| // SPDX-FileCopyrightText: 2020-2024 Junekey Jeon |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // SPDX-License-Identifier: BSL-1.0 |
| // SPDX-License-Identifier: MIT |
| |
| // This file is an adjusted copy of https://github.com/jk-jeon/dragonbox |
| // Junekey Jeon agreed to license this file under MIT license explicitly for |
| // usage in yaml-cpp. |
| // |
| // Changes to the original dragonbox library: |
| // - Added additional license information and information at top |
| // - Wrapped the 'jkj' namespace in an additional 'YAML' namespace |
| |
| #ifndef JKJ_HEADER_DRAGONBOX |
| #define JKJ_HEADER_DRAGONBOX |
| |
| // Attribute for storing static data into a dedicated place, e.g. flash memory. Every ODR-used |
| // static data declaration will be decorated with this macro. The users may define this macro, |
| // before including the library headers, into whatever they want. |
| #ifndef JKJ_STATIC_DATA_SECTION |
| #define JKJ_STATIC_DATA_SECTION |
| #else |
| #define JKJ_STATIC_DATA_SECTION_DEFINED 1 |
| #endif |
| |
| // To use the library with toolchains without standard C++ headers, the users may define this macro |
| // into their custom namespace which contains the defintions of all the standard C++ library |
| // features used in this header. (The list can be found below.) |
| #ifndef JKJ_STD_REPLACEMENT_NAMESPACE |
| #define JKJ_STD_REPLACEMENT_NAMESPACE std |
| #include <cassert> |
| #include <cstdint> |
| #include <cstring> |
| #include <limits> |
| #include <type_traits> |
| |
| #ifdef __has_include |
| #if __has_include(<version>) |
| #include <version> |
| #endif |
| #endif |
| #else |
| #define JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED 1 |
| #endif |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Language feature detections. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| // C++14 constexpr |
| #if defined(__cpp_constexpr) && __cpp_constexpr >= 201304L |
| #define JKJ_HAS_CONSTEXPR14 1 |
| #elif __cplusplus >= 201402L |
| #define JKJ_HAS_CONSTEXPR14 1 |
| #elif defined(_MSC_VER) && _MSC_VER >= 1910 && _MSVC_LANG >= 201402L |
| #define JKJ_HAS_CONSTEXPR14 1 |
| #else |
| #define JKJ_HAS_CONSTEXPR14 0 |
| #endif |
| |
| #if JKJ_HAS_CONSTEXPR14 |
| #define JKJ_CONSTEXPR14 constexpr |
| #else |
| #define JKJ_CONSTEXPR14 |
| #endif |
| |
| // C++17 constexpr lambdas |
| #if defined(__cpp_constexpr) && __cpp_constexpr >= 201603L |
| #define JKJ_HAS_CONSTEXPR17 1 |
| #elif __cplusplus >= 201703L |
| #define JKJ_HAS_CONSTEXPR17 1 |
| #elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L |
| #define JKJ_HAS_CONSTEXPR17 1 |
| #else |
| #define JKJ_HAS_CONSTEXPR17 0 |
| #endif |
| |
| // C++17 inline variables |
| #if defined(__cpp_inline_variables) && __cpp_inline_variables >= 201606L |
| #define JKJ_HAS_INLINE_VARIABLE 1 |
| #elif __cplusplus >= 201703L |
| #define JKJ_HAS_INLINE_VARIABLE 1 |
| #elif defined(_MSC_VER) && _MSC_VER >= 1912 && _MSVC_LANG >= 201703L |
| #define JKJ_HAS_INLINE_VARIABLE 1 |
| #else |
| #define JKJ_HAS_INLINE_VARIABLE 0 |
| #endif |
| |
| #if JKJ_HAS_INLINE_VARIABLE |
| #define JKJ_INLINE_VARIABLE inline constexpr |
| #else |
| #define JKJ_INLINE_VARIABLE static constexpr |
| #endif |
| |
| // C++17 if constexpr |
| #if defined(__cpp_if_constexpr) && __cpp_if_constexpr >= 201606L |
| #define JKJ_HAS_IF_CONSTEXPR 1 |
| #elif __cplusplus >= 201703L |
| #define JKJ_HAS_IF_CONSTEXPR 1 |
| #elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L |
| #define JKJ_HAS_IF_CONSTEXPR 1 |
| #else |
| #define JKJ_HAS_IF_CONSTEXPR 0 |
| #endif |
| |
| #if JKJ_HAS_IF_CONSTEXPR |
| #define JKJ_IF_CONSTEXPR if constexpr |
| #else |
| #define JKJ_IF_CONSTEXPR if |
| #endif |
| |
| // C++20 std::bit_cast |
| #if JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED |
| #if JKJ_STD_REPLACEMENT_HAS_BIT_CAST |
| #define JKJ_HAS_BIT_CAST 1 |
| #else |
| #define JKJ_HAS_BIT_CAST 0 |
| #endif |
| #elif defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L |
| #include <bit> |
| #define JKJ_HAS_BIT_CAST 1 |
| #else |
| #define JKJ_HAS_BIT_CAST 0 |
| #endif |
| |
| // C++23 if consteval or C++20 std::is_constant_evaluated |
| #if defined(__cpp_if_consteval) && __cpp_is_consteval >= 202106L |
| #define JKJ_IF_CONSTEVAL if consteval |
| #define JKJ_IF_NOT_CONSTEVAL if !consteval |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 1 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 0 |
| #elif JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED |
| #if JKJ_STD_REPLACEMENT_HAS_IS_CONSTANT_EVALUATED |
| #define JKJ_IF_CONSTEVAL if (stdr::is_constant_evaluated()) |
| #define JKJ_IF_NOT_CONSTEVAL if (!stdr::is_constant_evaluated()) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 1 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 1 |
| #elif JKJ_HAS_IF_CONSTEXPR |
| #define JKJ_IF_CONSTEVAL if constexpr (false) |
| #define JKJ_IF_NOT_CONSTEVAL if constexpr (true) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 0 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 0 |
| #else |
| #define JKJ_IF_CONSTEVAL if (false) |
| #define JKJ_IF_NOT_CONSTEVAL if (true) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 0 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 0 |
| #endif |
| #else |
| #if defined(__cpp_lib_is_constant_evaluated) && __cpp_lib_is_constant_evaluated >= 201811L |
| #define JKJ_IF_CONSTEVAL if (stdr::is_constant_evaluated()) |
| #define JKJ_IF_NOT_CONSTEVAL if (!stdr::is_constant_evaluated()) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 1 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 1 |
| #elif JKJ_HAS_IF_CONSTEXPR |
| #define JKJ_IF_CONSTEVAL if constexpr (false) |
| #define JKJ_IF_NOT_CONSTEVAL if constexpr (true) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 0 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 0 |
| #else |
| #define JKJ_IF_CONSTEVAL if (false) |
| #define JKJ_IF_NOT_CONSTEVAL if (true) |
| #define JKJ_CAN_BRANCH_ON_CONSTEVAL 0 |
| #define JKJ_USE_IS_CONSTANT_EVALUATED 0 |
| #endif |
| #endif |
| |
| #if JKJ_CAN_BRANCH_ON_CONSTEVAL && JKJ_HAS_BIT_CAST |
| #define JKJ_CONSTEXPR20 constexpr |
| #else |
| #define JKJ_CONSTEXPR20 |
| #endif |
| |
| // Suppress additional buffer overrun check. |
| // I have no idea why MSVC thinks some functions here are vulnerable to the buffer overrun |
| // attacks. No, they aren't. |
| #if defined(__GNUC__) || defined(__clang__) |
| #define JKJ_SAFEBUFFERS |
| #define JKJ_FORCEINLINE inline __attribute__((always_inline)) |
| #elif defined(_MSC_VER) |
| #define JKJ_SAFEBUFFERS __declspec(safebuffers) |
| #define JKJ_FORCEINLINE __forceinline |
| #else |
| #define JKJ_SAFEBUFFERS |
| #define JKJ_FORCEINLINE inline |
| #endif |
| |
| #if defined(__has_builtin) |
| #define JKJ_HAS_BUILTIN(x) __has_builtin(x) |
| #else |
| #define JKJ_HAS_BUILTIN(x) false |
| #endif |
| |
| #if defined(_MSC_VER) |
| #include <intrin.h> |
| #elif defined(__INTEL_COMPILER) |
| #include <immintrin.h> |
| #endif |
| |
| namespace YAML { |
| namespace jkj { |
| namespace dragonbox { |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // The Compatibility layer for toolchains without standard C++ headers. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| namespace detail { |
| namespace stdr { |
| // <bit> |
| #if JKJ_HAS_BIT_CAST |
| using JKJ_STD_REPLACEMENT_NAMESPACE::bit_cast; |
| #endif |
| |
| // <cassert> |
| // We need assert() macro, but it is not namespaced anyway, so nothing to do here. |
| |
| // <cstdint> |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_least8_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_least16_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_least32_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_fast8_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_fast16_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::int_fast32_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least8_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least16_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least32_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least64_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast8_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast16_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast32_t; |
| // We need INT32_C, UINT32_C and UINT64_C macros too, but again there is nothing to do |
| // here. |
| |
| // <cstring> |
| using JKJ_STD_REPLACEMENT_NAMESPACE::size_t; |
| using JKJ_STD_REPLACEMENT_NAMESPACE::memcpy; |
| |
| // <limits> |
| template <class T> |
| using numeric_limits = JKJ_STD_REPLACEMENT_NAMESPACE::numeric_limits<T>; |
| |
| // <type_traits> |
| template <bool cond, class T = void> |
| using enable_if = JKJ_STD_REPLACEMENT_NAMESPACE::enable_if<cond, T>; |
| template <class T> |
| using add_rvalue_reference = JKJ_STD_REPLACEMENT_NAMESPACE::add_rvalue_reference<T>; |
| template <bool cond, class T_true, class T_false> |
| using conditional = JKJ_STD_REPLACEMENT_NAMESPACE::conditional<cond, T_true, T_false>; |
| #if JKJ_USE_IS_CONSTANT_EVALUATED |
| using JKJ_STD_REPLACEMENT_NAMESPACE::is_constant_evaluated; |
| #endif |
| template <class T1, class T2> |
| using is_same = JKJ_STD_REPLACEMENT_NAMESPACE::is_same<T1, T2>; |
| #if !JKJ_HAS_BIT_CAST |
| template <class T> |
| using is_trivially_copyable = JKJ_STD_REPLACEMENT_NAMESPACE::is_trivially_copyable<T>; |
| #endif |
| template <class T> |
| using is_integral = JKJ_STD_REPLACEMENT_NAMESPACE::is_integral<T>; |
| template <class T> |
| using is_signed = JKJ_STD_REPLACEMENT_NAMESPACE::is_signed<T>; |
| template <class T> |
| using is_unsigned = JKJ_STD_REPLACEMENT_NAMESPACE::is_unsigned<T>; |
| } |
| } |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Some general utilities for C++11-compatibility. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| namespace detail { |
| #if !JKJ_HAS_CONSTEXPR17 |
| template <stdr::size_t... indices> |
| struct index_sequence {}; |
| |
| template <stdr::size_t current, stdr::size_t total, class Dummy, stdr::size_t... indices> |
| struct make_index_sequence_impl { |
| using type = typename make_index_sequence_impl<current + 1, total, Dummy, indices..., |
| current>::type; |
| }; |
| |
| template <stdr::size_t total, class Dummy, stdr::size_t... indices> |
| struct make_index_sequence_impl<total, total, Dummy, indices...> { |
| using type = index_sequence<indices...>; |
| }; |
| |
| template <stdr::size_t N> |
| using make_index_sequence = typename make_index_sequence_impl<0, N, void>::type; |
| #endif |
| |
| // Available since C++11, but including <utility> just for this is an overkill. |
| template <class T> |
| typename stdr::add_rvalue_reference<T>::type declval() noexcept; |
| |
| // Similarly, including <array> is an overkill. |
| template <class T, stdr::size_t N> |
| struct array { |
| T data_[N]; |
| constexpr T operator[](stdr::size_t idx) const noexcept { return data_[idx]; } |
| JKJ_CONSTEXPR14 T& operator[](stdr::size_t idx) noexcept { return data_[idx]; } |
| }; |
| } |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Some basic features for encoding/decoding IEEE-754 formats. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| namespace detail { |
| template <class T> |
| struct physical_bits { |
| static constexpr stdr::size_t value = |
| sizeof(T) * stdr::numeric_limits<unsigned char>::digits; |
| }; |
| template <class T> |
| struct value_bits { |
| static constexpr stdr::size_t value = stdr::numeric_limits< |
| typename stdr::enable_if<stdr::is_integral<T>::value, T>::type>::digits; |
| }; |
| |
| template <typename To, typename From> |
| JKJ_CONSTEXPR20 To bit_cast(const From& from) { |
| #if JKJ_HAS_BIT_CAST |
| return stdr::bit_cast<To>(from); |
| #else |
| static_assert(sizeof(From) == sizeof(To), ""); |
| static_assert(stdr::is_trivially_copyable<To>::value, ""); |
| static_assert(stdr::is_trivially_copyable<From>::value, ""); |
| To to; |
| stdr::memcpy(&to, &from, sizeof(To)); |
| return to; |
| #endif |
| } |
| } |
| |
| // These classes expose encoding specs of IEEE-754-like floating-point formats. |
| // Currently available formats are IEEE-754 binary32 & IEEE-754 binary64. |
| |
| struct ieee754_binary32 { |
| static constexpr int total_bits = 32; |
| static constexpr int significand_bits = 23; |
| static constexpr int exponent_bits = 8; |
| static constexpr int min_exponent = -126; |
| static constexpr int max_exponent = 127; |
| static constexpr int exponent_bias = -127; |
| static constexpr int decimal_significand_digits = 9; |
| static constexpr int decimal_exponent_digits = 2; |
| }; |
| struct ieee754_binary64 { |
| static constexpr int total_bits = 64; |
| static constexpr int significand_bits = 52; |
| static constexpr int exponent_bits = 11; |
| static constexpr int min_exponent = -1022; |
| static constexpr int max_exponent = 1023; |
| static constexpr int exponent_bias = -1023; |
| static constexpr int decimal_significand_digits = 17; |
| static constexpr int decimal_exponent_digits = 3; |
| }; |
| |
| // A floating-point format traits class defines ways to interpret a bit pattern of given size as |
| // an encoding of floating-point number. This is an implementation of such a traits class, |
| // supporting ways to interpret IEEE-754 binary floating-point numbers. |
| template <class Format, class CarrierUInt, class ExponentInt = int> |
| struct ieee754_binary_traits { |
| // CarrierUInt needs to have enough size to hold the entire contents of floating-point |
| // numbers. The actual bits are assumed to be aligned to the LSB, and every other bits are |
| // assumed to be zeroed. |
| static_assert(detail::value_bits<CarrierUInt>::value >= Format::total_bits, |
| "jkj::dragonbox: insufficient number of bits"); |
| static_assert(detail::stdr::is_unsigned<CarrierUInt>::value, ""); |
| |
| // ExponentUInt needs to be large enough to hold (unsigned) exponent bits as well as the |
| // (signed) actual exponent. |
| // TODO: static overflow guard against intermediate computations. |
| static_assert(detail::value_bits<ExponentInt>::value >= Format::exponent_bits + 1, |
| "jkj::dragonbox: insufficient number of bits"); |
| static_assert(detail::stdr::is_signed<ExponentInt>::value, ""); |
| |
| using format = Format; |
| using carrier_uint = CarrierUInt; |
| static constexpr int carrier_bits = int(detail::value_bits<carrier_uint>::value); |
| using exponent_int = ExponentInt; |
| |
| // Extract exponent bits from a bit pattern. |
| // The result must be aligned to the LSB so that there is no additional zero paddings |
| // on the right. This function does not do bias adjustment. |
| static constexpr exponent_int extract_exponent_bits(carrier_uint u) noexcept { |
| return exponent_int((u >> format::significand_bits) & |
| ((exponent_int(1) << format::exponent_bits) - 1)); |
| } |
| |
| // Extract significand bits from a bit pattern. |
| // The result must be aligned to the LSB so that there is no additional zero paddings |
| // on the right. The result does not contain the implicit bit. |
| static constexpr carrier_uint extract_significand_bits(carrier_uint u) noexcept { |
| return carrier_uint(u & ((carrier_uint(1) << format::significand_bits) - 1u)); |
| } |
| |
| // Remove the exponent bits and extract significand bits together with the sign bit. |
| static constexpr carrier_uint remove_exponent_bits(carrier_uint u) noexcept { |
| return carrier_uint(u & ~(((carrier_uint(1) << format::exponent_bits) - 1u) |
| << format::significand_bits)); |
| } |
| |
| // Shift the obtained signed significand bits to the left by 1 to remove the sign bit. |
| static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept { |
| return carrier_uint((carrier_uint(u) << 1) & |
| ((((carrier_uint(1) << (Format::total_bits - 1)) - 1u) << 1) | 1u)); |
| } |
| |
| // Obtain the actual value of the binary exponent from the extracted exponent bits. |
| static constexpr exponent_int binary_exponent(exponent_int exponent_bits) noexcept { |
| return exponent_int(exponent_bits == 0 ? format::min_exponent |
| : exponent_bits + format::exponent_bias); |
| } |
| |
| // Obtain the actual value of the binary significand from the extracted significand bits |
| // and exponent bits. |
| static constexpr carrier_uint binary_significand(carrier_uint significand_bits, |
| exponent_int exponent_bits) noexcept { |
| return carrier_uint( |
| exponent_bits == 0 |
| ? significand_bits |
| : (significand_bits | (carrier_uint(1) << format::significand_bits))); |
| } |
| |
| /* Various boolean observer functions */ |
| |
| static constexpr bool is_nonzero(carrier_uint u) noexcept { |
| return (u & ((carrier_uint(1) << (format::significand_bits + format::exponent_bits)) - |
| 1u)) != 0; |
| } |
| static constexpr bool is_positive(carrier_uint u) noexcept { |
| return u < (carrier_uint(1) << (format::significand_bits + format::exponent_bits)); |
| } |
| static constexpr bool is_negative(carrier_uint u) noexcept { return !is_positive(u); } |
| static constexpr bool is_finite(exponent_int exponent_bits) noexcept { |
| return exponent_bits != ((exponent_int(1) << format::exponent_bits) - 1); |
| } |
| static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept { |
| return ((u << 1) & |
| ((((carrier_uint(1) << (Format::total_bits - 1)) - 1u) << 1) | 1u)) == 0; |
| } |
| static constexpr bool has_even_significand_bits(carrier_uint u) noexcept { |
| return u % 2 == 0; |
| } |
| }; |
| |
| // Convert between bit patterns stored in carrier_uint and instances of an actual |
| // floating-point type. Depending on format and carrier_uint, this operation might not |
| // be possible for some specific bit patterns. However, the contract is that u always |
| // denotes a valid bit pattern, so the functions here are assumed to be noexcept. |
| // Users might specialize this class to change the behavior for certain types. |
| // The default provided by the library is to treat the given floating-point type Float as either |
| // IEEE-754 binary32 or IEEE-754 binary64, depending on the bitwise size of Float. |
| template <class Float> |
| struct default_float_bit_carrier_conversion_traits { |
| // Guards against types that have different internal representations than IEEE-754 |
| // binary32/64. I don't know if there is a truly reliable way of detecting IEEE-754 binary |
| // formats. I just did my best here. Note that in some cases |
| // numeric_limits<Float>::is_iec559 may report false even if the internal representation is |
| // IEEE-754 compatible. In such a case, the user can specialize this traits template and |
| // remove this static sanity check in order to make Dragonbox work for Float. |
| static_assert(detail::stdr::numeric_limits<Float>::is_iec559 && |
| detail::stdr::numeric_limits<Float>::radix == 2 && |
| (detail::physical_bits<Float>::value == 32 || |
| detail::physical_bits<Float>::value == 64), |
| "jkj::dragonbox: Float may not be of IEEE-754 binary32/binary64"); |
| |
| // Specifies the unsigned integer type to hold bitwise value of Float. |
| using carrier_uint = |
| typename detail::stdr::conditional<detail::physical_bits<Float>::value == 32, |
| detail::stdr::uint_least32_t, |
| detail::stdr::uint_least64_t>::type; |
| |
| // Specifies the floating-point format. |
| using format = typename detail::stdr::conditional<detail::physical_bits<Float>::value == 32, |
| ieee754_binary32, ieee754_binary64>::type; |
| |
| // Converts the floating-point type into the bit-carrier unsigned integer type. |
| static JKJ_CONSTEXPR20 carrier_uint float_to_carrier(Float x) noexcept { |
| return detail::bit_cast<carrier_uint>(x); |
| } |
| |
| // Converts the bit-carrier unsigned integer type into the floating-point type. |
| static JKJ_CONSTEXPR20 Float carrier_to_float(carrier_uint x) noexcept { |
| return detail::bit_cast<Float>(x); |
| } |
| }; |
| |
| // Convenient wrappers for floating-point traits classes. |
| // In order to reduce the argument passing overhead, these classes should be as simple as |
| // possible (e.g., no inheritance, no private non-static data member, etc.; this is an |
| // unfortunate fact about common ABI convention). |
| |
| template <class FormatTraits> |
| struct signed_significand_bits { |
| using format_traits = FormatTraits; |
| using carrier_uint = typename format_traits::carrier_uint; |
| |
| carrier_uint u; |
| |
| signed_significand_bits() = default; |
| constexpr explicit signed_significand_bits(carrier_uint bit_pattern) noexcept |
| : u{bit_pattern} {} |
| |
| // Shift the obtained signed significand bits to the left by 1 to remove the sign bit. |
| constexpr carrier_uint remove_sign_bit_and_shift() const noexcept { |
| return format_traits::remove_sign_bit_and_shift(u); |
| } |
| |
| constexpr bool is_positive() const noexcept { return format_traits::is_positive(u); } |
| constexpr bool is_negative() const noexcept { return format_traits::is_negative(u); } |
| constexpr bool has_all_zero_significand_bits() const noexcept { |
| return format_traits::has_all_zero_significand_bits(u); |
| } |
| constexpr bool has_even_significand_bits() const noexcept { |
| return format_traits::has_even_significand_bits(u); |
| } |
| }; |
| |
| template <class FormatTraits> |
| struct float_bits { |
| using format_traits = FormatTraits; |
| using carrier_uint = typename format_traits::carrier_uint; |
| using exponent_int = typename format_traits::exponent_int; |
| |
| carrier_uint u; |
| |
| float_bits() = default; |
| constexpr explicit float_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {} |
| |
| // Extract exponent bits from a bit pattern. |
| // The result must be aligned to the LSB so that there is no additional zero paddings |
| // on the right. This function does not do bias adjustment. |
| constexpr exponent_int extract_exponent_bits() const noexcept { |
| return format_traits::extract_exponent_bits(u); |
| } |
| |
| // Extract significand bits from a bit pattern. |
| // The result must be aligned to the LSB so that there is no additional zero paddings |
| // on the right. The result does not contain the implicit bit. |
| constexpr carrier_uint extract_significand_bits() const noexcept { |
| return format_traits::extract_significand_bits(u); |
| } |
| |
| // Remove the exponent bits and extract significand bits together with the sign bit. |
| constexpr signed_significand_bits<format_traits> remove_exponent_bits() const noexcept { |
| return signed_significand_bits<format_traits>(format_traits::remove_exponent_bits(u)); |
| } |
| |
| // Obtain the actual value of the binary exponent from the extracted exponent bits. |
| static constexpr exponent_int binary_exponent(exponent_int exponent_bits) noexcept { |
| return format_traits::binary_exponent(exponent_bits); |
| } |
| constexpr exponent_int binary_exponent() const noexcept { |
| return binary_exponent(extract_exponent_bits()); |
| } |
| |
| // Obtain the actual value of the binary exponent from the extracted significand bits |
| // and exponent bits. |
| static constexpr carrier_uint binary_significand(carrier_uint significand_bits, |
| exponent_int exponent_bits) noexcept { |
| return format_traits::binary_significand(significand_bits, exponent_bits); |
| } |
| constexpr carrier_uint binary_significand() const noexcept { |
| return binary_significand(extract_significand_bits(), extract_exponent_bits()); |
| } |
| |
| constexpr bool is_nonzero() const noexcept { return format_traits::is_nonzero(u); } |
| constexpr bool is_positive() const noexcept { return format_traits::is_positive(u); } |
| constexpr bool is_negative() const noexcept { return format_traits::is_negative(u); } |
| constexpr bool is_finite(exponent_int exponent_bits) const noexcept { |
| return format_traits::is_finite(exponent_bits); |
| } |
| constexpr bool is_finite() const noexcept { |
| return format_traits::is_finite(extract_exponent_bits()); |
| } |
| constexpr bool has_even_significand_bits() const noexcept { |
| return format_traits::has_even_significand_bits(u); |
| } |
| }; |
| |
| template <class Float, |
| class ConversionTraits = default_float_bit_carrier_conversion_traits<Float>, |
| class FormatTraits = ieee754_binary_traits<typename ConversionTraits::format, |
| typename ConversionTraits::carrier_uint>> |
| JKJ_CONSTEXPR20 float_bits<FormatTraits> make_float_bits(Float x) noexcept { |
| return float_bits<FormatTraits>(ConversionTraits::float_to_carrier(x)); |
| } |
| |
| namespace detail { |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Bit operation intrinsics. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| namespace bits { |
| // Most compilers should be able to optimize this into the ROR instruction. |
| // n is assumed to be at most of bit_width bits. |
| template <stdr::size_t bit_width, class UInt> |
| JKJ_CONSTEXPR14 UInt rotr(UInt n, unsigned int r) noexcept { |
| static_assert(bit_width > 0, "jkj::dragonbox: rotation bit-width must be positive"); |
| static_assert(bit_width <= value_bits<UInt>::value, |
| "jkj::dragonbox: rotation bit-width is too large"); |
| r &= (bit_width - 1); |
| return (n >> r) | (n << ((bit_width - r) & (bit_width - 1))); |
| } |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Utilities for wide unsigned integer arithmetic. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| namespace wuint { |
| // Compilers might support built-in 128-bit integer types. However, it seems that |
| // emulating them with a pair of 64-bit integers actually produces a better code, |
| // so we avoid using those built-ins. That said, they are still useful for |
| // implementing 64-bit x 64-bit -> 128-bit multiplication. |
| |
| // clang-format off |
| #if defined(__SIZEOF_INT128__) |
| // To silence "error: ISO C++ does not support '__int128' for 'type name' |
| // [-Wpedantic]" |
| #if defined(__GNUC__) |
| __extension__ |
| #endif |
| using builtin_uint128_t = unsigned __int128; |
| #endif |
| // clang-format on |
| |
| struct uint128 { |
| uint128() = default; |
| |
| stdr::uint_least64_t high_; |
| stdr::uint_least64_t low_; |
| |
| constexpr uint128(stdr::uint_least64_t high, stdr::uint_least64_t low) noexcept |
| : high_{high}, low_{low} {} |
| |
| constexpr stdr::uint_least64_t high() const noexcept { return high_; } |
| constexpr stdr::uint_least64_t low() const noexcept { return low_; } |
| |
| JKJ_CONSTEXPR20 uint128& operator+=(stdr::uint_least64_t n) & noexcept { |
| auto const generic_impl = [&] { |
| auto const sum = (low_ + n) & UINT64_C(0xffffffffffffffff); |
| high_ += (sum < low_ ? 1 : 0); |
| low_ = sum; |
| }; |
| // To suppress warning. |
| static_cast<void>(generic_impl); |
| |
| JKJ_IF_CONSTEXPR(value_bits<stdr::uint_least64_t>::value > 64) { |
| generic_impl(); |
| return *this; |
| } |
| |
| JKJ_IF_CONSTEVAL { |
| generic_impl(); |
| return *this; |
| } |
| |
| // See https://github.com/fmtlib/fmt/pull/2985. |
| #if JKJ_HAS_BUILTIN(__builtin_addcll) && !defined(__ibmxl__) |
| JKJ_IF_CONSTEXPR( |
| stdr::is_same<stdr::uint_least64_t, unsigned long long>::value) { |
| unsigned long long carry{}; |
| low_ = stdr::uint_least64_t(__builtin_addcll(low_, n, 0, &carry)); |
| high_ = stdr::uint_least64_t(__builtin_addcll(high_, 0, carry, &carry)); |
| return *this; |
| } |
| #endif |
| #if JKJ_HAS_BUILTIN(__builtin_addcl) && !defined(__ibmxl__) |
| JKJ_IF_CONSTEXPR(stdr::is_same<stdr::uint_least64_t, unsigned long>::value) { |
| unsigned long carry{}; |
| low_ = stdr::uint_least64_t( |
| __builtin_addcl(static_cast<unsigned long>(low_), |
| static_cast<unsigned long>(n), 0, &carry)); |
| high_ = stdr::uint_least64_t( |
| __builtin_addcl(static_cast<unsigned long>(high_), 0, carry, &carry)); |
| return *this; |
| } |
| #endif |
| #if JKJ_HAS_BUILTIN(__builtin_addc) && !defined(__ibmxl__) |
| JKJ_IF_CONSTEXPR(stdr::is_same<stdr::uint_least64_t, unsigned int>::value) { |
| unsigned int carry{}; |
| low_ = stdr::uint_least64_t(__builtin_addc(static_cast<unsigned int>(low_), |
| static_cast<unsigned int>(n), 0, |
| &carry)); |
| high_ = stdr::uint_least64_t( |
| __builtin_addc(static_cast<unsigned int>(high_), 0, carry, &carry)); |
| return *this; |
| } |
| #endif |
| |
| #if JKJ_HAS_BUILTIN(__builtin_ia32_addcarry_u64) |
| // __builtin_ia32_addcarry_u64 is not documented, but it seems it takes unsigned |
| // long long arguments. |
| unsigned long long result{}; |
| auto const carry = __builtin_ia32_addcarry_u64(0, low_, n, &result); |
| low_ = stdr::uint_least64_t(result); |
| __builtin_ia32_addcarry_u64(carry, high_, 0, &result); |
| high_ = stdr::uint_least64_t(result); |
| #elif defined(_MSC_VER) && defined(_M_X64) |
| // On MSVC, uint_least64_t and __int64 must be unsigned long long; see |
| // https://learn.microsoft.com/en-us/cpp/c-runtime-library/standard-types |
| // and https://learn.microsoft.com/en-us/cpp/cpp/int8-int16-int32-int64. |
| static_assert(stdr::is_same<unsigned long long, stdr::uint_least64_t>::value, |
| ""); |
| auto const carry = _addcarry_u64(0, low_, n, &low_); |
| _addcarry_u64(carry, high_, 0, &high_); |
| #elif defined(__INTEL_COMPILER) && (defined(_M_X64) || defined(__x86_64)) |
| // Cannot find any documentation on how things are defined, but hopefully this |
| // is always true... |
| static_assert(stdr::is_same<unsigned __int64, stdr::uint_least64_t>::value, ""); |
| auto const carry = _addcarry_u64(0, low_, n, &low_); |
| _addcarry_u64(carry, high_, 0, &high_); |
| #else |
| generic_impl(); |
| #endif |
| return *this; |
| } |
| }; |
| |
| inline JKJ_CONSTEXPR20 stdr::uint_least64_t umul64(stdr::uint_least32_t x, |
| stdr::uint_least32_t y) noexcept { |
| #if defined(_MSC_VER) && defined(_M_IX86) |
| JKJ_IF_NOT_CONSTEVAL { return __emulu(x, y); } |
| #endif |
| return x * stdr::uint_least64_t(y); |
| } |
| |
| // Get 128-bit result of multiplication of two 64-bit unsigned integers. |
| JKJ_SAFEBUFFERS inline JKJ_CONSTEXPR20 uint128 |
| umul128(stdr::uint_least64_t x, stdr::uint_least64_t y) noexcept { |
| auto const generic_impl = [=]() -> uint128 { |
| auto const a = stdr::uint_least32_t(x >> 32); |
| auto const b = stdr::uint_least32_t(x); |
| auto const c = stdr::uint_least32_t(y >> 32); |
| auto const d = stdr::uint_least32_t(y); |
| |
| auto const ac = umul64(a, c); |
| auto const bc = umul64(b, c); |
| auto const ad = umul64(a, d); |
| auto const bd = umul64(b, d); |
| |
| auto const intermediate = |
| (bd >> 32) + stdr::uint_least32_t(ad) + stdr::uint_least32_t(bc); |
| |
| return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), |
| (intermediate << 32) + stdr::uint_least32_t(bd)}; |
| }; |
| // To silence warning. |
| static_cast<void>(generic_impl); |
| |
| #if defined(__SIZEOF_INT128__) |
| auto const result = builtin_uint128_t(x) * builtin_uint128_t(y); |
| return {stdr::uint_least64_t(result >> 64), stdr::uint_least64_t(result)}; |
| #elif defined(_MSC_VER) && defined(_M_X64) |
| JKJ_IF_CONSTEVAL { |
| // This redundant variable is to workaround MSVC's codegen bug caused by the |
| // interaction of NRVO and intrinsics. |
| auto const result = generic_impl(); |
| return result; |
| } |
| uint128 result; |
| #if defined(__AVX2__) |
| result.low_ = _mulx_u64(x, y, &result.high_); |
| #else |
| result.low_ = _umul128(x, y, &result.high_); |
| #endif |
| return result; |
| #else |
| return generic_impl(); |
| #endif |
| } |
| |
| // Get high half of the 128-bit result of multiplication of two 64-bit unsigned |
| // integers. |
| JKJ_SAFEBUFFERS inline JKJ_CONSTEXPR20 stdr::uint_least64_t |
| umul128_upper64(stdr::uint_least64_t x, stdr::uint_least64_t y) noexcept { |
| auto const generic_impl = [=]() -> stdr::uint_least64_t { |
| auto const a = stdr::uint_least32_t(x >> 32); |
| auto const b = stdr::uint_least32_t(x); |
| auto const c = stdr::uint_least32_t(y >> 32); |
| auto const d = stdr::uint_least32_t(y); |
| |
| auto const ac = umul64(a, c); |
| auto const bc = umul64(b, c); |
| auto const ad = umul64(a, d); |
| auto const bd = umul64(b, d); |
| |
| auto const intermediate = |
| (bd >> 32) + stdr::uint_least32_t(ad) + stdr::uint_least32_t(bc); |
| |
| return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); |
| }; |
| // To silence warning. |
| static_cast<void>(generic_impl); |
| |
| #if defined(__SIZEOF_INT128__) |
| auto const result = builtin_uint128_t(x) * builtin_uint128_t(y); |
| return stdr::uint_least64_t(result >> 64); |
| #elif defined(_MSC_VER) && defined(_M_X64) |
| JKJ_IF_CONSTEVAL { |
| // This redundant variable is to workaround MSVC's codegen bug caused by the |
| // interaction of NRVO and intrinsics. |
| auto const result = generic_impl(); |
| return result; |
| } |
| stdr::uint_least64_t result; |
| #if defined(__AVX2__) |
| _mulx_u64(x, y, &result); |
| #else |
| result = __umulh(x, y); |
| #endif |
| return result; |
| #else |
| return generic_impl(); |
| #endif |
| } |
| |
| // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit |
| // unsigned integer. |
| JKJ_SAFEBUFFERS inline JKJ_CONSTEXPR20 uint128 umul192_upper128(stdr::uint_least64_t x, |
| uint128 y) noexcept { |
| auto r = umul128(x, y.high()); |
| r += umul128_upper64(x, y.low()); |
| return r; |
| } |
| |
| // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit |
| // unsigned integer. |
| inline JKJ_CONSTEXPR20 stdr::uint_least64_t |
| umul96_upper64(stdr::uint_least32_t x, stdr::uint_least64_t y) noexcept { |
| #if defined(__SIZEOF_INT128__) || (defined(_MSC_VER) && defined(_M_X64)) |
| return umul128_upper64(stdr::uint_least64_t(x) << 32, y); |
| #else |
| auto const yh = stdr::uint_least32_t(y >> 32); |
| auto const yl = stdr::uint_least32_t(y); |
| |
| auto const xyh = umul64(x, yh); |
| auto const xyl = umul64(x, yl); |
| |
| return xyh + (xyl >> 32); |
| #endif |
| } |
| |
| // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit |
| // unsigned integer. |
| JKJ_SAFEBUFFERS inline JKJ_CONSTEXPR20 uint128 umul192_lower128(stdr::uint_least64_t x, |
| uint128 y) noexcept { |
| auto const high = x * y.high(); |
| auto const high_low = umul128(x, y.low()); |
| return {(high + high_low.high()) & UINT64_C(0xffffffffffffffff), high_low.low()}; |
| } |
| |
| // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit |
| // unsigned integer. |
| constexpr stdr::uint_least64_t umul96_lower64(stdr::uint_least32_t x, |
| stdr::uint_least64_t y) noexcept { |
| return (x * y) & UINT64_C(0xffffffffffffffff); |
| } |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Some simple utilities for constexpr computation. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <int k, class Int> |
| constexpr Int compute_power(Int a) noexcept { |
| static_assert(k >= 0, ""); |
| #if JKJ_HAS_CONSTEXPR14 |
| Int p = 1; |
| for (int i = 0; i < k; ++i) { |
| p *= a; |
| } |
| return p; |
| #else |
| return k == 0 ? 1 |
| : k % 2 == 0 ? compute_power<k / 2, Int>(a * a) |
| : a * compute_power<k / 2, Int>(a * a); |
| #endif |
| } |
| |
| template <int a, class UInt> |
| constexpr int count_factors(UInt n) noexcept { |
| static_assert(a > 1, ""); |
| #if JKJ_HAS_CONSTEXPR14 |
| int c = 0; |
| while (n % a == 0) { |
| n /= a; |
| ++c; |
| } |
| return c; |
| #else |
| return n % a == 0 ? count_factors<a, UInt>(n / a) + 1 : 0; |
| #endif |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Utilities for fast/constexpr log computation. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| namespace log { |
| static_assert((stdr::int_fast32_t(-1) >> 1) == stdr::int_fast32_t(-1) && |
| (stdr::int_fast16_t(-1) >> 1) == stdr::int_fast16_t(-1), |
| "jkj::dragonbox: right-shift for signed integers must be arithmetic"); |
| |
| // For constexpr computation. |
| // Returns -1 when n = 0. |
| template <class UInt> |
| constexpr int floor_log2(UInt n) noexcept { |
| #if JKJ_HAS_CONSTEXPR14 |
| int count = -1; |
| while (n != 0) { |
| ++count; |
| n >>= 1; |
| } |
| return count; |
| #else |
| return n == 0 ? -1 : floor_log2<UInt>(n / 2) + 1; |
| #endif |
| } |
| |
| template <template <stdr::size_t> class Info, stdr::int_least32_t min_exponent, |
| stdr::int_least32_t max_exponent, stdr::size_t current_tier, |
| stdr::int_least32_t supported_min_exponent = Info<current_tier>::min_exponent, |
| stdr::int_least32_t supported_max_exponent = Info<current_tier>::max_exponent> |
| constexpr bool is_in_range(int) noexcept { |
| return min_exponent >= supported_min_exponent && |
| max_exponent <= supported_max_exponent; |
| } |
| template <template <stdr::size_t> class Info, stdr::int_least32_t min_exponent, |
| stdr::int_least32_t max_exponent, stdr::size_t current_tier> |
| constexpr bool is_in_range(...) noexcept { |
| // Supposed to be always false, but formally dependent on the template parameters. |
| static_assert(min_exponent > max_exponent, |
| "jkj::dragonbox: exponent range is too wide"); |
| return false; |
| } |
| |
| template <template <stdr::size_t> class Info, stdr::int_least32_t min_exponent, |
| stdr::int_least32_t max_exponent, stdr::size_t current_tier = 0, |
| bool = is_in_range<Info, min_exponent, max_exponent, current_tier>(0)> |
| struct compute_impl; |
| |
| template <template <stdr::size_t> class Info, stdr::int_least32_t min_exponent, |
| stdr::int_least32_t max_exponent, stdr::size_t current_tier> |
| struct compute_impl<Info, min_exponent, max_exponent, current_tier, true> { |
| using info = Info<current_tier>; |
| using default_return_type = typename info::default_return_type; |
| template <class ReturnType, class Int> |
| static constexpr ReturnType compute(Int e) noexcept { |
| #if JKJ_HAS_CONSTEXPR14 |
| assert(min_exponent <= e && e <= max_exponent); |
| #endif |
| // The sign is irrelevant for the mathematical validity of the formula, but |
| // assuming positivity makes the overflow analysis simpler. |
| static_assert(info::multiply >= 0 && info::subtract >= 0, ""); |
| return static_cast<ReturnType>((e * info::multiply - info::subtract) >> |
| info::shift); |
| } |
| }; |
| |
| template <template <stdr::size_t> class Info, stdr::int_least32_t min_exponent, |
| stdr::int_least32_t max_exponent, stdr::size_t current_tier> |
| struct compute_impl<Info, min_exponent, max_exponent, current_tier, false> { |
| using next_tier = compute_impl<Info, min_exponent, max_exponent, current_tier + 1>; |
| using default_return_type = typename next_tier::default_return_type; |
| template <class ReturnType, class Int> |
| static constexpr ReturnType compute(Int e) noexcept { |
| return next_tier::template compute<ReturnType>(e); |
| } |
| }; |
| |
| template <stdr::size_t tier> |
| struct floor_log10_pow2_info; |
| template <> |
| struct floor_log10_pow2_info<0> { |
| using default_return_type = stdr::int_fast8_t; |
| static constexpr stdr::int_fast16_t multiply = 77; |
| static constexpr stdr::int_fast16_t subtract = 0; |
| static constexpr stdr::size_t shift = 8; |
| static constexpr stdr::int_least32_t min_exponent = -102; |
| static constexpr stdr::int_least32_t max_exponent = 102; |
| }; |
| template <> |
| struct floor_log10_pow2_info<1> { |
| using default_return_type = stdr::int_fast8_t; |
| // 24-bits are enough in fact. |
| static constexpr stdr::int_fast32_t multiply = 1233; |
| static constexpr stdr::int_fast32_t subtract = 0; |
| static constexpr stdr::size_t shift = 12; |
| // Formula itself holds on [-680,680]; [-425,425] is to ensure that the output is |
| // within [-127,127]. |
| static constexpr stdr::int_least32_t min_exponent = -425; |
| static constexpr stdr::int_least32_t max_exponent = 425; |
| }; |
| template <> |
| struct floor_log10_pow2_info<2> { |
| using default_return_type = stdr::int_fast16_t; |
| static constexpr stdr::int_fast32_t multiply = INT32_C(315653); |
| static constexpr stdr::int_fast32_t subtract = 0; |
| static constexpr stdr::size_t shift = 20; |
| static constexpr stdr::int_least32_t min_exponent = -2620; |
| static constexpr stdr::int_least32_t max_exponent = 2620; |
| }; |
| template <stdr::int_least32_t min_exponent = -2620, |
| stdr::int_least32_t max_exponent = 2620, |
| class ReturnType = typename compute_impl<floor_log10_pow2_info, min_exponent, |
| max_exponent>::default_return_type, |
| class Int> |
| constexpr ReturnType floor_log10_pow2(Int e) noexcept { |
| return compute_impl<floor_log10_pow2_info, min_exponent, |
| max_exponent>::template compute<ReturnType>(e); |
| } |
| |
| template <stdr::size_t tier> |
| struct floor_log2_pow10_info; |
| template <> |
| struct floor_log2_pow10_info<0> { |
| using default_return_type = stdr::int_fast8_t; |
| static constexpr stdr::int_fast16_t multiply = 53; |
| static constexpr stdr::int_fast16_t subtract = 0; |
| static constexpr stdr::size_t shift = 4; |
| static constexpr stdr::int_least32_t min_exponent = -15; |
| static constexpr stdr::int_least32_t max_exponent = 18; |
| }; |
| template <> |
| struct floor_log2_pow10_info<1> { |
| using default_return_type = stdr::int_fast16_t; |
| // 24-bits are enough in fact. |
| static constexpr stdr::int_fast32_t multiply = 1701; |
| static constexpr stdr::int_fast32_t subtract = 0; |
| static constexpr stdr::size_t shift = 9; |
| static constexpr stdr::int_least32_t min_exponent = -58; |
| static constexpr stdr::int_least32_t max_exponent = 58; |
| }; |
| template <> |
| struct floor_log2_pow10_info<2> { |
| using default_return_type = stdr::int_fast16_t; |
| static constexpr stdr::int_fast32_t multiply = INT32_C(1741647); |
| static constexpr stdr::int_fast32_t subtract = 0; |
| static constexpr stdr::size_t shift = 19; |
| // Formula itself holds on [-4003,4003]; [-1233,1233] is to ensure no overflow. |
| static constexpr stdr::int_least32_t min_exponent = -1233; |
| static constexpr stdr::int_least32_t max_exponent = 1233; |
| }; |
| template <stdr::int_least32_t min_exponent = -1233, |
| stdr::int_least32_t max_exponent = 1233, |
| class ReturnType = typename compute_impl<floor_log2_pow10_info, min_exponent, |
| max_exponent>::default_return_type, |
| class Int> |
| constexpr ReturnType floor_log2_pow10(Int e) noexcept { |
| return compute_impl<floor_log2_pow10_info, min_exponent, |
| max_exponent>::template compute<ReturnType>(e); |
| } |
| |
| template <stdr::size_t tier> |
| struct floor_log10_pow2_minus_log10_4_over_3_info; |
| template <> |
| struct floor_log10_pow2_minus_log10_4_over_3_info<0> { |
| using default_return_type = stdr::int_fast8_t; |
| static constexpr stdr::int_fast16_t multiply = 77; |
| static constexpr stdr::int_fast16_t subtract = 31; |
| static constexpr stdr::size_t shift = 8; |
| static constexpr stdr::int_least32_t min_exponent = -75; |
| static constexpr stdr::int_least32_t max_exponent = 129; |
| }; |
| template <> |
| struct floor_log10_pow2_minus_log10_4_over_3_info<1> { |
| using default_return_type = stdr::int_fast8_t; |
| // 24-bits are enough in fact. |
| static constexpr stdr::int_fast32_t multiply = 19728; |
| static constexpr stdr::int_fast32_t subtract = 8241; |
| static constexpr stdr::size_t shift = 16; |
| // Formula itself holds on [-849,315]; [-424,315] is to ensure that the output is |
| // within [-127,127]. |
| static constexpr stdr::int_least32_t min_exponent = -424; |
| static constexpr stdr::int_least32_t max_exponent = 315; |
| }; |
| template <> |
| struct floor_log10_pow2_minus_log10_4_over_3_info<2> { |
| using default_return_type = stdr::int_fast16_t; |
| static constexpr stdr::int_fast32_t multiply = INT32_C(631305); |
| static constexpr stdr::int_fast32_t subtract = INT32_C(261663); |
| static constexpr stdr::size_t shift = 21; |
| static constexpr stdr::int_least32_t min_exponent = -2985; |
| static constexpr stdr::int_least32_t max_exponent = 2936; |
| }; |
| template <stdr::int_least32_t min_exponent = -2985, |
| stdr::int_least32_t max_exponent = 2936, |
| class ReturnType = |
| typename compute_impl<floor_log10_pow2_minus_log10_4_over_3_info, |
| min_exponent, max_exponent>::default_return_type, |
| class Int> |
| constexpr ReturnType floor_log10_pow2_minus_log10_4_over_3(Int e) noexcept { |
| return compute_impl<floor_log10_pow2_minus_log10_4_over_3_info, min_exponent, |
| max_exponent>::template compute<ReturnType>(e); |
| } |
| |
| template <stdr::size_t tier> |
| struct floor_log5_pow2_info; |
| template <> |
| struct floor_log5_pow2_info<0> { |
| using default_return_type = stdr::int_fast32_t; |
| static constexpr stdr::int_fast32_t multiply = INT32_C(225799); |
| static constexpr stdr::int_fast32_t subtract = 0; |
| static constexpr stdr::size_t shift = 19; |
| static constexpr stdr::int_least32_t min_exponent = -1831; |
| static constexpr stdr::int_least32_t max_exponent = 1831; |
| }; |
| template <stdr::int_least32_t min_exponent = -1831, |
| stdr::int_least32_t max_exponent = 1831, |
| class ReturnType = typename compute_impl<floor_log5_pow2_info, min_exponent, |
| max_exponent>::default_return_type, |
| class Int> |
| constexpr ReturnType floor_log5_pow2(Int e) noexcept { |
| return compute_impl<floor_log5_pow2_info, min_exponent, |
| max_exponent>::template compute<ReturnType>(e); |
| } |
| |
| template <stdr::size_t tier> |
| struct floor_log5_pow2_minus_log5_3_info; |
| template <> |
| struct floor_log5_pow2_minus_log5_3_info<0> { |
| using default_return_type = stdr::int_fast32_t; |
| static constexpr stdr::int_fast32_t multiply = INT32_C(451597); |
| static constexpr stdr::int_fast32_t subtract = INT32_C(715764); |
| static constexpr stdr::size_t shift = 20; |
| static constexpr stdr::int_least32_t min_exponent = -3543; |
| static constexpr stdr::int_least32_t max_exponent = 2427; |
| }; |
| template <stdr::int_least32_t min_exponent = -3543, |
| stdr::int_least32_t max_exponent = 2427, |
| class ReturnType = |
| typename compute_impl<floor_log5_pow2_minus_log5_3_info, min_exponent, |
| max_exponent>::default_return_type, |
| class Int> |
| constexpr ReturnType floor_log5_pow2_minus_log5_3(Int e) noexcept { |
| return compute_impl<floor_log5_pow2_minus_log5_3_info, min_exponent, |
| max_exponent>::template compute<ReturnType>(e); |
| } |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Utilities for fast divisibility tests. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| namespace div { |
| // Replace n by floor(n / 10^N). |
| // Returns true if and only if n is divisible by 10^N. |
| // Precondition: n <= 10^(N+1) |
| // !!It takes an in-out parameter!! |
| template <int N, class UInt> |
| struct divide_by_pow10_info; |
| |
| template <class UInt> |
| struct divide_by_pow10_info<1, UInt> { |
| static constexpr stdr::uint_fast32_t magic_number = 6554; |
| static constexpr int shift_amount = 16; |
| }; |
| |
| template <> |
| struct divide_by_pow10_info<1, stdr::uint_least8_t> { |
| static constexpr stdr::uint_fast16_t magic_number = 103; |
| static constexpr int shift_amount = 10; |
| }; |
| |
| template <> |
| struct divide_by_pow10_info<1, stdr::uint_least16_t> { |
| static constexpr stdr::uint_fast16_t magic_number = 103; |
| static constexpr int shift_amount = 10; |
| }; |
| |
| template <class UInt> |
| struct divide_by_pow10_info<2, UInt> { |
| static constexpr stdr::uint_fast32_t magic_number = 656; |
| static constexpr int shift_amount = 16; |
| }; |
| |
| template <> |
| struct divide_by_pow10_info<2, stdr::uint_least16_t> { |
| static constexpr stdr::uint_fast32_t magic_number = 41; |
| static constexpr int shift_amount = 12; |
| }; |
| |
| template <int N, class UInt> |
| JKJ_CONSTEXPR14 bool check_divisibility_and_divide_by_pow10(UInt& n) noexcept { |
| // Make sure the computation for max_n does not overflow. |
| static_assert(N + 1 <= log::floor_log10_pow2(int(value_bits<UInt>::value)), ""); |
| assert(n <= compute_power<N + 1>(UInt(10))); |
| |
| using info = divide_by_pow10_info<N, UInt>; |
| using intermediate_type = decltype(info::magic_number); |
| auto const prod = intermediate_type(n * info::magic_number); |
| |
| constexpr auto mask = |
| intermediate_type((intermediate_type(1) << info::shift_amount) - 1); |
| bool const result = ((prod & mask) < info::magic_number); |
| |
| n = UInt(prod >> info::shift_amount); |
| return result; |
| } |
| |
| // Compute floor(n / 10^N) for small n and N. |
| // Precondition: n <= 10^(N+1) |
| template <int N, class UInt> |
| JKJ_CONSTEXPR14 UInt small_division_by_pow10(UInt n) noexcept { |
| // Make sure the computation for max_n does not overflow. |
| static_assert(N + 1 <= log::floor_log10_pow2(int(value_bits<UInt>::value)), ""); |
| assert(n <= compute_power<N + 1>(UInt(10))); |
| |
| return UInt((n * divide_by_pow10_info<N, UInt>::magic_number) >> |
| divide_by_pow10_info<N, UInt>::shift_amount); |
| } |
| |
| // Compute floor(n / 10^N) for small N. |
| // Precondition: n <= n_max |
| template <int N, class UInt, UInt n_max> |
| JKJ_CONSTEXPR20 UInt divide_by_pow10(UInt n) noexcept { |
| static_assert(N >= 0, ""); |
| |
| // Specialize for 32-bit division by 10. |
| // Without the bound on n_max (which compilers these days never leverage), the |
| // minimum needed amount of shift is larger than 32. Hence, this may generate better |
| // code for 32-bit or smaller architectures. Even for 64-bit architectures, it seems |
| // compilers tend to generate mov + mul instead of a single imul for an unknown |
| // reason if we just write n / 10. |
| JKJ_IF_CONSTEXPR(stdr::is_same<UInt, stdr::uint_least32_t>::value && N == 1 && |
| n_max <= UINT32_C(1073741828)) { |
| return UInt(wuint::umul64(n, UINT32_C(429496730)) >> 32); |
| } |
| // Specialize for 64-bit division by 10. |
| // Without the bound on n_max (which compilers these days never leverage), the |
| // minimum needed amount of shift is larger than 64. |
| else JKJ_IF_CONSTEXPR(stdr::is_same<UInt, stdr::uint_least64_t>::value && N == 1 && |
| n_max <= UINT64_C(4611686018427387908)) { |
| return UInt(wuint::umul128_upper64(n, UINT64_C(1844674407370955162))); |
| } |
| // Specialize for 32-bit division by 100. |
| // It seems compilers tend to generate mov + mul instead of a single imul for an |
| // unknown reason if we just write n / 100. |
| else JKJ_IF_CONSTEXPR(stdr::is_same<UInt, stdr::uint_least32_t>::value && N == 2) { |
| return UInt(wuint::umul64(n, UINT32_C(1374389535)) >> 37); |
| } |
| // Specialize for 64-bit division by 1000. |
| // Without the bound on n_max (which compilers these days never leverage), the |
| // smallest magic number for this computation does not fit into 64-bits. |
| else JKJ_IF_CONSTEXPR(stdr::is_same<UInt, stdr::uint_least64_t>::value && N == 3 && |
| n_max <= UINT64_C(15534100272597517998)) { |
| return UInt(wuint::umul128_upper64(n, UINT64_C(4722366482869645214)) >> 8); |
| } |
| else { |
| constexpr auto divisor = compute_power<N>(UInt(10)); |
| return n / divisor; |
| } |
| } |
| } |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Return types for the main interface function. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <class SignificandType, class ExponentType, bool is_signed, bool trailing_zero_flag> |
| struct decimal_fp; |
| |
| template <class SignificandType, class ExponentType> |
| struct decimal_fp<SignificandType, ExponentType, false, false> { |
| SignificandType significand; |
| ExponentType exponent; |
| }; |
| |
| template <class SignificandType, class ExponentType> |
| struct decimal_fp<SignificandType, ExponentType, true, false> { |
| SignificandType significand; |
| ExponentType exponent; |
| bool is_negative; |
| }; |
| |
| template <class SignificandType, class ExponentType> |
| struct decimal_fp<SignificandType, ExponentType, false, true> { |
| SignificandType significand; |
| ExponentType exponent; |
| bool may_have_trailing_zeros; |
| }; |
| |
| template <class SignificandType, class ExponentType> |
| struct decimal_fp<SignificandType, ExponentType, true, true> { |
| SignificandType significand; |
| ExponentType exponent; |
| bool may_have_trailing_zeros; |
| bool is_negative; |
| }; |
| |
| template <class SignificandType, class ExponentType, bool trailing_zero_flag = false> |
| using unsigned_decimal_fp = |
| decimal_fp<SignificandType, ExponentType, false, trailing_zero_flag>; |
| |
| template <class SignificandType, class ExponentType, bool trailing_zero_flag = false> |
| using signed_decimal_fp = decimal_fp<SignificandType, ExponentType, true, trailing_zero_flag>; |
| |
| template <class SignificandType, class ExponentType> |
| constexpr signed_decimal_fp<SignificandType, ExponentType, false> |
| add_sign_to_unsigned_decimal_fp( |
| bool is_negative, unsigned_decimal_fp<SignificandType, ExponentType, false> r) noexcept { |
| return {r.significand, r.exponent, is_negative}; |
| } |
| |
| template <class SignificandType, class ExponentType> |
| constexpr signed_decimal_fp<SignificandType, ExponentType, true> |
| add_sign_to_unsigned_decimal_fp( |
| bool is_negative, unsigned_decimal_fp<SignificandType, ExponentType, true> r) noexcept { |
| return {r.significand, r.exponent, r.may_have_trailing_zeros, is_negative}; |
| } |
| |
| namespace detail { |
| template <class UnsignedDecimalFp> |
| struct unsigned_decimal_fp_to_signed; |
| |
| template <class SignificandType, class ExponentType, bool trailing_zero_flag> |
| struct unsigned_decimal_fp_to_signed< |
| unsigned_decimal_fp<SignificandType, ExponentType, trailing_zero_flag>> { |
| using type = signed_decimal_fp<SignificandType, ExponentType, trailing_zero_flag>; |
| }; |
| |
| template <class UnsignedDecimalFp> |
| using unsigned_decimal_fp_to_signed_t = |
| typename unsigned_decimal_fp_to_signed<UnsignedDecimalFp>::type; |
| } |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Computed cache entries. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <class FloatFormat, class Dummy = void> |
| struct cache_holder; |
| |
| template <class Dummy> |
| struct cache_holder<ieee754_binary32, Dummy> { |
| using cache_entry_type = detail::stdr::uint_least64_t; |
| static constexpr int cache_bits = 64; |
| static constexpr int min_k = -31; |
| static constexpr int max_k = 46; |
| static constexpr detail::array<cache_entry_type, detail::stdr::size_t(max_k - min_k + 1)> |
| cache JKJ_STATIC_DATA_SECTION = { |
| {UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), |
| UINT64_C(0xcad2f7f5359a3b3f), UINT64_C(0xfd87b5f28300ca0e), |
| UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), |
| UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), |
| UINT64_C(0xc16d9a0095928a28), UINT64_C(0xf1c90080baf72cb2), |
| UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), |
| UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), |
| UINT64_C(0xb877aa3236a4b44a), UINT64_C(0xe69594bec44de15c), |
| UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), |
| UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), |
| UINT64_C(0xafebff0bcb24aaff), UINT64_C(0xdbe6fecebdedd5bf), |
| UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), |
| UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), |
| UINT64_C(0xa7c5ac471b478424), UINT64_C(0xd1b71758e219652c), |
| UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), |
| UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), |
| UINT64_C(0xa000000000000000), UINT64_C(0xc800000000000000), |
| UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), |
| UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), |
| UINT64_C(0x9896800000000000), UINT64_C(0xbebc200000000000), |
| UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), |
| UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), |
| UINT64_C(0x9184e72a00000000), UINT64_C(0xb5e620f480000000), |
| UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), |
| UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), |
| UINT64_C(0x8ac7230489e80000), UINT64_C(0xad78ebc5ac620000), |
| UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), |
| UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), |
| UINT64_C(0x84595161401484a0), UINT64_C(0xa56fa5b99019a5c8), |
| UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), |
| UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), |
| UINT64_C(0xfc6f7c4045812297), UINT64_C(0x9dc5ada82b70b59e), |
| UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), |
| UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), |
| UINT64_C(0xf0bdc21abb48db21), UINT64_C(0x96769950b50d88f5), |
| UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), |
| UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), |
| UINT64_C(0xe596b7b0c643c71a), UINT64_C(0x8f7e32ce7bea5c70), |
| UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}}; |
| }; |
| #if !JKJ_HAS_INLINE_VARIABLE |
| // decltype(...) should not depend on Dummy; see |
| // https://stackoverflow.com/questions/76438400/decltype-on-static-variable-in-template-class. |
| template <class Dummy> |
| constexpr decltype(cache_holder<ieee754_binary32>::cache) |
| cache_holder<ieee754_binary32, Dummy>::cache; |
| #endif |
| |
| template <class Dummy> |
| struct cache_holder<ieee754_binary64, Dummy> { |
| using cache_entry_type = detail::wuint::uint128; |
| static constexpr int cache_bits = 128; |
| static constexpr int min_k = -292; |
| static constexpr int max_k = 326; |
| static constexpr detail::array<cache_entry_type, detail::stdr::size_t(max_k - min_k + 1)> |
| cache JKJ_STATIC_DATA_SECTION = { |
| {{UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, |
| {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, |
| {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, |
| {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, |
| {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, |
| {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, |
| {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, |
| {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, |
| {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, |
| {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, |
| {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, |
| {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, |
| {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, |
| {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, |
| {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, |
| {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, |
| {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, |
| {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, |
| {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, |
| {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, |
| {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, |
| {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, |
| {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, |
| {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, |
| {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, |
| {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, |
| {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, |
| {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, |
| {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, |
| {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, |
| {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, |
| {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, |
| {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, |
| {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, |
| {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, |
| {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, |
| {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, |
| {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, |
| {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, |
| {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, |
| {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, |
| {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, |
| {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, |
| {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, |
| {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, |
| {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, |
| {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, |
| {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, |
| {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, |
| {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, |
| {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, |
| {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, |
| {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, |
| {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, |
| {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, |
| {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, |
| {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, |
| {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, |
| {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, |
| {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, |
| {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, |
| {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, |
| {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, |
| {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, |
| {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, |
| {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, |
| {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, |
| {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, |
| {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, |
| {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, |
| {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, |
| {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, |
| {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, |
| {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, |
| {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, |
| {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, |
| {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, |
| {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, |
| {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, |
| {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, |
| {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, |
| {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, |
| {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, |
| {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, |
| {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, |
| {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, |
| {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, |
| {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, |
| {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, |
| {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, |
| {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, |
| {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, |
| {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, |
| {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, |
| {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, |
| {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, |
| {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, |
| {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, |
| {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, |
| {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, |
| {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, |
| {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, |
| {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, |
| {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, |
| {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, |
| {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, |
| {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, |
| {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, |
| {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, |
| {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, |
| {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, |
| {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, |
| {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, |
| {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, |
| {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, |
| {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, |
| {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, |
| {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, |
| {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, |
| {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, |
| {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, |
| {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, |
| {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, |
| {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, |
| {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, |
| {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, |
| {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, |
| {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, |
| {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, |
| {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, |
| {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, |
| {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, |
| {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, |
| {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, |
| {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, |
| {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, |
| {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, |
| {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, |
| {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, |
| {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, |
| {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, |
| {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, |
| {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, |
| {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, |
| {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, |
| {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, |
| {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, |
| {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, |
| {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, |
| {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, |
| {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, |
| {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, |
| {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, |
| {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, |
| {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, |
| {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, |
| {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, |
| {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, |
| {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, |
| {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, |
| {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, |
| {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, |
| {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, |
| {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, |
| {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, |
| {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, |
| {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, |
| {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, |
| {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, |
| {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, |
| {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, |
| {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, |
| {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, |
| {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, |
| {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, |
| {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, |
| {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, |
| {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, |
| {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, |
| {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, |
| {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, |
| {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, |
| {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, |
| {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, |
| {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, |
| {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, |
| {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, |
| {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, |
| {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, |
| {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, |
| {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, |
| {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, |
| {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, |
| {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, |
| {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, |
| {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, |
| {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, |
| {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, |
| {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, |
| {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, |
| {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, |
| {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, |
| {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, |
| {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, |
| {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, |
| {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, |
| {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, |
| {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, |
| {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, |
| {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, |
| {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, |
| {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, |
| {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, |
| {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, |
| {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, |
| {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, |
| {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, |
| {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, |
| {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, |
| {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, |
| {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, |
| {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, |
| {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, |
| {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, |
| {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, |
| {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, |
| {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, |
| {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, |
| {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, |
| {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, |
| {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, |
| {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, |
| {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, |
| {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, |
| {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, |
| {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, |
| {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, |
| {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, |
| {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, |
| {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, |
| {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, |
| {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, |
| {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, |
| {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, |
| {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, |
| {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, |
| {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, |
| {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, |
| {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, |
| {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, |
| {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, |
| {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, |
| {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, |
| {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, |
| {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, |
| {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, |
| {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, |
| {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, |
| {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, |
| {UINT64_C(0xa6274bbdd0fadd61), UINT64_C(0xecb1ad8aeacdd58f)}, |
| {UINT64_C(0xcfb11ead453994ba), UINT64_C(0x67de18eda5814af3)}, |
| {UINT64_C(0x81ceb32c4b43fcf4), UINT64_C(0x80eacf948770ced8)}, |
| {UINT64_C(0xa2425ff75e14fc31), UINT64_C(0xa1258379a94d028e)}, |
| {UINT64_C(0xcad2f7f5359a3b3e), UINT64_C(0x096ee45813a04331)}, |
| {UINT64_C(0xfd87b5f28300ca0d), UINT64_C(0x8bca9d6e188853fd)}, |
| {UINT64_C(0x9e74d1b791e07e48), UINT64_C(0x775ea264cf55347e)}, |
| {UINT64_C(0xc612062576589dda), UINT64_C(0x95364afe032a819e)}, |
| {UINT64_C(0xf79687aed3eec551), UINT64_C(0x3a83ddbd83f52205)}, |
| {UINT64_C(0x9abe14cd44753b52), UINT64_C(0xc4926a9672793543)}, |
| {UINT64_C(0xc16d9a0095928a27), UINT64_C(0x75b7053c0f178294)}, |
| {UINT64_C(0xf1c90080baf72cb1), UINT64_C(0x5324c68b12dd6339)}, |
| {UINT64_C(0x971da05074da7bee), UINT64_C(0xd3f6fc16ebca5e04)}, |
| {UINT64_C(0xbce5086492111aea), UINT64_C(0x88f4bb1ca6bcf585)}, |
| {UINT64_C(0xec1e4a7db69561a5), UINT64_C(0x2b31e9e3d06c32e6)}, |
| {UINT64_C(0x9392ee8e921d5d07), UINT64_C(0x3aff322e62439fd0)}, |
| {UINT64_C(0xb877aa3236a4b449), UINT64_C(0x09befeb9fad487c3)}, |
| {UINT64_C(0xe69594bec44de15b), UINT64_C(0x4c2ebe687989a9b4)}, |
| {UINT64_C(0x901d7cf73ab0acd9), UINT64_C(0x0f9d37014bf60a11)}, |
| {UINT64_C(0xb424dc35095cd80f), UINT64_C(0x538484c19ef38c95)}, |
| {UINT64_C(0xe12e13424bb40e13), UINT64_C(0x2865a5f206b06fba)}, |
| {UINT64_C(0x8cbccc096f5088cb), UINT64_C(0xf93f87b7442e45d4)}, |
| {UINT64_C(0xafebff0bcb24aafe), UINT64_C(0xf78f69a51539d749)}, |
| {UINT64_C(0xdbe6fecebdedd5be), UINT64_C(0xb573440e5a884d1c)}, |
| {UINT64_C(0x89705f4136b4a597), UINT64_C(0x31680a88f8953031)}, |
| {UINT64_C(0xabcc77118461cefc), UINT64_C(0xfdc20d2b36ba7c3e)}, |
| {UINT64_C(0xd6bf94d5e57a42bc), UINT64_C(0x3d32907604691b4d)}, |
| {UINT64_C(0x8637bd05af6c69b5), UINT64_C(0xa63f9a49c2c1b110)}, |
| {UINT64_C(0xa7c5ac471b478423), UINT64_C(0x0fcf80dc33721d54)}, |
| {UINT64_C(0xd1b71758e219652b), UINT64_C(0xd3c36113404ea4a9)}, |
| {UINT64_C(0x83126e978d4fdf3b), UINT64_C(0x645a1cac083126ea)}, |
| {UINT64_C(0xa3d70a3d70a3d70a), UINT64_C(0x3d70a3d70a3d70a4)}, |
| {UINT64_C(0xcccccccccccccccc), UINT64_C(0xcccccccccccccccd)}, |
| {UINT64_C(0x8000000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xa000000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xc800000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xfa00000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x9c40000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xc350000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xf424000000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x9896800000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xbebc200000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xee6b280000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x9502f90000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xba43b74000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xe8d4a51000000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x9184e72a00000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, |
| {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, |
| {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, |
| {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, |
| {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, |
| {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, |
| {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, |
| {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, |
| {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, |
| {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, |
| {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, |
| {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, |
| {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, |
| {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, |
| {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, |
| {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, |
| {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, |
| {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, |
| {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, |
| {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, |
| {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, |
| {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, |
| {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, |
| {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, |
| {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, |
| {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, |
| {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, |
| {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, |
| {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, |
| {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, |
| {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, |
| {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, |
| {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, |
| {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, |
| {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, |
| {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, |
| {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, |
| {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, |
| {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, |
| {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, |
| {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, |
| {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, |
| {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, |
| {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, |
| {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, |
| {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, |
| {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, |
| {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, |
| {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, |
| {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, |
| {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, |
| {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, |
| {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, |
| {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, |
| {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, |
| {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, |
| {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, |
| {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, |
| {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, |
| {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, |
| {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, |
| {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, |
| {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, |
| {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, |
| {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, |
| {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, |
| {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, |
| {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, |
| {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, |
| {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, |
| {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, |
| {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, |
| {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, |
| {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, |
| {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, |
| {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, |
| {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, |
| {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, |
| {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, |
| {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, |
| {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, |
| {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, |
| {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, |
| {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, |
| {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, |
| {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, |
| {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, |
| {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, |
| {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, |
| {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, |
| {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, |
| {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, |
| {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, |
| {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, |
| {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, |
| {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, |
| {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, |
| {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, |
| {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, |
| {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, |
| {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, |
| {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, |
| {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, |
| {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, |
| {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, |
| {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, |
| {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, |
| {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, |
| {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, |
| {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, |
| {UINT64_C(0x899504ae72497eba), UINT64_C(0x6a06494a791c53a9)}, |
| {UINT64_C(0xabfa45da0edbde69), UINT64_C(0x0487db9d17636893)}, |
| {UINT64_C(0xd6f8d7509292d603), UINT64_C(0x45a9d2845d3c42b7)}, |
| {UINT64_C(0x865b86925b9bc5c2), UINT64_C(0x0b8a2392ba45a9b3)}, |
| {UINT64_C(0xa7f26836f282b732), UINT64_C(0x8e6cac7768d7141f)}, |
| {UINT64_C(0xd1ef0244af2364ff), UINT64_C(0x3207d795430cd927)}, |
| {UINT64_C(0x8335616aed761f1f), UINT64_C(0x7f44e6bd49e807b9)}, |
| {UINT64_C(0xa402b9c5a8d3a6e7), UINT64_C(0x5f16206c9c6209a7)}, |
| {UINT64_C(0xcd036837130890a1), UINT64_C(0x36dba887c37a8c10)}, |
| {UINT64_C(0x802221226be55a64), UINT64_C(0xc2494954da2c978a)}, |
| {UINT64_C(0xa02aa96b06deb0fd), UINT64_C(0xf2db9baa10b7bd6d)}, |
| {UINT64_C(0xc83553c5c8965d3d), UINT64_C(0x6f92829494e5acc8)}, |
| {UINT64_C(0xfa42a8b73abbf48c), UINT64_C(0xcb772339ba1f17fa)}, |
| {UINT64_C(0x9c69a97284b578d7), UINT64_C(0xff2a760414536efc)}, |
| {UINT64_C(0xc38413cf25e2d70d), UINT64_C(0xfef5138519684abb)}, |
| {UINT64_C(0xf46518c2ef5b8cd1), UINT64_C(0x7eb258665fc25d6a)}, |
| {UINT64_C(0x98bf2f79d5993802), UINT64_C(0xef2f773ffbd97a62)}, |
| {UINT64_C(0xbeeefb584aff8603), UINT64_C(0xaafb550ffacfd8fb)}, |
| {UINT64_C(0xeeaaba2e5dbf6784), UINT64_C(0x95ba2a53f983cf39)}, |
| {UINT64_C(0x952ab45cfa97a0b2), UINT64_C(0xdd945a747bf26184)}, |
| {UINT64_C(0xba756174393d88df), UINT64_C(0x94f971119aeef9e5)}, |
| {UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, |
| {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, |
| {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, |
| {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, |
| {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, |
| {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, |
| {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, |
| {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, |
| {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, |
| {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, |
| {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, |
| {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, |
| {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, |
| {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, |
| {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, |
| {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, |
| {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, |
| {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, |
| {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, |
| {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, |
| {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, |
| {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, |
| {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, |
| {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, |
| {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, |
| {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, |
| {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, |
| {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, |
| {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, |
| {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, |
| {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, |
| {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, |
| {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, |
| {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, |
| {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, |
| {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, |
| {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, |
| {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, |
| {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, |
| {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, |
| {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, |
| {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, |
| {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, |
| {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, |
| {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, |
| {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, |
| {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, |
| {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, |
| {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, |
| {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, |
| {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, |
| {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, |
| {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, |
| {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, |
| {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, |
| {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, |
| {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, |
| {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, |
| {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, |
| {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, |
| {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, |
| {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, |
| {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, |
| {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, |
| {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, |
| {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, |
| {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, |
| {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, |
| {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, |
| {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, |
| {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, |
| {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, |
| {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, |
| {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, |
| {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, |
| {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, |
| {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, |
| {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, |
| {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, |
| {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, |
| {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, |
| {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, |
| {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, |
| {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, |
| {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, |
| {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, |
| {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, |
| {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, |
| {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, |
| {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, |
| {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, |
| {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, |
| {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, |
| {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, |
| {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, |
| {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, |
| {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, |
| {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, |
| {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, |
| {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, |
| {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, |
| {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, |
| {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, |
| {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, |
| {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, |
| {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, |
| {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, |
| {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, |
| {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, |
| {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, |
| {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, |
| {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, |
| {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, |
| {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, |
| {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, |
| {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, |
| {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, |
| {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, |
| {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, |
| {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, |
| {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, |
| {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, |
| {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, |
| {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, |
| {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, |
| {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, |
| {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, |
| {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, |
| {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, |
| {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, |
| {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, |
| {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, |
| {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, |
| {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, |
| {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, |
| {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, |
| {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, |
| {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, |
| {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, |
| {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, |
| {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, |
| {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, |
| {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, |
| {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, |
| {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, |
| {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, |
| {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, |
| {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, |
| {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, |
| {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, |
| {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, |
| {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, |
| {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, |
| {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, |
| {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, |
| {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, |
| {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, |
| {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, |
| {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, |
| {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, |
| {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, |
| {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, |
| {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, |
| {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, |
| {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, |
| {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, |
| {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, |
| {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, |
| {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}}; |
| }; |
| #if !JKJ_HAS_INLINE_VARIABLE |
| // decltype(...) should not depend on Dummy; see |
| // https://stackoverflow.com/questions/76438400/decltype-on-static-variable-in-template-class. |
| template <class Dummy> |
| constexpr decltype(cache_holder<ieee754_binary64>::cache) |
| cache_holder<ieee754_binary64, Dummy>::cache; |
| #endif |
| |
| // Compressed cache. |
| template <class FloatFormat, class Dummy = void> |
| struct compressed_cache_holder { |
| using cache_entry_type = typename cache_holder<FloatFormat>::cache_entry_type; |
| static constexpr int cache_bits = cache_holder<FloatFormat>::cache_bits; |
| static constexpr int min_k = cache_holder<FloatFormat>::min_k; |
| static constexpr int max_k = cache_holder<FloatFormat>::max_k; |
| |
| template <class ShiftAmountType, class DecimalExponentType> |
| static constexpr cache_entry_type get_cache(DecimalExponentType k) noexcept { |
| return cache_holder<FloatFormat>::cache[k - min_k]; |
| } |
| }; |
| |
| template <class Dummy> |
| struct compressed_cache_holder<ieee754_binary32, Dummy> { |
| using cache_entry_type = cache_holder<ieee754_binary32>::cache_entry_type; |
| static constexpr int cache_bits = cache_holder<ieee754_binary32>::cache_bits; |
| static constexpr int min_k = cache_holder<ieee754_binary32>::min_k; |
| static constexpr int max_k = cache_holder<ieee754_binary32>::max_k; |
| static constexpr int compression_ratio = 13; |
| static constexpr detail::stdr::size_t compressed_table_size = |
| detail::stdr::size_t((max_k - min_k + compression_ratio) / compression_ratio); |
| static constexpr detail::stdr::size_t pow5_table_size = |
| detail::stdr::size_t((compression_ratio + 1) / 2); |
| |
| using cache_holder_t = detail::array<cache_entry_type, compressed_table_size>; |
| using pow5_holder_t = detail::array<detail::stdr::uint_least16_t, pow5_table_size>; |
| |
| #if JKJ_HAS_CONSTEXPR17 |
| static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION = [] { |
| cache_holder_t res{}; |
| for (detail::stdr::size_t i = 0; i < compressed_table_size; ++i) { |
| res[i] = cache_holder<ieee754_binary32>::cache[i * compression_ratio]; |
| } |
| return res; |
| }(); |
| static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = [] { |
| pow5_holder_t res{}; |
| detail::stdr::uint_least16_t p = 1; |
| for (detail::stdr::size_t i = 0; i < pow5_table_size; ++i) { |
| res[i] = p; |
| p *= 5; |
| } |
| return res; |
| }(); |
| #else |
| template <detail::stdr::size_t... indices> |
| static constexpr cache_holder_t make_cache(detail::index_sequence<indices...>) { |
| return {cache_holder<ieee754_binary32>::cache[indices * compression_ratio]...}; |
| } |
| static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION = |
| make_cache(detail::make_index_sequence<compressed_table_size>{}); |
| |
| template <detail::stdr::size_t... indices> |
| static constexpr pow5_holder_t make_pow5_table(detail::index_sequence<indices...>) { |
| return {detail::compute_power<indices>(detail::stdr::uint_least16_t(5))...}; |
| } |
| static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = |
| make_pow5_table(detail::make_index_sequence<pow5_table_size>{}); |
| #endif |
| |
| template <class ShiftAmountType, class DecimalExponentType> |
| static JKJ_CONSTEXPR20 cache_entry_type get_cache(DecimalExponentType k) noexcept { |
| // Compute the base index. |
| // Supposed to compute (k - min_k) / compression_ratio. |
| static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); |
| static_assert(max_k - min_k <= detail::stdr::numeric_limits<DecimalExponentType>::max(), |
| ""); |
| auto const cache_index = |
| DecimalExponentType(detail::stdr::uint_fast16_t(DecimalExponentType(k - min_k) * |
| detail::stdr::int_fast16_t(79)) >> |
| 10); |
| auto const kb = DecimalExponentType(cache_index * compression_ratio + min_k); |
| auto const offset = DecimalExponentType(k - kb); |
| |
| // Get the base cache. |
| auto const base_cache = cache[cache_index]; |
| |
| if (offset == 0) { |
| return base_cache; |
| } |
| else { |
| // Compute the required amount of bit-shift. |
| auto const alpha = |
| ShiftAmountType(detail::log::floor_log2_pow10<min_k, max_k>(k) - |
| detail::log::floor_log2_pow10<min_k, max_k>(kb) - offset); |
| assert(alpha > 0 && alpha < 64); |
| |
| // Try to recover the real cache. |
| auto const pow5 = |
| offset >= 7 |
| ? detail::stdr::uint_fast32_t(detail::stdr::uint_fast32_t(pow5_table[6]) * |
| pow5_table[offset - 6]) |
| : detail::stdr::uint_fast32_t(pow5_table[offset]); |
| auto mul_result = detail::wuint::umul128(base_cache, pow5); |
| auto const recovered_cache = |
| cache_entry_type((((mul_result.high() << ShiftAmountType(64 - alpha)) | |
| (mul_result.low() >> alpha)) + |
| 1) & |
| UINT64_C(0xffffffffffffffff)); |
| assert(recovered_cache != 0); |
| |
| return recovered_cache; |
| } |
| } |
| }; |
| #if !JKJ_HAS_INLINE_VARIABLE |
| template <class Dummy> |
| constexpr typename compressed_cache_holder<ieee754_binary32, Dummy>::cache_holder_t |
| compressed_cache_holder<ieee754_binary32, Dummy>::cache; |
| template <class Dummy> |
| constexpr typename compressed_cache_holder<ieee754_binary32, Dummy>::pow5_holder_t |
| compressed_cache_holder<ieee754_binary32, Dummy>::pow5_table; |
| #endif |
| |
| template <class Dummy> |
| struct compressed_cache_holder<ieee754_binary64, Dummy> { |
| using cache_entry_type = cache_holder<ieee754_binary64>::cache_entry_type; |
| static constexpr int cache_bits = cache_holder<ieee754_binary64>::cache_bits; |
| static constexpr int min_k = cache_holder<ieee754_binary64>::min_k; |
| static constexpr int max_k = cache_holder<ieee754_binary64>::max_k; |
| static constexpr int compression_ratio = 27; |
| static constexpr detail::stdr::size_t compressed_table_size = |
| detail::stdr::size_t((max_k - min_k + compression_ratio) / compression_ratio); |
| static constexpr detail::stdr::size_t pow5_table_size = |
| detail::stdr::size_t(compression_ratio); |
| |
| using cache_holder_t = detail::array<cache_entry_type, compressed_table_size>; |
| using pow5_holder_t = detail::array<detail::stdr::uint_least64_t, pow5_table_size>; |
| |
| #if JKJ_HAS_CONSTEXPR17 |
| static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION = [] { |
| cache_holder_t res{}; |
| for (detail::stdr::size_t i = 0; i < compressed_table_size; ++i) { |
| res[i] = cache_holder<ieee754_binary64>::cache[i * compression_ratio]; |
| } |
| return res; |
| }(); |
| static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = [] { |
| pow5_holder_t res{}; |
| detail::stdr::uint_least64_t p = 1; |
| for (detail::stdr::size_t i = 0; i < pow5_table_size; ++i) { |
| res[i] = p; |
| p *= 5; |
| } |
| return res; |
| }(); |
| #else |
| template <detail::stdr::size_t... indices> |
| static constexpr cache_holder_t make_cache(detail::index_sequence<indices...>) { |
| return {cache_holder<ieee754_binary64>::cache[indices * compression_ratio]...}; |
| } |
| static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION = |
| make_cache(detail::make_index_sequence<compressed_table_size>{}); |
| |
| template <detail::stdr::size_t... indices> |
| static constexpr pow5_holder_t make_pow5_table(detail::index_sequence<indices...>) { |
| return {detail::compute_power<indices>(detail::stdr::uint_least64_t(5))...}; |
| } |
| static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = |
| make_pow5_table(detail::make_index_sequence<pow5_table_size>{}); |
| #endif |
| |
| template <class ShiftAmountType, class DecimalExponentType> |
| static JKJ_CONSTEXPR20 cache_entry_type get_cache(DecimalExponentType k) noexcept { |
| // Compute the base index. |
| // Supposed to compute (k - min_k) / compression_ratio. |
| static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); |
| static_assert(max_k - min_k <= detail::stdr::numeric_limits<DecimalExponentType>::max(), |
| ""); |
| auto const cache_index = |
| DecimalExponentType(detail::stdr::uint_fast32_t(DecimalExponentType(k - min_k) * |
| detail::stdr::int_fast32_t(607)) >> |
| 14); |
| auto const kb = DecimalExponentType(cache_index * compression_ratio + min_k); |
| auto const offset = DecimalExponentType(k - kb); |
| |
| // Get the base cache. |
| auto const base_cache = cache[cache_index]; |
| |
| if (offset == 0) { |
| return base_cache; |
| } |
| else { |
| // Compute the required amount of bit-shift. |
| auto const alpha = |
| ShiftAmountType(detail::log::floor_log2_pow10<min_k, max_k>(k) - |
| detail::log::floor_log2_pow10<min_k, max_k>(kb) - offset); |
| assert(alpha > 0 && alpha < 64); |
| |
| // Try to recover the real cache. |
| auto const pow5 = pow5_table[offset]; |
| auto recovered_cache = detail::wuint::umul128(base_cache.high(), pow5); |
| auto const middle_low = detail::wuint::umul128(base_cache.low(), pow5); |
| |
| recovered_cache += middle_low.high(); |
| |
| auto const high_to_middle = detail::stdr::uint_least64_t( |
| (recovered_cache.high() << ShiftAmountType(64 - alpha)) & |
| UINT64_C(0xffffffffffffffff)); |
| auto const middle_to_low = detail::stdr::uint_least64_t( |
| (recovered_cache.low() << ShiftAmountType(64 - alpha)) & |
| UINT64_C(0xffffffffffffffff)); |
| |
| recovered_cache = {(recovered_cache.low() >> alpha) | high_to_middle, |
| ((middle_low.low() >> alpha) | middle_to_low)}; |
| |
| assert(recovered_cache.low() != UINT64_C(0xffffffffffffffff)); |
| recovered_cache = {recovered_cache.high(), |
| detail::stdr::uint_least64_t(recovered_cache.low() + 1)}; |
| |
| return recovered_cache; |
| } |
| } |
| }; |
| #if !JKJ_HAS_INLINE_VARIABLE |
| template <class Dummy> |
| constexpr typename compressed_cache_holder<ieee754_binary64, Dummy>::cache_holder_t |
| compressed_cache_holder<ieee754_binary64, Dummy>::cache; |
| template <class Dummy> |
| constexpr typename compressed_cache_holder<ieee754_binary64, Dummy>::pow5_holder_t |
| compressed_cache_holder<ieee754_binary64, Dummy>::pow5_table; |
| #endif |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Forward declarations of user-specializable templates used in the main algorithm. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| // Remove trailing zeros from significand and add the number of removed zeros into |
| // exponent. |
| template <class TrailingZeroPolicy, class Format, class DecimalSignificand, |
| class DecimalExponentType> |
| struct remove_trailing_zeros_traits; |
| |
| // Users can specialize this traits class to make Dragonbox work with their own formats. |
| // However, this requires detailed knowledge on how the algorithm works, so it is recommended to |
| // read through the paper. |
| template <class FormatTraits, class CacheEntryType, detail::stdr::size_t cache_bits_> |
| struct multiplication_traits; |
| |
| // A collection of some common definitions to reduce boilerplate. |
| template <class FormatTraits, class CacheEntryType, detail::stdr::size_t cache_bits_> |
| struct multiplication_traits_base { |
| using format = typename FormatTraits::format; |
| static constexpr int significand_bits = format::significand_bits; |
| static constexpr int total_bits = format::total_bits; |
| using carrier_uint = typename FormatTraits::carrier_uint; |
| using cache_entry_type = CacheEntryType; |
| static constexpr int cache_bits = int(cache_bits_); |
| |
| struct compute_mul_result { |
| carrier_uint integer_part; |
| bool is_integer; |
| }; |
| struct compute_mul_parity_result { |
| bool parity; |
| bool is_integer; |
| }; |
| }; |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Policies. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| namespace detail { |
| template <class T> |
| struct dummy {}; |
| } |
| |
| namespace policy { |
| namespace sign { |
| JKJ_INLINE_VARIABLE struct ignore_t { |
| using sign_policy = ignore_t; |
| static constexpr bool return_has_sign = false; |
| |
| #if defined(_MSC_VER) && !defined(__clang__) |
| // See |
| // https://developercommunity.visualstudio.com/t/Failure-to-optimize-intrinsics/10628226 |
| template <class SignedSignificandBits, class DecimalSignificand, |
| class DecimalExponentType> |
| static constexpr decimal_fp<DecimalSignificand, DecimalExponentType, false, false> |
| handle_sign( |
| SignedSignificandBits, |
| decimal_fp<DecimalSignificand, DecimalExponentType, false, false> r) noexcept { |
| return {r.significand, r.exponent}; |
| } |
| template <class SignedSignificandBits, class DecimalSignificand, |
| class DecimalExponentType> |
| static constexpr decimal_fp<DecimalSignificand, DecimalExponentType, false, true> |
| handle_sign( |
| SignedSignificandBits, |
| decimal_fp<DecimalSignificand, DecimalExponentType, false, true> r) noexcept { |
| return {r.significand, r.exponent, r.may_have_trailing_zeros}; |
| } |
| #else |
| template <class SignedSignificandBits, class UnsignedDecimalFp> |
| static constexpr UnsignedDecimalFp handle_sign(SignedSignificandBits, |
| UnsignedDecimalFp r) noexcept { |
| return r; |
| } |
| #endif |
| } ignore = {}; |
| |
| JKJ_INLINE_VARIABLE struct return_sign_t { |
| using sign_policy = return_sign_t; |
| static constexpr bool return_has_sign = true; |
| |
| template <class SignedSignificandBits, class UnsignedDecimalFp> |
| static constexpr detail::unsigned_decimal_fp_to_signed_t<UnsignedDecimalFp> |
| handle_sign(SignedSignificandBits s, UnsignedDecimalFp r) noexcept { |
| return add_sign_to_unsigned_decimal_fp(s.is_negative(), r); |
| } |
| } return_sign = {}; |
| } |
| |
| namespace trailing_zero { |
| JKJ_INLINE_VARIABLE struct ignore_t { |
| using trailing_zero_policy = ignore_t; |
| static constexpr bool report_trailing_zeros = false; |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| on_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent}; |
| } |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| no_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent}; |
| } |
| } ignore = {}; |
| |
| JKJ_INLINE_VARIABLE struct remove_t { |
| using trailing_zero_policy = remove_t; |
| static constexpr bool report_trailing_zeros = false; |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 |
| unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| on_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| remove_trailing_zeros_traits< |
| remove_t, Format, DecimalSignificand, |
| DecimalExponentType>::remove_trailing_zeros(significand, exponent); |
| return {significand, exponent}; |
| } |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| no_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent}; |
| } |
| } remove = {}; |
| |
| JKJ_INLINE_VARIABLE struct remove_compact_t { |
| using trailing_zero_policy = remove_compact_t; |
| static constexpr bool report_trailing_zeros = false; |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 |
| unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| on_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| remove_trailing_zeros_traits< |
| remove_compact_t, Format, DecimalSignificand, |
| DecimalExponentType>::remove_trailing_zeros(significand, exponent); |
| return {significand, exponent}; |
| } |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, false> |
| no_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent}; |
| } |
| } remove_compact = {}; |
| |
| JKJ_INLINE_VARIABLE struct report_t { |
| using trailing_zero_policy = report_t; |
| static constexpr bool report_trailing_zeros = true; |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, true> |
| on_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent, true}; |
| } |
| |
| template <class Format, class DecimalSignificand, class DecimalExponentType> |
| static constexpr unsigned_decimal_fp<DecimalSignificand, DecimalExponentType, true> |
| no_trailing_zeros(DecimalSignificand significand, |
| DecimalExponentType exponent) noexcept { |
| return {significand, exponent, false}; |
| } |
| } report = {}; |
| } |
| |
| namespace decimal_to_binary_rounding { |
| enum class tag_t { to_nearest, left_closed_directed, right_closed_directed }; |
| |
| namespace interval_type { |
| struct symmetric_boundary { |
| static constexpr bool is_symmetric = true; |
| bool is_closed; |
| constexpr bool include_left_endpoint() const noexcept { return is_closed; } |
| constexpr bool include_right_endpoint() const noexcept { return is_closed; } |
| }; |
| struct asymmetric_boundary { |
| static constexpr bool is_symmetric = false; |
| bool is_left_closed; |
| constexpr bool include_left_endpoint() const noexcept { return is_left_closed; } |
| constexpr bool include_right_endpoint() const noexcept { |
| return !is_left_closed; |
| } |
| }; |
| struct closed { |
| static constexpr bool is_symmetric = true; |
| static constexpr bool include_left_endpoint() noexcept { return true; } |
| static constexpr bool include_right_endpoint() noexcept { return true; } |
| }; |
| struct open { |
| static constexpr bool is_symmetric = true; |
| static constexpr bool include_left_endpoint() noexcept { return false; } |
| static constexpr bool include_right_endpoint() noexcept { return false; } |
| }; |
| struct left_closed_right_open { |
| static constexpr bool is_symmetric = false; |
| static constexpr bool include_left_endpoint() noexcept { return true; } |
| static constexpr bool include_right_endpoint() noexcept { return false; } |
| }; |
| struct right_closed_left_open { |
| static constexpr bool is_symmetric = false; |
| static constexpr bool include_left_endpoint() noexcept { return false; } |
| static constexpr bool include_right_endpoint() noexcept { return true; } |
| }; |
| } |
| |
| JKJ_INLINE_VARIABLE struct nearest_to_even_t { |
| using decimal_to_binary_rounding_policy = nearest_to_even_t; |
| using interval_type_provider = nearest_to_even_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_to_even_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_to_even_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::symmetric_boundary |
| normal_interval(SignedSignificandBits s) noexcept { |
| return {s.has_even_significand_bits()}; |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::closed |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| } nearest_to_even = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_to_odd_t { |
| using decimal_to_binary_rounding_policy = nearest_to_odd_t; |
| using interval_type_provider = nearest_to_odd_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_to_odd_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_to_odd_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::symmetric_boundary |
| normal_interval(SignedSignificandBits s) noexcept { |
| return {!s.has_even_significand_bits()}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::open |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| } nearest_to_odd = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_toward_plus_infinity_t { |
| using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity_t; |
| using interval_type_provider = nearest_toward_plus_infinity_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_toward_plus_infinity_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_toward_plus_infinity_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::asymmetric_boundary |
| normal_interval(SignedSignificandBits s) noexcept { |
| return {!s.is_negative()}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::asymmetric_boundary |
| shorter_interval(SignedSignificandBits s) noexcept { |
| return {!s.is_negative()}; |
| } |
| } nearest_toward_plus_infinity = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_toward_minus_infinity_t { |
| using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity_t; |
| using interval_type_provider = nearest_toward_minus_infinity_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_toward_minus_infinity_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_toward_minus_infinity_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::asymmetric_boundary |
| normal_interval(SignedSignificandBits s) noexcept { |
| return {s.is_negative()}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::asymmetric_boundary |
| shorter_interval(SignedSignificandBits s) noexcept { |
| return {s.is_negative()}; |
| } |
| } nearest_toward_minus_infinity = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_toward_zero_t { |
| using decimal_to_binary_rounding_policy = nearest_toward_zero_t; |
| using interval_type_provider = nearest_toward_zero_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_toward_zero_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_toward_zero_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::right_closed_left_open |
| normal_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::right_closed_left_open |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| } nearest_toward_zero = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_away_from_zero_t { |
| using decimal_to_binary_rounding_policy = nearest_away_from_zero_t; |
| using interval_type_provider = nearest_away_from_zero_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| dragonbox::detail::declval<nearest_away_from_zero_t>(), Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(nearest_away_from_zero_t{}, args...); |
| } |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::left_closed_right_open |
| normal_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::left_closed_right_open |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| } nearest_away_from_zero = {}; |
| |
| namespace detail { |
| struct nearest_always_closed_t { |
| using interval_type_provider = nearest_always_closed_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::closed |
| normal_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::closed |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| }; |
| struct nearest_always_open_t { |
| using interval_type_provider = nearest_always_open_t; |
| static constexpr auto tag = tag_t::to_nearest; |
| |
| template <class SignedSignificandBits> |
| static constexpr interval_type::open |
| normal_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| template <class SignedSignificandBits> |
| static constexpr interval_type::open |
| shorter_interval(SignedSignificandBits) noexcept { |
| return {}; |
| } |
| }; |
| } |
| |
| JKJ_INLINE_VARIABLE struct nearest_to_even_static_boundary_t { |
| using decimal_to_binary_rounding_policy = nearest_to_even_static_boundary_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::nearest_always_closed_t{}, Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.has_even_significand_bits() |
| ? f(detail::nearest_always_closed_t{}, args...) |
| : f(detail::nearest_always_open_t{}, args...); |
| } |
| } nearest_to_even_static_boundary = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_to_odd_static_boundary_t { |
| using decimal_to_binary_rounding_policy = nearest_to_odd_static_boundary_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::nearest_always_closed_t{}, Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.has_even_significand_bits() |
| ? f(detail::nearest_always_open_t{}, args...) |
| : f(detail::nearest_always_closed_t{}, args...); |
| } |
| } nearest_to_odd_static_boundary = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_toward_plus_infinity_static_boundary_t { |
| using decimal_to_binary_rounding_policy = |
| nearest_toward_plus_infinity_static_boundary_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE |
| JKJ_SAFEBUFFERS static constexpr decltype(Func{}(nearest_toward_zero, |
| Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.is_negative() ? f(nearest_toward_zero, args...) |
| : f(nearest_away_from_zero, args...); |
| } |
| } nearest_toward_plus_infinity_static_boundary = {}; |
| |
| JKJ_INLINE_VARIABLE struct nearest_toward_minus_infinity_static_boundary_t { |
| using decimal_to_binary_rounding_policy = |
| nearest_toward_minus_infinity_static_boundary_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE |
| JKJ_SAFEBUFFERS static constexpr decltype(Func{}(nearest_toward_zero, |
| Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.is_negative() ? f(nearest_away_from_zero, args...) |
| : f(nearest_toward_zero, args...); |
| } |
| } nearest_toward_minus_infinity_static_boundary = {}; |
| |
| namespace detail { |
| struct left_closed_directed_t { |
| static constexpr auto tag = tag_t::left_closed_directed; |
| }; |
| struct right_closed_directed_t { |
| static constexpr auto tag = tag_t::right_closed_directed; |
| }; |
| } |
| |
| JKJ_INLINE_VARIABLE struct toward_plus_infinity_t { |
| using decimal_to_binary_rounding_policy = toward_plus_infinity_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::left_closed_directed_t{}, Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.is_negative() ? f(detail::left_closed_directed_t{}, args...) |
| : f(detail::right_closed_directed_t{}, args...); |
| } |
| } toward_plus_infinity = {}; |
| |
| JKJ_INLINE_VARIABLE struct toward_minus_infinity_t { |
| using decimal_to_binary_rounding_policy = toward_minus_infinity_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::left_closed_directed_t{}, Args{}...)) |
| delegate(SignedSignificandBits s, Func f, Args... args) noexcept { |
| return s.is_negative() ? f(detail::right_closed_directed_t{}, args...) |
| : f(detail::left_closed_directed_t{}, args...); |
| } |
| } toward_minus_infinity = {}; |
| |
| JKJ_INLINE_VARIABLE struct toward_zero_t { |
| using decimal_to_binary_rounding_policy = toward_zero_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::left_closed_directed_t{}, Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(detail::left_closed_directed_t{}, args...); |
| } |
| } toward_zero = {}; |
| |
| JKJ_INLINE_VARIABLE struct away_from_zero_t { |
| using decimal_to_binary_rounding_policy = away_from_zero_t; |
| |
| template <class SignedSignificandBits, class Func, class... Args> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static constexpr decltype(Func{}( |
| detail::right_closed_directed_t{}, Args{}...)) |
| delegate(SignedSignificandBits, Func f, Args... args) noexcept { |
| return f(detail::right_closed_directed_t{}, args...); |
| } |
| } away_from_zero = {}; |
| } |
| |
| namespace binary_to_decimal_rounding { |
| // (Always assumes nearest rounding modes, as there can be no tie for other rounding |
| // modes.) |
| enum class tag_t { do_not_care, to_even, to_odd, away_from_zero, toward_zero }; |
| |
| // The parameter significand corresponds to 10\tilde{s}+t in the paper. |
| |
| JKJ_INLINE_VARIABLE struct do_not_care_t { |
| using binary_to_decimal_rounding_policy = do_not_care_t; |
| static constexpr auto tag = tag_t::do_not_care; |
| |
| template <class CarrierUInt> |
| static constexpr bool prefer_round_down(CarrierUInt) noexcept { |
| return false; |
| } |
| } do_not_care = {}; |
| |
| JKJ_INLINE_VARIABLE struct to_even_t { |
| using binary_to_decimal_rounding_policy = to_even_t; |
| static constexpr auto tag = tag_t::to_even; |
| |
| template <class CarrierUInt> |
| static constexpr bool prefer_round_down(CarrierUInt significand) noexcept { |
| return significand % 2 != 0; |
| } |
| } to_even = {}; |
| |
| JKJ_INLINE_VARIABLE struct to_odd_t { |
| using binary_to_decimal_rounding_policy = to_odd_t; |
| static constexpr auto tag = tag_t::to_odd; |
| |
| template <class CarrierUInt> |
| static constexpr bool prefer_round_down(CarrierUInt significand) noexcept { |
| return significand % 2 == 0; |
| } |
| } to_odd = {}; |
| |
| JKJ_INLINE_VARIABLE struct away_from_zero_t { |
| using binary_to_decimal_rounding_policy = away_from_zero_t; |
| static constexpr auto tag = tag_t::away_from_zero; |
| |
| template <class CarrierUInt> |
| static constexpr bool prefer_round_down(CarrierUInt) noexcept { |
| return false; |
| } |
| } away_from_zero = {}; |
| |
| JKJ_INLINE_VARIABLE struct toward_zero_t { |
| using binary_to_decimal_rounding_policy = toward_zero_t; |
| static constexpr auto tag = tag_t::toward_zero; |
| |
| template <class CarrierUInt> |
| static constexpr bool prefer_round_down(CarrierUInt) noexcept { |
| return true; |
| } |
| } toward_zero = {}; |
| } |
| |
| namespace cache { |
| JKJ_INLINE_VARIABLE struct full_t { |
| using cache_policy = full_t; |
| template <class FloatFormat> |
| using cache_holder_type = cache_holder<FloatFormat>; |
| |
| template <class FloatFormat, class ShiftAmountType, class DecimalExponentType> |
| static constexpr typename cache_holder_type<FloatFormat>::cache_entry_type |
| get_cache(DecimalExponentType k) noexcept { |
| #if JKJ_HAS_CONSTEXPR14 |
| assert(k >= cache_holder_type<FloatFormat>::min_k && |
| k <= cache_holder_type<FloatFormat>::max_k); |
| #endif |
| return cache_holder_type<FloatFormat>::cache[detail::stdr::size_t( |
| k - cache_holder_type<FloatFormat>::min_k)]; |
| } |
| } full = {}; |
| |
| JKJ_INLINE_VARIABLE struct compact_t { |
| using cache_policy = compact_t; |
| template <class FloatFormat> |
| using cache_holder_type = compressed_cache_holder<FloatFormat>; |
| |
| template <class FloatFormat, class ShiftAmountType, class DecimalExponentType> |
| static JKJ_CONSTEXPR20 typename cache_holder<FloatFormat>::cache_entry_type |
| get_cache(DecimalExponentType k) noexcept { |
| assert(k >= cache_holder<FloatFormat>::min_k && |
| k <= cache_holder<FloatFormat>::max_k); |
| |
| return cache_holder_type<FloatFormat>::template get_cache<ShiftAmountType>(k); |
| } |
| } compact = {}; |
| } |
| |
| namespace preferred_integer_types { |
| JKJ_INLINE_VARIABLE struct match_t { |
| using preferred_integer_types_policy = match_t; |
| |
| template <class FormatTraits, detail::stdr::uint_least64_t upper_bound> |
| using remainder_type = typename FormatTraits::carrier_uint; |
| |
| template <class FormatTraits, detail::stdr::int_least32_t lower_bound, |
| detail::stdr::uint_least32_t upper_bound> |
| using decimal_exponent_type = typename FormatTraits::exponent_int; |
| |
| template <class FormatTraits> |
| using shift_amount_type = typename FormatTraits::exponent_int; |
| } match; |
| |
| JKJ_INLINE_VARIABLE struct prefer_32_t { |
| using preferred_integer_types_policy = prefer_32_t; |
| |
| template <class FormatTraits, detail::stdr::uint_least64_t upper_bound> |
| using remainder_type = typename detail::stdr::conditional< |
| upper_bound <= |
| detail::stdr::numeric_limits<detail::stdr::uint_least32_t>::max(), |
| detail::stdr::uint_least32_t, typename FormatTraits::carrier_uint>::type; |
| |
| template <class FormatTraits, detail::stdr::int_least32_t lower_bound, |
| detail::stdr::uint_least32_t upper_bound> |
| using decimal_exponent_type = typename detail::stdr::conditional< |
| FormatTraits::format::exponent_bits <= |
| detail::value_bits<detail::stdr::int_least32_t>::value, |
| detail::stdr::int_least32_t, typename FormatTraits::exponent_int>::type; |
| |
| template <class FormatTraits> |
| using shift_amount_type = detail::stdr::int_least32_t; |
| } prefer_32; |
| |
| JKJ_INLINE_VARIABLE struct minimal_t { |
| using preferred_integer_types_policy = minimal_t; |
| |
| template <class FormatTraits, detail::stdr::uint_least64_t upper_bound> |
| using remainder_type = typename detail::stdr::conditional< |
| upper_bound <= detail::stdr::numeric_limits<detail::stdr::uint_least8_t>::max(), |
| detail::stdr::uint_least8_t, |
| typename detail::stdr::conditional< |
| upper_bound <= |
| detail::stdr::numeric_limits<detail::stdr::uint_least16_t>::max(), |
| detail::stdr::uint_least16_t, |
| typename detail::stdr::conditional< |
| upper_bound <= |
| detail::stdr::numeric_limits<detail::stdr::uint_least32_t>::max(), |
| detail::stdr::uint_least32_t, |
| typename detail::stdr::conditional< |
| upper_bound <= detail::stdr::numeric_limits< |
| detail::stdr::uint_least64_t>::max(), |
| detail::stdr::uint_least64_t, |
| typename FormatTraits::carrier_uint>::type>::type>::type>::type; |
| |
| template <class FormatTraits, detail::stdr::int_least32_t lower_bound, |
| detail::stdr::uint_least32_t upper_bound> |
| using decimal_exponent_type = typename detail::stdr::conditional< |
| lower_bound >= |
| detail::stdr::numeric_limits<detail::stdr::int_least8_t>::min() && |
| upper_bound <= |
| detail::stdr::numeric_limits<detail::stdr::int_least8_t>::max(), |
| detail::stdr::int_least8_t, |
| typename detail::stdr::conditional< |
| lower_bound >= |
| detail::stdr::numeric_limits<detail::stdr::int_least16_t>::min() && |
| upper_bound <= |
| detail::stdr::numeric_limits<detail::stdr::int_least16_t>::max(), |
| detail::stdr::int_least16_t, |
| typename detail::stdr::conditional< |
| lower_bound >= detail::stdr::numeric_limits< |
| detail::stdr::int_least32_t>::min() && |
| upper_bound <= detail::stdr::numeric_limits< |
| detail::stdr::int_least32_t>::max(), |
| detail::stdr::int_least32_t, |
| typename FormatTraits::exponent_int>::type>::type>::type; |
| |
| template <class FormatTraits> |
| using shift_amount_type = detail::stdr::int_least8_t; |
| } minimal; |
| } |
| } |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Specializations of user-specializable templates used in the main algorithm. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <class DecimalExponentType> |
| struct remove_trailing_zeros_traits<policy::trailing_zero::remove_t, ieee754_binary32, |
| detail::stdr::uint_least32_t, DecimalExponentType> { |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 void |
| remove_trailing_zeros(detail::stdr::uint_least32_t& significand, |
| DecimalExponentType& exponent) noexcept { |
| // See https://github.com/jk-jeon/rtz_benchmark. |
| // The idea of branchless search below is by reddit users r/pigeon768 and |
| // r/TheoreticalDumbass. |
| |
| auto r = detail::bits::rotr<32>( |
| detail::stdr::uint_least32_t(significand * UINT32_C(184254097)), 4); |
| auto b = r < UINT32_C(429497); |
| auto s = detail::stdr::size_t(b); |
| significand = b ? r : significand; |
| |
| r = detail::bits::rotr<32>( |
| detail::stdr::uint_least32_t(significand * UINT32_C(42949673)), 2); |
| b = r < UINT32_C(42949673); |
| s = s * 2 + b; |
| significand = b ? r : significand; |
| |
| r = detail::bits::rotr<32>( |
| detail::stdr::uint_least32_t(significand * UINT32_C(1288490189)), 1); |
| b = r < UINT32_C(429496730); |
| s = s * 2 + b; |
| significand = b ? r : significand; |
| |
| exponent += s; |
| } |
| }; |
| |
| template <class DecimalExponentType> |
| struct remove_trailing_zeros_traits<policy::trailing_zero::remove_t, ieee754_binary64, |
| detail::stdr::uint_least64_t, DecimalExponentType> { |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 void |
| remove_trailing_zeros(detail::stdr::uint_least64_t& significand, |
| DecimalExponentType& exponent) noexcept { |
| // See https://github.com/jk-jeon/rtz_benchmark. |
| // The idea of branchless search below is by reddit users r/pigeon768 and |
| // r/TheoreticalDumbass. |
| |
| auto r = detail::bits::rotr<64>( |
| detail::stdr::uint_least64_t(significand * UINT64_C(28999941890838049)), 8); |
| auto b = r < UINT64_C(184467440738); |
| auto s = detail::stdr::size_t(b); |
| significand = b ? r : significand; |
| |
| r = detail::bits::rotr<64>( |
| detail::stdr::uint_least64_t(significand * UINT64_C(182622766329724561)), 4); |
| b = r < UINT64_C(1844674407370956); |
| s = s * 2 + b; |
| significand = b ? r : significand; |
| |
| r = detail::bits::rotr<64>( |
| detail::stdr::uint_least64_t(significand * UINT64_C(10330176681277348905)), 2); |
| b = r < UINT64_C(184467440737095517); |
| s = s * 2 + b; |
| significand = b ? r : significand; |
| |
| r = detail::bits::rotr<64>( |
| detail::stdr::uint_least64_t(significand * UINT32_C(14757395258967641293)), 1); |
| b = r < UINT64_C(1844674407370955162); |
| s = s * 2 + b; |
| significand = b ? r : significand; |
| |
| exponent += s; |
| } |
| }; |
| |
| template <class DecimalExponentType> |
| struct remove_trailing_zeros_traits<policy::trailing_zero::remove_compact_t, ieee754_binary32, |
| detail::stdr::uint_least32_t, DecimalExponentType> { |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 void |
| remove_trailing_zeros(detail::stdr::uint_least32_t& significand, |
| DecimalExponentType& exponent) noexcept { |
| // See https://github.com/jk-jeon/rtz_benchmark. |
| while (true) { |
| auto const r = detail::stdr::uint_least32_t(significand * UINT32_C(1288490189)); |
| if (r < UINT32_C(429496731)) { |
| significand = detail::stdr::uint_least32_t(r >> 1); |
| exponent += 1; |
| } |
| else { |
| break; |
| } |
| } |
| } |
| }; |
| |
| template <class DecimalExponentType> |
| struct remove_trailing_zeros_traits<policy::trailing_zero::remove_compact_t, ieee754_binary64, |
| detail::stdr::uint_least64_t, DecimalExponentType> { |
| JKJ_FORCEINLINE static JKJ_CONSTEXPR14 void |
| remove_trailing_zeros(detail::stdr::uint_least64_t& significand, |
| DecimalExponentType& exponent) noexcept { |
| // See https://github.com/jk-jeon/rtz_benchmark. |
| while (true) { |
| auto const r = |
| detail::stdr::uint_least64_t(significand * UINT64_C(5534023222112865485)); |
| if (r < UINT64_C(1844674407370955163)) { |
| significand = detail::stdr::uint_least64_t(r >> 1); |
| exponent += 1; |
| } |
| else { |
| break; |
| } |
| } |
| } |
| }; |
| |
| template <class ExponentInt> |
| struct multiplication_traits< |
| ieee754_binary_traits<ieee754_binary32, detail::stdr::uint_least32_t, ExponentInt>, |
| detail::stdr::uint_least64_t, 64> |
| : public multiplication_traits_base< |
| ieee754_binary_traits<ieee754_binary32, detail::stdr::uint_least32_t>, |
| detail::stdr::uint_least64_t, 64> { |
| static JKJ_CONSTEXPR20 compute_mul_result |
| compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept { |
| auto const r = detail::wuint::umul96_upper64(u, cache); |
| return {carrier_uint(r >> 32), carrier_uint(r) == 0}; |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr detail::stdr::uint_least64_t compute_delta(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return detail::stdr::uint_least64_t(cache >> ShiftAmountType(cache_bits - 1 - beta)); |
| } |
| |
| template <class ShiftAmountType> |
| static JKJ_CONSTEXPR20 compute_mul_parity_result compute_mul_parity( |
| carrier_uint two_f, cache_entry_type const& cache, ShiftAmountType beta) noexcept { |
| assert(beta >= 1); |
| assert(beta <= 32); |
| |
| auto const r = detail::wuint::umul96_lower64(two_f, cache); |
| return {((r >> ShiftAmountType(64 - beta)) & 1) != 0, |
| (UINT32_C(0xffffffff) & (r >> ShiftAmountType(32 - beta))) == 0}; |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return carrier_uint((cache - (cache >> (significand_bits + 2))) >> |
| ShiftAmountType(cache_bits - significand_bits - 1 - beta)); |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return carrier_uint((cache + (cache >> (significand_bits + 1))) >> |
| ShiftAmountType(cache_bits - significand_bits - 1 - beta)); |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return (carrier_uint(cache >> |
| ShiftAmountType(cache_bits - significand_bits - 2 - beta)) + |
| 1) / |
| 2; |
| } |
| }; |
| |
| template <class ExponentInt> |
| struct multiplication_traits< |
| ieee754_binary_traits<ieee754_binary64, detail::stdr::uint_least64_t, ExponentInt>, |
| detail::wuint::uint128, 128> |
| : public multiplication_traits_base< |
| ieee754_binary_traits<ieee754_binary64, detail::stdr::uint_least64_t>, |
| detail::wuint::uint128, 128> { |
| static JKJ_CONSTEXPR20 compute_mul_result |
| compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept { |
| auto const r = detail::wuint::umul192_upper128(u, cache); |
| return {r.high(), r.low() == 0}; |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr detail::stdr::uint_least64_t compute_delta(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return detail::stdr::uint_least64_t(cache.high() >> |
| ShiftAmountType(total_bits - 1 - beta)); |
| } |
| |
| template <class ShiftAmountType> |
| static JKJ_CONSTEXPR20 compute_mul_parity_result compute_mul_parity( |
| carrier_uint two_f, cache_entry_type const& cache, ShiftAmountType beta) noexcept { |
| assert(beta >= 1); |
| assert(beta < 64); |
| |
| auto const r = detail::wuint::umul192_lower128(two_f, cache); |
| return {((r.high() >> ShiftAmountType(64 - beta)) & 1) != 0, |
| (((r.high() << beta) & UINT64_C(0xffffffffffffffff)) | |
| (r.low() >> ShiftAmountType(64 - beta))) == 0}; |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return (cache.high() - (cache.high() >> (significand_bits + 2))) >> |
| ShiftAmountType(total_bits - significand_bits - 1 - beta); |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return (cache.high() + (cache.high() >> (significand_bits + 1))) >> |
| ShiftAmountType(total_bits - significand_bits - 1 - beta); |
| } |
| |
| template <class ShiftAmountType> |
| static constexpr carrier_uint |
| compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, |
| ShiftAmountType beta) noexcept { |
| return ((cache.high() >> ShiftAmountType(total_bits - significand_bits - 2 - beta)) + |
| 1) / |
| 2; |
| } |
| }; |
| |
| namespace detail { |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // The main algorithm. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <class FormatTraits> |
| struct impl : private FormatTraits::format { |
| using format = typename FormatTraits::format; |
| using carrier_uint = typename FormatTraits::carrier_uint; |
| static constexpr int carrier_bits = FormatTraits::carrier_bits; |
| using exponent_int = typename FormatTraits::exponent_int; |
| |
| using format::significand_bits; |
| using format::min_exponent; |
| using format::max_exponent; |
| using format::exponent_bias; |
| |
| static constexpr int kappa = |
| log::floor_log10_pow2(carrier_bits - significand_bits - 2) - 1; |
| static_assert(kappa >= 1, ""); |
| static_assert(carrier_bits >= significand_bits + 2 + log::floor_log2_pow10(kappa + 1), |
| ""); |
| |
| static constexpr int min(int x, int y) noexcept { return x < y ? x : y; } |
| static constexpr int max(int x, int y) noexcept { return x > y ? x : y; } |
| |
| static constexpr int min_k = |
| min(-log::floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), |
| -log::floor_log10_pow2(max_exponent - significand_bits) + kappa); |
| |
| // We do invoke shorter_interval_case for exponent == min_exponent case, |
| // so we should not add 1 here. |
| static constexpr int max_k = |
| max(-log::floor_log10_pow2_minus_log10_4_over_3(min_exponent - |
| significand_bits /*+ 1*/), |
| -log::floor_log10_pow2(min_exponent - significand_bits) + kappa); |
| |
| static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2; |
| static constexpr int case_shorter_interval_left_endpoint_upper_threshold = |
| 2 + |
| log::floor_log2( |
| compute_power< |
| count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) / |
| 3); |
| |
| static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0; |
| static constexpr int case_shorter_interval_right_endpoint_upper_threshold = |
| 2 + |
| log::floor_log2( |
| compute_power< |
| count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) / |
| 3); |
| |
| static constexpr int shorter_interval_tie_lower_threshold = |
| -log::floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits; |
| static constexpr int shorter_interval_tie_upper_threshold = |
| -log::floor_log5_pow2(significand_bits + 2) - 2 - significand_bits; |
| |
| template <class PreferredIntegerTypesPolicy> |
| using remainder_type = typename PreferredIntegerTypesPolicy::template remainder_type< |
| FormatTraits, compute_power<kappa + 1>(detail::stdr::uint_least64_t(10))>; |
| |
| template <class PreferredIntegerTypesPolicy> |
| using decimal_exponent_type = |
| typename PreferredIntegerTypesPolicy::template decimal_exponent_type< |
| FormatTraits, detail::stdr::int_least32_t(min(-max_k, min_k)), |
| detail::stdr::int_least32_t(max(max_k, -min_k + kappa + 1))>; |
| |
| template <class SignPolicy, class TrailingZeroPolicy, class PreferredIntegerTypesPolicy> |
| using return_type = |
| decimal_fp<carrier_uint, decimal_exponent_type<PreferredIntegerTypesPolicy>, |
| SignPolicy::return_has_sign, TrailingZeroPolicy::report_trailing_zeros>; |
| |
| //// The main algorithm assumes the input is a normal/subnormal finite number. |
| |
| template <class SignPolicy, class TrailingZeroPolicy, class IntervalTypeProvider, |
| class BinaryToDecimalRoundingPolicy, class CachePolicy, |
| class PreferredIntegerTypesPolicy> |
| JKJ_SAFEBUFFERS static JKJ_CONSTEXPR20 |
| return_type<SignPolicy, TrailingZeroPolicy, PreferredIntegerTypesPolicy> |
| compute_nearest(signed_significand_bits<FormatTraits> s, |
| exponent_int exponent_bits) noexcept { |
| using cache_holder_type = typename CachePolicy::template cache_holder_type<format>; |
| static_assert( |
| min_k >= cache_holder_type::min_k && max_k <= cache_holder_type::max_k, ""); |
| |
| using remainder_type_ = remainder_type<PreferredIntegerTypesPolicy>; |
| using decimal_exponent_type_ = decimal_exponent_type<PreferredIntegerTypesPolicy>; |
| using shift_amount_type = |
| typename PreferredIntegerTypesPolicy::template shift_amount_type<FormatTraits>; |
| |
| using multiplication_traits_ = |
| multiplication_traits<FormatTraits, |
| typename cache_holder_type::cache_entry_type, |
| cache_holder_type::cache_bits>; |
| |
| auto two_fc = s.remove_sign_bit_and_shift(); |
| auto binary_exponent = exponent_bits; |
| |
| // Is the input a normal number? |
| if (binary_exponent != 0) { |
| binary_exponent += format::exponent_bias - format::significand_bits; |
| |
| // Shorter interval case; proceed like Schubfach. |
| // One might think this condition is wrong, since when exponent_bits == |
| // 1 and two_fc == 0, the interval is actually regular. However, it |
| // turns out that this seemingly wrong condition is actually fine, |
| // because the end result is anyway the same. |
| // |
| // [binary32] |
| // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 |
| // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 |
| // fc * 2^e = 1.175'494'35... * 10^-38 |
| // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 |
| // |
| // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. |
| // 1.175'494'3 * 10^-38 is also a correct shortest representation that |
| // will be rejected if we assume shorter interval, but 1.175'494'4 * |
| // 10^-38 is closer to the true value so it doesn't matter. |
| // |
| // [binary64] |
| // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 |
| // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 |
| // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 |
| // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 |
| // |
| // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * |
| // 10^-308. This is indeed of the shortest length, and it is the unique |
| // one closest to the true value among valid representations of the same |
| // length. |
| static_assert(stdr::is_same<format, ieee754_binary32>::value || |
| stdr::is_same<format, ieee754_binary64>::value, |
| ""); |
| |
| // Shorter interval case. |
| if (two_fc == 0) { |
| auto interval_type = IntervalTypeProvider::shorter_interval(s); |
| |
| // Compute k and beta. |
| auto const minus_k = log::floor_log10_pow2_minus_log10_4_over_3< |
| min_exponent - format::significand_bits, |
| max_exponent - format::significand_bits, decimal_exponent_type_>( |
| binary_exponent); |
| auto const beta = shift_amount_type( |
| binary_exponent + |
| log::floor_log2_pow10<min_k, max_k>(decimal_exponent_type_(-minus_k))); |
| |
| // Compute xi and zi. |
| auto const cache = |
| CachePolicy::template get_cache<format, shift_amount_type>( |
| decimal_exponent_type_(-minus_k)); |
| |
| auto xi = |
| multiplication_traits_::compute_left_endpoint_for_shorter_interval_case( |
| cache, beta); |
| auto zi = multiplication_traits_:: |
| compute_right_endpoint_for_shorter_interval_case(cache, beta); |
| |
| // If we don't accept the right endpoint and |
| // if the right endpoint is an integer, decrease it. |
| if (!interval_type.include_right_endpoint() && |
| is_right_endpoint_integer_shorter_interval(binary_exponent)) { |
| --zi; |
| } |
| // If we don't accept the left endpoint or |
| // if the left endpoint is not an integer, increase it. |
| if (!interval_type.include_left_endpoint() || |
| !is_left_endpoint_integer_shorter_interval(binary_exponent)) { |
| ++xi; |
| } |
| |
| // Try bigger divisor. |
| // zi is at most floor((f_c + 1/2) * 2^e * 10^k0). |
| // Substituting f_c = 2^p and k0 = -floor(log10(3 * 2^(e-2))), we get |
| // zi <= floor((2^(p+1) + 1) * 20/3) <= ceil((2^(p+1) + 1)/3) * 20. |
| // This computation does not overflow for any of the formats I care about. |
| carrier_uint decimal_significand = div::divide_by_pow10< |
| 1, carrier_uint, |
| carrier_uint( |
| ((((carrier_uint(1) << (significand_bits + 1)) + 1) / 3) + 1) * |
| 20)>(zi); |
| |
| // If succeed, remove trailing zeros if necessary and return. |
| if (decimal_significand * 10 >= xi) { |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template on_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + 1))); |
| } |
| |
| // Otherwise, compute the round-up of y. |
| decimal_significand = |
| multiplication_traits_::compute_round_up_for_shorter_interval_case( |
| cache, beta); |
| |
| // When tie occurs, choose one of them according to the rule. |
| if (BinaryToDecimalRoundingPolicy::prefer_round_down(decimal_significand) && |
| binary_exponent >= shorter_interval_tie_lower_threshold && |
| binary_exponent <= shorter_interval_tie_upper_threshold) { |
| --decimal_significand; |
| } |
| else if (decimal_significand < xi) { |
| ++decimal_significand; |
| } |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template no_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k))); |
| } |
| |
| // Normal interval case. |
| two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); |
| } |
| // Is the input a subnormal number? |
| else { |
| // Normal interval case. |
| binary_exponent = format::min_exponent - format::significand_bits; |
| } |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 1: Schubfach multiplier calculation. |
| ////////////////////////////////////////////////////////////////////// |
| |
| auto interval_type = IntervalTypeProvider::normal_interval(s); |
| |
| // Compute k and beta. |
| auto const minus_k = decimal_exponent_type_( |
| log::floor_log10_pow2<min_exponent - format::significand_bits, |
| max_exponent - format::significand_bits, |
| decimal_exponent_type_>(binary_exponent) - |
| kappa); |
| auto const cache = CachePolicy::template get_cache<format, shift_amount_type>( |
| decimal_exponent_type_(-minus_k)); |
| auto const beta = |
| shift_amount_type(binary_exponent + log::floor_log2_pow10<min_k, max_k>( |
| decimal_exponent_type_(-minus_k))); |
| |
| // Compute zi and deltai. |
| // 10^kappa <= deltai < 10^(kappa + 1) |
| auto const deltai = static_cast<remainder_type_>( |
| multiplication_traits_::compute_delta(cache, beta)); |
| // For the case of binary32, the result of integer check is not correct for |
| // 29711844 * 2^-82 |
| // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 |
| // and 29711844 * 2^-81 |
| // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, |
| // and they are the unique counterexamples. However, since 29711844 is even, |
| // this does not cause any problem for the endpoints calculations; it can only |
| // cause a problem when we need to perform integer check for the center. |
| // Fortunately, with these inputs, that branch is never executed, so we are |
| // fine. |
| auto const z_result = |
| multiplication_traits_::compute_mul(carrier_uint((two_fc | 1) << beta), cache); |
| |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 2: Try larger divisor; remove trailing zeros if necessary. |
| ////////////////////////////////////////////////////////////////////// |
| |
| constexpr auto big_divisor = compute_power<kappa + 1>(remainder_type_(10)); |
| constexpr auto small_divisor = compute_power<kappa>(remainder_type_(10)); |
| |
| // Using an upper bound on zi, we might be able to optimize the division |
| // better than the compiler; we are computing zi / big_divisor here. |
| carrier_uint decimal_significand = div::divide_by_pow10< |
| kappa + 1, carrier_uint, |
| carrier_uint((carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1)>( |
| z_result.integer_part); |
| auto r = remainder_type_(z_result.integer_part - big_divisor * decimal_significand); |
| |
| do { |
| if (r < deltai) { |
| // Exclude the right endpoint if necessary. |
| if ((r | remainder_type_(!z_result.is_integer) | |
| remainder_type_(interval_type.include_right_endpoint())) == 0) { |
| JKJ_IF_CONSTEXPR( |
| BinaryToDecimalRoundingPolicy::tag == |
| policy::binary_to_decimal_rounding::tag_t::do_not_care) { |
| decimal_significand *= 10; |
| --decimal_significand; |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template no_trailing_zeros<format>( |
| decimal_significand, |
| decimal_exponent_type_(minus_k + kappa))); |
| } |
| else { |
| --decimal_significand; |
| r = big_divisor; |
| break; |
| } |
| } |
| } |
| else if (r > deltai) { |
| break; |
| } |
| else { |
| // r == deltai; compare fractional parts. |
| auto const x_result = multiplication_traits_::compute_mul_parity( |
| carrier_uint(two_fc - 1), cache, beta); |
| |
| if (!(x_result.parity | |
| (x_result.is_integer & interval_type.include_left_endpoint()))) { |
| break; |
| } |
| } |
| |
| // We may need to remove trailing zeros. |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template on_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa + 1))); |
| } while (false); |
| |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 3: Find the significand with the smaller divisor. |
| ////////////////////////////////////////////////////////////////////// |
| |
| decimal_significand *= 10; |
| |
| JKJ_IF_CONSTEXPR(BinaryToDecimalRoundingPolicy::tag == |
| policy::binary_to_decimal_rounding::tag_t::do_not_care) { |
| // Normally, we want to compute |
| // significand += r / small_divisor |
| // and return, but we need to take care of the case that the resulting |
| // value is exactly the right endpoint, while that is not included in the |
| // interval. |
| if (!interval_type.include_right_endpoint()) { |
| // Is r divisible by 10^kappa? |
| if (div::check_divisibility_and_divide_by_pow10<kappa>(r) && |
| z_result.is_integer) { |
| // This should be in the interval. |
| decimal_significand += r - 1; |
| } |
| else { |
| decimal_significand += r; |
| } |
| } |
| else { |
| decimal_significand += div::small_division_by_pow10<kappa>(r); |
| } |
| } |
| else { |
| // delta is equal to 10^(kappa + elog10(2) - floor(elog10(2))), so dist cannot |
| // be larger than r. |
| auto dist = remainder_type_(r - (deltai / 2) + (small_divisor / 2)); |
| bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; |
| |
| // Is dist divisible by 10^kappa? |
| bool const divisible_by_small_divisor = |
| div::check_divisibility_and_divide_by_pow10<kappa>(dist); |
| |
| // Add dist / 10^kappa to the significand. |
| decimal_significand += dist; |
| |
| if (divisible_by_small_divisor) { |
| // Check z^(f) >= epsilon^(f). |
| // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, |
| // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). |
| // Since there are only 2 possibilities, we only need to care about the |
| // parity. Also, zi and r should have the same parity since the divisor |
| // is an even number. |
| auto const y_result = |
| multiplication_traits_::compute_mul_parity(two_fc, cache, beta); |
| if (y_result.parity != approx_y_parity) { |
| --decimal_significand; |
| } |
| else { |
| // If z^(f) >= epsilon^(f), we might have a tie |
| // when z^(f) == epsilon^(f), or equivalently, when y is an integer. |
| // For tie-to-up case, we can just choose the upper one. |
| if (BinaryToDecimalRoundingPolicy::prefer_round_down( |
| decimal_significand) & |
| y_result.is_integer) { |
| --decimal_significand; |
| } |
| } |
| } |
| } |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template no_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa))); |
| } |
| |
| template <class SignPolicy, class TrailingZeroPolicy, class CachePolicy, |
| class PreferredIntegerTypesPolicy> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static JKJ_CONSTEXPR20 |
| return_type<SignPolicy, TrailingZeroPolicy, PreferredIntegerTypesPolicy> |
| compute_left_closed_directed(signed_significand_bits<FormatTraits> s, |
| exponent_int exponent_bits) noexcept { |
| using cache_holder_type = typename CachePolicy::template cache_holder_type<format>; |
| static_assert( |
| min_k >= cache_holder_type::min_k && max_k <= cache_holder_type::max_k, ""); |
| |
| using remainder_type_ = remainder_type<PreferredIntegerTypesPolicy>; |
| using decimal_exponent_type_ = decimal_exponent_type<PreferredIntegerTypesPolicy>; |
| using shift_amount_type = |
| typename PreferredIntegerTypesPolicy::template shift_amount_type<FormatTraits>; |
| |
| using multiplication_traits_ = |
| multiplication_traits<FormatTraits, |
| typename cache_holder_type::cache_entry_type, |
| cache_holder_type::cache_bits>; |
| |
| auto two_fc = s.remove_sign_bit_and_shift(); |
| auto binary_exponent = exponent_bits; |
| |
| // Is the input a normal number? |
| if (binary_exponent != 0) { |
| binary_exponent += format::exponent_bias - format::significand_bits; |
| two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); |
| } |
| // Is the input a subnormal number? |
| else { |
| binary_exponent = format::min_exponent - format::significand_bits; |
| } |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 1: Schubfach multiplier calculation. |
| ////////////////////////////////////////////////////////////////////// |
| |
| // Compute k and beta. |
| auto const minus_k = decimal_exponent_type_( |
| log::floor_log10_pow2<format::min_exponent - format::significand_bits, |
| format::max_exponent - format::significand_bits, |
| decimal_exponent_type_>(binary_exponent) - |
| kappa); |
| auto const cache = CachePolicy::template get_cache<format, shift_amount_type>( |
| decimal_exponent_type_(-minus_k)); |
| auto const beta = |
| shift_amount_type(binary_exponent + log::floor_log2_pow10<min_k, max_k>( |
| decimal_exponent_type_(-minus_k))); |
| |
| // Compute xi and deltai. |
| // 10^kappa <= deltai < 10^(kappa + 1) |
| auto const deltai = static_cast<remainder_type_>( |
| multiplication_traits_::compute_delta(cache, beta)); |
| auto x_result = |
| multiplication_traits_::compute_mul(carrier_uint(two_fc << beta), cache); |
| |
| // Deal with the unique exceptional cases |
| // 29711844 * 2^-82 |
| // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 |
| // and 29711844 * 2^-81 |
| // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17 |
| // for binary32. |
| JKJ_IF_CONSTEXPR(stdr::is_same<format, ieee754_binary32>::value) { |
| if (binary_exponent <= -80) { |
| x_result.is_integer = false; |
| } |
| } |
| |
| if (!x_result.is_integer) { |
| ++x_result.integer_part; |
| } |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 2: Try larger divisor; remove trailing zeros if necessary. |
| ////////////////////////////////////////////////////////////////////// |
| |
| constexpr auto big_divisor = compute_power<kappa + 1>(remainder_type_(10)); |
| |
| // Using an upper bound on xi, we might be able to optimize the division |
| // better than the compiler; we are computing xi / big_divisor here. |
| carrier_uint decimal_significand = div::divide_by_pow10< |
| kappa + 1, carrier_uint, |
| carrier_uint((carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1)>( |
| x_result.integer_part); |
| auto r = remainder_type_(x_result.integer_part - big_divisor * decimal_significand); |
| |
| if (r != 0) { |
| ++decimal_significand; |
| r = remainder_type_(big_divisor - r); |
| } |
| |
| do { |
| if (r > deltai) { |
| break; |
| } |
| else if (r == deltai) { |
| // Compare the fractional parts. |
| // This branch is never taken for the exceptional cases |
| // 2f_c = 29711482, e = -81 |
| // (6.1442649164096937243516663440523473127541365101933479309082... * |
| // 10^-18) and 2f_c = 29711482, e = -80 |
| // (1.2288529832819387448703332688104694625508273020386695861816... * |
| // 10^-17). |
| // For the case of compressed cache for binary32, there is another |
| // exceptional case 2f_c = 33554430, e = -10 (16383.9990234375). In this |
| // case, the recovered cache is two large to make compute_mul_parity |
| // mistakenly conclude that z is not an integer, but actually z = 16384 is |
| // an integer. |
| JKJ_IF_CONSTEXPR( |
| stdr::is_same<cache_holder_type, |
| compressed_cache_holder<ieee754_binary32>>::value) { |
| if (two_fc == 33554430 && binary_exponent == -10) { |
| break; |
| } |
| } |
| auto const z_result = multiplication_traits_::compute_mul_parity( |
| carrier_uint(two_fc + 2), cache, beta); |
| if (z_result.parity || z_result.is_integer) { |
| break; |
| } |
| } |
| |
| // The ceiling is inside, so we are done. |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template on_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa + 1))); |
| } while (false); |
| |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 3: Find the significand with the smaller divisor. |
| ////////////////////////////////////////////////////////////////////// |
| |
| decimal_significand *= 10; |
| decimal_significand -= div::small_division_by_pow10<kappa>(r); |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template no_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa))); |
| } |
| |
| template <class SignPolicy, class TrailingZeroPolicy, class CachePolicy, |
| class PreferredIntegerTypesPolicy> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS static JKJ_CONSTEXPR20 |
| return_type<SignPolicy, TrailingZeroPolicy, PreferredIntegerTypesPolicy> |
| compute_right_closed_directed(signed_significand_bits<FormatTraits> s, |
| exponent_int exponent_bits) noexcept { |
| using cache_holder_type = typename CachePolicy::template cache_holder_type<format>; |
| static_assert( |
| min_k >= cache_holder_type::min_k && max_k <= cache_holder_type::max_k, ""); |
| |
| using remainder_type_ = remainder_type<PreferredIntegerTypesPolicy>; |
| using decimal_exponent_type_ = decimal_exponent_type<PreferredIntegerTypesPolicy>; |
| using shift_amount_type = |
| typename PreferredIntegerTypesPolicy::template shift_amount_type<FormatTraits>; |
| |
| using multiplication_traits_ = |
| multiplication_traits<FormatTraits, |
| typename cache_holder_type::cache_entry_type, |
| cache_holder_type::cache_bits>; |
| |
| auto two_fc = s.remove_sign_bit_and_shift(); |
| auto binary_exponent = exponent_bits; |
| bool shorter_interval = false; |
| |
| // Is the input a normal number? |
| if (binary_exponent != 0) { |
| if (two_fc == 0 && binary_exponent != 1) { |
| shorter_interval = true; |
| } |
| binary_exponent += format::exponent_bias - format::significand_bits; |
| two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); |
| } |
| // Is the input a subnormal number? |
| else { |
| binary_exponent = format::min_exponent - format::significand_bits; |
| } |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 1: Schubfach multiplier calculation. |
| ////////////////////////////////////////////////////////////////////// |
| |
| // Compute k and beta. |
| auto const minus_k = decimal_exponent_type_( |
| log::floor_log10_pow2<format::min_exponent - format::significand_bits, |
| format::max_exponent - format::significand_bits, |
| decimal_exponent_type_>( |
| exponent_int(binary_exponent - (shorter_interval ? 1 : 0))) - |
| kappa); |
| auto const cache = CachePolicy::template get_cache<format, shift_amount_type>( |
| decimal_exponent_type_(-minus_k)); |
| auto const beta = shift_amount_type( |
| binary_exponent + log::floor_log2_pow10(decimal_exponent_type_(-minus_k))); |
| |
| // Compute zi and deltai. |
| // 10^kappa <= deltai < 10^(kappa + 1) |
| auto const deltai = |
| static_cast<remainder_type_>(multiplication_traits_::compute_delta( |
| cache, shift_amount_type(beta - (shorter_interval ? 1 : 0)))); |
| carrier_uint const zi = |
| multiplication_traits_::compute_mul(carrier_uint(two_fc << beta), cache) |
| .integer_part; |
| |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 2: Try larger divisor; remove trailing zeros if necessary. |
| ////////////////////////////////////////////////////////////////////// |
| |
| constexpr auto big_divisor = compute_power<kappa + 1>(remainder_type_(10)); |
| |
| // Using an upper bound on zi, we might be able to optimize the division better |
| // than the compiler; we are computing zi / big_divisor here. |
| carrier_uint decimal_significand = div::divide_by_pow10< |
| kappa + 1, carrier_uint, |
| carrier_uint((carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1)>( |
| zi); |
| auto const r = remainder_type_(zi - big_divisor * decimal_significand); |
| |
| do { |
| if (r > deltai) { |
| break; |
| } |
| else if (r == deltai) { |
| // Compare the fractional parts. |
| if (!multiplication_traits_::compute_mul_parity( |
| carrier_uint(two_fc - (shorter_interval ? 1 : 2)), cache, beta) |
| .parity) { |
| break; |
| } |
| } |
| |
| // The floor is inside, so we are done. |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template on_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa + 1))); |
| } while (false); |
| |
| |
| ////////////////////////////////////////////////////////////////////// |
| // Step 3: Find the significand with the small divisor. |
| ////////////////////////////////////////////////////////////////////// |
| |
| decimal_significand *= 10; |
| decimal_significand += div::small_division_by_pow10<kappa>(r); |
| return SignPolicy::handle_sign( |
| s, TrailingZeroPolicy::template no_trailing_zeros<format>( |
| decimal_significand, decimal_exponent_type_(minus_k + kappa))); |
| } |
| |
| static constexpr bool |
| is_right_endpoint_integer_shorter_interval(exponent_int binary_exponent) noexcept { |
| return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && |
| binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; |
| } |
| |
| static constexpr bool |
| is_left_endpoint_integer_shorter_interval(exponent_int binary_exponent) noexcept { |
| return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && |
| binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; |
| } |
| }; |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // Policy holder. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| // The library will specify a list of accepted kinds of policies and their defaults, |
| // and the user will pass a list of policies parameters. The policy parameters are |
| // supposed to be stateless and only convey information through their types. |
| // The aim of the helper classes/functions given below is to do the following: |
| // 1. Check if the policy parameters given by the user are all valid; that means, |
| // each of them should be at least of one of the kinds specified by the library. |
| // If that's not the case, then the compilation fails. |
| // 2. Check if multiple policy parameters for the same kind is specified by the |
| // user. If that's the case, then the compilation fails. |
| // 3. Build a class deriving from all policies the user have given, and also from |
| // the default policies if the user did not specify one for some kinds. |
| // The library considers a certain policy parameter to belong to a specific kind if and only |
| // if the parameter's type has a member type with a specific name; for example, it belongs |
| // to "sign policy" kind if there is a member type sign_policy. |
| |
| // For a given kind, find a policy belonging to that kind. |
| // Check if there are more than one such policies. |
| enum class policy_found_info { not_found, unique, repeated }; |
| template <class Policy, policy_found_info info> |
| struct found_policy_pair { |
| // Either the policy parameter type given by the user, or the default policy. |
| using policy = Policy; |
| static constexpr auto found_info = info; |
| }; |
| |
| template <class KindDetector, class DefaultPolicy> |
| struct detector_default_pair { |
| using kind_detector = KindDetector; |
| |
| // Iterate through all given policy parameter types and see if there is a policy |
| // parameter type belonging to the policy kind specified by KindDetector. |
| // 1. If there is none, get_found_policy_pair returns |
| // found_policy_pair<DefaultPolicy, policy_found_info::not_found>. |
| // 2. If there is only one parameter type belonging to the specified kind, then |
| // get_found_policy_pair returns |
| // found_policy_pair<Policy, policy_found_info::unique> |
| // where Policy is the unique parameter type belonging to the specified kind. |
| // 3. If there are multiple parameter types belonging to the specified kind, then |
| // get_found_policy_pair returns |
| // found_policy_pair<FirstPolicy, policy_found_info::repeated> |
| // where FirstPolicy is the first parameter type belonging to the specified kind. |
| // The compilation must fail if this happens. |
| // This is done by first setting FoundPolicyInfo below to |
| // found_policy_pair<DefaultPolicy, policy_found_info::not_found>, and then iterate |
| // over Policies, replacing FoundPolicyInfo by the appropriate one if a parameter |
| // type belonging to the specified kind is found. |
| |
| template <class FoundPolicyInfo, class... Policies> |
| struct get_found_policy_pair_impl; |
| |
| template <class FoundPolicyInfo> |
| struct get_found_policy_pair_impl<FoundPolicyInfo> { |
| using type = FoundPolicyInfo; |
| }; |
| |
| template <class FoundPolicyInfo, class FirstPolicy, class... RemainingPolicies> |
| struct get_found_policy_pair_impl<FoundPolicyInfo, FirstPolicy, RemainingPolicies...> { |
| using type = typename stdr::conditional< |
| KindDetector{}(dummy<FirstPolicy>{}), |
| typename stdr::conditional< |
| FoundPolicyInfo::found_info == policy_found_info::not_found, |
| typename get_found_policy_pair_impl< |
| found_policy_pair<FirstPolicy, policy_found_info::unique>, |
| RemainingPolicies...>::type, |
| typename get_found_policy_pair_impl< |
| found_policy_pair<FirstPolicy, policy_found_info::repeated>, |
| RemainingPolicies...>::type>::type, |
| typename get_found_policy_pair_impl<FoundPolicyInfo, |
| RemainingPolicies...>::type>::type; |
| }; |
| |
| template <class... Policies> |
| using get_found_policy_pair = typename get_found_policy_pair_impl< |
| found_policy_pair<DefaultPolicy, policy_found_info::not_found>, Policies...>::type; |
| }; |
| |
| // Simple typelist of detector_default_pair's. |
| template <class... DetectorDefaultPairs> |
| struct detector_default_pair_list {}; |
| |
| // Check if a given policy belongs to one of the kinds specified by the library. |
| template <class Policy> |
| constexpr bool check_policy_validity(dummy<Policy>, detector_default_pair_list<>) noexcept { |
| return false; |
| } |
| template <class Policy, class FirstDetectorDefaultPair, |
| class... RemainingDetectorDefaultPairs> |
| constexpr bool check_policy_validity( |
| dummy<Policy>, detector_default_pair_list<FirstDetectorDefaultPair, |
| RemainingDetectorDefaultPairs...>) noexcept { |
| return typename FirstDetectorDefaultPair::kind_detector{}(dummy<Policy>{}) || |
| check_policy_validity( |
| dummy<Policy>{}, |
| detector_default_pair_list<RemainingDetectorDefaultPairs...>{}); |
| } |
| |
| // Check if all of policies belong to some of the kinds specified by the library. |
| template <class DetectorDefaultPairList> |
| constexpr bool check_policy_list_validity(DetectorDefaultPairList) noexcept { |
| return true; |
| } |
| template <class DetectorDefaultPairList, class FirstPolicy, class... RemainingPolicies> |
| constexpr bool check_policy_list_validity(DetectorDefaultPairList, |
| dummy<FirstPolicy> first_policy, |
| dummy<RemainingPolicies>... remaining_policies) { |
| return check_policy_validity(first_policy, DetectorDefaultPairList{}) && |
| check_policy_list_validity(DetectorDefaultPairList{}, remaining_policies...); |
| } |
| |
| // Actual policy holder class deriving from all specified policy types. |
| template <class... Policies> |
| struct policy_holder : Policies... {}; |
| |
| // Iterate through the library-specified list of base-default pairs, i.e., the list of |
| // policy kinds and their defaults. For each base-default pair, call |
| // base_default_pair::get_found_policy_pair on the list of user-specified list of |
| // policies to get found_policy_pair, and build the list of them. |
| |
| template <bool repeated_, class... FoundPolicyPairs> |
| struct found_policy_pair_list { |
| // This will be set to be true if and only if there exists at least one |
| // found_policy_pair inside FoundPolicyPairs with |
| // found_info == policy_found_info::repeated, in which case the compilation must |
| // fail. |
| static constexpr bool repeated = repeated_; |
| }; |
| |
| // Iterate through DetectorDefaultPairList and augment FoundPolicyPairList by one at each |
| // iteration. |
| template <class DetectorDefaultPairList, class FoundPolicyPairList, class... Policies> |
| struct make_policy_pair_list_impl; |
| |
| // When there is no more detector-default pair to iterate, then the current |
| // found_policy_pair_list is the final result. |
| template <bool repeated, class... FoundPolicyPairs, class... Policies> |
| struct make_policy_pair_list_impl<detector_default_pair_list<>, |
| found_policy_pair_list<repeated, FoundPolicyPairs...>, |
| Policies...> { |
| using type = found_policy_pair_list<repeated, FoundPolicyPairs...>; |
| }; |
| |
| // For the first detector-default pair in the remaining list, call |
| // detector_default_pair::get_found_policy_pair on Policies and add the returned |
| // found_policy_pair into the current list of found_policy_pair's, and move to the next |
| // detector-default pair. |
| template <class FirstDetectorDefaultPair, class... RemainingDetectorDefaultPairs, |
| bool repeated, class... FoundPolicyPairs, class... Policies> |
| struct make_policy_pair_list_impl< |
| detector_default_pair_list<FirstDetectorDefaultPair, RemainingDetectorDefaultPairs...>, |
| found_policy_pair_list<repeated, FoundPolicyPairs...>, Policies...> { |
| using new_found_policy_pair = |
| typename FirstDetectorDefaultPair::template get_found_policy_pair<Policies...>; |
| |
| using type = typename make_policy_pair_list_impl< |
| detector_default_pair_list<RemainingDetectorDefaultPairs...>, |
| found_policy_pair_list<(repeated || new_found_policy_pair::found_info == |
| policy_found_info::repeated), |
| new_found_policy_pair, FoundPolicyPairs...>, |
| Policies...>::type; |
| }; |
| |
| template <class DetectorDefaultPairList, class... Policies> |
| using policy_pair_list = |
| typename make_policy_pair_list_impl<DetectorDefaultPairList, |
| found_policy_pair_list<false>, Policies...>::type; |
| |
| // Unpack FoundPolicyPairList into found_policy_pair's and build the policy_holder type |
| // from the corresponding typelist of found_policy_pair::policy's. |
| template <class FoundPolicyPairList, class... RawPolicies> |
| struct convert_to_policy_holder_impl; |
| |
| template <bool repeated, class... RawPolicies> |
| struct convert_to_policy_holder_impl<found_policy_pair_list<repeated>, RawPolicies...> { |
| using type = policy_holder<RawPolicies...>; |
| }; |
| |
| template <bool repeated, class FirstFoundPolicyPair, class... RemainingFoundPolicyPairs, |
| class... RawPolicies> |
| struct convert_to_policy_holder_impl< |
| found_policy_pair_list<repeated, FirstFoundPolicyPair, RemainingFoundPolicyPairs...>, |
| RawPolicies...> { |
| using type = typename convert_to_policy_holder_impl< |
| found_policy_pair_list<repeated, RemainingFoundPolicyPairs...>, |
| typename FirstFoundPolicyPair::policy, RawPolicies...>::type; |
| }; |
| |
| template <class FoundPolicyPairList> |
| using convert_to_policy_holder = |
| typename convert_to_policy_holder_impl<FoundPolicyPairList>::type; |
| |
| template <class DetectorDefaultPairList, class... Policies> |
| struct make_policy_holder_impl { |
| static_assert(check_policy_list_validity(DetectorDefaultPairList{}, |
| dummy<Policies>{}...), |
| "jkj::dragonbox: an invalid policy is specified"); |
| |
| static_assert( |
| !policy_pair_list<DetectorDefaultPairList, Policies...>::repeated, |
| "jkj::dragonbox: at most one policy should be specified for each policy kind"); |
| |
| using type = |
| convert_to_policy_holder<policy_pair_list<DetectorDefaultPairList, Policies...>>; |
| }; |
| |
| template <class DetectorDefaultPairList, class... Policies> |
| using make_policy_holder = |
| typename make_policy_holder_impl<DetectorDefaultPairList, Policies...>::type; |
| |
| |
| // Policy kind detectors. |
| struct is_sign_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::sign_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| struct is_trailing_zero_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::trailing_zero_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| struct is_decimal_to_binary_rounding_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::decimal_to_binary_rounding_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| struct is_binary_to_decimal_rounding_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::binary_to_decimal_rounding_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| struct is_cache_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::cache_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| struct is_preferred_integer_types_policy { |
| constexpr bool operator()(...) const noexcept { return false; } |
| template <class Policy, class = typename Policy::preferred_integer_types_policy> |
| constexpr bool operator()(dummy<Policy>) const noexcept { |
| return true; |
| } |
| }; |
| |
| template <class... Policies> |
| using to_decimal_policy_holder = make_policy_holder< |
| detector_default_pair_list< |
| detector_default_pair<is_sign_policy, policy::sign::return_sign_t>, |
| detector_default_pair<is_trailing_zero_policy, policy::trailing_zero::remove_t>, |
| detector_default_pair<is_decimal_to_binary_rounding_policy, |
| policy::decimal_to_binary_rounding::nearest_to_even_t>, |
| detector_default_pair<is_binary_to_decimal_rounding_policy, |
| policy::binary_to_decimal_rounding::to_even_t>, |
| detector_default_pair<is_cache_policy, policy::cache::full_t>, |
| detector_default_pair<is_preferred_integer_types_policy, |
| policy::preferred_integer_types::match_t>>, |
| Policies...>; |
| |
| template <class FormatTraits, class... Policies> |
| using to_decimal_return_type = typename impl<FormatTraits>::template return_type< |
| typename to_decimal_policy_holder<Policies...>::sign_policy, |
| typename to_decimal_policy_holder<Policies...>::trailing_zero_policy, |
| typename to_decimal_policy_holder<Policies...>::preferred_integer_types_policy>; |
| |
| template <class FormatTraits, class PolicyHolder> |
| struct to_decimal_dispatcher { |
| using sign_policy = typename PolicyHolder::sign_policy; |
| using trailing_zero_policy = typename PolicyHolder::trailing_zero_policy; |
| using binary_to_decimal_rounding_policy = |
| typename PolicyHolder::binary_to_decimal_rounding_policy; |
| using cache_policy = typename PolicyHolder::cache_policy; |
| using preferred_integer_types_policy = |
| typename PolicyHolder::preferred_integer_types_policy; |
| using return_type = |
| typename impl<FormatTraits>::template return_type<sign_policy, trailing_zero_policy, |
| preferred_integer_types_policy>; |
| |
| template <class IntervalTypeProvider> |
| JKJ_FORCEINLINE JKJ_SAFEBUFFERS JKJ_CONSTEXPR20 return_type |
| operator()(IntervalTypeProvider, signed_significand_bits<FormatTraits> s, |
| typename FormatTraits::exponent_int exponent_bits) noexcept { |
| constexpr auto tag = IntervalTypeProvider::tag; |
| |
| JKJ_IF_CONSTEXPR(tag == policy::decimal_to_binary_rounding::tag_t::to_nearest) { |
| return impl<FormatTraits>::template compute_nearest< |
| sign_policy, trailing_zero_policy, IntervalTypeProvider, |
| binary_to_decimal_rounding_policy, cache_policy, |
| preferred_integer_types_policy>(s, exponent_bits); |
| } |
| else JKJ_IF_CONSTEXPR( |
| tag == policy::decimal_to_binary_rounding::tag_t::left_closed_directed) { |
| return impl<FormatTraits>::template compute_left_closed_directed< |
| sign_policy, trailing_zero_policy, cache_policy, |
| preferred_integer_types_policy>(s, exponent_bits); |
| } |
| else { |
| #if JKJ_HAS_IF_CONSTEXPR |
| static_assert( |
| tag == policy::decimal_to_binary_rounding::tag_t::right_closed_directed, |
| ""); |
| #endif |
| return impl<FormatTraits>::template compute_right_closed_directed< |
| sign_policy, trailing_zero_policy, cache_policy, |
| preferred_integer_types_policy>(s, exponent_bits); |
| } |
| } |
| }; |
| } |
| |
| |
| //////////////////////////////////////////////////////////////////////////////////////// |
| // The interface function. |
| //////////////////////////////////////////////////////////////////////////////////////// |
| |
| template <class FormatTraits, class ExponentBits, class... Policies> |
| JKJ_FORCEINLINE |
| JKJ_SAFEBUFFERS JKJ_CONSTEXPR20 detail::to_decimal_return_type<FormatTraits, Policies...> |
| to_decimal_ex(signed_significand_bits<FormatTraits> s, ExponentBits exponent_bits, |
| Policies...) noexcept { |
| // Build policy holder type. |
| using policy_holder = detail::to_decimal_policy_holder<Policies...>; |
| |
| return policy_holder::delegate( |
| s, detail::to_decimal_dispatcher<FormatTraits, policy_holder>{}, s, exponent_bits); |
| } |
| |
| template <class Float, |
| class ConversionTraits = default_float_bit_carrier_conversion_traits<Float>, |
| class FormatTraits = ieee754_binary_traits<typename ConversionTraits::format, |
| typename ConversionTraits::carrier_uint>, |
| class... Policies> |
| JKJ_FORCEINLINE |
| JKJ_SAFEBUFFERS JKJ_CONSTEXPR20 detail::to_decimal_return_type<FormatTraits, Policies...> |
| to_decimal(Float x, Policies... policies) noexcept { |
| auto const br = make_float_bits<Float, ConversionTraits, FormatTraits>(x); |
| auto const exponent_bits = br.extract_exponent_bits(); |
| auto const s = br.remove_exponent_bits(); |
| assert(br.is_finite() && br.is_nonzero()); |
| |
| return to_decimal_ex(s, exponent_bits, policies...); |
| } |
| } |
| } |
| } |
| |
| #undef JKJ_HAS_BUILTIN |
| #undef JKJ_FORCEINLINE |
| #undef JKJ_SAFEBUFFERS |
| #undef JKJ_CONSTEXPR20 |
| #undef JKJ_USE_IS_CONSTANT_EVALUATED |
| #undef JKJ_CAN_BRANCH_ON_CONSTEVAL |
| #undef JKJ_IF_NOT_CONSTEVAL |
| #undef JKJ_IF_CONSTEVAL |
| #undef JKJ_HAS_BIT_CAST |
| #undef JKJ_IF_CONSTEXPR |
| #undef JKJ_HAS_IF_CONSTEXPR |
| #undef JKJ_INLINE_VARIABLE |
| #undef JKJ_HAS_INLINE_VARIABLE |
| #undef JKJ_HAS_CONSTEXPR17 |
| #undef JKJ_CONSTEXPR14 |
| #undef JKJ_HAS_CONSTEXPR14 |
| #if JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED |
| #undef JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED |
| #else |
| #undef JKJ_STD_REPLACEMENT_NAMESPACE |
| #endif |
| #if JKJ_STATIC_DATA_SECTION_DEFINED |
| #undef JKJ_STATIC_DATA_SECTION_DEFINED |
| #else |
| #undef JKJ_STATIC_DATA_SECTION |
| #endif |
| |
| #endif |
