traits_type>& os, const soft_double& f) -> std::basic_ostream<char_type, traits_type>&;
template<typename char_type, typename traits_type> auto operator>>(std::basic_istream<char_type, traits_type>& is, soft_double& f) -> std::basic_istream<char_type, traits_type>&;
#endif // !WIDE_DECIMAL_DISABLE_IOSTREAM
constexpr auto (isnan) (soft_double x) -> bool;
constexpr auto (isinf) (soft_double x) -> bool;
constexpr auto (isfinite)(soft_double x) -> bool;
constexpr auto abs (soft_double x) -> soft_double;
constexpr auto fabs (soft_double x) -> soft_double;
constexpr auto fmod (soft_double v1, soft_double v2) -> soft_double;
constexpr auto frexp (soft_double x, int* expptr) -> soft_double;
constexpr auto ldexp (soft_double x, int expval) -> soft_double;
constexpr auto floor (soft_double x) -> soft_double;
constexpr auto ceil (soft_double x) -> soft_double;
constexpr auto sqrt (soft_double x) -> soft_double;
constexpr auto exp (soft_double x) -> soft_double;
constexpr auto log (soft_double x) -> soft_double;
constexpr auto pow (soft_double x, soft_double a) -> soft_double;
constexpr auto sin (soft_double x) -> soft_double;
constexpr auto cos (soft_double x) -> soft_double;
constexpr auto tan (soft_double x) -> soft_double;
constexpr auto asin (soft_double x) -> soft_double;
constexpr auto acos (soft_double x) -> soft_double;
constexpr auto atan (soft_double x) -> soft_double;
constexpr auto sinh (soft_double x) -> soft_double;
constexpr auto cosh (soft_double x) -> soft_double;
constexpr auto tanh (soft_double x) -> soft_double;
template<typename UnsignedIntegralType,
typename std::enable_if<( std::is_integral<UnsignedIntegralType>::value
&& std::is_unsigned<UnsignedIntegralType>::value)>::type const* = nullptr>
constexpr auto pow(soft_double x, UnsignedIntegralType u) -> soft_double;
template<typename SignedIntegralType,
typename std::enable_if<( std::is_integral<SignedIntegralType>::value
&& std::is_signed <SignedIntegralType>::value)>::type const* = nullptr>
constexpr auto pow(soft_double x, SignedIntegralType n) -> soft_double;
class soft_double final
{
public:
static_assert(sizeof(float) == static_cast<std::size_t>(UINT8_C(4)),
"Error: This template is designed for built-in float having 4 bytes");
using representation_type = std::uint64_t;
constexpr soft_double() noexcept = default;
template<typename UnsignedIntegralType,
typename std::enable_if<( std::is_integral<UnsignedIntegralType>::value
&& std::is_unsigned<UnsignedIntegralType>::value
&& (sizeof(UnsignedIntegralType) <= sizeof(std::uint32_t)))>::type const* = nullptr>
constexpr soft_double(UnsignedIntegralType u) noexcept : my_value(my_ui32_to_f64(static_cast<std::uint32_t>(u))) { } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
template<typename UnsignedIntegralType,
typename std::enable_if<( std::is_integral<UnsignedIntegralType>::value
&& std::is_unsigned<UnsignedIntegralType>::value
&& (!(sizeof(UnsignedIntegralType) <= sizeof(std::uint32_t))))>::type const* = nullptr>
constexpr soft_double(UnsignedIntegralType u) noexcept : my_value(my_ui64_to_f64(static_cast<std::uint64_t>(u))) { } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
template<typename SignedIntegralType,
typename std::enable_if<( std::is_integral<SignedIntegralType>::value
&& std::is_signed <SignedIntegralType>::value
&& (sizeof(SignedIntegralType) <= sizeof(int32_t)))>::type const* = nullptr>
constexpr soft_double(SignedIntegralType n) noexcept : my_value(my__i32_to_f64(static_cast<std::int32_t>(n))) { } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
template<typename SignedIntegralType,
typename std::enable_if<( std::is_integral<SignedIntegralType>::value
&& std::is_signed <SignedIntegralType>::value
&& (!(sizeof(SignedIntegralType) <= sizeof(int32_t))))>::type const* = nullptr>
constexpr soft_double(SignedIntegralType n) noexcept : my_value(my__i64_to_f64(static_cast<std::int64_t>(n))) { } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr soft_double(float f) noexcept // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
: my_value
(
((detail::expF32UI(detail::uz_type<float>(f).get_u()) == static_cast<std::int16_t>(INT8_C(0))) && (detail::fracF32UI(detail::uz_type<float>(f).get_u()) == static_cast<std::uint32_t>(UINT8_C(0)))) // NOLINT(cppcoreguidelines-pro-type-union-access)
? detail::packToF64UI
(
detail::signF32UI(detail::uz_type<float>(f).get_u()), // NOLINT(cppcoreguidelines-pro-type-union-access)
static_cast<int>(INT8_C(0)),
static_cast<int>(INT8_C(0))
)
: detail::packToF64UI
(
detail::signF32UI(detail::uz_type<float>(f).get_u()), // NOLINT(cppcoreguidelines-pro-type-union-access)
static_cast<std::int32_t>
(
static_cast<std::int32_t>(detail::expF32UI(detail::uz_type<float>(f).get_u())) // NOLINT(cppcoreguidelines-pro-type-union-access)
+ static_cast<std::int32_t>(INT16_C(0x380))
),
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>
(
detail::fracF32UI(detail::uz_type<float>(f).get_u()) // NOLINT(cppcoreguidelines-pro-type-union-access)
) << static_cast<unsigned>(UINT8_C(29))
)
)
) { }
constexpr soft_double(double d) noexcept // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
: my_value(detail::uz_type<double>(d).get_u()) { } // NOLINT(cppcoreguidelines-pro-type-union-access)
constexpr soft_double(long double ld) noexcept // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
: my_value(detail::uz_type<double>(static_cast<double>(ld)).get_u()) { } // NOLINT(cppcoreguidelines-pro-type-union-access)
constexpr soft_double(const soft_double& other) noexcept : my_value(other.my_value) { }; // NOLINT(hicpp-use-equals-default,modernize-use-equals-default)
constexpr soft_double(soft_double&& other) noexcept
: my_value(other.my_value) { }
explicit constexpr soft_double(std::uint64_t n, detail::nothing&&) noexcept // NOLINT(hicpp-named-parameter,readability-named-parameter)
: my_value(static_cast<std::uint64_t>(n)) { }
constexpr auto operator=(const soft_double& other) noexcept -> soft_double&
{
if(this != &other)
{
my_value = other.my_value;
}
return *this;
}
constexpr auto operator=(soft_double&& other) noexcept -> soft_double&
{
my_value = other.my_value;
return *this;
}
~soft_double() = default;
SOFT_DOUBLE_NODISCARD constexpr auto representation() const -> representation_type { return my_value; }
SOFT_DOUBLE_NODISCARD constexpr auto crepresentation() const -> representation_type { return my_value; }
static constexpr auto get_rep(const soft_double& a) -> representation_type { return a.crepresentation(); }
constexpr operator signed char () const { return static_cast<signed char> (f64_to__i32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator signed short () const { return static_cast<signed short> (f64_to__i32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
constexpr operator signed int () const { return static_cast<signed int> (f64_to__i32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator signed long () const { return static_cast<signed long> (f64_to__i64(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
constexpr operator signed long long() const { return static_cast<signed long long>(f64_to__i64(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
constexpr operator unsigned char () const { return static_cast<unsigned char> (f64_to_ui32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator unsigned short () const { return static_cast<unsigned short> (f64_to_ui32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
constexpr operator unsigned int () const { return static_cast<unsigned int> (f64_to_ui32(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator unsigned long () const { return static_cast<unsigned long> (f64_to_ui64(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
constexpr operator unsigned long long() const { return static_cast<unsigned long long>(f64_to_ui64(my_value)); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions,google-runtime-int)
private:
template<typename FloatingPointType>
SOFT_DOUBLE_NODISCARD constexpr auto to_float() const -> typename std::enable_if<( (sizeof(FloatingPointType) == 4)
&& std::numeric_limits<FloatingPointType>::is_iec559), FloatingPointType>::type
{
return f64_to_f32(my_value);
}
template<typename FloatingPointType>
SOFT_DOUBLE_NODISCARD constexpr auto to_float() const -> typename std::enable_if<( (sizeof(FloatingPointType) == static_cast<std::size_t>(UINT8_C(8)))
&& std::numeric_limits<FloatingPointType>::is_iec559), FloatingPointType>::type
{
return static_cast<FloatingPointType>(*static_cast<const volatile FloatingPointType*>(static_cast<const volatile void*>(this))); // NOLINT(bugprone-casting-through-void)
}
public:
constexpr operator float () const noexcept { return to_float<float>(); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator double () const noexcept { return to_float<double>(); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr operator long double() const noexcept { return static_cast<long double>(to_float<double>()); } // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
constexpr auto operator+=(const soft_double& other) -> soft_double& { my_value = f64_add(my_value, other.my_value); return *this; }
constexpr auto operator-=(const soft_double& other) -> soft_double& { my_value = f64_sub(my_value, other.my_value); return *this; }
constexpr auto operator*=(const soft_double& other) -> soft_double& { my_value = f64_mul(my_value, other.my_value); return *this; }
constexpr auto operator/=(const soft_double& other) -> soft_double& { my_value = f64_div(my_value, other.my_value); return *this; }
// Operators pre-increment and pre-decrement.
constexpr auto operator++() -> soft_double& { return *this += my_value_one(); }
constexpr auto operator--() -> soft_double& { return *this -= my_value_one(); }
// Operators post-increment and post-decrement.
constexpr auto operator++(int) -> soft_double { const soft_double w(*this); static_cast<void>(++(*this)); return w; } // NOLINT(performance-no-automatic-move)
constexpr auto operator--(int) -> soft_double { const soft_double w(*this); static_cast<void>(--(*this)); return w; } // NOLINT(performance-no-automatic-move)
constexpr auto operator+() const -> const soft_double& { return *this; }
constexpr auto operator-() const -> soft_double { return soft_double { my_value ^ static_cast<std::uint64_t>(static_cast<std::uint64_t>(UINT8_C(1)) << static_cast<unsigned>(UINT8_C(63))), detail::nothing{} }; }
static constexpr auto my_value_zero () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0)), detail::nothing{} }; }
static constexpr auto my_value_one () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x3FF0000000000000)), detail::nothing{} }; }
static constexpr auto my_value_two () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x4000000000000000)), detail::nothing{} }; }
static constexpr auto my_value_half () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x3FE0000000000000)), detail::nothing{} }; }
static constexpr auto my_value_pi () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(4614256656552045848)), detail::nothing{} }; }
static constexpr auto my_value_pi_half() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x3FF921FB54442D18)), detail::nothing{} }; }
static constexpr auto my_value_ln2 () -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(4604418534313441775)), detail::nothing{} }; }
static constexpr auto my_value_min() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(4503599627370496)), detail::nothing{} }; }
static constexpr auto my_value_max() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(9218868437227405311)), detail::nothing{} }; }
static constexpr auto my_value_lowest() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(18442240474082181119)),detail::nothing{} }; }
static constexpr auto my_value_epsilon() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(4372995238176751616)), detail::nothing{} }; }
static constexpr auto my_value_round_error() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x3FE0000000000000)), detail::nothing{} }; }
static constexpr auto my_value_denorm_min() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(1)), detail::nothing{} }; }
static constexpr auto my_value_infinity() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x7FF0000000000000)), detail::nothing{} }; }
static constexpr auto my_value_quiet_NaN() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0xFFF8000000000000)), detail::nothing{} }; }
static constexpr auto my_value_signaling_NaN() -> soft_double { return soft_double { static_cast<std::uint64_t>(UINT64_C(0x7FF8000000000000)), detail::nothing{} }; }
private:
representation_type my_value { };
static constexpr auto my_le(const soft_double& a, const soft_double& b) -> bool
{
return (detail::signF64UI(a.my_value) != detail::signF64UI(b.my_value))
? (detail::signF64UI(a.my_value) || (static_cast<std::uint64_t>(a.my_value | b.my_value) & static_cast<std::uint64_t>(UINT64_C(0x7FFFFFFFFFFFFFFF))) == static_cast<std::uint64_t>(UINT8_C(0)))
: (a.my_value == b.my_value) || (( static_cast<unsigned>(detail::signF64UI(a.my_value) ? static_cast<unsigned>(UINT8_C(1)) : static_cast<unsigned>(UINT8_C(0)))
^ static_cast<unsigned>((a.my_value < b.my_value) ? static_cast<unsigned>(UINT8_C(1)) : static_cast<unsigned>(UINT8_C(0)))) != static_cast<unsigned>(UINT8_C(0)));
}
static constexpr auto my_lt(const soft_double& a, const soft_double& b) -> bool
{
return (detail::signF64UI(a.my_value) != detail::signF64UI(b.my_value))
? (detail::signF64UI(a.my_value) && (static_cast<std::uint64_t>(a.my_value | b.my_value) & static_cast<std::uint64_t>(UINT64_C(0x7FFFFFFFFFFFFFFF))) != static_cast<std::uint64_t>(UINT8_C(0)))
: (a.my_value != b.my_value) && (( static_cast<unsigned>(detail::signF64UI(a.my_value) ? static_cast<unsigned>(UINT8_C(1)) : static_cast<unsigned>(UINT8_C(0)))
^ static_cast<unsigned>((a.my_value < b.my_value) ? static_cast<unsigned>(UINT8_C(1)) : static_cast<unsigned>(UINT8_C(0)))) != static_cast<unsigned>(UINT8_C(0)));
}
static constexpr auto sign_ab(const std::uint64_t a, const std::uint64_t b) -> bool
{
const auto signA = detail::signF64UI(a);
const auto signB = detail::signF64UI(b);
return
static_cast<std::uint_fast8_t>
(
static_cast<std::uint_fast8_t>(signA ? static_cast<std::uint_fast8_t>(UINT8_C(1)) : static_cast<std::uint_fast8_t>(UINT8_C(0)))
^ static_cast<std::uint_fast8_t>(signB ? static_cast<std::uint_fast8_t>(UINT8_C(1)) : static_cast<std::uint_fast8_t>(UINT8_C(0)))
) != static_cast<std::uint_fast8_t>(UINT8_C(0));
}
static constexpr auto f64_add(const std::uint64_t a, const std::uint64_t b) -> std::uint64_t
{
const auto signA = detail::signF64UI(a);
return ((signA == detail::signF64UI(b)) ? softfloat_addMagsF64(a, b, signA)
: softfloat_subMagsF64(a, b, signA));
}
static constexpr auto f64_sub(const std::uint64_t a, const std::uint64_t b) -> std::uint64_t
{
const auto signA = detail::signF64UI(a);
return ((signA == detail::signF64UI(b)) ? softfloat_subMagsF64(a, b, signA)
: softfloat_addMagsF64(a, b, signA));
}
static constexpr auto f64_mul(const std::uint64_t a, const std::uint64_t b) -> std::uint64_t
{
const auto expA = detail::expF64UI (a);
const auto expB = detail::expF64UI (b);
auto sigA = detail::fracF64UI(a);
auto sigB = detail::fracF64UI(b);
const auto signZ = sign_ab(a, b);
auto result = std::uint64_t { };
const auto a_is_zero = ( (expA == static_cast<std::int16_t> ( INT8_C(0)))
&& (sigA == static_cast<std::uint64_t>(UINT8_C(0))));
if( a_is_zero
|| ( (expB == static_cast<std::int16_t> ( INT8_C(0)))
&& (sigB == static_cast<std::uint64_t>(UINT8_C(0)))))
{
result = detail::packToF64UI(signZ, static_cast<int>(INT8_C(0)), static_cast<int>(INT8_C(0)));
}
else
{
auto expZ =
static_cast<std::int16_t>
(
static_cast<std::int16_t>(expA + expB)
- static_cast<std::int16_t>(INT16_C(0x3FF))
);
sigA =
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>
(
sigA | static_cast<std::uint64_t>(UINT64_C(0x0010000000000000))
) << static_cast<unsigned>(UINT8_C(10))
);
sigB =
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>
(
sigB | static_cast<std::uint64_t>(UINT64_C(0x0010000000000000))
) << static_cast<unsigned>(UINT8_C(11))
);
// Compute the 128-bit product of sigA and sigB.
const auto a32 = static_cast<std::uint32_t>(sigA >> static_cast<unsigned>(UINT8_C(32)));
const auto a0 = static_cast<std::uint32_t>(sigA);
const auto b32 = static_cast<std::uint32_t>(sigB >> static_cast<unsigned>(UINT8_C(32)));
const auto b0 = static_cast<std::uint32_t>(sigB);
const auto mid1 = static_cast<std::uint64_t>( (static_cast<std::uint64_t>(a32)) * b0);
auto mid = static_cast<std::uint64_t>(mid1 + static_cast<std::uint64_t>((static_cast<std::uint64_t>(b32)) * a0));
auto sig128Z =
detail::uint128_compound
{
static_cast<std::uint64_t>(static_cast<std::uint64_t>(a0) * b0),
static_cast<std::uint64_t>
(
static_cast<std::uint64_t>(static_cast<std::uint64_t>(a32) * b32)
+ static_cast<std::uint32_t>(mid >> static_cast<unsigned>(UINT8_C(32)))
)
};
if(mid < mid1)
{
sig128Z.v1 =
static_cast<std::uint64_t>
(
sig128Z.v1
+ static_cast<std::uint64_t>(UINT64_C(0x100000000))
);
}
mid = static_cast<std::uint64_t>(mid << static_cast<unsigned>(UINT8_C(32)));
sig128Z.v0 = static_cast<std::uint64_t>(sig128Z.v0 + mid);
sig128Z.v1 =
static_cast<std::uint64_t>
(
sig128Z.v1
+ static_cast<std::uint_fast8_t>
(
(sig128Z.v0 < mid)
? static_cast<std::uint_fast8_t>(UINT8_C(1))
: static_cast<std::uint_fast8_t>(UINT8_C(0))
)
);
if(sig128Z.v0 != static_cast<std::uint64_t>(UINT8_C(0)))
{
sig128Z.v1 =
static_cast<std::uint64_t>
(
sig128Z.v1
| static_cast<std::uint_fast8_t>(UINT8_C(1))
);
}
if(sig128Z.v1 < static_cast<std::uint64_t>(UINT64_C(0x4000000000000000)))
{
--expZ;
sig128Z.v1 <<= static_cast<unsigned>(UINT8_C(1));
}
result = softfloat_roundPackToF64(signZ, expZ, sig128Z.v1);
}
return result;
}
static constexpr auto f64_div(const std::uint64_t a, const std::uint64_t b) -> std::uint64_t
{
const auto expA = detail::expF64UI(a);
auto sigA = detail::fracF64UI(a);
const auto signZ = sign_ab(a, b);
auto result = std::uint64_t { };
const auto a_is_zero = ( (expA == static_cast<std::int16_t> ( INT8_C(0)))
&& (sigA == static_cast<std::uint64_t>(UINT8_C(0))));
if(a_is_zero)
{
result = detail::packToF64UI(signZ, static_cast<int>(INT8_C(0)), static_cast<int>(INT8_C(0)));
}
else
{
auto expZ =
static_cast<std::int16_t>
(
static_cast<std::int16_t>(expA - detail::expF64UI(b))
+ static_cast<std::int16_t>(INT16_C(0x3FE))
);
sigA =
static_cast<std::uint64_t>
(
sigA
| static_cast<std::uint64_t>(UINT64_C(0x0010000000000000))
);
auto sigB =
static_cast<std::uint64_t>
(
detail::fracF64UI(b)
| static_cast<std::uint64_t>(UINT64_C(0x0010000000000000))
);
if(sigA < sigB)
{
--expZ;
sigA = static_cast<std::uint64_t>(sigA << static_cast<unsigned>(UINT8_C(11)));
}
else
{
sigA = static_cast<std::uint64_t>(sigA << static_cast<unsigned>(UINT8_C(10)));
}
sigB <<= static_cast<unsigned>(UINT8_C(11));
const auto recip32 =
static_cast<std::uint32_t>
(
detail::softfloat_approxRecip32_1(static_cast<std::uint32_t>(sigB >> static_cast<unsigned>(UINT8_C(32))))
- static_cast<unsigned>(UINT8_C(2))