// Copyright 2020-2024 Junekey Jeon
//
// The contents of this file may be used under the terms of
// the Apache License v2.0 with LLVM Exceptions.
//
//    (See accompanying file LICENSE-Apache or copy at
//     https://llvm.org/foundation/relicensing/LICENSE.txt)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE-Boost or copy at
//     https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.

#ifndef GLZ_JKJ_HEADER_DRAGONBOX
#define GLZ_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 GLZ_JKJ_STATIC_DATA_SECTION
#define GLZ_JKJ_STATIC_DATA_SECTION
#else
#define GLZ_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 GLZ_JKJ_STD_REPLACEMENT_NAMESPACE
#define GLZ_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 GLZ_JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED 1
#endif

////////////////////////////////////////////////////////////////////////////////////////
// Language feature detections.
////////////////////////////////////////////////////////////////////////////////////////

// C++14 constexpr
#if defined(__cpp_constexpr) && __cpp_constexpr >= 201304L
#define GLZ_JKJ_HAS_CONSTEXPR14 1
#elif __cplusplus >= 201402L
#define GLZ_JKJ_HAS_CONSTEXPR14 1
#elif defined(_MSC_VER) && _MSC_VER >= 1910 && _MSVC_LANG >= 201402L
#define GLZ_JKJ_HAS_CONSTEXPR14 1
#else
#define GLZ_JKJ_HAS_CONSTEXPR14 0
#endif

#if GLZ_JKJ_HAS_CONSTEXPR14
#define GLZ_JKJ_CONSTEXPR14 constexpr
#else
#define GLZ_JKJ_CONSTEXPR14
#endif

// C++17 constexpr lambdas
#if defined(__cpp_constexpr) && __cpp_constexpr >= 201603L
#define GLZ_JKJ_HAS_CONSTEXPR17 1
#elif __cplusplus >= 201703L
#define GLZ_JKJ_HAS_CONSTEXPR17 1
#elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L
#define GLZ_JKJ_HAS_CONSTEXPR17 1
#else
#define GLZ_JKJ_HAS_CONSTEXPR17 0
#endif

// C++17 inline variables
#if defined(__cpp_inline_variables) && __cpp_inline_variables >= 201606L
#define GLZ_JKJ_HAS_INLINE_VARIABLE 1
#elif __cplusplus >= 201703L
#define GLZ_JKJ_HAS_INLINE_VARIABLE 1
#elif defined(_MSC_VER) && _MSC_VER >= 1912 && _MSVC_LANG >= 201703L
#define GLZ_JKJ_HAS_INLINE_VARIABLE 1
#else
#define GLZ_JKJ_HAS_INLINE_VARIABLE 0
#endif

#if GLZ_JKJ_HAS_INLINE_VARIABLE
#define GLZ_JKJ_INLINE_VARIABLE inline constexpr
#else
#define GLZ_JKJ_INLINE_VARIABLE static constexpr
#endif

// C++17 if constexpr
#if defined(__cpp_if_constexpr) && __cpp_if_constexpr >= 201606L
#define GLZ_JKJ_HAS_IF_CONSTEXPR 1
#elif __cplusplus >= 201703L
#define GLZ_JKJ_HAS_IF_CONSTEXPR 1
#elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L
#define GLZ_JKJ_HAS_IF_CONSTEXPR 1
#else
#define GLZ_JKJ_HAS_IF_CONSTEXPR 0
#endif

#if GLZ_JKJ_HAS_IF_CONSTEXPR
#define GLZ_JKJ_IF_CONSTEXPR if constexpr
#else
#define GLZ_JKJ_IF_CONSTEXPR if
#endif

// C++20 std::bit_cast
#if GLZ_JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED
#if GLZ_JKJ_STD_REPLACEMENT_HAS_BIT_CAST
#define GLZ_JKJ_HAS_BIT_CAST 1
#else
#define GLZ_JKJ_HAS_BIT_CAST 0
#endif
#elif defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
#include <bit>
#define GLZ_JKJ_HAS_BIT_CAST 1
#else
#define GLZ_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 GLZ_JKJ_IF_CONSTEVAL if consteval
#define GLZ_JKJ_IF_NOT_CONSTEVAL if !consteval
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 1
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 0
#elif GLZ_JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED
#if GLZ_JKJ_STD_REPLACEMENT_HAS_IS_CONSTANT_EVALUATED
#define GLZ_JKJ_IF_CONSTEVAL if (stdr::is_constant_evaluated())
#define GLZ_JKJ_IF_NOT_CONSTEVAL if (!stdr::is_constant_evaluated())
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 1
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 1
#elif GLZ_JKJ_HAS_IF_CONSTEXPR
#define GLZ_JKJ_IF_CONSTEVAL if constexpr (false)
#define GLZ_JKJ_IF_NOT_CONSTEVAL if constexpr (true)
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 0
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 0
#else
#define GLZ_JKJ_IF_CONSTEVAL if (false)
#define GLZ_JKJ_IF_NOT_CONSTEVAL if (true)
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 0
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 0
#endif
#else
#if defined(__cpp_lib_is_constant_evaluated) && __cpp_lib_is_constant_evaluated >= 201811L
#define GLZ_JKJ_IF_CONSTEVAL if (stdr::is_constant_evaluated())
#define GLZ_JKJ_IF_NOT_CONSTEVAL if (!stdr::is_constant_evaluated())
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 1
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 1
#elif GLZ_JKJ_HAS_IF_CONSTEXPR
#define GLZ_JKJ_IF_CONSTEVAL if constexpr (false)
#define GLZ_JKJ_IF_NOT_CONSTEVAL if constexpr (true)
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 0
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 0
#else
#define GLZ_JKJ_IF_CONSTEVAL if (false)
#define GLZ_JKJ_IF_NOT_CONSTEVAL if (true)
#define GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL 0
#define GLZ_JKJ_USE_IS_CONSTANT_EVALUATED 0
#endif
#endif

#if GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL && GLZ_JKJ_HAS_BIT_CAST
#define GLZ_JKJ_CONSTEXPR20 constexpr
#else
#define GLZ_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 GLZ_JKJ_SAFEBUFFERS
#define GLZ_JKJ_FORCEINLINE inline __attribute__((always_inline))
#elif defined(_MSC_VER)
#define GLZ_JKJ_SAFEBUFFERS __declspec(safebuffers)
#define GLZ_JKJ_FORCEINLINE __forceinline
#else
#define GLZ_JKJ_SAFEBUFFERS
#define GLZ_JKJ_FORCEINLINE inline
#endif

#if defined(__has_builtin)
#define GLZ_JKJ_HAS_BUILTIN(x) __has_builtin(x)
#else
#define GLZ_JKJ_HAS_BUILTIN(x) false
#endif

#if defined(_MSC_VER)
#include <intrin.h>
#elif defined(__INTEL_COMPILER)
#include <immintrin.h>
#endif

namespace glz::jkj
{
   namespace dragonbox
   {
      ////////////////////////////////////////////////////////////////////////////////////////
      // The Compatibility layer for toolchains without standard C++ headers.
      ////////////////////////////////////////////////////////////////////////////////////////
      namespace detail
      {
         namespace stdr
         {
            // <bit>
#if GLZ_JKJ_HAS_BIT_CAST
            using GLZ_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 GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_fast16_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_fast32_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_fast8_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_least16_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_least32_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::int_least8_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast16_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast32_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_fast8_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_least16_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_least32_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_least64_t;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::uint_least8_t;
            // We need INT32_C, UINT32_C and UINT64_C macros too, but again there is nothing to do
            // here.

            // <cstring>
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::memcpy;
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::size_t;

            // <limits>
            template <class T>
            using numeric_limits = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::numeric_limits<T>;

            // <type_traits>
            template <bool cond, class T = void>
            using enable_if = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::enable_if<cond, T>;
            template <class T>
            using add_rvalue_reference = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::add_rvalue_reference<T>;
            template <bool cond, class T_true, class T_false>
            using conditional = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::conditional<cond, T_true, T_false>;
#if GLZ_JKJ_USE_IS_CONSTANT_EVALUATED
            using GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_constant_evaluated;
#endif
            template <class T1, class T2>
            using is_same = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_same<T1, T2>;
#if !GLZ_JKJ_HAS_BIT_CAST
            template <class T>
            using is_trivially_copyable = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_trivially_copyable<T>;
#endif
            template <class T>
            using is_integral = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_integral<T>;
            template <class T>
            using is_signed = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_signed<T>;
            template <class T>
            using is_unsigned = GLZ_JKJ_STD_REPLACEMENT_NAMESPACE::is_unsigned<T>;
         }
      }

      ////////////////////////////////////////////////////////////////////////////////////////
      // Some general utilities for C++11-compatibility.
      ////////////////////////////////////////////////////////////////////////////////////////
      namespace detail
      {
#if !GLZ_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]; }
            GLZ_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>
         GLZ_JKJ_CONSTEXPR20 To bit_cast(const From& from)
         {
#if GLZ_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 GLZ_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 GLZ_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>>
      GLZ_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>
            GLZ_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_; }

               GLZ_JKJ_CONSTEXPR20 uint128& operator+=(stdr::uint_least64_t n) & noexcept
               {
                  const auto 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);

                  GLZ_JKJ_IF_CONSTEXPR(value_bits<stdr::uint_least64_t>::value > 64)
                  {
                     generic_impl();
                     return *this;
                  }

                  GLZ_JKJ_IF_CONSTEVAL
                  {
                     generic_impl();
                     return *this;
                  }

                  // See https://github.com/fmtlib/fmt/pull/2985.
#if GLZ_JKJ_HAS_BUILTIN(__builtin_addcll) && !defined(__ibmxl__)
                  GLZ_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 GLZ_JKJ_HAS_BUILTIN(__builtin_addcl) && !defined(__ibmxl__)
                  GLZ_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 GLZ_JKJ_HAS_BUILTIN(__builtin_addc) && !defined(__ibmxl__)
                  GLZ_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 GLZ_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{};
                  const auto 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, "");
                  const auto 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, "");
                  const auto carry = _addcarry_u64(0, low_, n, &low_);
                  _addcarry_u64(carry, high_, 0, &high_);
#else
                  generic_impl();
#endif
                  return *this;
               }
            };

            inline GLZ_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)
               GLZ_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.
            GLZ_JKJ_SAFEBUFFERS inline GLZ_JKJ_CONSTEXPR20 uint128 umul128(stdr::uint_least64_t x,
                                                                           stdr::uint_least64_t y) noexcept
            {
               const auto 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__)
               const auto 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)
               GLZ_JKJ_IF_CONSTEVAL
               {
                  // This redundant variable is to workaround MSVC's codegen bug caused by the
                  // interaction of NRVO and intrinsics.
                  const auto 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.
            GLZ_JKJ_SAFEBUFFERS inline GLZ_JKJ_CONSTEXPR20 stdr::uint_least64_t umul128_upper64(
               stdr::uint_least64_t x, stdr::uint_least64_t y) noexcept
            {
               const auto 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__)
               const auto result = builtin_uint128_t(x) * builtin_uint128_t(y);
               return stdr::uint_least64_t(result >> 64);
#elif defined(_MSC_VER) && defined(_M_X64)
               GLZ_JKJ_IF_CONSTEVAL
               {
                  // This redundant variable is to workaround MSVC's codegen bug caused by the
                  // interaction of NRVO and intrinsics.
                  const auto 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.
            GLZ_JKJ_SAFEBUFFERS inline GLZ_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 GLZ_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
               const auto yh = stdr::uint_least32_t(y >> 32);
               const auto yl = stdr::uint_least32_t(y);

               const auto xyh = umul64(x, yh);
               const auto 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.
            GLZ_JKJ_SAFEBUFFERS inline GLZ_JKJ_CONSTEXPR20 uint128 umul192_lower128(stdr::uint_least64_t x,
                                                                                    uint128 y) noexcept
            {
               const auto high = x * y.high();
               const auto 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 GLZ_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 GLZ_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 GLZ_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 GLZ_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>
            GLZ_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);
               const auto prod = intermediate_type(n * info::magic_number);

               constexpr auto mask = intermediate_type((intermediate_type(1) << info::shift_amount) - 1);
               const bool 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>
            GLZ_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>
            GLZ_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.
               GLZ_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 GLZ_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 GLZ_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 GLZ_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
            GLZ_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 !GLZ_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
            GLZ_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 !GLZ_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 GLZ_JKJ_HAS_CONSTEXPR17
         static constexpr cache_holder_t cache GLZ_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 GLZ_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 GLZ_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 GLZ_JKJ_STATIC_DATA_SECTION =
            make_pow5_table(detail::make_index_sequence<pow5_table_size>{});
#endif

         template <class ShiftAmountType, class DecimalExponentType>
         static GLZ_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)(), "");
            const auto cache_index = DecimalExponentType(
               detail::stdr::uint_fast16_t(DecimalExponentType(k - min_k) * detail::stdr::int_fast16_t(79)) >> 10);
            const auto kb = DecimalExponentType(cache_index * compression_ratio + min_k);
            const auto offset = DecimalExponentType(k - kb);

            // Get the base cache.
            const auto base_cache = cache[cache_index];

            if (offset == 0) {
               return base_cache;
            }
            else {
               // Compute the required amount of bit-shift.
               const auto 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.
               const auto 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);
               const auto 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 !GLZ_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 GLZ_JKJ_HAS_CONSTEXPR17
         static constexpr cache_holder_t cache GLZ_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 GLZ_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 GLZ_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 GLZ_JKJ_STATIC_DATA_SECTION =
            make_pow5_table(detail::make_index_sequence<pow5_table_size>{});
#endif

         template <class ShiftAmountType, class DecimalExponentType>
         static GLZ_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)(), "");
            const auto cache_index = DecimalExponentType(
               detail::stdr::uint_fast32_t(DecimalExponentType(k - min_k) * detail::stdr::int_fast32_t(607)) >> 14);
            const auto kb = DecimalExponentType(cache_index * compression_ratio + min_k);
            const auto offset = DecimalExponentType(k - kb);

            // Get the base cache.
            const auto base_cache = cache[cache_index];

            if (offset == 0) {
               return base_cache;
            }
            else {
               // Compute the required amount of bit-shift.
               const auto 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.
               const auto pow5 = pow5_table[offset];
               auto recovered_cache = detail::wuint::umul128(base_cache.high(), pow5);
               const auto middle_low = detail::wuint::umul128(base_cache.low(), pow5);

               recovered_cache += middle_low.high();

               const auto high_to_middle = detail::stdr::uint_least64_t(
                  (recovered_cache.high() << ShiftAmountType(64 - alpha)) & UINT64_C(0xffffffffffffffff));
               const auto 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 !GLZ_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
         {
            GLZ_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 = {};

            GLZ_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
         {
            GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE static GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE static GLZ_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 = {};

            GLZ_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; }
               };
            }

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 {};
                  }
               };
            }

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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;
               };
            }

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_JKJ_INLINE_VARIABLE struct toward_zero_t
            {
               using decimal_to_binary_rounding_policy = toward_zero_t;

               template <class SignedSignificandBits, class Func, class... Args>
               GLZ_JKJ_FORCEINLINE GLZ_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 = {};

            GLZ_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>
               GLZ_JKJ_FORCEINLINE GLZ_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.

            GLZ_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 = {};

            GLZ_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 = {};

            GLZ_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 = {};

            GLZ_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 = {};

            GLZ_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
         {
            GLZ_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 GLZ_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 = {};

            GLZ_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 GLZ_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
         {
            GLZ_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;

            GLZ_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;

            GLZ_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>
      {
         GLZ_JKJ_FORCEINLINE static GLZ_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>
      {
         GLZ_JKJ_FORCEINLINE static GLZ_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>
      {
         GLZ_JKJ_FORCEINLINE static GLZ_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) {
               const auto 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>
      {
         GLZ_JKJ_FORCEINLINE static GLZ_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) {
               const auto 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 GLZ_JKJ_CONSTEXPR20 compute_mul_result compute_mul(carrier_uint u,
                                                                   const cache_entry_type& cache) noexcept
         {
            const auto 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(const cache_entry_type& cache,
                                                                     ShiftAmountType beta) noexcept
         {
            return detail::stdr::uint_least64_t(cache >> ShiftAmountType(cache_bits - 1 - beta));
         }

         template <class ShiftAmountType>
         static GLZ_JKJ_CONSTEXPR20 compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
                                                                                 const cache_entry_type& cache,
                                                                                 ShiftAmountType beta) noexcept
         {
            assert(beta >= 1);
            assert(beta <= 32);

            const auto 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(const cache_entry_type& 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(const cache_entry_type& 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(const cache_entry_type& 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 GLZ_JKJ_CONSTEXPR20 compute_mul_result compute_mul(carrier_uint u,
                                                                   const cache_entry_type& cache) noexcept
         {
            const auto 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(const cache_entry_type& cache,
                                                                     ShiftAmountType beta) noexcept
         {
            return detail::stdr::uint_least64_t(cache.high() >> ShiftAmountType(total_bits - 1 - beta));
         }

         template <class ShiftAmountType>
         static GLZ_JKJ_CONSTEXPR20 compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
                                                                                 const cache_entry_type& cache,
                                                                                 ShiftAmountType beta) noexcept
         {
            assert(beta >= 1);
            assert(beta < 64);

            const auto 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(const cache_entry_type& 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(const cache_entry_type& 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(const cache_entry_type& 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::exponent_bias;
            using format::max_exponent;
            using format::min_exponent;
            using format::significand_bits;

            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), "");
#undef min
#undef max
            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>
            GLZ_JKJ_SAFEBUFFERS static GLZ_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.
                     const auto 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);
                     const auto beta = shift_amount_type(
                        binary_exponent + log::floor_log2_pow10<min_k, max_k>(decimal_exponent_type_(-minus_k)));

                     // Compute xi and zi.
                     const auto 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.
               const auto 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);
               const auto cache =
                  CachePolicy::template get_cache<format, shift_amount_type>(decimal_exponent_type_(-minus_k));
               const auto 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)
               const auto 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.
               const auto 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) {
                        GLZ_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.
                     const auto 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;

               GLZ_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));
                  const bool approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0;

                  // Is dist divisible by 10^kappa?
                  const bool 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.
                     const auto 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>
            GLZ_JKJ_FORCEINLINE GLZ_JKJ_SAFEBUFFERS static GLZ_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.
               const auto 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);
               const auto cache =
                  CachePolicy::template get_cache<format, shift_amount_type>(decimal_exponent_type_(-minus_k));
               const auto 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)
               const auto 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.
               GLZ_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.
                     GLZ_JKJ_IF_CONSTEXPR(
                        stdr::is_same<cache_holder_type, compressed_cache_holder<ieee754_binary32>>::value)
                     {
                        if (two_fc == 33554430 && binary_exponent == -10) {
                           break;
                        }
                     }
                     const auto 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>
            GLZ_JKJ_FORCEINLINE GLZ_JKJ_SAFEBUFFERS static GLZ_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.
               const auto 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);
               const auto cache =
                  CachePolicy::template get_cache<format, shift_amount_type>(decimal_exponent_type_(-minus_k));
               const auto 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)
               const auto deltai = static_cast<remainder_type_>(
                  multiplication_traits_::compute_delta(cache, shift_amount_type(beta - (shorter_interval ? 1 : 0))));
               const carrier_uint 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);
               const auto 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()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::sign_policy>
            constexpr bool operator()(dummy<Policy>) noexcept
            {
               return true;
            }
         };
         struct is_trailing_zero_policy
         {
            constexpr bool operator()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::trailing_zero_policy>
            constexpr bool operator()(dummy<Policy>) noexcept
            {
               return true;
            }
         };
         struct is_decimal_to_binary_rounding_policy
         {
            constexpr bool operator()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::decimal_to_binary_rounding_policy>
            constexpr bool operator()(dummy<Policy>) noexcept
            {
               return true;
            }
         };
         struct is_binary_to_decimal_rounding_policy
         {
            constexpr bool operator()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::binary_to_decimal_rounding_policy>
            constexpr bool operator()(dummy<Policy>) noexcept
            {
               return true;
            }
         };
         struct is_cache_policy
         {
            constexpr bool operator()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::cache_policy>
            constexpr bool operator()(dummy<Policy>) noexcept
            {
               return true;
            }
         };
         struct is_preferred_integer_types_policy
         {
            constexpr bool operator()(...) noexcept { return false; }
            template <class Policy, class = typename Policy::preferred_integer_types_policy>
            constexpr bool operator()(dummy<Policy>) 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>
            GLZ_JKJ_FORCEINLINE GLZ_JKJ_SAFEBUFFERS GLZ_JKJ_CONSTEXPR20 return_type
            operator()(IntervalTypeProvider, signed_significand_bits<FormatTraits> s,
                       typename FormatTraits::exponent_int exponent_bits) noexcept
            {
               constexpr auto tag = IntervalTypeProvider::tag;

               GLZ_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 GLZ_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 GLZ_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>
      GLZ_JKJ_FORCEINLINE GLZ_JKJ_SAFEBUFFERS GLZ_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>
      GLZ_JKJ_FORCEINLINE GLZ_JKJ_SAFEBUFFERS GLZ_JKJ_CONSTEXPR20
         detail::to_decimal_return_type<FormatTraits, Policies...>
         to_decimal(Float x, Policies... policies) noexcept
      {
         const auto br = make_float_bits<Float, ConversionTraits, FormatTraits>(x);
         const auto exponent_bits = br.extract_exponent_bits();
         const auto s = br.remove_exponent_bits();
         assert(br.is_finite() && br.is_nonzero());

         return to_decimal_ex(s, exponent_bits, policies...);
      }
   }
}

#undef GLZ_JKJ_HAS_BUILTIN
#undef GLZ_JKJ_FORCEINLINE
#undef GLZ_JKJ_SAFEBUFFERS
#undef GLZ_JKJ_CONSTEXPR20
#undef GLZ_JKJ_USE_IS_CONSTANT_EVALUATED
#undef GLZ_JKJ_CAN_BRANCH_ON_CONSTEVAL
#undef GLZ_JKJ_IF_NOT_CONSTEVAL
#undef GLZ_JKJ_IF_CONSTEVAL
#undef GLZ_JKJ_HAS_BIT_CAST
#undef GLZ_JKJ_IF_CONSTEXPR
#undef GLZ_JKJ_HAS_IF_CONSTEXPR
#undef GLZ_JKJ_INLINE_VARIABLE
#undef GLZ_JKJ_HAS_INLINE_VARIABLE
#undef GLZ_JKJ_HAS_CONSTEXPR17
#undef GLZ_JKJ_CONSTEXPR14
#undef GLZ_JKJ_HAS_CONSTEXPR14
#if GLZ_JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED
#undef GLZ_JKJ_STD_REPLACEMENT_NAMESPACE_DEFINED
#else
#undef GLZ_JKJ_STD_REPLACEMENT_NAMESPACE
#endif
#if GLZ_JKJ_STATIC_DATA_SECTION_DEFINED
#undef GLZ_JKJ_STATIC_DATA_SECTION_DEFINED
#else
#undef GLZ_JKJ_STATIC_DATA_SECTION
#endif

#endif
