// Copyright 2020 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.

#pragma once

#include <daw/json/impl/version.h>

#include <daw/daw_algorithm.h>
#include <daw/daw_attributes.h>
#include <daw/daw_bit_cast.h>
#include <daw/daw_cpp_feature_check.h>
#include <daw/daw_is_constant_evaluated.h>
#include <daw/daw_likely.h>

#include <cassert>
#include <climits>
#include <cstdint>
#include <cstring>
#include <limits>
#include <type_traits>

#if defined( DAW_HAS_MSVC )
#include <intrin.h>
#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__ ) or defined( __clang__ )
#define JKJ_SAFEBUFFERS
#elif defined( _MSC_VER )
#define JKJ_SAFEBUFFERS __declspec( safebuffers )
#else
#define JKJ_SAFEBUFFERS
#endif

namespace daw::jkj::dragonbox {
	inline namespace DAW_JSON_VER {
		namespace detail {
			template<class T>
			inline constexpr std::size_t physical_bits =
			  sizeof( T ) * std::numeric_limits<unsigned char>::digits;

			template<class T>
			inline constexpr std::size_t value_bits =
			  std::numeric_limits<std::enable_if_t<std::is_unsigned_v<T>, T>>::digits;
		} // namespace detail

		enum class ieee754_format { binary32, binary64 };

		template<ieee754_format format_>
		struct ieee754_format_info;

		template<>
		struct ieee754_format_info<ieee754_format::binary32> {
			static constexpr auto format = ieee754_format::binary32;
			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_digits = 9;
		};

		template<>
		struct ieee754_format_info<ieee754_format::binary64> {
			static constexpr auto format = ieee754_format::binary64;
			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_digits = 17;
		};

		// To reduce boilerplates
		template<class T>
		struct default_ieee754_traits {
			static_assert( detail::physical_bits<T> == 32 or
			               detail::physical_bits<T> == 64 );

			using type = T;
			static constexpr ieee754_format format = detail::physical_bits<T> == 32
			                                           ? ieee754_format::binary32
			                                           : ieee754_format::binary64;

			using carrier_uint = daw::conditional_t<detail::physical_bits<T> == 32,
			                                        std::uint32_t, std::uint64_t>;
			static_assert( sizeof( carrier_uint ) == sizeof( T ) );

			static constexpr int carrier_bits =
			  static_cast<int>( detail::physical_bits<carrier_uint> );

			static inline constexpr T carrier_to_float( carrier_uint u ) noexcept {
				return DAW_BIT_CAST( T, u );
			}

			static inline constexpr carrier_uint float_to_carrier( T x ) noexcept {
				return DAW_BIT_CAST( carrier_uint, x );
			}

			static inline constexpr unsigned int
			extract_exponent_bits( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr int exponent_bits =
				  ieee754_format_info<format>::exponent_bits;
				static_assert( detail::value_bits<unsigned int> > exponent_bits );
				constexpr unsigned exponent_bits_mask = ( 1U << exponent_bits ) - 1U;
				return static_cast<unsigned int>( ( u >> significand_bits ) &
				                                  exponent_bits_mask );
			}

			static inline constexpr carrier_uint
			extract_significand_bits( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr auto significand_bits_mask =
				  carrier_uint( ( carrier_uint( 1 ) << significand_bits ) - 1 );
				return carrier_uint( u & significand_bits_mask );
			}

			// Allows positive zero and positive NaN's, but not allow negative zero
			static inline constexpr bool is_positive( carrier_uint u ) noexcept {
				return ( u >> ( carrier_bits - 1 ) ) == 0;
			}
			// Allows negative zero and negative NaN's, but not allow positive zero
			static inline constexpr bool is_negative( carrier_uint u ) noexcept {
				return ( u >> ( carrier_bits - 1 ) ) != 0;
			}

			static constexpr int exponent_bias =
			  1 - ( 1 << ( carrier_bits -
			               ieee754_format_info<format>::significand_bits - 2 ) );

			static inline constexpr bool is_finite( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr int exponent_bits =
				  ieee754_format_info<format>::exponent_bits;
				constexpr auto exponent_bits_mask = carrier_uint(
				  ( ( carrier_uint( 1 ) << exponent_bits ) - 1 ) << significand_bits );

				return ( u & exponent_bits_mask ) != exponent_bits_mask;
			}
			static inline constexpr bool is_nonzero( carrier_uint u ) noexcept {
				return ( u << 1 ) != 0;
			}
			// Allows positive and negative zeros
			static inline constexpr bool is_subnormal( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr int exponent_bits =
				  ieee754_format_info<format>::exponent_bits;
				constexpr auto exponent_bits_mask = carrier_uint(
				  ( ( carrier_uint( 1 ) << exponent_bits ) - 1 ) << significand_bits );

				return ( u & exponent_bits_mask ) == 0;
			}
			static inline constexpr bool
			is_positive_infinity( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr int exponent_bits =
				  ieee754_format_info<format>::exponent_bits;
				constexpr auto positive_infinity =
				  carrier_uint( ( carrier_uint( 1 ) << exponent_bits ) - 1 )
				  << significand_bits;
				return u == positive_infinity;
			}
			static inline constexpr bool
			is_negative_infinity( carrier_uint u ) noexcept {
				constexpr int significand_bits =
				  ieee754_format_info<format>::significand_bits;
				constexpr int exponent_bits =
				  ieee754_format_info<format>::exponent_bits;
				constexpr auto negative_infinity =
				  ( carrier_uint( ( carrier_uint( 1 ) << exponent_bits ) - 1 )
				    << significand_bits ) |
				  ( carrier_uint( 1 ) << ( carrier_bits - 1 ) );
				return u == negative_infinity;
			}
			static inline constexpr bool is_infinity( carrier_uint u ) noexcept {
				return is_positive_infinity( u ) or is_negative_infinity( u );
			}
			static inline constexpr bool is_nan( carrier_uint u ) noexcept {
				return not is_finite( u ) and ( extract_significand_bits( u ) != 0 );
			}
		};

		// Speciailze this class template for possible extensions
		template<class T>
		struct ieee754_traits : default_ieee754_traits<T> {
			// I don't know if there is a truly reliable way of detecting
			// IEEE-754 binary32/binary64 formats; I just did my best here
			static_assert(
			  std::numeric_limits<T>::is_iec559 and
			    std::numeric_limits<T>::radix == 2 and
			    ( detail::physical_bits<T> == 32 or detail::physical_bits<T> == 64 ),
			  "default_ieee754_traits only worsk for 32-bits or 64-bits types "
			  "supporting binary32 or binary64 formatsnot " );
		};

		// Convenient wrapper for ieee754_traits
		// In order to reduce the argument passing overhead,
		// this class should be as simple as possible
		// (e.g., no inheritance, no private non-static data member, etc.;
		// this is an unfortunate fact about x64 calling convention)
		template<class T>
		struct ieee754_bits {
			using carrier_uint = typename ieee754_traits<T>::carrier_uint;
			carrier_uint u;

			ieee754_bits( ) = default;
			inline constexpr explicit ieee754_bits( carrier_uint _u ) noexcept
			  : u{ _u } {}
			inline constexpr explicit ieee754_bits( T x ) noexcept
			  : u{ ieee754_traits<T>::float_to_carrier( x ) } {}

			[[nodiscard]] inline constexpr T to_float( ) const noexcept {
				return ieee754_traits<T>::carrier_to_float( u );
			}

			[[nodiscard]] inline constexpr carrier_uint
			extract_significand_bits( ) const noexcept {
				return ieee754_traits<T>::extract_significand_bits( u );
			}

			[[nodiscard]] inline constexpr unsigned
			extract_exponent_bits( ) const noexcept {
				return ieee754_traits<T>::extract_exponent_bits( u );
			}

			[[nodiscard]] inline constexpr carrier_uint
			binary_significand( ) const noexcept {
				using format_info = ieee754_format_info<ieee754_traits<T>::format>;
				auto s = extract_significand_bits( );
				if( extract_exponent_bits( ) == 0 ) {
					return s;
				} else {
					return s | ( carrier_uint( 1 ) << format_info::significand_bits );
				}
			}

			[[nodiscard]] inline constexpr int binary_exponent( ) const noexcept {
				using format_info = ieee754_format_info<ieee754_traits<T>::format>;
				auto e = extract_exponent_bits( );
				if( e == 0 ) {
					return format_info::min_exponent;
				} else {
					return e + format_info::exponent_bias;
				}
			}

			[[nodiscard]] inline constexpr bool is_finite( ) const noexcept {
				return ieee754_traits<T>::is_finite( u );
			}

			[[nodiscard]] inline constexpr bool is_nonzero( ) const noexcept {
				return ieee754_traits<T>::is_nonzero( u );
			}
			// Allows positive and negative zeros
			[[nodiscard]] inline constexpr bool is_subnormal( ) const noexcept {
				return ieee754_traits<T>::is_subnormal( u );
			}
			// Allows positive zero and positive NaN's, but not allow negative zero
			[[nodiscard]] inline constexpr bool is_positive( ) const noexcept {
				return ieee754_traits<T>::is_positive( u );
			}
			// Allows negative zero and negative NaN's, but not allow positive zero
			[[nodiscard]] inline constexpr bool is_negative( ) const noexcept {
				return ieee754_traits<T>::is_negative( u );
			}

			[[nodiscard]] inline constexpr bool
			is_positive_infinity( ) const noexcept {
				return ieee754_traits<T>::is_positive_infinity( u );
			}

			[[nodiscard]] inline constexpr bool
			is_negative_infinity( ) const noexcept {
				return ieee754_traits<T>::is_negative_infinity( u );
			}
			// Allows both plus and minus infinities
			[[nodiscard]] inline constexpr bool is_infinity( ) const noexcept {
				return ieee754_traits<T>::is_infinity( u );
			}
			[[nodiscard]] inline constexpr bool is_nan( ) const noexcept {
				return ieee754_traits<T>::is_nan( u );
			}
		};

		template<class T>
		ieee754_bits( T ) -> ieee754_bits<T>;

		namespace detail {
			////////////////////////////////////////////////////////////////////////////////////////
			// Utilities for wide unsigned integer arithmetic
			////////////////////////////////////////////////////////////////////////////////////////

			namespace wuint {
				struct uint128 {
					uint128( ) = default;

#if( defined( __GNUC__ ) or defined( __clang__ ) ) and \
  defined( __SIZEOF_INT128__ ) and defined( __x86_64__ )
#if defined( __GNUC__ )
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic"
#endif
					unsigned __int128 internal_;

					constexpr uint128( std::uint64_t high, std::uint64_t low ) noexcept
					  : internal_{
					      ( static_cast<unsigned __int128>( low ) ) |
					      ( ( static_cast<unsigned __int128>( high ) ) << 64 ) } {}

					constexpr uint128( unsigned __int128 u ) noexcept
					  : internal_{ u } {}
#if defined( __GNUC__ )
#pragma GCC diagnostic pop
#endif
					[[nodiscard]] constexpr std::uint64_t high( ) const noexcept {
						return std::uint64_t( internal_ >> 64 );
					}

					[[nodiscard]] constexpr std::uint64_t low( ) const noexcept {
						return std::uint64_t( internal_ );
					}

					constexpr uint128 &operator+=( std::uint64_t n ) & noexcept {
						internal_ += n;
						return *this;
					}
#else
					std::uint64_t high_;
					std::uint64_t low_;

					constexpr uint128( std::uint64_t high, std::uint64_t low ) noexcept
					  : high_{ high }
					  , low_{ low } {}

					[[nodiscard]] constexpr std::uint64_t high( ) const noexcept {
						return high_;
					}

					[[nodiscard]] constexpr std::uint64_t low( ) const noexcept {
						return low_;
					}

					constexpr uint128 &operator+=( std::uint64_t n ) & noexcept {
#if defined( DAW_IS_CONSTANT_EVALUATED ) and defined( DAW_HAS_MSVC ) and \
  defined( _M_X64 )
						if( not DAW_IS_CONSTANT_EVALUATED( ) ) {
							auto carry = _addcarry_u64( 0, low_, n, &low_ );
							_addcarry_u64( carry, high_, 0, &high_ );
							return *this;
						}
#endif
						auto sum = low_ + n;
						high_ += ( sum < low_ ? 1 : 0 );
						low_ = sum;
						return *this;
					}
#endif
				};

				// Get 128-bit result of multiplication of two 64-bit unsigned
				// integers
				[[nodiscard]] JKJ_SAFEBUFFERS inline constexpr uint128
				umul128( std::uint64_t x, std::uint64_t y ) noexcept {
#if( defined( __GNUC__ ) or defined( __clang__ ) ) and \
  defined( __SIZEOF_INT128__ ) and defined( __x86_64__ )
#if defined( __GNUC__ )
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic"
#endif
					return static_cast<unsigned __int128>( x ) *
					       static_cast<unsigned __int128>( y );
#if defined( __GNUC__ )
#pragma GCC diagnostic pop
#endif
#elif defined( _MSC_VER ) and defined( _M_X64 ) and \
  defined( DAW_IS_CONSTANT_EVALUATED )
					if( DAW_IS_CONSTANT_EVALUATED( ) ) {
						constexpr auto mask =
						  ( std::uint64_t( 1 ) << 32 ) - std::uint64_t( 1 );

						auto a = x >> 32;
						auto b = x & mask;
						auto c = y >> 32;
						auto d = y & mask;

						auto ac = a * c;
						auto bc = b * c;
						auto ad = a * d;
						auto bd = b * d;

						auto intermediate = ( bd >> 32 ) + ( ad & mask ) + ( bc & mask );

						return { ac + ( intermediate >> 32 ) + ( ad >> 32 ) + ( bc >> 32 ),
						         ( intermediate << 32 ) + ( bd & mask ) };
					}
					uint128 result;
					result.low_ = _umul128( x, y, &result.high_ );
					return result;
#else
					constexpr auto mask =
					  ( std::uint64_t( 1 ) << 32 ) - std::uint64_t( 1 );

					auto a = x >> 32;
					auto b = x & mask;
					auto c = y >> 32;
					auto d = y & mask;

					auto ac = a * c;
					auto bc = b * c;
					auto ad = a * d;
					auto bd = b * d;

					auto intermediate = ( bd >> 32 ) + ( ad & mask ) + ( bc & mask );

					return { ac + ( intermediate >> 32 ) + ( ad >> 32 ) + ( bc >> 32 ),
					         ( intermediate << 32 ) + ( bd & mask ) };
#endif
				}

				[[nodiscard]] JKJ_SAFEBUFFERS inline constexpr std::uint64_t
				umul128_upper64( std::uint64_t x, std::uint64_t y ) noexcept {
#if( defined( __GNUC__ ) or defined( __clang__ ) ) and \
  defined( __SIZEOF_INT128__ ) and defined( __x86_64__ )
#if defined( __GNUC__ )
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic"
#endif
					auto p = static_cast<unsigned __int128>( x ) *
					         static_cast<unsigned __int128>( y );
					return std::uint64_t( p >> 64 );
#if defined( __GNUC__ )
#pragma GCC diagnostic pop
#endif
#elif defined( DAW_IS_CONSTANT_EVALUATED ) and defined( _MSC_VER ) and \
  defined( _M_X64 )
					if( DAW_IS_CONSTANT_EVALUATED( ) ) {
						constexpr auto mask =
						  ( std::uint64_t( 1 ) << 32 ) - std::uint64_t( 1 );

						auto a = x >> 32;
						auto b = x & mask;
						auto c = y >> 32;
						auto d = y & mask;

						auto ac = a * c;
						auto bc = b * c;
						auto ad = a * d;
						auto bd = b * d;

						auto intermediate = ( bd >> 32 ) + ( ad & mask ) + ( bc & mask );

						return ac + ( intermediate >> 32 ) + ( ad >> 32 ) + ( bc >> 32 );
					} else {
						return __umulh( x, y );
					}
#else
					constexpr auto mask =
					  ( std::uint64_t( 1 ) << 32 ) - std::uint64_t( 1 );

					auto a = x >> 32;
					auto b = x & mask;
					auto c = y >> 32;
					auto d = y & mask;

					auto ac = a * c;
					auto bc = b * c;
					auto ad = a * d;
					auto bd = b * d;

					auto intermediate = ( bd >> 32 ) + ( ad & mask ) + ( bc & mask );

					return ac + ( intermediate >> 32 ) + ( ad >> 32 ) + ( bc >> 32 );
#endif
				}

				// Get upper 64-bits of multiplication of a 64-bit unsigned integer
				// and a 128-bit unsigned integer
				[[nodiscard]] JKJ_SAFEBUFFERS inline constexpr std::uint64_t
				umul192_upper64( std::uint64_t x, uint128 y ) noexcept {
					auto g0 = umul128( x, y.high( ) );
					g0 += umul128_upper64( x, y.low( ) );
					return g0.high( );
				}

				// Get upper 32-bits of multiplication of a 32-bit unsigned integer
				// and a 64-bit unsigned integer
				[[nodiscard]] inline constexpr std::uint32_t
				umul96_upper32( std::uint32_t x, std::uint64_t y ) noexcept {
					return std::uint32_t( umul128_upper64( x, y ) );
				}

				// Get middle 64-bits of multiplication of a 64-bit unsigned integer
				// and a 128-bit unsigned integer
				[[nodiscard]] JKJ_SAFEBUFFERS inline constexpr std::uint64_t
				umul192_middle64( std::uint64_t x, uint128 y ) noexcept {
					auto g01 = x * y.high( );
					auto g10 = umul128_upper64( x, y.low( ) );
					return g01 + g10;
				}

				// Get middle 32-bits of multiplication of a 32-bit unsigned integer
				// and a 64-bit unsigned integer
				[[nodiscard]] inline constexpr std::uint64_t
				umul96_lower64( std::uint32_t x, std::uint64_t y ) noexcept {
					return x * y;
				}
			} // namespace wuint

			template<int k, class Int>
			[[nodiscard]] inline constexpr Int compute_power( Int a ) noexcept {
				static_assert( k >= 0 );
				Int p = 1;
				for( int i = 0; i < k; ++i ) {
					p *= a;
				}
				return p;
			}

			template<int a, class UInt>
			[[nodiscard]] inline constexpr int count_factors( UInt n ) noexcept {
				static_assert( a > 1 );
				int c = 0;
				while( n % a == 0 ) {
					n /= a;
					++c;
				}
				return c;
			}

			////////////////////////////////////////////////////////////////////////////////////////
			// Utilities for fast/constexpr log computation
			////////////////////////////////////////////////////////////////////////////////////////

			namespace log {
				[[nodiscard]] inline constexpr std::int32_t
				floor_shift( std::uint32_t integer_part,
				             std::uint64_t fractional_digits,
				             std::size_t shift_amount ) noexcept {
					assert( shift_amount < 32 );
					// Ensure no overflow
					assert( shift_amount == 0 or
					        integer_part <
					          ( std::uint32_t( 1 ) << ( 32 - shift_amount ) ) );

					return shift_amount == 0
					         ? static_cast<std::int32_t>( integer_part )
					         : static_cast<std::int32_t>(
					             ( integer_part
					               << static_cast<std::uint32_t>( shift_amount ) ) |
					             ( fractional_digits >> ( 64U - shift_amount ) ) );
				}

				// Compute floor(e * c - s)
				template<std::uint32_t c_integer_part,
				         std::uint64_t c_fractional_digits, std::size_t shift_amount,
				         std::int32_t max_exponent, std::uint32_t s_integer_part = 0,
				         std::uint64_t s_fractional_digits = 0>
				[[nodiscard]] inline constexpr int compute( int e ) noexcept {
					assert( e <= max_exponent and e >= -max_exponent );
					constexpr auto c =
					  floor_shift( c_integer_part, c_fractional_digits, shift_amount );
					constexpr auto s =
					  floor_shift( s_integer_part, s_fractional_digits, shift_amount );
					return static_cast<int>( ( std::int32_t( e ) * c - s ) >>
					                         shift_amount );
				}

				inline constexpr std::uint64_t log10_2_fractional_digits{
				  0x4d10'4d42'7de7'fbcc };
				inline constexpr std::uint64_t log10_4_over_3_fractional_digits{
				  0x1ffb'fc2b'bc78'0375 };
				inline constexpr std::size_t floor_log10_pow2_shift_amount = 22;

				inline constexpr std::uint64_t log2_10_fractional_digits{
				  0x5269'e12f'346e'2bf9 };
				inline constexpr std::size_t floor_log2_pow10_shift_amount = 19;

				inline constexpr std::uint64_t log5_2_fractional_digits{
				  0x6e40'd1a4'143d'cb94 };
				inline constexpr std::uint64_t log5_3_fractional_digits{
				  0xaebf'4791'5d44'3b24 };
				inline constexpr std::size_t floor_log5_pow2_shift_amount = 20;

				// For constexpr computation
				// Returns -1 when n = 0
				template<class UInt>
				[[nodiscard]] inline constexpr int floor_log2( UInt n ) noexcept {
					int count = -1;
					while( n != 0 ) {
						++count;
						n >>= 1;
					}
					return count;
				}

				[[nodiscard]] inline constexpr int floor_log10_pow2( int e ) noexcept {
					using namespace log;
					return compute<0, log10_2_fractional_digits,
					               floor_log10_pow2_shift_amount, 1700>( e );
				}

				[[nodiscard]] inline constexpr int floor_log2_pow10( int e ) noexcept {
					using namespace log;
					return compute<3, log2_10_fractional_digits,
					               floor_log2_pow10_shift_amount, 1233>( e );
				}

				[[nodiscard]] inline constexpr int floor_log5_pow2( int e ) noexcept {
					using namespace log;
					return compute<0, log5_2_fractional_digits,
					               floor_log5_pow2_shift_amount, 1492>( e );
				}

				[[nodiscard]] inline constexpr int
				floor_log5_pow2_minus_log5_3( int e ) noexcept {
					using namespace log;
					return compute<0, log5_2_fractional_digits,
					               floor_log5_pow2_shift_amount, 2427, 0,
					               log5_3_fractional_digits>( e );
				}

				[[nodiscard]] inline constexpr int
				floor_log10_pow2_minus_log10_4_over_3( int e ) noexcept {
					using namespace log;
					return compute<0, log10_2_fractional_digits,
					               floor_log10_pow2_shift_amount, 1700, 0,
					               log10_4_over_3_fractional_digits>( e );
				}
			} // namespace log

			////////////////////////////////////////////////////////////////////////////////////////
			// Utilities for fast divisibility test
			////////////////////////////////////////////////////////////////////////////////////////

			namespace div {
				template<class UInt, UInt a>
				[[nodiscard]] inline constexpr UInt modular_inverse(
				  int bit_width = static_cast<int>( value_bits<UInt> ) ) noexcept {
					// By Euler's theorem, a^phi(2^n) == 1 (mod 2^n),
					// where phi(2^n) = 2^(n-1), so the modular inverse of a is
					// a^(2^(n-1) - 1) = a^(1 + 2 + 2^2 + ... + 2^(n-2))
					std::common_type_t<UInt, unsigned int> mod_inverse = 1;
					for( int i = 1; i < bit_width; ++i ) {
						mod_inverse = mod_inverse * mod_inverse * a;
					}
					if( bit_width < static_cast<int>( value_bits<UInt> ) ) {
						auto mask = UInt( ( UInt( 1 ) << bit_width ) - 1 );
						return UInt( mod_inverse & mask );
					} else {
						return UInt( mod_inverse );
					}
				}

				template<class UInt, UInt a, int N>
				struct table_t {
					static_assert( std::is_unsigned_v<UInt> );
					static_assert( a % 2 != 0 );
					static_assert( N > 0 );

					static constexpr int size = N;
					UInt mod_inv[N];
					UInt max_quotients[N];
				};

				template<class UInt, UInt a, int N>
				struct table_holder {
					static constexpr table_t<UInt, a, N> table = [] {
						constexpr auto mod_inverse = modular_inverse<UInt, a>( );
						table_t<UInt, a, N> tbl{ };
						std::common_type_t<UInt, unsigned int> pow_of_mod_inverse = 1;
						UInt pow_of_a = 1;
						for( int i = 0; i < N; ++i ) {
							tbl.mod_inv[i] = UInt( pow_of_mod_inverse );
							tbl.max_quotients[i] =
							  UInt( ( std::numeric_limits<UInt>::max )( ) / pow_of_a );

							pow_of_mod_inverse *= mod_inverse;
							pow_of_a *= a;
						}

						return tbl;
					}( );
				};

				template<std::size_t table_size, class UInt>
				[[nodiscard]] inline constexpr bool
				divisible_by_power_of_5( UInt x, unsigned exp ) noexcept {
					auto const &table =
					  table_holder<UInt, 5, static_cast<int>( table_size )>::table;
					assert( exp < static_cast<unsigned>( table.size ) );
					return ( x * table.mod_inv[exp] ) <= table.max_quotients[exp];
				}

				template<class UInt>
				[[nodiscard]] inline constexpr bool
				divisible_by_power_of_2( UInt x, unsigned exp ) noexcept {
					assert( exp >= 1 );
					assert( x != 0 );
					return daw::cxmath::count_trailing_zeros( x ) >= exp;
					/*
#if JKJ_HAS_COUNTR_ZERO_INTRINSIC
					return bits::countr_zero( x ) >= int( exp );
#else
					if( exp >= int( value_bits<UInt> ) ) {
					  return false;
					}
					return x == ( ( x >> exp ) << exp );
#endif
					 */
				}

				// Replace n by floor(n / 5^N)
				// Returns true if and only if n is divisible by 5^N
				// Precondition: n <= 2 * 5^(N+1)
				template<int N>
				struct check_divisibility_and_divide_by_pow5_info;

				template<>
				struct check_divisibility_and_divide_by_pow5_info<1> {
					static constexpr std::uint32_t magic_number = 0xcccd;
					static constexpr int bits_for_comparison = 16;
					static constexpr std::uint32_t threshold = 0x3333;
					static constexpr int shift_amount = 18;
				};

				template<>
				struct check_divisibility_and_divide_by_pow5_info<2> {
					static constexpr std::uint32_t magic_number = 0xa429;
					static constexpr int bits_for_comparison = 8;
					static constexpr std::uint32_t threshold = 0x0a;
					static constexpr int shift_amount = 20;
				};

				template<int N>
				[[nodiscard]] inline constexpr bool
				check_divisibility_and_divide_by_pow5( std::uint32_t &n ) noexcept {
					// Make sure the computation for max_n does not overflow
					static_assert( N + 1 <= log::floor_log5_pow2( 31 ) );
					assert( n <= compute_power<N + 1>( std::uint32_t( 5 ) ) * 2 );

					using info = check_divisibility_and_divide_by_pow5_info<N>;
					n *= info::magic_number;
					constexpr std::uint32_t comparison_mask =
					  info::bits_for_comparison >= 32
					    ? ( std::numeric_limits<std::uint32_t>::max )( )
					    : std::uint32_t(
					        ( std::uint32_t( 1 ) << info::bits_for_comparison ) - 1 );

					if( ( n & comparison_mask ) <= info::threshold ) {
						n >>= info::shift_amount;
						return true;
					} else {
						n >>= info::shift_amount;
						return false;
					}
				}

				// Compute floor(n / 10^N) for small n and N
				// Precondition: n <= 10^(N+1)
				template<int N>
				struct small_division_by_pow10_info;

				template<>
				struct small_division_by_pow10_info<1> {
					static constexpr std::uint32_t magic_number = 0xcccd;
					static constexpr int shift_amount = 19;
				};

				template<>
				struct small_division_by_pow10_info<2> {
					static constexpr std::uint32_t magic_number = 0xa3d8;
					static constexpr int shift_amount = 22;
				};

				template<int N>
				[[nodiscard]] inline constexpr std::uint32_t
				small_division_by_pow10( std::uint32_t n ) noexcept {
					assert( n <= compute_power<N + 1>( std::uint32_t( 10 ) ) );
					return ( n * small_division_by_pow10_info<N>::magic_number ) >>
					       small_division_by_pow10_info<N>::shift_amount;
				}

				// Compute floor(n / 10^N) for small N
				// Precondition: n <= 2^a * 5^b (a = max_pow2, b = max_pow5)
				template<int N, int max_pow2, int max_pow5, class UInt>
				[[nodiscard]] inline constexpr UInt divide_by_pow10( UInt n ) noexcept {
					static_assert( N >= 0 );

					// Ensure no overflow
					static_assert( max_pow2 +
					                 ( log::floor_log2_pow10( max_pow5 ) - max_pow5 ) <
					               value_bits<UInt> );

					// Specialize for 64bit division by 1000
					// Ensure that the correctness condition is met
					if constexpr( std::is_same_v<UInt, std::uint64_t> and N == 3 and
					              max_pow2 + ( log::floor_log2_pow10( N + max_pow5 ) -
					                           ( N + max_pow5 ) ) <
					                70 ) {
						return wuint::umul128_upper64( n, 0x8312'6e97'8d4f'df3c ) >> 9;
					} else {
						constexpr auto divisor = compute_power<N>( UInt( 10 ) );
						return n / divisor;
					}
				}
			} // namespace div
		} // namespace detail

		////////////////////////////////////////////////////////////////////////////////////////
		// DIY floating-point data type
		////////////////////////////////////////////////////////////////////////////////////////

		template<class Float, bool is_signed, bool trailing_zero_flag>
		struct fp_t;

		template<class Float>
		struct fp_t<Float, false, false> {
			using float_type = Float;
			using carrier_uint = typename ieee754_traits<Float>::carrier_uint;

			carrier_uint significand;
			int exponent;
		};

		template<class Float>
		struct fp_t<Float, true, false> {
			using float_type = Float;
			using carrier_uint = typename ieee754_traits<Float>::carrier_uint;

			carrier_uint significand;
			int exponent;
			bool is_negative;
		};

		template<class Float>
		struct fp_t<Float, false, true> {
			using float_type = Float;
			using carrier_uint = typename ieee754_traits<Float>::carrier_uint;

			carrier_uint significand;
			int exponent;
			bool may_have_trailing_zeros;
		};

		template<class Float>
		struct fp_t<Float, true, true> {
			using float_type = Float;
			using carrier_uint = typename ieee754_traits<Float>::carrier_uint;

			carrier_uint significand;
			int exponent;
			bool is_negative;
			bool may_have_trailing_zeros;
		};

		template<class Float>
		using unsigned_fp_t = fp_t<Float, false, false>;

		template<class Float>
		using signed_fp_t = fp_t<Float, true, false>;

		////////////////////////////////////////////////////////////////////////////////////////
		// Computed cache entries
		////////////////////////////////////////////////////////////////////////////////////////

		namespace detail {
			template<ieee754_format format>
			struct cache_holder;

			template<>
			struct cache_holder<ieee754_format::binary32> {
				using cache_entry_type = std::uint64_t;
				static constexpr int cache_bits = 64;
				static constexpr int min_k = -31;
				static constexpr int max_k = 46;
				static constexpr cache_entry_type cache[] = {
				  0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f,
				  0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, 0xc612062576589ddb,
				  0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28,
				  0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb,
				  0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a,
				  0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810,
				  0xe12e13424bb40e14, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff,
				  0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd,
				  0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424,
				  0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b,
				  0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000,
				  0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000,
				  0xc350000000000000, 0xf424000000000000, 0x9896800000000000,
				  0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000,
				  0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000,
				  0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000,
				  0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000,
				  0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000,
				  0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0,
				  0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984,
				  0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296,
				  0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6,
				  0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20,
				  0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd,
				  0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719,
				  0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e };
			};

			template<>
			struct cache_holder<ieee754_format::binary64> {
				using cache_entry_type = wuint::uint128;
				static constexpr int cache_bits = 128;
				static constexpr int min_k = -292;
				static constexpr int max_k = 326;
				static constexpr cache_entry_type cache[] = {
				  { 0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b },
				  { 0x9faacf3df73609b1, 0x77b191618c54e9ad },
				  { 0xc795830d75038c1d, 0xd59df5b9ef6a2418 },
				  { 0xf97ae3d0d2446f25, 0x4b0573286b44ad1e },
				  { 0x9becce62836ac577, 0x4ee367f9430aec33 },
				  { 0xc2e801fb244576d5, 0x229c41f793cda740 },
				  { 0xf3a20279ed56d48a, 0x6b43527578c11110 },
				  { 0x9845418c345644d6, 0x830a13896b78aaaa },
				  { 0xbe5691ef416bd60c, 0x23cc986bc656d554 },
				  { 0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9 },
				  { 0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa },
				  { 0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54 },
				  { 0xe858ad248f5c22c9, 0xd1b3400f8f9cff69 },
				  { 0x91376c36d99995be, 0x23100809b9c21fa2 },
				  { 0xb58547448ffffb2d, 0xabd40a0c2832a78b },
				  { 0xe2e69915b3fff9f9, 0x16c90c8f323f516d },
				  { 0x8dd01fad907ffc3b, 0xae3da7d97f6792e4 },
				  { 0xb1442798f49ffb4a, 0x99cd11cfdf41779d },
				  { 0xdd95317f31c7fa1d, 0x40405643d711d584 },
				  { 0x8a7d3eef7f1cfc52, 0x482835ea666b2573 },
				  { 0xad1c8eab5ee43b66, 0xda3243650005eed0 },
				  { 0xd863b256369d4a40, 0x90bed43e40076a83 },
				  { 0x873e4f75e2224e68, 0x5a7744a6e804a292 },
				  { 0xa90de3535aaae202, 0x711515d0a205cb37 },
				  { 0xd3515c2831559a83, 0x0d5a5b44ca873e04 },
				  { 0x8412d9991ed58091, 0xe858790afe9486c3 },
				  { 0xa5178fff668ae0b6, 0x626e974dbe39a873 },
				  { 0xce5d73ff402d98e3, 0xfb0a3d212dc81290 },
				  { 0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a },
				  { 0xa139029f6a239f72, 0x1c1fffc1ebc44e81 },
				  { 0xc987434744ac874e, 0xa327ffb266b56221 },
				  { 0xfbe9141915d7a922, 0x4bf1ff9f0062baa9 },
				  { 0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa },
				  { 0xc4ce17b399107c22, 0xcb550fb4384d21d4 },
				  { 0xf6019da07f549b2b, 0x7e2a53a146606a49 },
				  { 0x99c102844f94e0fb, 0x2eda7444cbfc426e },
				  { 0xc0314325637a1939, 0xfa911155fefb5309 },
				  { 0xf03d93eebc589f88, 0x793555ab7eba27cb },
				  { 0x96267c7535b763b5, 0x4bc1558b2f3458df },
				  { 0xbbb01b9283253ca2, 0x9eb1aaedfb016f17 },
				  { 0xea9c227723ee8bcb, 0x465e15a979c1cadd },
				  { 0x92a1958a7675175f, 0x0bfacd89ec191eca },
				  { 0xb749faed14125d36, 0xcef980ec671f667c },
				  { 0xe51c79a85916f484, 0x82b7e12780e7401b },
				  { 0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811 },
				  { 0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16 },
				  { 0xdfbdcece67006ac9, 0x67a791e093e1d49b },
				  { 0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1 },
				  { 0xaecc49914078536d, 0x58fae9f773886e19 },
				  { 0xda7f5bf590966848, 0xaf39a475506a899f },
				  { 0x888f99797a5e012d, 0x6d8406c952429604 },
				  { 0xaab37fd7d8f58178, 0xc8e5087ba6d33b84 },
				  { 0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65 },
				  { 0x855c3be0a17fcd26, 0x5cf2eea09a550680 },
				  { 0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f },
				  { 0xd0601d8efc57b08b, 0xf13b94daf124da27 },
				  { 0x823c12795db6ce57, 0x76c53d08d6b70859 },
				  { 0xa2cb1717b52481ed, 0x54768c4b0c64ca6f },
				  { 0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a },
				  { 0xfe5d54150b090b02, 0xd3f93b35435d7c4d },
				  { 0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0 },
				  { 0xc6b8e9b0709f109a, 0x359ab6419ca1091c },
				  { 0xf867241c8cc6d4c0, 0xc30163d203c94b63 },
				  { 0x9b407691d7fc44f8, 0x79e0de63425dcf1e },
				  { 0xc21094364dfb5636, 0x985915fc12f542e5 },
				  { 0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e },
				  { 0x979cf3ca6cec5b5a, 0xa705992ceecf9c43 },
				  { 0xbd8430bd08277231, 0x50c6ff782a838354 },
				  { 0xece53cec4a314ebd, 0xa4f8bf5635246429 },
				  { 0x940f4613ae5ed136, 0x871b7795e136be9a },
				  { 0xb913179899f68584, 0x28e2557b59846e40 },
				  { 0xe757dd7ec07426e5, 0x331aeada2fe589d0 },
				  { 0x9096ea6f3848984f, 0x3ff0d2c85def7622 },
				  { 0xb4bca50b065abe63, 0x0fed077a756b53aa },
				  { 0xe1ebce4dc7f16dfb, 0xd3e8495912c62895 },
				  { 0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d },
				  { 0xb080392cc4349dec, 0xbd8d794d96aacfb4 },
				  { 0xdca04777f541c567, 0xecf0d7a0fc5583a1 },
				  { 0x89e42caaf9491b60, 0xf41686c49db57245 },
				  { 0xac5d37d5b79b6239, 0x311c2875c522ced6 },
				  { 0xd77485cb25823ac7, 0x7d633293366b828c },
				  { 0x86a8d39ef77164bc, 0xae5dff9c02033198 },
				  { 0xa8530886b54dbdeb, 0xd9f57f830283fdfd },
				  { 0xd267caa862a12d66, 0xd072df63c324fd7c },
				  { 0x8380dea93da4bc60, 0x4247cb9e59f71e6e },
				  { 0xa46116538d0deb78, 0x52d9be85f074e609 },
				  { 0xcd795be870516656, 0x67902e276c921f8c },
				  { 0x806bd9714632dff6, 0x00ba1cd8a3db53b7 },
				  { 0xa086cfcd97bf97f3, 0x80e8a40eccd228a5 },
				  { 0xc8a883c0fdaf7df0, 0x6122cd128006b2ce },
				  { 0xfad2a4b13d1b5d6c, 0x796b805720085f82 },
				  { 0x9cc3a6eec6311a63, 0xcbe3303674053bb1 },
				  { 0xc3f490aa77bd60fc, 0xbedbfc4411068a9d },
				  { 0xf4f1b4d515acb93b, 0xee92fb5515482d45 },
				  { 0x991711052d8bf3c5, 0x751bdd152d4d1c4b },
				  { 0xbf5cd54678eef0b6, 0xd262d45a78a0635e },
				  { 0xef340a98172aace4, 0x86fb897116c87c35 },
				  { 0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1 },
				  { 0xbae0a846d2195712, 0x8974836059cca10a },
				  { 0xe998d258869facd7, 0x2bd1a438703fc94c },
				  { 0x91ff83775423cc06, 0x7b6306a34627ddd0 },
				  { 0xb67f6455292cbf08, 0x1a3bc84c17b1d543 },
				  { 0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94 },
				  { 0x8e938662882af53e, 0x547eb47b7282ee9d },
				  { 0xb23867fb2a35b28d, 0xe99e619a4f23aa44 },
				  { 0xdec681f9f4c31f31, 0x6405fa00e2ec94d5 },
				  { 0x8b3c113c38f9f37e, 0xde83bc408dd3dd05 },
				  { 0xae0b158b4738705e, 0x9624ab50b148d446 },
				  { 0xd98ddaee19068c76, 0x3badd624dd9b0958 },
				  { 0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7 },
				  { 0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d },
				  { 0xd47487cc8470652b, 0x7647c32000696720 },
				  { 0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074 },
				  { 0xa5fb0a17c777cf09, 0xf468107100525891 },
				  { 0xcf79cc9db955c2cc, 0x7182148d4066eeb5 },
				  { 0x81ac1fe293d599bf, 0xc6f14cd848405531 },
				  { 0xa21727db38cb002f, 0xb8ada00e5a506a7d },
				  { 0xca9cf1d206fdc03b, 0xa6d90811f0e4851d },
				  { 0xfd442e4688bd304a, 0x908f4a166d1da664 },
				  { 0x9e4a9cec15763e2e, 0x9a598e4e043287ff },
				  { 0xc5dd44271ad3cdba, 0x40eff1e1853f29fe },
				  { 0xf7549530e188c128, 0xd12bee59e68ef47d },
				  { 0x9a94dd3e8cf578b9, 0x82bb74f8301958cf },
				  { 0xc13a148e3032d6e7, 0xe36a52363c1faf02 },
				  { 0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2 },
				  { 0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba },
				  { 0xbcb2b812db11a5de, 0x7415d448f6b6f0e8 },
				  { 0xebdf661791d60f56, 0x111b495b3464ad22 },
				  { 0x936b9fcebb25c995, 0xcab10dd900beec35 },
				  { 0xb84687c269ef3bfb, 0x3d5d514f40eea743 },
				  { 0xe65829b3046b0afa, 0x0cb4a5a3112a5113 },
				  { 0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac },
				  { 0xb3f4e093db73a093, 0x59ed216765690f57 },
				  { 0xe0f218b8d25088b8, 0x306869c13ec3532d },
				  { 0x8c974f7383725573, 0x1e414218c73a13fc },
				  { 0xafbd2350644eeacf, 0xe5d1929ef90898fb },
				  { 0xdbac6c247d62a583, 0xdf45f746b74abf3a },
				  { 0x894bc396ce5da772, 0x6b8bba8c328eb784 },
				  { 0xab9eb47c81f5114f, 0x066ea92f3f326565 },
				  { 0xd686619ba27255a2, 0xc80a537b0efefebe },
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				  { 0xb454e4a179dd1877, 0x29babe4598c311fb },
				  { 0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a },
				  { 0x8ce2529e2734bb1d, 0x1899e4a65f58660c },
				  { 0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f },
				  { 0xdc21a1171d42645d, 0x76707543f4fa1f73 },
				  { 0x899504ae72497eba, 0x6a06494a791c53a8 },
				  { 0xabfa45da0edbde69, 0x0487db9d17636892 },
				  { 0xd6f8d7509292d603, 0x45a9d2845d3c42b6 },
				  { 0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2 },
				  { 0xa7f26836f282b732, 0x8e6cac7768d7141e },
				  { 0xd1ef0244af2364ff, 0x3207d795430cd926 },
				  { 0x8335616aed761f1f, 0x7f44e6bd49e807b8 },
				  { 0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6 },
				  { 0xcd036837130890a1, 0x36dba887c37a8c0f },
				  { 0x802221226be55a64, 0xc2494954da2c9789 },
				  { 0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c },
				  { 0xc83553c5c8965d3d, 0x6f92829494e5acc7 },
				  { 0xfa42a8b73abbf48c, 0xcb772339ba1f17f9 },
				  { 0x9c69a97284b578d7, 0xff2a760414536efb },
				  { 0xc38413cf25e2d70d, 0xfef5138519684aba },
				  { 0xf46518c2ef5b8cd1, 0x7eb258665fc25d69 },
				  { 0x98bf2f79d5993802, 0xef2f773ffbd97a61 },
				  { 0xbeeefb584aff8603, 0xaafb550ffacfd8fa },
				  { 0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38 },
				  { 0x952ab45cfa97a0b2, 0xdd945a747bf26183 },
				  { 0xba756174393d88df, 0x94f971119aeef9e4 },
				  { 0xe912b9d1478ceb17, 0x7a37cd5601aab85d },
				  { 0x91abb422ccb812ee, 0xac62e055c10ab33a },
				  { 0xb616a12b7fe617aa, 0x577b986b314d6009 },
				  { 0xe39c49765fdf9d94, 0xed5a7e85fda0b80b },
				  { 0x8e41ade9fbebc27d, 0x14588f13be847307 },
				  { 0xb1d219647ae6b31c, 0x596eb2d8ae258fc8 },
				  { 0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb },
				  { 0x8aec23d680043bee, 0x25de7bb9480d5854 },
				  { 0xada72ccc20054ae9, 0xaf561aa79a10ae6a },
				  { 0xd910f7ff28069da4, 0x1b2ba1518094da04 },
				  { 0x87aa9aff79042286, 0x90fb44d2f05d0842 },
				  { 0xa99541bf57452b28, 0x353a1607ac744a53 },
				  { 0xd3fa922f2d1675f2, 0x42889b8997915ce8 },
				  { 0x847c9b5d7c2e09b7, 0x69956135febada11 },
				  { 0xa59bc234db398c25, 0x43fab9837e699095 },
				  { 0xcf02b2c21207ef2e, 0x94f967e45e03f4bb },
				  { 0x8161afb94b44f57d, 0x1d1be0eebac278f5 },
				  { 0xa1ba1ba79e1632dc, 0x6462d92a69731732 },
				  { 0xca28a291859bbf93, 0x7d7b8f7503cfdcfe },
				  { 0xfcb2cb35e702af78, 0x5cda735244c3d43e },
				  { 0x9defbf01b061adab, 0x3a0888136afa64a7 },
				  { 0xc56baec21c7a1916, 0x088aaa1845b8fdd0 },
				  { 0xf6c69a72a3989f5b, 0x8aad549e57273d45 },
				  { 0x9a3c2087a63f6399, 0x36ac54e2f678864b },
				  { 0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd },
				  { 0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5 },
				  { 0x969eb7c47859e743, 0x9f644ae5a4b1b325 },
				  { 0xbc4665b596706114, 0x873d5d9f0dde1fee },
				  { 0xeb57ff22fc0c7959, 0xa90cb506d155a7ea },
				  { 0x9316ff75dd87cbd8, 0x09a7f12442d588f2 },
				  { 0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f },
				  { 0xe5d3ef282a242e81, 0x8f1668c8a86da5fa },
				  { 0x8fa475791a569d10, 0xf96e017d694487bc },
				  { 0xb38d92d760ec4455, 0x37c981dcc395a9ac },
				  { 0xe070f78d3927556a, 0x85bbe253f47b1417 },
				  { 0x8c469ab843b89562, 0x93956d7478ccec8e },
				  { 0xaf58416654a6babb, 0x387ac8d1970027b2 },
				  { 0xdb2e51bfe9d0696a, 0x06997b05fcc0319e },
				  { 0x88fcf317f22241e2, 0x441fece3bdf81f03 },
				  { 0xab3c2fddeeaad25a, 0xd527e81cad7626c3 },
				  { 0xd60b3bd56a5586f1, 0x8a71e223d8d3b074 },
				  { 0x85c7056562757456, 0xf6872d5667844e49 },
				  { 0xa738c6bebb12d16c, 0xb428f8ac016561db },
				  { 0xd106f86e69d785c7, 0xe13336d701beba52 },
				  { 0x82a45b450226b39c, 0xecc0024661173473 },
				  { 0xa34d721642b06084, 0x27f002d7f95d0190 },
				  { 0xcc20ce9bd35c78a5, 0x31ec038df7b441f4 },
				  { 0xff290242c83396ce, 0x7e67047175a15271 },
				  { 0x9f79a169bd203e41, 0x0f0062c6e984d386 },
				  { 0xc75809c42c684dd1, 0x52c07b78a3e60868 },
				  { 0xf92e0c3537826145, 0xa7709a56ccdf8a82 },
				  { 0x9bbcc7a142b17ccb, 0x88a66076400bb691 },
				  { 0xc2abf989935ddbfe, 0x6acff893d00ea435 },
				  { 0xf356f7ebf83552fe, 0x0583f6b8c4124d43 },
				  { 0x98165af37b2153de, 0xc3727a337a8b704a },
				  { 0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c },
				  { 0xeda2ee1c7064130c, 0x1162def06f79df73 },
				  { 0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8 },
				  { 0xb9a74a0637ce2ee1, 0x6d953e2bd7173692 },
				  { 0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437 },
				  { 0x910ab1d4db9914a0, 0x1d9c9892400a22a2 },
				  { 0xb54d5e4a127f59c8, 0x2503beb6d00cab4b },
				  { 0xe2a0b5dc971f303a, 0x2e44ae64840fd61d },
				  { 0x8da471a9de737e24, 0x5ceaecfed289e5d2 },
				  { 0xb10d8e1456105dad, 0x7425a83e872c5f47 },
				  { 0xdd50f1996b947518, 0xd12f124e28f77719 },
				  { 0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f },
				  { 0xace73cbfdc0bfb7b, 0x636cc64d1001550b },
				  { 0xd8210befd30efa5a, 0x3c47f7e05401aa4e },
				  { 0x8714a775e3e95c78, 0x65acfaec34810a71 },
				  { 0xa8d9d1535ce3b396, 0x7f1839a741a14d0d },
				  { 0xd31045a8341ca07c, 0x1ede48111209a050 },
				  { 0x83ea2b892091e44d, 0x934aed0aab460432 },
				  { 0xa4e4b66b68b65d60, 0xf81da84d5617853f },
				  { 0xce1de40642e3f4b9, 0x36251260ab9d668e },
				  { 0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019 },
				  { 0xa1075a24e4421730, 0xb24cf65b8612f81f },
				  { 0xc94930ae1d529cfc, 0xdee033f26797b627 },
				  { 0xfb9b7cd9a4a7443c, 0x169840ef017da3b1 },
				  { 0x9d412e0806e88aa5, 0x8e1f289560ee864e },
				  { 0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2 },
				  { 0xf5b5d7ec8acb58a2, 0xae10af696774b1db },
				  { 0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29 },
				  { 0xbff610b0cc6edd3f, 0x17fd090a58d32af3 },
				  { 0xeff394dcff8a948e, 0xddfc4b4cef07f5b0 },
				  { 0x95f83d0a1fb69cd9, 0x4abdaf101564f98e },
				  { 0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1 },
				  { 0xea53df5fd18d5513, 0x84c86189216dc5ed },
				  { 0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4 },
				  { 0xb7118682dbb66a77, 0x3fbc8c33221dc2a1 },
				  { 0xe4d5e82392a40515, 0x0fabaf3feaa5334a },
				  { 0x8f05b1163ba6832d, 0x29cb4d87f2a7400e },
				  { 0xb2c71d5bca9023f8, 0x743e20e9ef511012 },
				  { 0xdf78e4b2bd342cf6, 0x914da9246b255416 },
				  { 0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e },
				  { 0xae9672aba3d0c320, 0xa184ac2473b529b1 },
				  { 0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e },
				  { 0x8865899617fb1871, 0x7e2fa67c7a658892 },
				  { 0xaa7eebfb9df9de8d, 0xddbb901b98feeab7 },
				  { 0xd51ea6fa85785631, 0x552a74227f3ea565 },
				  { 0x8533285c936b35de, 0xd53a88958f87275f },
				  { 0xa67ff273b8460356, 0x8a892abaf368f137 },
				  { 0xd01fef10a657842c, 0x2d2b7569b0432d85 },
				  { 0x8213f56a67f6b29b, 0x9c3b29620e29fc73 },
				  { 0xa298f2c501f45f42, 0x8349f3ba91b47b8f },
				  { 0xcb3f2f7642717713, 0x241c70a936219a73 },
				  { 0xfe0efb53d30dd4d7, 0xed238cd383aa0110 },
				  { 0x9ec95d1463e8a506, 0xf4363804324a40aa },
				  { 0xc67bb4597ce2ce48, 0xb143c6053edcd0d5 },
				  { 0xf81aa16fdc1b81da, 0xdd94b7868e94050a },
				  { 0x9b10a4e5e9913128, 0xca7cf2b4191c8326 },
				  { 0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0 },
				  { 0xf24a01a73cf2dccf, 0xbc633b39673c8cec },
				  { 0x976e41088617ca01, 0xd5be0503e085d813 },
				  { 0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18 },
				  { 0xec9c459d51852ba2, 0xddf8e7d60ed1219e },
				  { 0x93e1ab8252f33b45, 0xcabb90e5c942b503 },
				  { 0xb8da1662e7b00a17, 0x3d6a751f3b936243 },
				  { 0xe7109bfba19c0c9d, 0x0cc512670a783ad4 },
				  { 0x906a617d450187e2, 0x27fb2b80668b24c5 },
				  { 0xb484f9dc9641e9da, 0xb1f9f660802dedf6 },
				  { 0xe1a63853bbd26451, 0x5e7873f8a0396973 },
				  { 0x8d07e33455637eb2, 0xdb0b487b6423e1e8 },
				  { 0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62 },
				  { 0xdc5c5301c56b75f7, 0x7641a140cc7810fb },
				  { 0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d },
				  { 0xac2820d9623bf429, 0x546345fa9fbdcd44 },
				  { 0xd732290fbacaf133, 0xa97c177947ad4095 },
				  { 0x867f59a9d4bed6c0, 0x49ed8eabcccc485d },
				  { 0xa81f301449ee8c70, 0x5c68f256bfff5a74 },
				  { 0xd226fc195c6a2f8c, 0x73832eec6fff3111 },
				  { 0x83585d8fd9c25db7, 0xc831fd53c5ff7eab },
				  { 0xa42e74f3d032f525, 0xba3e7ca8b77f5e55 },
				  { 0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb },
				  { 0x80444b5e7aa7cf85, 0x7980d163cf5b81b3 },
				  { 0xa0555e361951c366, 0xd7e105bcc332621f },
				  { 0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7 },
				  { 0xfa856334878fc150, 0xb14f98f6f0feb951 },
				  { 0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3 },
				  { 0xc3b8358109e84f07, 0x0a862f80ec4700c8 },
				  { 0xf4a642e14c6262c8, 0xcd27bb612758c0fa },
				  { 0x98e7e9cccfbd7dbd, 0x8038d51cb897789c },
				  { 0xbf21e44003acdd2c, 0xe0470a63e6bd56c3 },
				  { 0xeeea5d5004981478, 0x1858ccfce06cac74 },
				  { 0x95527a5202df0ccb, 0x0f37801e0c43ebc8 },
				  { 0xbaa718e68396cffd, 0xd30560258f54e6ba },
				  { 0xe950df20247c83fd, 0x47c6b82ef32a2069 },
				  { 0x91d28b7416cdd27e, 0x4cdc331d57fa5441 },
				  { 0xb6472e511c81471d, 0xe0133fe4adf8e952 },
				  { 0xe3d8f9e563a198e5, 0x58180fddd97723a6 },
				  { 0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648 },
				  { 0xb201833b35d63f73, 0x2cd2cc6551e513da },
				  { 0xde81e40a034bcf4f, 0xf8077f7ea65e58d1 },
				  { 0x8b112e86420f6191, 0xfb04afaf27faf782 },
				  { 0xadd57a27d29339f6, 0x79c5db9af1f9b563 },
				  { 0xd94ad8b1c7380874, 0x18375281ae7822bc },
				  { 0x87cec76f1c830548, 0x8f2293910d0b15b5 },
				  { 0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22 },
				  { 0xd433179d9c8cb841, 0x5fa60692a46151eb },
				  { 0x849feec281d7f328, 0xdbc7c41ba6bcd333 },
				  { 0xa5c7ea73224deff3, 0x12b9b522906c0800 },
				  { 0xcf39e50feae16bef, 0xd768226b34870a00 },
				  { 0x81842f29f2cce375, 0xe6a1158300d46640 },
				  { 0xa1e53af46f801c53, 0x60495ae3c1097fd0 },
				  { 0xca5e89b18b602368, 0x385bb19cb14bdfc4 },
				  { 0xfcf62c1dee382c42, 0x46729e03dd9ed7b5 },
				  { 0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1 },
				  { 0xc5a05277621be293, 0xc7098b7305241885 },
				  { 0xf70867153aa2db38, 0xb8cbee4fc66d1ea7 } };
			};

			// Compressed cache for double
			struct compressed_cache_detail {
				static constexpr int compression_ratio = 27;
				static constexpr std::size_t compressed_table_size =
				  ( cache_holder<ieee754_format::binary64>::max_k -
				    cache_holder<ieee754_format::binary64>::min_k +
				    compression_ratio ) /
				  compression_ratio;

				struct cache_holder_t {
					wuint::uint128 table[compressed_table_size];
				};
				static constexpr cache_holder_t cache = [] {
					cache_holder_t res{ };
					for( std::size_t i = 0; i < compressed_table_size; ++i ) {
						res.table[i] =
						  cache_holder<ieee754_format::binary64>::cache[i *
						                                                compression_ratio];
					}
					return res;
				}( );

				struct pow5_holder_t {
					std::uint64_t table[compression_ratio];
				};
				static constexpr pow5_holder_t pow5 = [] {
					pow5_holder_t res{ };
					std::uint64_t p = 1;
					for( std::uint64_t &item : res.table ) {
						item = p;
						p *= 5;
					}
					return res;
				}( );

				static constexpr std::uint32_t errors[] = {
				  0x50001400, 0x54044100, 0x54014555, 0x55954415, 0x54115555,
				  0x00000001, 0x50000000, 0x00104000, 0x54010004, 0x05004001,
				  0x55555544, 0x41545555, 0x54040551, 0x15445545, 0x51555514,
				  0x10000015, 0x00101100, 0x01100015, 0x00000000, 0x00000000,
				  0x00000000, 0x00000000, 0x04450514, 0x45414110, 0x55555145,
				  0x50544050, 0x15040155, 0x11054140, 0x50111514, 0x11451454,
				  0x00400541, 0x00000000, 0x55555450, 0x10056551, 0x10054011,
				  0x55551014, 0x69514555, 0x05151109, 0x00155555 };
			};
		} // namespace detail

		////////////////////////////////////////////////////////////////////////////////////////
		// Policies
		////////////////////////////////////////////////////////////////////////////////////////

		namespace detail {
			// Forward declare the implementation class
			template<class Float>
			struct impl;

			namespace policy_impl {
				// Sign policy
				namespace sign {
					struct base {};

					struct ignore : base {
						using sign_policy = ignore;
						static constexpr bool return_has_sign = false;

						template<class Float, class Fp>
						static inline constexpr void handle_sign( ieee754_bits<Float>,
						                                          Fp & ) noexcept {}
					};

					struct return_sign : base {
						using sign_policy = return_sign;
						static inline constexpr bool return_has_sign = true;

						template<class Float, class Fp>
						static inline constexpr void handle_sign( ieee754_bits<Float> br,
						                                          Fp &fp ) noexcept {
							fp.is_negative = br.is_negative( );
						}
					};
				} // namespace sign

				// Trailing zero policy
				namespace trailing_zero {
					struct base {};

					struct ignore : base {
						using trailing_zero_policy = ignore;
						static constexpr bool report_trailing_zeros = false;

						template<class Fp>
						static inline constexpr void on_trailing_zeros( Fp & ) noexcept {}

						template<class Fp>
						static inline constexpr void no_trailing_zeros( Fp & ) noexcept {}
					};

					struct remove : base {
						using trailing_zero_policy = remove;
						static constexpr bool report_trailing_zeros = false;

						template<class Fp>
						static inline constexpr void on_trailing_zeros( Fp &fp ) noexcept {
							fp.exponent +=
							  impl<typename Fp::float_type>::remove_trailing_zeros(
							    fp.significand );
						}

						template<class Fp>
						static inline constexpr void no_trailing_zeros( Fp & ) noexcept {}
					};

					struct report : base {
						using trailing_zero_policy = report;
						static constexpr bool report_trailing_zeros = true;

						template<class Fp>
						static inline constexpr void on_trailing_zeros( Fp &fp ) noexcept {
							fp.may_have_trailing_zeros = true;
						}

						template<class Fp>
						static inline constexpr void no_trailing_zeros( Fp &fp ) noexcept {
							fp.may_have_trailing_zeros = false;
						}
					};
				} // namespace trailing_zero

				// Rounding mode policy
				namespace rounding_mode {
					struct base {};

					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;
							[[nodiscard]] inline constexpr bool
							include_left_endpoint( ) const noexcept {
								return is_closed;
							}

							[[nodiscard]] inline constexpr bool
							include_right_endpoint( ) const noexcept {
								return is_closed;
							}
						};
						struct asymmetric_boundary {
							static constexpr bool is_symmetric = false;
							bool is_left_closed;
							[[nodiscard]] inline constexpr bool
							include_left_endpoint( ) const noexcept {
								return is_left_closed;
							}

							[[nodiscard]] inline constexpr bool
							include_right_endpoint( ) const noexcept {
								return not is_left_closed;
							}
						};
						struct closed {
							static constexpr bool is_symmetric = true;
							[[nodiscard]] static inline constexpr bool
							include_left_endpoint( ) noexcept {
								return true;
							}
							[[nodiscard]] static inline constexpr bool
							include_right_endpoint( ) noexcept {
								return true;
							}
						};
						struct open {
							static constexpr bool is_symmetric = true;
							[[nodiscard]] static inline constexpr bool
							include_left_endpoint( ) noexcept {
								return false;
							}
							[[nodiscard]] static inline constexpr bool
							include_right_endpoint( ) noexcept {
								return false;
							}
						};
						struct left_closed_right_open {
							static constexpr bool is_symmetric = false;
							[[nodiscard]] static inline constexpr bool
							include_left_endpoint( ) noexcept {
								return true;
							}
							[[nodiscard]] static inline constexpr bool
							include_right_endpoint( ) noexcept {
								return false;
							}
						};
						struct right_closed_left_open {
							static constexpr bool is_symmetric = false;
							[[nodiscard]] static inline constexpr bool
							include_left_endpoint( ) noexcept {
								return false;
							}
							[[nodiscard]] static inline constexpr bool
							include_right_endpoint( ) noexcept {
								return true;
							}
						};
					} // namespace interval_type

					struct nearest_to_even : base {
						using rounding_mode_policy = nearest_to_even;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_to_even{ } );
						}

						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  symmetric_boundary
						  interval_type_normal( ieee754_bits<Float> br ) noexcept {
							return { br.u % 2 == 0 };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::closed
						interval_type_shorter( ieee754_bits<Float> ) noexcept {
							return { };
						}
					};
					struct nearest_to_odd : base {
						using rounding_mode_policy = nearest_to_odd;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_to_odd{ } );
						}

						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  symmetric_boundary
						  interval_type_normal( ieee754_bits<Float> br ) noexcept {
							return { br.u % 2 != 0 };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::closed
						interval_type_shorter( ieee754_bits<Float> ) noexcept {
							return { };
						}
					};
					struct nearest_toward_plus_infinity : base {
						using rounding_mode_policy = nearest_toward_plus_infinity;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_toward_plus_infinity{ } );
						}

						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  asymmetric_boundary
						  interval_type_normal( ieee754_bits<Float> br ) noexcept {
							return { not br.is_negative( ) };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  asymmetric_boundary
						  interval_type_shorter( ieee754_bits<Float> br ) noexcept {
							return { not br.is_negative( ) };
						}
					};
					struct nearest_toward_minus_infinity : base {
						using rounding_mode_policy = nearest_toward_minus_infinity;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_toward_minus_infinity{ } );
						}

						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  asymmetric_boundary
						  interval_type_normal( ieee754_bits<Float> br ) noexcept {
							return { br.is_negative( ) };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  asymmetric_boundary
						  interval_type_shorter( ieee754_bits<Float> br ) noexcept {
							return { br.is_negative( ) };
						}
					};
					struct nearest_toward_zero : base {
						using rounding_mode_policy = nearest_toward_zero;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_toward_zero{ } );
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  right_closed_left_open
						  interval_type_normal( ieee754_bits<Float> ) noexcept {
							return { };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  right_closed_left_open
						  interval_type_shorter( ieee754_bits<Float> ) noexcept {
							return { };
						}
					};
					struct nearest_away_from_zero : base {
						using rounding_mode_policy = nearest_away_from_zero;
						static constexpr auto tag = tag_t::to_nearest;

						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( nearest_away_from_zero{ } );
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  left_closed_right_open
						  interval_type_normal( ieee754_bits<Float> ) noexcept {
							return { };
						}
						template<class Float>
						[[nodiscard]] static inline constexpr interval_type::
						  left_closed_right_open
						  interval_type_shorter( ieee754_bits<Float> ) noexcept {
							return { };
						}
					};

					namespace detail {
						struct nearest_always_closed {
							static constexpr auto tag = tag_t::to_nearest;

							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::closed
							interval_type_normal( ieee754_bits<Float> ) noexcept {
								return { };
							}
							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::closed
							interval_type_shorter( ieee754_bits<Float> ) noexcept {
								return { };
							}
						};

						struct nearest_always_open {
							static constexpr auto tag = tag_t::to_nearest;

							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::open
							interval_type_normal( ieee754_bits<Float> ) noexcept {
								return { };
							}
							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::open
							interval_type_shorter( ieee754_bits<Float> ) noexcept {
								return { };
							}
						};
					} // namespace detail

					struct nearest_to_even_static_boundary : base {
						using rounding_mode_policy = nearest_to_even_static_boundary;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.u % 2 == 0 ) {
								return f( detail::nearest_always_closed{ } );
							} else {
								return f( detail::nearest_always_open{ } );
							}
						}
					};

					struct nearest_to_odd_static_boundary : base {
						using rounding_mode_policy = nearest_to_odd_static_boundary;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.u % 2 == 0 ) {
								return f( detail::nearest_always_open{ } );
							} else {
								return f( detail::nearest_always_closed{ } );
							}
						}
					};

					struct nearest_toward_plus_infinity_static_boundary : base {
						using rounding_mode_policy =
						  nearest_toward_plus_infinity_static_boundary;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.is_negative( ) ) {
								return f( nearest_toward_zero{ } );
							} else {
								return f( nearest_away_from_zero{ } );
							}
						}
					};

					struct nearest_toward_minus_infinity_static_boundary : base {
						using rounding_mode_policy =
						  nearest_toward_minus_infinity_static_boundary;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.is_negative( ) ) {
								return f( nearest_away_from_zero{ } );
							} else {
								return f( nearest_toward_zero{ } );
							}
						}
					};

					namespace detail {
						struct left_closed_directed {
							static constexpr auto tag = tag_t::left_closed_directed;

							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::
							  left_closed_right_open
							  interval_type_normal( ieee754_bits<Float> ) noexcept {
								return { };
							}
						};
						struct right_closed_directed {
							static constexpr auto tag = tag_t::right_closed_directed;

							template<class Float>
							[[nodiscard]] static inline constexpr interval_type::
							  right_closed_left_open
							  interval_type_normal( ieee754_bits<Float> ) noexcept {
								return { };
							}
						};
					} // namespace detail

					struct toward_plus_infinity : base {
						using rounding_mode_policy = toward_plus_infinity;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.is_negative( ) ) {
								return f( detail::left_closed_directed{ } );
							} else {
								return f( detail::right_closed_directed{ } );
							}
						}
					};

					struct toward_minus_infinity : base {
						using rounding_mode_policy = toward_minus_infinity;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float> br, Func &&f ) noexcept {
							if( br.is_negative( ) ) {
								return f( detail::right_closed_directed{ } );
							} else {
								return f( detail::left_closed_directed{ } );
							}
						}
					};

					struct toward_zero : base {
						using rounding_mode_policy = toward_zero;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( detail::left_closed_directed{ } );
						}
					};

					struct away_from_zero : base {
						using rounding_mode_policy = away_from_zero;
						template<class Float, class Func>
						[[nodiscard]] static inline constexpr auto
						delegate( ieee754_bits<Float>, Func &&f ) noexcept {
							return f( detail::right_closed_directed{ } );
						}
					};
				} // namespace rounding_mode

				// Correct rounding policy
				namespace correct_rounding {
					struct base {};

					enum class tag_t {
						do_not_care,
						to_even,
						to_odd,
						away_from_zero,
						toward_zero
					};

					struct do_not_care : base {
						using correct_rounding_policy = do_not_care;
						static constexpr auto tag = tag_t::do_not_care;

						template<class Fp>
						static constexpr inline void break_rounding_tie( Fp & ) noexcept {}
					};

					struct to_even : base {
						using correct_rounding_policy = to_even;
						static constexpr auto tag = tag_t::to_even;

						template<class Fp>
						static constexpr inline void break_rounding_tie( Fp &fp ) noexcept {
							fp.significand =
							  fp.significand % 2 == 0 ? fp.significand : fp.significand - 1;
						}
					};

					struct to_odd : base {
						using correct_rounding_policy = to_odd;
						static constexpr auto tag = tag_t::to_odd;

						template<class Fp>
						static inline constexpr void break_rounding_tie( Fp &fp ) noexcept {
							fp.significand =
							  fp.significand % 2 != 0 ? fp.significand : fp.significand - 1;
						}
					};

					struct away_from_zero : base {
						using correct_rounding_policy = away_from_zero;
						static constexpr auto tag = tag_t::away_from_zero;

						template<class Fp>
						static constexpr inline void
						break_rounding_tie( Fp & /*fp*/ ) noexcept {}
					};

					struct toward_zero : base {
						using correct_rounding_policy = toward_zero;
						static constexpr auto tag = tag_t::toward_zero;

						template<class Fp>
						static constexpr inline void break_rounding_tie( Fp &fp ) noexcept {
							--fp.significand;
						}
					};
				} // namespace correct_rounding

				namespace cache {
					struct base {};

					struct normal : base {
						using cache_policy = normal;
						template<ieee754_format format>
						[[nodiscard]] static inline constexpr
						  typename cache_holder<format>::cache_entry_type
						  get_cache( int k ) noexcept {
							assert( k >= cache_holder<format>::min_k and
							        k <= cache_holder<format>::max_k );
							return cache_holder<format>::cache[std::size_t(
							  k - cache_holder<format>::min_k )];
						}
					};

					struct compressed : base {
						using cache_policy = compressed;
						template<ieee754_format format>
						[[nodiscard]] static inline constexpr
						  typename cache_holder<format>::cache_entry_type
						  get_cache( int k ) noexcept {
							assert( k >= cache_holder<format>::min_k and
							        k <= cache_holder<format>::max_k );

							if constexpr( format == ieee754_format::binary64 ) {
								// Compute base index
								auto cache_index = ( k - cache_holder<format>::min_k ) /
								                   compressed_cache_detail::compression_ratio;
								auto kb =
								  cache_index * compressed_cache_detail::compression_ratio +
								  cache_holder<format>::min_k;
								auto offset = k - kb;

								// Get base cache
								auto base_cache =
								  compressed_cache_detail::cache.table[cache_index];

								if( offset == 0 ) {
									return base_cache;
								} else {
									// Compute the required amount of bit-shift
									auto alpha = log::floor_log2_pow10( kb + offset ) -
									             log::floor_log2_pow10( kb ) - offset;
									assert( alpha > 0 and alpha < 64 );

									// Try to recover the real cache
									auto pow5 = compressed_cache_detail::pow5.table[offset];
									auto recovered_cache =
									  wuint::umul128( base_cache.high( ), pow5 );
									auto middle_low = wuint::umul128(
									  base_cache.low( ) - ( kb < 0 ? 1 : 0 ), pow5 );

									recovered_cache += middle_low.high( );

									auto high_to_middle = recovered_cache.high( )
									                      << ( 64 - alpha );
									auto middle_to_low = recovered_cache.low( ) << ( 64 - alpha );

									recovered_cache = wuint::uint128{
									  ( recovered_cache.low( ) >> alpha ) | high_to_middle,
									  ( ( middle_low.low( ) >> alpha ) | middle_to_low ) };

									if( kb < 0 ) {
										recovered_cache += 1;
									}

									// Get error
									auto error_idx = ( k - cache_holder<format>::min_k ) / 16;
									auto error =
									  ( compressed_cache_detail::errors[error_idx] >>
									    ( ( k - cache_holder<format>::min_k ) % 16 ) * 2 ) &
									  0x3;

									// Add the error back
									assert( recovered_cache.low( ) + error >=
									        recovered_cache.low( ) );
									recovered_cache = { recovered_cache.high( ),
									                    recovered_cache.low( ) + error };

									return recovered_cache;
								}
							} else {
								return cache_holder<format>::cache[std::size_t(
								  k - cache_holder<format>::min_k )];
							}
						}
					};
				} // namespace cache

				namespace input_validation {
					struct base {};

					struct assert_finite : base {
						using input_validation_policy = assert_finite;
						template<class Float>
						static inline constexpr void
						validate_input( ieee754_bits<Float> br ) noexcept {
							(void)br;
							assert( br.is_finite( ) );
						}
					};

					struct do_nothing : base {
						using input_validation_policy = do_nothing;
						template<class Float>
						static inline constexpr void
						validate_input( ieee754_bits<Float> ) noexcept {}
					};
				} // namespace input_validation
			} // namespace policy_impl
		} // namespace detail

		namespace policy {
			namespace sign {
				inline constexpr auto ignore = detail::policy_impl::sign::ignore{ };
				inline constexpr auto return_sign =
				  detail::policy_impl::sign::return_sign{ };
			} // namespace sign

			namespace trailing_zero {
				inline constexpr auto ignore =
				  detail::policy_impl::trailing_zero::ignore{ };
				inline constexpr auto remove =
				  detail::policy_impl::trailing_zero::remove{ };
				inline constexpr auto report =
				  detail::policy_impl::trailing_zero::report{ };
			} // namespace trailing_zero

			namespace rounding_mode {
				inline constexpr auto nearest_to_even =
				  detail::policy_impl::rounding_mode::nearest_to_even{ };
				inline constexpr auto nearest_to_odd =
				  detail::policy_impl::rounding_mode::nearest_to_odd{ };
				inline constexpr auto nearest_toward_plus_infinity =
				  detail::policy_impl::rounding_mode::nearest_toward_plus_infinity{ };
				inline constexpr auto nearest_toward_minus_infinity =
				  detail::policy_impl::rounding_mode::nearest_toward_minus_infinity{ };
				inline constexpr auto nearest_toward_zero =
				  detail::policy_impl::rounding_mode::nearest_toward_zero{ };
				inline constexpr auto nearest_away_from_zero =
				  detail::policy_impl::rounding_mode::nearest_away_from_zero{ };

				inline constexpr auto nearest_to_even_static_boundary = detail::
				  policy_impl::rounding_mode::nearest_to_even_static_boundary{ };
				inline constexpr auto nearest_to_odd_static_boundary =
				  detail::policy_impl::rounding_mode::nearest_to_odd_static_boundary{ };
				inline constexpr auto nearest_toward_plus_infinity_static_boundary =
				  detail::policy_impl::rounding_mode::
				    nearest_toward_plus_infinity_static_boundary{ };
				inline constexpr auto nearest_toward_minus_infinity_static_boundary =
				  detail::policy_impl::rounding_mode::
				    nearest_toward_minus_infinity_static_boundary{ };

				inline constexpr auto toward_plus_infinity =
				  detail::policy_impl::rounding_mode::toward_plus_infinity{ };
				inline constexpr auto toward_minus_infinity =
				  detail::policy_impl::rounding_mode::toward_minus_infinity{ };
				inline constexpr auto toward_zero =
				  detail::policy_impl::rounding_mode::toward_zero{ };
				inline constexpr auto away_from_zero =
				  detail::policy_impl::rounding_mode::away_from_zero{ };
			} // namespace rounding_mode

			namespace correct_rounding {
				inline constexpr auto do_not_care =
				  detail::policy_impl::correct_rounding::do_not_care{ };
				inline constexpr auto to_even =
				  detail::policy_impl::correct_rounding::to_even{ };
				inline constexpr auto to_odd =
				  detail::policy_impl::correct_rounding::to_odd{ };
				inline constexpr auto away_from_zero =
				  detail::policy_impl::correct_rounding::away_from_zero{ };
				inline constexpr auto toward_zero =
				  detail::policy_impl::correct_rounding::toward_zero{ };
			} // namespace correct_rounding

			namespace cache {
				inline constexpr auto normal = detail::policy_impl::cache::normal{ };
				inline constexpr auto compressed =
				  detail::policy_impl::cache::compressed{ };
			} // namespace cache

			namespace input_validation {
				inline constexpr auto assert_finite =
				  detail::policy_impl::input_validation::assert_finite{ };
				inline constexpr auto do_nothing =
				  detail::policy_impl::input_validation::do_nothing{ };
			} // namespace input_validation
		} // namespace policy

		namespace detail {
			////////////////////////////////////////////////////////////////////////////////////////
			// The main algorithm
			////////////////////////////////////////////////////////////////////////////////////////

			// Get sign/decimal significand/decimal exponent from
			// the bit representation of a floating-point number
			template<class Float>
			struct impl : private ieee754_traits<Float>,
			              private ieee754_format_info<ieee754_traits<Float>::format> {
				using carrier_uint = typename ieee754_traits<Float>::carrier_uint;

				using ieee754_traits<Float>::format;
				using ieee754_traits<Float>::carrier_bits;
				using ieee754_format_info<format>::significand_bits;
				using ieee754_format_info<format>::min_exponent;
				using ieee754_format_info<format>::max_exponent;
				using ieee754_format_info<format>::exponent_bias;
				using ieee754_format_info<format>::decimal_digits;

				static constexpr int kappa = format == ieee754_format::binary32 ? 1 : 2;
				static_assert( kappa >= 1 );
				static_assert( carrier_bits >= significand_bits + 2 +
				                                 log::floor_log2_pow10( kappa + 1 ) );

				static constexpr int min_k = [] {
					constexpr auto a = -log::floor_log10_pow2_minus_log10_4_over_3(
					  int( max_exponent - significand_bits ) );
					constexpr auto b =
					  -log::floor_log10_pow2( int( max_exponent - significand_bits ) ) +
					  kappa;
					return a < b ? a : b;
				}( );
				static_assert( min_k >= cache_holder<format>::min_k );

				static constexpr int max_k = [] {
					constexpr auto a = -log::floor_log10_pow2_minus_log10_4_over_3(
					  int( min_exponent - significand_bits + 1 ) );
					constexpr auto b =
					  -log::floor_log10_pow2( int( min_exponent - significand_bits ) ) +
					  kappa;
					return a > b ? a : b;
				}( );
				static_assert( max_k <= cache_holder<format>::max_k );

				using cache_entry_type =
				  typename cache_holder<format>::cache_entry_type;
				static constexpr auto cache_bits = cache_holder<format>::cache_bits;

				static constexpr int max_power_of_factor_of_5 =
				  log::floor_log5_pow2( int( significand_bits + 2 ) );
				static constexpr int divisibility_check_by_5_threshold =
				  log::floor_log2_pow10( max_power_of_factor_of_5 + kappa + 1 );

				static constexpr int case_fc_pm_half_lower_threshold =
				  -kappa - log::floor_log5_pow2( kappa );
				static constexpr int case_fc_pm_half_upper_threshold =
				  log::floor_log2_pow10( kappa + 1 );

				static constexpr int case_fc_lower_threshold =
				  -kappa - 1 - log::floor_log5_pow2( kappa + 1 );
				static constexpr int case_fc_upper_threshold =
				  log::floor_log2_pow10( kappa + 1 );

				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;

				//// The main algorithm assumes the input is a normal/subnormal finite
				/// number

				template<class ReturnType, class IntervalTypeProvider, class SignPolicy,
				         class TrailingZeroPolicy, class CorrectRoundingPolicy,
				         class CachePolicy>
				[[nodiscard]] JKJ_SAFEBUFFERS static constexpr inline ReturnType
				compute_nearest( ieee754_bits<Float> const br ) noexcept {
					//////////////////////////////////////////////////////////////////////
					// Step 1: integer promotion & Schubfach multiplier calculation
					//////////////////////////////////////////////////////////////////////

					ReturnType ret_value{ };

					SignPolicy::handle_sign( br, ret_value );

					auto significand = br.extract_significand_bits( );
					auto exponent = int( br.extract_exponent_bits( ) );

					// Deal with normal/subnormal dichotomy
					if( exponent != 0 ) {
						exponent += exponent_bias - significand_bits;

						// Shorter interval case; proceed like Schubfach
						if( significand == 0 ) {
							shorter_interval_case<TrailingZeroPolicy, CorrectRoundingPolicy,
							                      CachePolicy>(
							  ret_value, exponent,
							  IntervalTypeProvider::interval_type_shorter( br ) );
							return ret_value;
						}

						significand |= ( carrier_uint( 1 ) << significand_bits );
					}
					// Subnormal case; interval is always regular
					else {
						exponent = min_exponent - significand_bits;
					}

					auto const interval_type =
					  IntervalTypeProvider::interval_type_normal( br );

					// Compute k and beta
					int const minus_k = log::floor_log10_pow2( exponent ) - kappa;
					auto const cache =
					  CachePolicy::template get_cache<format>( -minus_k );
					int const beta_minus_1 = exponent + log::floor_log2_pow10( -minus_k );

					// Compute zi and deltai
					// 10^kappa <= deltai < 10^(kappa + 1)
					auto const deltai = compute_delta( cache, beta_minus_1 );
					carrier_uint const two_fc = significand << 1;
					carrier_uint const two_fr = two_fc | 1;
					carrier_uint const zi = compute_mul( two_fr << beta_minus_1, cache );

					//////////////////////////////////////////////////////////////////////
					// Step 2: Try larger divisor; remove trailing zeros if necessary
					//////////////////////////////////////////////////////////////////////

					constexpr auto big_divisor =
					  compute_power<kappa + 1>( std::uint32_t( 10 ) );
					constexpr auto small_divisor =
					  compute_power<kappa>( std::uint32_t( 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
					ret_value.significand =
					  div::divide_by_pow10<kappa + 1, significand_bits + kappa + 2,
					                       kappa + 1>( zi );
					auto r = std::uint32_t( zi - big_divisor * ret_value.significand );

					auto const small_divisor_case_label = [&] {
						//////////////////////////////////////////////////////////////////////
						// Step 3: Find the significand with the smaller divisor
						//////////////////////////////////////////////////////////////////////
						TrailingZeroPolicy::no_trailing_zeros( ret_value );
						ret_value.significand *= 10;
						ret_value.exponent = minus_k + kappa;

						constexpr auto mask = ( std::uint32_t( 1 ) << kappa ) - 1;

						if constexpr( CorrectRoundingPolicy::tag ==
						              policy_impl::correct_rounding::tag_t::do_not_care ) {
							// Normally, we want to compute
							// ret_value.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( not interval_type.include_right_endpoint( ) ) {
								// Is r divisible by 2^kappa?
								if( ( r & mask ) == 0 ) {
									r >>= kappa;

									// Is r divisible by 5^kappa?
									if( div::check_divisibility_and_divide_by_pow5<kappa>( r ) and
									    is_product_integer<integer_check_case_id::fc_pm_half>(
									      two_fr, exponent, minus_k ) ) {
										// This should be in the interval
										ret_value.significand += r - 1;
									} else {
										ret_value.significand += r;
									}
								} else {
									ret_value.significand +=
									  div::small_division_by_pow10<kappa>( r );
								}
							} else {
								ret_value.significand +=
								  div::small_division_by_pow10<kappa>( r );
							}
						} else {
							auto dist = r - ( deltai / 2 ) + ( small_divisor / 2 );

							// Is dist divisible by 2^kappa?
							if( ( dist & mask ) == 0 ) {
								bool const approx_y_parity =
								  ( ( dist ^ ( small_divisor / 2 ) ) & 1 ) != 0;
								dist >>= kappa;

								// Is dist divisible by 5^kappa?
								if( div::check_divisibility_and_divide_by_pow5<kappa>(
								      dist ) ) {
									ret_value.significand += dist;

									// 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
									if( compute_mul_parity( two_fc, cache, beta_minus_1 ) !=
									    approx_y_parity ) {
										--ret_value.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 constexpr( CorrectRoundingPolicy::tag !=
										              policy_impl::correct_rounding::tag_t::
										                away_from_zero ) {
											if( is_product_integer<integer_check_case_id::fc>(
											      two_fc, exponent, minus_k ) ) {
												CorrectRoundingPolicy::break_rounding_tie( ret_value );
											}
										}
									}
								}
								// Is dist not divisible by 5^kappa?
								else {
									ret_value.significand += dist;
								}
							}
							// Is dist not divisible by 2^kappa?
							else {
								// Since we know dist is small, we might be able to optimize
								// the division better than the compiler; we are computing
								// dist / small_divisor here
								ret_value.significand +=
								  div::small_division_by_pow10<kappa>( dist );
							}
						}
						return ret_value;
					};

					if( r > deltai ) {
						return small_divisor_case_label( );
					} else if( r < deltai ) {
						// Exclude the right endpoint if necessary
						if( r == 0 and not interval_type.include_right_endpoint( ) and
						    is_product_integer<integer_check_case_id::fc_pm_half>(
						      two_fr, exponent, minus_k ) ) {
							if constexpr( CorrectRoundingPolicy::tag ==
							              policy_impl::correct_rounding::tag_t::
							                do_not_care ) {
								ret_value.significand *= 10;
								ret_value.exponent = minus_k + kappa;
								--ret_value.significand;
								return ret_value;
							} else {
								--ret_value.significand;
								r = big_divisor;
								return small_divisor_case_label( );
							}
						}
					} else {
						// r == deltai; compare fractional parts
						// Check conditions in the order different from the paper
						// to take advantage of short-circuiting
						auto const two_fl = two_fc - 1;
						if( ( not interval_type.include_left_endpoint( ) or
						      not is_product_integer<integer_check_case_id::fc_pm_half>(
						        two_fl, exponent, minus_k ) ) and
						    not compute_mul_parity( two_fl, cache, beta_minus_1 ) ) {
							return small_divisor_case_label( );
						}
					}
					ret_value.exponent = minus_k + kappa + 1;

					// We may need to remove trailing zeros
					TrailingZeroPolicy::on_trailing_zeros( ret_value );
					return ret_value;
				}

				template<class TrailingZeroPolicy, class CorrectRoundingPolicy,
				         class CachePolicy, class ReturnType, class IntervalType>
				DAW_ATTRIB_INLINE JKJ_SAFEBUFFERS static constexpr void
				shorter_interval_case( ReturnType &ret_value, int const exponent,
				                       IntervalType const interval_type ) noexcept {
					// Compute k and beta
					int const minus_k =
					  log::floor_log10_pow2_minus_log10_4_over_3( exponent );
					int const beta_minus_1 = exponent + log::floor_log2_pow10( -minus_k );

					// Compute xi and zi
					auto const cache =
					  CachePolicy::template get_cache<format>( -minus_k );

					auto xi = compute_left_endpoint_for_shorter_interval_case(
					  cache, beta_minus_1 );
					auto zi = compute_right_endpoint_for_shorter_interval_case(
					  cache, beta_minus_1 );

					// If we don't accept the right endpoint and
					// if the right endpoint is an integer, decrease it
					if( not interval_type.include_right_endpoint( ) and
					    is_right_endpoint_integer_shorter_interval( exponent ) ) {
						--zi;
					}
					// If we don't accept the left endpoint or
					// if the left endpoint is not an integer, increase it
					if( not interval_type.include_left_endpoint( ) or
					    not is_left_endpoint_integer_shorter_interval( exponent ) ) {
						++xi;
					}

					// Try bigger divisor
					ret_value.significand = zi / 10;

					// If succeed, remove trailing zeros if necessary and return
					if( ret_value.significand * 10 >= xi ) {
						ret_value.exponent = minus_k + 1;
						TrailingZeroPolicy::on_trailing_zeros( ret_value );
						return;
					}

					// Otherwise, compute the round-up of y
					TrailingZeroPolicy::no_trailing_zeros( ret_value );
					ret_value.significand =
					  compute_round_up_for_shorter_interval_case( cache, beta_minus_1 );
					ret_value.exponent = minus_k;

					// When tie occurs, choose one of them according to the rule
					if constexpr( CorrectRoundingPolicy::tag !=
					                policy_impl::correct_rounding::tag_t::do_not_care and
					              CorrectRoundingPolicy::tag !=
					                policy_impl::correct_rounding::tag_t::
					                  away_from_zero ) {
						if( exponent >= shorter_interval_tie_lower_threshold and
						    exponent <= shorter_interval_tie_upper_threshold ) {
							CorrectRoundingPolicy::break_rounding_tie( ret_value );
						} else if( ret_value.significand < xi ) {
							++ret_value.significand;
						}
					} else {
						if( ret_value.significand < xi ) {
							++ret_value.significand;
						}
					}
				}

				template<class ReturnType, class SignPolicy, class TrailingZeroPolicy,
				         class CachePolicy>
				[[nodiscard]] JKJ_SAFEBUFFERS static inline constexpr ReturnType
				compute_left_closed_directed( ieee754_bits<Float> const br ) noexcept {
					//////////////////////////////////////////////////////////////////////
					// Step 1: integer promotion & Schubfach multiplier calculation
					//////////////////////////////////////////////////////////////////////

					ReturnType ret_value;

					SignPolicy::handle_sign( br, ret_value );

					auto significand = br.extract_significand_bits( );
					auto exponent = int( br.extract_exponent_bits( ) );

					// Deal with normal/subnormal dichotomy
					if( exponent != 0 ) {
						exponent += exponent_bias - significand_bits;
						significand |= ( carrier_uint( 1 ) << significand_bits );
					}
					// Subnormal case; interval is always regular
					else {
						exponent = min_exponent - significand_bits;
					}

					// Compute k and beta
					int const minus_k = log::floor_log10_pow2( exponent ) - kappa;
					auto const cache =
					  CachePolicy::template get_cache<format>( -minus_k );
					int const beta = exponent + log::floor_log2_pow10( -minus_k ) + 1;

					// Compute xi and deltai
					// 10^kappa <= deltai < 10^(kappa + 1)
					auto const deltai = compute_delta( cache, beta - 1 );
					carrier_uint xi = compute_mul( significand << beta, cache );

					if( not is_product_integer<integer_check_case_id::fc>(
					      significand, exponent + 1, minus_k ) ) {
						++xi;
					}

					//////////////////////////////////////////////////////////////////////
					// Step 2: Try larger divisor; remove trailing zeros if necessary
					//////////////////////////////////////////////////////////////////////

					constexpr auto big_divisor =
					  compute_power<kappa + 1>( std::uint32_t( 10 ) );
					/*** REMOVE
					constexpr auto small_divisor =
					  compute_power<kappa>( std::uint32_t( 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
					ret_value.significand =
					  div::divide_by_pow10<kappa + 1, significand_bits + kappa + 2,
					                       kappa + 1>( xi );
					auto r = std::uint32_t( xi - big_divisor * ret_value.significand );

					if( r != 0 ) {
						++ret_value.significand;
						r = big_divisor - r;
					}

					auto const small_divisor_case_label = [&] {
						//////////////////////////////////////////////////////////////////////
						// Step 3: Find the significand with the smaller divisor
						//////////////////////////////////////////////////////////////////////
						ret_value.significand *= 10;
						ret_value.significand -= div::small_division_by_pow10<kappa>( r );
						ret_value.exponent = minus_k + kappa;
						TrailingZeroPolicy::no_trailing_zeros( ret_value );
						return ret_value;
					};

					if( r > deltai ) {
						return small_divisor_case_label( );
					} else if( r == deltai ) {
						// Compare the fractional parts
						if( compute_mul_parity( significand + 1, cache, beta ) or
						    is_product_integer<integer_check_case_id::fc>(
						      significand + 1, exponent + 1, minus_k ) ) {
							return small_divisor_case_label( );
						}
					}

					// The ceiling is inside, so we are done
					ret_value.exponent = minus_k + kappa + 1;
					TrailingZeroPolicy::on_trailing_zeros( ret_value );
					return ret_value;
				}

				template<class ReturnType, class SignPolicy, class TrailingZeroPolicy,
				         class CachePolicy>
				[[nodiscard]] JKJ_SAFEBUFFERS static inline ReturnType
				compute_right_closed_directed( ieee754_bits<Float> const br ) noexcept {
					//////////////////////////////////////////////////////////////////////
					// Step 1: integer promotion & Schubfach multiplier calculation
					//////////////////////////////////////////////////////////////////////

					ReturnType ret_value;

					SignPolicy::handle_sign( br, ret_value );

					auto significand = br.extract_significand_bits( );
					auto exponent = int( br.extract_exponent_bits( ) );

					// Deal with normal/subnormal dichotomy
					bool closer_boundary = false;
					if( exponent != 0 ) {
						exponent += exponent_bias - significand_bits;
						if( significand == 0 ) {
							closer_boundary = true;
						}
						significand |= ( carrier_uint( 1 ) << significand_bits );
					}
					// Subnormal case; interval is always regular
					else {
						exponent = min_exponent - significand_bits;
					}

					// Compute k and beta
					int const minus_k =
					  log::floor_log10_pow2( exponent - ( closer_boundary ? 1 : 0 ) ) -
					  kappa;
					auto const cache =
					  CachePolicy::template get_cache<format>( -minus_k );
					int const beta = exponent + log::floor_log2_pow10( -minus_k ) + 1;

					// Compute zi and deltai
					// 10^kappa <= deltai < 10^(kappa + 1)
					auto const deltai = closer_boundary
					                      ? compute_delta( cache, beta - 2 )
					                      : compute_delta( cache, beta - 1 );
					carrier_uint const zi = compute_mul( significand << beta, cache );

					//////////////////////////////////////////////////////////////////////
					// Step 2: Try larger divisor; remove trailing zeros if necessary
					//////////////////////////////////////////////////////////////////////

					constexpr auto big_divisor =
					  compute_power<kappa + 1>( std::uint32_t( 10 ) );
					constexpr auto small_divisor =
					  compute_power<kappa>( std::uint32_t( 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
					ret_value.significand =
					  div::divide_by_pow10<kappa + 1, significand_bits + kappa + 2,
					                       kappa + 1>( zi );
					auto const r =
					  std::uint32_t( zi - big_divisor * ret_value.significand );

					auto const small_divisor_case_label = [&] {
						//////////////////////////////////////////////////////////////////////
						// Step 3: Find the significand with the small divisor
						//////////////////////////////////////////////////////////////////////
						ret_value.significand *= 10;
						ret_value.significand += div::small_division_by_pow10<kappa>( r );
						ret_value.exponent = minus_k + kappa;
						TrailingZeroPolicy::no_trailing_zeros( ret_value );
						return ret_value;
					};

					if( r > deltai ) {
						return small_divisor_case_label( );
					} else if( r == deltai ) {
						// Compare the fractional parts
						if( closer_boundary ) {
							if( not compute_mul_parity( ( significand * 2 ) - 1, cache,
							                            beta - 1 ) ) {
								return small_divisor_case_label( );
							}
						} else {
							if( not compute_mul_parity( significand - 1, cache, beta ) ) {
								return small_divisor_case_label( );
							}
						}
					}

					// The floor is inside, so we are done
					ret_value.exponent = minus_k + kappa + 1;
					TrailingZeroPolicy::on_trailing_zeros( ret_value );
					return ret_value;
				}

				// Remove trailing zeros from n and return the number of zeros removed
				[[nodiscard]] DAW_ATTRIB_INLINE static constexpr int
				remove_trailing_zeros( carrier_uint &n ) noexcept {
					constexpr auto max_power = [] {
						auto max_possible_significand =
						  ( std::numeric_limits<carrier_uint>::max )( ) /
						  compute_power<kappa + 1>( std::uint32_t( 10 ) );

						int k = 0;
						carrier_uint p = 1;
						while( p < max_possible_significand / 10 ) {
							p *= 10;
							++k;
						}
						return k;
					}( );

					auto t = static_cast<int>(
					  daw::cxmath::count_trailing_zeros( n ) ); // bits::countr_zero( n );
					if( t > max_power ) {
						t = max_power;
					}

					if constexpr( format == ieee754_format::binary32 ) {
						constexpr auto const &divtable =
						  div::table_holder<carrier_uint, 5, decimal_digits>::table;

						int s = 0;
						for( ; s < t - 1; s += 2 ) {
							if( n * divtable.mod_inv[2] > divtable.max_quotients[2] ) {
								break;
							}
							n *= divtable.mod_inv[2];
						}
						if( s < t and
						    n * divtable.mod_inv[1] <= divtable.max_quotients[1] ) {
							n *= divtable.mod_inv[1];
							++s;
						}
						n >>= s;
						return s;
					} else {
						static_assert( format == ieee754_format::binary64 );
						static_assert( kappa >= 2 );

						// Divide by 10^8 and reduce to 32-bits
						// Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17,
						// both of the quotient and the r should fit in 32-bits

						constexpr auto const &divtable =
						  div::table_holder<carrier_uint, 5, decimal_digits>::table;

						// If the number is divisible by 1'0000'0000, work with the
						// quotient
						if( t >= 8 ) {
							auto quotient_candidate = n * divtable.mod_inv[8];

							if( quotient_candidate <= divtable.max_quotients[8] ) {
								auto quotient = std::uint32_t( quotient_candidate >> 8 );

								constexpr auto mod_inverse =
								  std::uint32_t( divtable.mod_inv[1] );
								constexpr auto max_quotient =
								  ( std::numeric_limits<std::uint32_t>::max )( ) / 5;

								int s = 8;
								for( ; s < t; ++s ) {
									if( quotient * mod_inverse > max_quotient ) {
										break;
									}
									quotient *= mod_inverse;
								}
								quotient >>= ( s - 8 );
								n = quotient;
								return s;
							}
						}

						// Otherwise, work with the remainder
						auto quotient =
						  static_cast<std::uint32_t>( div::divide_by_pow10<8, 54, 0>( n ) );
						auto remainder = static_cast<std::uint32_t>(
						  static_cast<unsigned>( n ) - 1'0000'0000 * quotient );

						constexpr auto mod_inverse = std::uint32_t( divtable.mod_inv[1] );
						constexpr auto max_quotient =
						  ( std::numeric_limits<std::uint32_t>::max )( ) / 5;

						if( t == 0 or remainder * mod_inverse > max_quotient ) {
							return 0;
						}
						remainder *= mod_inverse;

						if( t == 1 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 1 ) + quotient * carrier_uint( 1000'0000 );
							return 1;
						}
						remainder *= mod_inverse;

						if( t == 2 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 2 ) + quotient * carrier_uint( 100'0000 );
							return 2;
						}
						remainder *= mod_inverse;

						if( t == 3 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 3 ) + quotient * carrier_uint( 10'0000 );
							return 3;
						}
						remainder *= mod_inverse;

						if( t == 4 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 4 ) + quotient * carrier_uint( 1'0000 );
							return 4;
						}
						remainder *= mod_inverse;

						if( t == 5 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 5 ) + quotient * carrier_uint( 1000 );
							return 5;
						}
						remainder *= mod_inverse;

						if( t == 6 or remainder * mod_inverse > max_quotient ) {
							n = ( remainder >> 6 ) + quotient * carrier_uint( 100 );
							return 6;
						}
						remainder *= mod_inverse;

						n = ( remainder >> 7 ) + quotient * carrier_uint( 10 );
						return 7;
					}
				}

				[[nodiscard]] static inline constexpr carrier_uint
				compute_mul( carrier_uint u, cache_entry_type const &cache ) noexcept {
					if constexpr( format == ieee754_format::binary32 ) {
						return wuint::umul96_upper32( u, cache );
					} else {
						return wuint::umul192_upper64( u, cache );
					}
				}

				[[nodiscard]] static inline std::uint32_t constexpr compute_delta(
				  cache_entry_type const &cache, int beta_minus_1 ) noexcept {
					if constexpr( format == ieee754_format::binary32 ) {
						return std::uint32_t( cache >> ( cache_bits - 1 - beta_minus_1 ) );
					} else {
						return std::uint32_t( cache.high( ) >>
						                      ( carrier_bits - 1 - beta_minus_1 ) );
					}
				}

				[[nodiscard]] static inline constexpr bool
				compute_mul_parity( carrier_uint two_f, cache_entry_type const &cache,
				                    int beta_minus_1 ) noexcept {
					assert( beta_minus_1 >= 1 );
					assert( beta_minus_1 < 64 );

					if constexpr( format == ieee754_format::binary32 ) {
						return ( ( wuint::umul96_lower64( two_f, cache ) >>
						           ( 64 - beta_minus_1 ) ) &
						         1 ) != 0;
					} else {
						return ( ( wuint::umul192_middle64( two_f, cache ) >>
						           ( 64 - beta_minus_1 ) ) &
						         1 ) != 0;
					}
				}

				[[nodiscard]] static inline constexpr carrier_uint
				compute_left_endpoint_for_shorter_interval_case(
				  cache_entry_type const &cache, int beta_minus_1 ) noexcept {
					if constexpr( format == ieee754_format::binary32 ) {
						return carrier_uint(
						  ( cache - ( cache >> ( significand_bits + 2 ) ) ) >>
						  ( cache_bits - significand_bits - 1 - beta_minus_1 ) );
					} else {
						return ( cache.high( ) -
						         ( cache.high( ) >> ( significand_bits + 2 ) ) ) >>
						       ( carrier_bits - significand_bits - 1 - beta_minus_1 );
					}
				}

				[[nodiscard]] static inline constexpr carrier_uint
				compute_right_endpoint_for_shorter_interval_case(
				  cache_entry_type const &cache, int beta_minus_1 ) noexcept {
					if constexpr( format == ieee754_format::binary32 ) {
						return carrier_uint(
						  ( cache + ( cache >> ( significand_bits + 1 ) ) ) >>
						  ( cache_bits - significand_bits - 1 - beta_minus_1 ) );
					} else {
						return ( cache.high( ) +
						         ( cache.high( ) >> ( significand_bits + 1 ) ) ) >>
						       ( carrier_bits - significand_bits - 1 - beta_minus_1 );
					}
				}

				[[nodiscard]] static inline constexpr carrier_uint
				compute_round_up_for_shorter_interval_case(
				  cache_entry_type const &cache, int beta_minus_1 ) noexcept {
					if constexpr( format == ieee754_format::binary32 ) {
						return ( carrier_uint( cache >> ( cache_bits - significand_bits -
						                                  2 - beta_minus_1 ) ) +
						         1 ) /
						       2;
					} else {
						return ( ( cache.high( ) >> ( carrier_bits - significand_bits - 2 -
						                              beta_minus_1 ) ) +
						         1 ) /
						       2;
					}
				}

				[[nodiscard]] static inline constexpr bool
				is_right_endpoint_integer_shorter_interval( int exponent ) noexcept {
					return exponent >=
					         case_shorter_interval_right_endpoint_lower_threshold and
					       exponent <=
					         case_shorter_interval_right_endpoint_upper_threshold;
				}

				[[nodiscard]] static inline constexpr bool
				is_left_endpoint_integer_shorter_interval( int exponent ) noexcept {
					return exponent >=
					         case_shorter_interval_left_endpoint_lower_threshold and
					       exponent <=
					         case_shorter_interval_left_endpoint_upper_threshold;
				}

				enum class integer_check_case_id { fc_pm_half, fc };
				template<integer_check_case_id case_id>
				[[nodiscard]] static inline constexpr bool
				is_product_integer( carrier_uint two_f, int exponent,
				                    int minus_k ) noexcept {
					// Case I: f = fc +- 1/2
					if constexpr( case_id == integer_check_case_id::fc_pm_half ) {
						if( exponent < case_fc_pm_half_lower_threshold ) {
							return false;
						}
						// For k >= 0
						else if( exponent <= case_fc_pm_half_upper_threshold ) {
							return true;
						}
						// For k < 0
						else if( exponent > divisibility_check_by_5_threshold ) {
							return false;
						} else {
							return div::divisible_by_power_of_5<max_power_of_factor_of_5 + 1>(
							  two_f, static_cast<unsigned>( minus_k ) );
						}
					}
					// Case II: f = fc + 1
					// Case III: f = fc
					else {
						// Exponent for 5 is negative
						if( exponent > divisibility_check_by_5_threshold ) {
							return false;
						} else if( exponent > case_fc_upper_threshold ) {
							return div::divisible_by_power_of_5<max_power_of_factor_of_5 + 1>(
							  two_f, static_cast<unsigned>( minus_k ) );
						}
						// Both exponents are nonnegative
						else if( exponent >= case_fc_lower_threshold ) {
							return true;
						}
						// Exponent for 2 is negative
						else {
							return div::divisible_by_power_of_2(
							  two_f, static_cast<unsigned>( minus_k - exponent + 1 ) );
						}
					}
				}
			};

			////////////////////////////////////////////////////////////////////////////////////////
			// Policy holder
			////////////////////////////////////////////////////////////////////////////////////////

			namespace policy_impl {
				// The library will specify a list of accepted kinds of policies and
				// their defaults, and the user will pass a list of policies. The aim
				// of helper classes/functions here 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 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.
				// A policy belongs to a certain kind if it is deriving from a base
				// class.

				// 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 {
					using policy = Policy;
					static constexpr auto found_info = info;
				};

				template<class Base, class DefaultPolicy>
				struct base_default_pair {
					using base = Base;

					template<class FoundPolicyInfo>
					[[nodiscard]] static constexpr FoundPolicyInfo
					get_policy_impl( FoundPolicyInfo ) {
						return { };
					}
					template<class FoundPolicyInfo, class FirstPolicy,
					         class... RemainingPolicies>
					[[nodiscard]] static constexpr auto
					get_policy_impl( FoundPolicyInfo, FirstPolicy,
					                 RemainingPolicies... remainings ) {
						if constexpr( std::is_base_of_v<Base, FirstPolicy> ) {
							if constexpr( FoundPolicyInfo::found_info ==
							              policy_found_info::not_found ) {
								return get_policy_impl(
								  found_policy_pair<FirstPolicy, policy_found_info::unique>{ },
								  remainings... );
							} else {
								return get_policy_impl(
								  found_policy_pair<FirstPolicy,
								                    policy_found_info::repeated>{ },
								  remainings... );
							}
						} else {
							return get_policy_impl( FoundPolicyInfo{ }, remainings... );
						}
					}

					template<class... Policies>
					[[nodiscard]] static constexpr auto
					get_policy( Policies... policies ) {
						return get_policy_impl(
						  found_policy_pair<DefaultPolicy, policy_found_info::not_found>{ },
						  policies... );
					}
				};
				template<class... BaseDefaultPairs>
				struct base_default_pair_list {};

				// Check if a given policy belongs to one of the kinds specified by
				// the library
				template<class Policy>
				[[nodiscard]] constexpr bool
				check_policy_validity( Policy, base_default_pair_list<> ) {
					return false;
				}
				template<class Policy, class FirstBaseDefaultPair,
				         class... RemainingBaseDefaultPairs>
				[[nodiscard]] constexpr bool check_policy_validity(
				  Policy, base_default_pair_list<FirstBaseDefaultPair,
				                                 RemainingBaseDefaultPairs...> ) {
					return std::is_base_of_v<typename FirstBaseDefaultPair::base,
					                         Policy> or
					       check_policy_validity(
					         Policy{ },
					         base_default_pair_list<RemainingBaseDefaultPairs...>{ } );
				}

				template<class BaseDefaultPairList>
				[[nodiscard]] constexpr bool
				check_policy_list_validity( BaseDefaultPairList ) {
					return true;
				}

				template<class BaseDefaultPairList, class FirstPolicy,
				         class... RemainingPolicies>
				[[nodiscard]] constexpr bool
				check_policy_list_validity( BaseDefaultPairList, FirstPolicy,
				                            RemainingPolicies... remaining_policies ) {
					return check_policy_validity( FirstPolicy{ },
					                              BaseDefaultPairList{ } ) and
					       check_policy_list_validity( BaseDefaultPairList{ },
					                                   remaining_policies... );
				}

				// Build policy_holder
				template<bool repeated_, class... FoundPolicyPairs>
				struct found_policy_pair_list {
					static constexpr bool repeated = repeated_;
				};

				template<class... Policies>
				struct policy_holder : Policies... {};

				template<bool repeated, class... FoundPolicyPairs, class... Policies>
				[[nodiscard]] constexpr auto make_policy_holder_impl(
				  base_default_pair_list<>,
				  found_policy_pair_list<repeated, FoundPolicyPairs...>, Policies... ) {
					return found_policy_pair_list<repeated, FoundPolicyPairs...>{ };
				}

				template<class FirstBaseDefaultPair, class... RemainingBaseDefaultPairs,
				         bool repeated, class... FoundPolicyPairs, class... Policies>
				[[nodiscard]] constexpr auto make_policy_holder_impl(
				  base_default_pair_list<FirstBaseDefaultPair,
				                         RemainingBaseDefaultPairs...>,
				  found_policy_pair_list<repeated, FoundPolicyPairs...>,
				  Policies... policies ) {
					using new_found_policy_pair =
					  decltype( FirstBaseDefaultPair::get_policy( policies... ) );

					return make_policy_holder_impl(
					  base_default_pair_list<RemainingBaseDefaultPairs...>{ },
					  found_policy_pair_list < repeated or
					    new_found_policy_pair::found_info == policy_found_info::repeated,
					  new_found_policy_pair, FoundPolicyPairs... > { }, policies... );
				}

				template<bool repeated, class... RawPolicies>
				[[nodiscard]] constexpr auto
				convert_to_policy_holder( found_policy_pair_list<repeated>,
				                          RawPolicies... ) {
					return policy_holder<RawPolicies...>{ };
				}

				template<bool repeated, class FirstFoundPolicyPair,
				         class... RemainingFoundPolicyPairs, class... RawPolicies>
				[[nodiscard]] constexpr auto convert_to_policy_holder(
				  found_policy_pair_list<repeated, FirstFoundPolicyPair,
				                         RemainingFoundPolicyPairs...>,
				  RawPolicies... policies ) {
					return convert_to_policy_holder(
					  found_policy_pair_list<repeated, RemainingFoundPolicyPairs...>{ },
					  typename FirstFoundPolicyPair::policy{ }, policies... );
				}

				template<class BaseDefaultPairList, class... Policies>
				[[nodiscard]] constexpr auto
				make_policy_holder( BaseDefaultPairList, Policies... policies ) {
					static_assert( check_policy_list_validity( BaseDefaultPairList{ },
					                                           Policies{ }... ),
					               "jkj::dragonbox: an invalid policy is specified" );

					using policy_pair_list = decltype( make_policy_holder_impl(
					  BaseDefaultPairList{ }, found_policy_pair_list<false>{ },
					  policies... ) );

					static_assert(
					  not policy_pair_list::repeated,
					  "jkj::dragonbox: each policy should be specified at most once" );

					return convert_to_policy_holder( policy_pair_list{ } );
				}
			} // namespace policy_impl
		} // namespace detail

		////////////////////////////////////////////////////////////////////////////////////////
		// The interface function
		////////////////////////////////////////////////////////////////////////////////////////

		namespace detail {
			namespace {
				template<typename Float, typename return_type, typename policy_holder,
				         typename Br>
				struct delegate_helper {
					Br br;

					template<typename TypeProvider>
					constexpr auto operator( )( TypeProvider ) const noexcept {
						using namespace detail::policy_impl;
						constexpr auto tag_tmp = TypeProvider::tag;

						if constexpr( tag_tmp == rounding_mode::tag_t::to_nearest ) {
							return detail::impl<Float>::template compute_nearest<
							  return_type, TypeProvider, typename policy_holder::sign_policy,
							  typename policy_holder::trailing_zero_policy,
							  typename policy_holder::correct_rounding_policy,
							  typename policy_holder::cache_policy>( br );
						} else if constexpr( tag_tmp ==
						                     rounding_mode::tag_t::left_closed_directed ) {
							return detail::impl<Float>::template compute_left_closed_directed<
							  return_type, typename policy_holder::sign_policy,
							  typename policy_holder::trailing_zero_policy,
							  typename policy_holder::cache_policy>( br );
						} else {
							return detail::impl<Float>::
							  template compute_right_closed_directed<
							    return_type, typename policy_holder::sign_policy,
							    typename policy_holder::trailing_zero_policy,
							    typename policy_holder::cache_policy>( br );
						}
					}
				};
			} // namespace
		} // namespace detail

		template<class Float, class... Policies>
		[[nodiscard]] JKJ_SAFEBUFFERS DAW_ATTRIB_INLINE constexpr auto
		to_decimal( Float x, Policies... policies ) {
			// Build policy holder type
			using namespace detail::policy_impl;
			using policy_holder = decltype( make_policy_holder(
			  base_default_pair_list<
			    base_default_pair<sign::base, sign::return_sign>,
			    base_default_pair<trailing_zero::base, trailing_zero::remove>,
			    base_default_pair<rounding_mode::base,
			                      rounding_mode::nearest_to_even>,
			    base_default_pair<correct_rounding::base, correct_rounding::to_even>,
			    base_default_pair<cache::base, cache::normal>,
			    base_default_pair<input_validation::base,
			                      input_validation::assert_finite>>{ },
			  policies... ) );

			using return_type = fp_t<Float, policy_holder::return_has_sign,
			                         policy_holder::report_trailing_zeros>;

			auto br = ieee754_bits( x );
			policy_holder::validate_input( br );

			return policy_holder::delegate(
			  br, detail::delegate_helper<Float, return_type, policy_holder,
			                              decltype( br )>{ br } );
		}
	} // namespace DAW_JSON_VER
} // namespace daw::jkj::dragonbox

#undef JKJ_HAS_COUNTR_ZERO_INTRINSIC
#undef JKJ_SAFEBUFFERS
