robot/include/boost/charconv/detail/dragonbox/dragonbox.hpp

// Copyright 2020-2022 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.
//
// Copyright 2023 Matt Borland
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt

#ifndef BOOST_CHARCONV_DETAIL_DRAGONBOX_HPP
#define BOOST_CHARCONV_DETAIL_DRAGONBOX_HPP

#include <boost/charconv/detail/config.hpp>
#include <boost/charconv/detail/dragonbox/dragonbox_common.hpp>
#include <boost/charconv/detail/bit_layouts.hpp>
#include <boost/charconv/detail/emulated128.hpp>
#include <boost/charconv/detail/buffer_sizing.hpp>
#include <boost/charconv/detail/to_chars_result.hpp>
#include <boost/charconv/chars_format.hpp>
#include <boost/core/bit.hpp>
#include <type_traits>
#include <limits>
#include <cstdint>
#include <cstring>

#ifdef BOOST_MSVC
# pragma warning(push)
# pragma warning(disable: 4127) // Conditional expression is constant (e.g. BOOST_IF_CONSTEXPR statements)
# pragma warning(disable: 4307) // Integral constant overflow (Only MSVC-14.1 issued this warning)
#endif

namespace boost { namespace charconv { namespace detail {

// A floating-point traits class defines ways to interpret a bit pattern of given size as an
// encoding of floating-point number. This is a default implementation of such a traits class,
// supporting ways to interpret 32-bits into a binary32-encoded floating-point number and to
// interpret 64-bits into a binary64-encoded floating-point number. Users might specialize this
// class to change the default behavior for certain types.

template <typename T>
struct dragonbox_float_traits 
{
    // 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 && std::numeric_limits<T>::radix == 2 &&
                  (physical_bits<T>::value == 32 || physical_bits<T>::value == 64),
                    "default_ieee754_traits only works for 32-bits or 64-bits types "
                    "supporting binary32 or binary64 formats!");

    // The type that is being viewed.
    using type = T;

    // Refers to the format specification class.
    using format = typename std::conditional<physical_bits<T>::value == 32, ieee754_binary32, ieee754_binary64>::type;

    // Defines an unsigned integer type that is large enough to carry a variable of type T.
    // Most of the operations will be done on this integer type.
    using carrier_uint =
        typename std::conditional<physical_bits<T>::value == 32, std::uint32_t, std::uint64_t>::type;

    static_assert(sizeof(carrier_uint) == sizeof(T), "Type T must have a unsigned type with the same number of bits");

    // Number of bits in the above unsigned integer type.
    static constexpr int carrier_bits = static_cast<int>(physical_bits<carrier_uint>::value);

    // Convert from carrier_uint into the original type.
    // Depending on the floating-point encoding format, this operation might not be possible for
    // some specific bit patterns. However, the contract is that u always denotes a
    // valid bit pattern, so this function must be assumed to be noexcept.
    static T carrier_to_float(carrier_uint u) noexcept
    {
        T x;
        std::memcpy(&x, &u, sizeof(carrier_uint));
        return x;
    }

    // Same as above.
    static carrier_uint float_to_carrier(T x) noexcept
    {
        carrier_uint u;
        std::memcpy(&u, &x, sizeof(carrier_uint));
        return u;
    }

    // Extract exponent bits from a bit pattern.
    // The result must be aligned to the LSB so that there is no additional zero paddings
    // on the right. This function does not do bias adjustment.
    static constexpr unsigned extract_exponent_bits(carrier_uint u) noexcept
    {
        return static_cast<unsigned>(u >> format::significand_bits) & ((static_cast<unsigned int>(1) << format::exponent_bits) - 1);
    }

    // Extract significand bits from a bit pattern.
    // The result must be aligned to the LSB so that there is no additional zero paddings
    // on the right. The result does not contain the implicit bit.
    static constexpr carrier_uint extract_significand_bits(carrier_uint u) noexcept 
    {
        return carrier_uint(u & carrier_uint((carrier_uint(1) << format::significand_bits) - 1));
    }

    // Remove the exponent bits and extract significand bits together with the sign bit.
    static constexpr carrier_uint remove_exponent_bits(carrier_uint u, unsigned int exponent_bits) noexcept
    {
        return u ^ (carrier_uint(exponent_bits) << format::significand_bits);
    }

    // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
    static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept {
        return carrier_uint(carrier_uint(u) << 1);
    }

    // The actual value of exponent is obtained by adding this value to the extracted exponent
    // bits.
    static constexpr int exponent_bias = 1 - (1 << (carrier_bits - format::significand_bits - 2));

    // Obtain the actual value of the binary exponent from the extracted exponent bits.
    static constexpr int binary_exponent(unsigned exponent_bits) noexcept 
    {
        return static_cast<int>(exponent_bits == 0 ? format::min_exponent : int(exponent_bits) + format::exponent_bias);
    }

    // Obtain the actual value of the binary exponent from the extracted significand bits and
    // exponent bits.
    static constexpr carrier_uint binary_significand(carrier_uint significand_bits, unsigned exponent_bits) noexcept
    {
        return exponent_bits == 0 ? significand_bits : significand_bits | (carrier_uint(1) << format::significand_bits);
    }

    /* Various boolean observer functions */

    static constexpr bool is_nonzero(carrier_uint u) noexcept
    { 
        return (u << 1) != 0;
    }

    static constexpr bool is_positive(carrier_uint u) noexcept
    {
        return u < (carrier_uint(1) << (format::significand_bits + format::exponent_bits));
    }

    static constexpr bool is_negative(carrier_uint u) noexcept
    { 
        return !is_positive(u);
    }

    static constexpr bool is_finite(unsigned exponent_bits) noexcept
    {
        return exponent_bits != ((1u << format::exponent_bits) - 1);
    }

    static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept
    {
        return (u << 1) == 0;
    }

    static constexpr bool has_even_significand_bits(carrier_uint u) noexcept
    {
        return u % 2 == 0;
    }
};

// Convenient wrappers for floating-point traits classes.
// In order to reduce the argument passing overhead, these classes should be as simple as
// possible (e.g., no inheritance, no private non-static data member, etc.; this is an
// unfortunate fact about common ABI convention).

template <typename T, typename Traits = dragonbox_float_traits<T>>
struct dragonbox_float_bits;

template <typename T, typename Traits = dragonbox_float_traits<T>>
struct dragonbox_signed_significand_bits;

template <typename T, typename Traits>
struct dragonbox_float_bits
{
    using type = T;
    using traits_type = Traits;
    using carrier_uint = typename traits_type::carrier_uint;

    carrier_uint u;

    dragonbox_float_bits() = default;
    constexpr explicit dragonbox_float_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {}
    constexpr explicit dragonbox_float_bits(T float_value) noexcept
        : u{traits_type::float_to_carrier(float_value)} {}

    T to_float() const noexcept
    { 
        return traits_type::carrier_to_float(u);
    }

    // Extract exponent bits from a bit pattern.
    // The result must be aligned to the LSB so that there is no additional zero paddings
    // on the right. This function does not do bias adjustment.
    constexpr unsigned int extract_exponent_bits() const noexcept
    {
        return traits_type::extract_exponent_bits(u);
    }

    // Extract significand bits from a bit pattern.
    // The result must be aligned to the LSB so that there is no additional zero paddings
    // on the right. The result does not contain the implicit bit.
    constexpr carrier_uint extract_significand_bits() const noexcept
    {
        return traits_type::extract_significand_bits(u);
    }

    // Remove the exponent bits and extract significand bits together with the sign bit.
    constexpr auto remove_exponent_bits(unsigned int exponent_bits) const noexcept -> dragonbox_signed_significand_bits<type, traits_type>
    {
        return dragonbox_signed_significand_bits<type, traits_type>(traits_type::remove_exponent_bits(u, exponent_bits));
    }

    // Obtain the actual value of the binary exponent from the extracted exponent bits.
    static constexpr int binary_exponent(unsigned exponent_bits) noexcept
    {
        return traits_type::binary_exponent(exponent_bits);
    }

    constexpr int binary_exponent() const noexcept
    {
        return binary_exponent(extract_exponent_bits());
    }

    // Obtain the actual value of the binary exponent from the extracted significand bits and
    // exponent bits.
    static constexpr carrier_uint binary_significand(carrier_uint significand_bits, unsigned exponent_bits) noexcept 
    {
        return traits_type::binary_significand(significand_bits, exponent_bits);
    }

    constexpr carrier_uint binary_significand() const noexcept 
    {
        return binary_significand(extract_significand_bits(), extract_exponent_bits());
    }

    constexpr bool is_nonzero() const noexcept 
    { 
        return traits_type::is_nonzero(u);
    }

    constexpr bool is_positive() const noexcept
    { 
        return traits_type::is_positive(u);
    }

    constexpr bool is_negative() const noexcept
    { 
        return traits_type::is_negative(u); 
    }

    constexpr bool is_finite(unsigned exponent_bits) const noexcept 
    {
        return traits_type::is_finite(exponent_bits);
    }

    constexpr bool is_finite() const noexcept 
    {
        return traits_type::is_finite(extract_exponent_bits());
    }

    constexpr bool has_even_significand_bits() const noexcept 
    {
        return traits_type::has_even_significand_bits(u);
    }
};

template <typename T, typename Traits>
struct dragonbox_signed_significand_bits
{
    using type = T;
    using traits_type = Traits;
    using carrier_uint = typename traits_type::carrier_uint;

    carrier_uint u;

    dragonbox_signed_significand_bits() = default;
    constexpr explicit dragonbox_signed_significand_bits(carrier_uint bit_pattern) noexcept
        : u{bit_pattern} {}

    // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
    constexpr carrier_uint remove_sign_bit_and_shift() const noexcept 
    {
        return traits_type::remove_sign_bit_and_shift(u);
    }

    constexpr bool is_positive() const noexcept
    { 
        return traits_type::is_positive(u);
    }

    constexpr bool is_negative() const noexcept
    { 
        return traits_type::is_negative(u); 
    }

    constexpr bool has_all_zero_significand_bits() const noexcept 
    {
        return traits_type::has_all_zero_significand_bits(u);
    }

    constexpr bool has_even_significand_bits() const noexcept 
    {
        return traits_type::has_even_significand_bits(u);
    }
};

    ////////////////////////////////////////////////////////////////////////////////////////
    // Utilities for fast divisibility tests.
    ////////////////////////////////////////////////////////////////////////////////////////

    namespace div {
        // Replace n by floor(n / 10^N).
        // Returns true if and only if n is divisible by 10^N.
        // Precondition: n <= 10^(N+1)
        // !!It takes an in-out parameter!!
        template <int N>
        struct divide_by_pow10_info;

        template <>
        struct divide_by_pow10_info<1>
        {
            static constexpr std::uint32_t magic_number = 6554;
            static constexpr int shift_amount = 16;
        };

        template <>
        struct divide_by_pow10_info<2>
        {
            static constexpr std::uint32_t magic_number = 656;
            static constexpr int shift_amount = 16;
        };

        template <int N>
        BOOST_CXX14_CONSTEXPR bool check_divisibility_and_divide_by_pow10(std::uint32_t& n) noexcept 
        {
            // Make sure the computation for max_n does not overflow.
            // static_assert(N + 1 <= log::floor_log10_pow2(31));
            BOOST_CHARCONV_ASSERT(n <= compute_power(UINT32_C(10), N + 1));

            using info = divide_by_pow10_info<N>;
            n *= info::magic_number;

            constexpr auto mask = std::uint32_t(std::uint32_t(1) << info::shift_amount) - 1;
            bool result = ((n & mask) < info::magic_number);

            n >>= info::shift_amount;
            return result;
        }

        // Compute floor(n / 10^N) for small n and N.
        // Precondition: n <= 10^(N+1)
        template <int N>
        BOOST_CXX14_CONSTEXPR std::uint32_t small_division_by_pow10(std::uint32_t n) noexcept
        {
            // Make sure the computation for max_n does not overflow.
            // static_assert(N + 1 <= log::floor_log10_pow2(31));
            BOOST_CHARCONV_ASSERT(n <= compute_power(UINT32_C(10), N + 1));

            return (n * divide_by_pow10_info<N>::magic_number) >> divide_by_pow10_info<N>::shift_amount;
        }

        // Compute floor(n / 10^N) for small N.
        // Precondition: n <= n_max
        template <unsigned N, typename UInt, UInt n_max>
        BOOST_CXX14_CONSTEXPR UInt divide_by_pow10(UInt n) noexcept 
        {

            // Specialize for 32-bit division by 100.
            // Compiler is supposed to generate the identical code for just writing
            // "n / 100", but for some reason MSVC generates an inefficient code
            // (mul + mov for no apparent reason, instead of single imul),
            // so we does this manually.
            BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint32_t>::value && N == 2) 
            {
                return static_cast<UInt>(umul64(static_cast<std::uint32_t>(n), UINT32_C(1374389535)) >> 37);
            }
            // Specialize for 64-bit division by 1000.
            // Ensure that the correctness condition is met.
            else BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint64_t>::value && N == 3 && n_max <= UINT64_C(15534100272597517998))
            {
                return static_cast<UInt>(umul128_upper64(n, UINT64_C(2361183241434822607)) >> 7);
            }
            else 
            {
                BOOST_CXX14_CONSTEXPR auto divisor = compute_power(static_cast<UInt>(10), N);
                return n / divisor;
            }
        }

        #ifdef BOOST_MSVC
        # pragma warning(push)
        # pragma warning(disable: 4100) // MSVC 14.0 does not have BOOST_ATTRIBUTE_UNUSED so we disable the warning
        #endif

        template <typename UInt>
        BOOST_CXX14_CONSTEXPR UInt divide_by_pow10(unsigned N, BOOST_ATTRIBUTE_UNUSED UInt n_max, UInt n) noexcept
        {
            BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint32_t>::value && N == 2) 
            {
                return static_cast<UInt>(umul64(static_cast<std::uint32_t>(n), static_cast<std::uint32_t>(1374389535)) >> UINT32_C(37));
            }
            // Specialize for 64-bit division by 1000.
            // Ensure that the correctness condition is met.
            else BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint64_t>::value && N == 3 && n_max <= UINT64_C(15534100272597517998))
            {
                return static_cast<UInt>(umul128_upper64(n, UINT64_C(2361183241434822607)) >> 7);
            }
            else 
            {
                auto divisor = compute_power(static_cast<UInt>(10), N);
                return n / divisor;
            }
        }

        #ifdef BOOST_MSVC
        # pragma warning(pop)
        #endif
    }

////////////////////////////////////////////////////////////////////////////////////////
// Return types for the main interface function.
////////////////////////////////////////////////////////////////////////////////////////

template <typename UInt, bool is_signed, bool trailing_zero_flag>
struct decimal_fp;

template <typename UInt>
struct decimal_fp<UInt, false, false>
{
    using carrier_uint = UInt;

    carrier_uint significand;
    int exponent;
};

template <typename UInt>
struct decimal_fp<UInt, true, false>
{
    using carrier_uint = UInt;

    carrier_uint significand;
    int exponent;
    bool is_negative;
};

template <typename UInt>
struct decimal_fp<UInt, false, true>
{
    using carrier_uint = UInt;

    carrier_uint significand;
    int exponent;
    bool may_have_trailing_zeros;
};

template <typename UInt>
struct decimal_fp<UInt, true, true>
{
    using carrier_uint = UInt;

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

template <typename UInt>
using unsigned_decimal_fp = decimal_fp<UInt, false, false>;

template <typename UInt>
using signed_decimal_fp = decimal_fp<UInt, true, false>;

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

#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
template <bool b>
struct cache_holder_ieee754_binary32_impl
#else
struct cache_holder_ieee754_binary32
#endif
{
    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, 0x813f3978f8940985,
        0xa18f07d736b90be6, 0xc9f2c9cd04674edf, 0xfc6f7c4045812297, 0x9dc5ada82b70b59e,
        0xc5371912364ce306, 0xf684df56c3e01bc7, 0x9a130b963a6c115d, 0xc097ce7bc90715b4,
        0xf0bdc21abb48db21, 0x96769950b50d88f5, 0xbc143fa4e250eb32, 0xeb194f8e1ae525fe,
        0x92efd1b8d0cf37bf, 0xb7abc627050305ae, 0xe596b7b0c643c71a, 0x8f7e32ce7bea5c70,
        0xb35dbf821ae4f38c, 0xe0352f62a19e306f};
};

#if defined(BOOST_NO_CXX17_INLINE_VARIABLES) && (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)

template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::cache_bits;
template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::min_k;
template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::max_k;
template <bool b> constexpr typename cache_holder_ieee754_binary32_impl<b>::cache_entry_type cache_holder_ieee754_binary32_impl<b>::cache[];

#endif

#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
using cache_holder_ieee754_binary32 = cache_holder_ieee754_binary32_impl<true>;
#endif

#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
template <bool b>
struct cache_holder_ieee754_binary64_impl
#else
struct cache_holder_ieee754_binary64
#endif
{
    using cache_entry_type = 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},
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        {0xf8ebad2b84e0d58b, 0xd2e0898765a7deb3}, {0x9b934c3b330c8577, 0x63cc55f49f88eb30},
        {0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fc}, {0xf316271c7fc3908a, 0x8bef464e3945ef7b},
        {0x97edd871cfda3a56, 0x97758bf0e3cbb5ad}, {0xbde94e8e43d0c8ec, 0x3d52eeed1cbea318},
        {0xed63a231d4c4fb27, 0x4ca7aaa863ee4bde}, {0x945e455f24fb1cf8, 0x8fe8caa93e74ef6b},
        {0xb975d6b6ee39e436, 0xb3e2fd538e122b45}, {0xe7d34c64a9c85d44, 0x60dbbca87196b617},
        {0x90e40fbeea1d3a4a, 0xbc8955e946fe31ce}, {0xb51d13aea4a488dd, 0x6babab6398bdbe42},
        {0xe264589a4dcdab14, 0xc696963c7eed2dd2}, {0x8d7eb76070a08aec, 0xfc1e1de5cf543ca3},
        {0xb0de65388cc8ada8, 0x3b25a55f43294bcc}, {0xdd15fe86affad912, 0x49ef0eb713f39ebf},
        {0x8a2dbf142dfcc7ab, 0x6e3569326c784338}, {0xacb92ed9397bf996, 0x49c2c37f07965405},
        {0xd7e77a8f87daf7fb, 0xdc33745ec97be907}, {0x86f0ac99b4e8dafd, 0x69a028bb3ded71a4},
        {0xa8acd7c0222311bc, 0xc40832ea0d68ce0d}, {0xd2d80db02aabd62b, 0xf50a3fa490c30191},
        {0x83c7088e1aab65db, 0x792667c6da79e0fb}, {0xa4b8cab1a1563f52, 0x577001b891185939},
        {0xcde6fd5e09abcf26, 0xed4c0226b55e6f87}, {0x80b05e5ac60b6178, 0x544f8158315b05b5},
        {0xa0dc75f1778e39d6, 0x696361ae3db1c722}, {0xc913936dd571c84c, 0x03bc3a19cd1e38ea},
        {0xfb5878494ace3a5f, 0x04ab48a04065c724}, {0x9d174b2dcec0e47b, 0x62eb0d64283f9c77},
        {0xc45d1df942711d9a, 0x3ba5d0bd324f8395}, {0xf5746577930d6500, 0xca8f44ec7ee3647a},
        {0x9968bf6abbe85f20, 0x7e998b13cf4e1ecc}, {0xbfc2ef456ae276e8, 0x9e3fedd8c321a67f},
        {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101f}, {0x95d04aee3b80ece5, 0xbba1f1d158724a13},
        {0xbb445da9ca61281f, 0x2a8a6e45ae8edc98}, {0xea1575143cf97226, 0xf52d09d71a3293be},
        {0x924d692ca61be758, 0x593c2626705f9c57}, {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836d},
        {0xe498f455c38b997a, 0x0b6dfb9c0f956448}, {0x8edf98b59a373fec, 0x4724bd4189bd5ead},
        {0xb2977ee300c50fe7, 0x58edec91ec2cb658}, {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ee},
        {0x8b865b215899f46c, 0xbd79e0d20082ee75}, {0xae67f1e9aec07187, 0xecd8590680a3aa12},
        {0xda01ee641a708de9, 0xe80e6f4820cc9496}, {0x884134fe908658b2, 0x3109058d147fdcde},
        {0xaa51823e34a7eede, 0xbd4b46f0599fd416}, {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91b},
        {0x850fadc09923329e, 0x03e2cf6bc604ddb1}, {0xa6539930bf6bff45, 0x84db8346b786151d},
        {0xcfe87f7cef46ff16, 0xe612641865679a64}, {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07f},
        {0xa26da3999aef7749, 0xe3be5e330f38f09e}, {0xcb090c8001ab551c, 0x5cadf5bfd3072cc6},
        {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f7}, {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afb},
        {0xc646d63501a1511d, 0xb281e1fd541501b9}, {0xf7d88bc24209a565, 0x1f225a7ca91a4227},
        {0x9ae757596946075f, 0x3375788de9b06959}, {0xc1a12d2fc3978937, 0x0052d6b1641c83af},
        {0xf209787bb47d6b84, 0xc0678c5dbd23a49b}, {0x9745eb4d50ce6332, 0xf840b7ba963646e1},
        {0xbd176620a501fbff, 0xb650e5a93bc3d899}, {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebf},
        {0x93ba47c980e98cdf, 0xc66f336c36b10138}, {0xb8a8d9bbe123f017, 0xb80b0047445d4185},
        {0xe6d3102ad96cec1d, 0xa60dc059157491e6}, {0x9043ea1ac7e41392, 0x87c89837ad68db30},
        {0xb454e4a179dd1877, 0x29babe4598c311fc}, {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67b},
        {0x8ce2529e2734bb1d, 0x1899e4a65f58660d}, {0xb01ae745b101e9e4, 0x5ec05dcff72e7f90},
        {0xdc21a1171d42645d, 0x76707543f4fa1f74}, {0x899504ae72497eba, 0x6a06494a791c53a9},
        {0xabfa45da0edbde69, 0x0487db9d17636893}, {0xd6f8d7509292d603, 0x45a9d2845d3c42b7},
        {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b3}, {0xa7f26836f282b732, 0x8e6cac7768d7141f},
        {0xd1ef0244af2364ff, 0x3207d795430cd927}, {0x8335616aed761f1f, 0x7f44e6bd49e807b9},
        {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a7}, {0xcd036837130890a1, 0x36dba887c37a8c10},
        {0x802221226be55a64, 0xc2494954da2c978a}, {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6d},
        {0xc83553c5c8965d3d, 0x6f92829494e5acc8}, {0xfa42a8b73abbf48c, 0xcb772339ba1f17fa},
        {0x9c69a97284b578d7, 0xff2a760414536efc}, {0xc38413cf25e2d70d, 0xfef5138519684abb},
        {0xf46518c2ef5b8cd1, 0x7eb258665fc25d6a}, {0x98bf2f79d5993802, 0xef2f773ffbd97a62},
        {0xbeeefb584aff8603, 0xaafb550ffacfd8fb}, {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf39},
        {0x952ab45cfa97a0b2, 0xdd945a747bf26184}, {0xba756174393d88df, 0x94f971119aeef9e5},
        {0xe912b9d1478ceb17, 0x7a37cd5601aab85e}, {0x91abb422ccb812ee, 0xac62e055c10ab33b},
        {0xb616a12b7fe617aa, 0x577b986b314d600a}, {0xe39c49765fdf9d94, 0xed5a7e85fda0b80c},
        {0x8e41ade9fbebc27d, 0x14588f13be847308}, {0xb1d219647ae6b31c, 0x596eb2d8ae258fc9},
        {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bc}, {0x8aec23d680043bee, 0x25de7bb9480d5855},
        {0xada72ccc20054ae9, 0xaf561aa79a10ae6b}, {0xd910f7ff28069da4, 0x1b2ba1518094da05},
        {0x87aa9aff79042286, 0x90fb44d2f05d0843}, {0xa99541bf57452b28, 0x353a1607ac744a54},
        {0xd3fa922f2d1675f2, 0x42889b8997915ce9}, {0x847c9b5d7c2e09b7, 0x69956135febada12},
        {0xa59bc234db398c25, 0x43fab9837e699096}, {0xcf02b2c21207ef2e, 0x94f967e45e03f4bc},
        {0x8161afb94b44f57d, 0x1d1be0eebac278f6}, {0xa1ba1ba79e1632dc, 0x6462d92a69731733},
        {0xca28a291859bbf93, 0x7d7b8f7503cfdcff}, {0xfcb2cb35e702af78, 0x5cda735244c3d43f},
        {0x9defbf01b061adab, 0x3a0888136afa64a8}, {0xc56baec21c7a1916, 0x088aaa1845b8fdd1},
        {0xf6c69a72a3989f5b, 0x8aad549e57273d46}, {0x9a3c2087a63f6399, 0x36ac54e2f678864c},
        {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7de}, {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d6},
        {0x969eb7c47859e743, 0x9f644ae5a4b1b326}, {0xbc4665b596706114, 0x873d5d9f0dde1fef},
        {0xeb57ff22fc0c7959, 0xa90cb506d155a7eb}, {0x9316ff75dd87cbd8, 0x09a7f12442d588f3},
        {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb30}, {0xe5d3ef282a242e81, 0x8f1668c8a86da5fb},
        {0x8fa475791a569d10, 0xf96e017d694487bd}, {0xb38d92d760ec4455, 0x37c981dcc395a9ad},
        {0xe070f78d3927556a, 0x85bbe253f47b1418}, {0x8c469ab843b89562, 0x93956d7478ccec8f},
        {0xaf58416654a6babb, 0x387ac8d1970027b3}, {0xdb2e51bfe9d0696a, 0x06997b05fcc0319f},
        {0x88fcf317f22241e2, 0x441fece3bdf81f04}, {0xab3c2fddeeaad25a, 0xd527e81cad7626c4},
        {0xd60b3bd56a5586f1, 0x8a71e223d8d3b075}, {0x85c7056562757456, 0xf6872d5667844e4a},
        {0xa738c6bebb12d16c, 0xb428f8ac016561dc}, {0xd106f86e69d785c7, 0xe13336d701beba53},
        {0x82a45b450226b39c, 0xecc0024661173474}, {0xa34d721642b06084, 0x27f002d7f95d0191},
        {0xcc20ce9bd35c78a5, 0x31ec038df7b441f5}, {0xff290242c83396ce, 0x7e67047175a15272},
        {0x9f79a169bd203e41, 0x0f0062c6e984d387}, {0xc75809c42c684dd1, 0x52c07b78a3e60869},
        {0xf92e0c3537826145, 0xa7709a56ccdf8a83}, {0x9bbcc7a142b17ccb, 0x88a66076400bb692},
        {0xc2abf989935ddbfe, 0x6acff893d00ea436}, {0xf356f7ebf83552fe, 0x0583f6b8c4124d44},
        {0x98165af37b2153de, 0xc3727a337a8b704b}, {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5d},
        {0xeda2ee1c7064130c, 0x1162def06f79df74}, {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba9},
        {0xb9a74a0637ce2ee1, 0x6d953e2bd7173693}, {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0438},
        {0x910ab1d4db9914a0, 0x1d9c9892400a22a3}, {0xb54d5e4a127f59c8, 0x2503beb6d00cab4c},
        {0xe2a0b5dc971f303a, 0x2e44ae64840fd61e}, {0x8da471a9de737e24, 0x5ceaecfed289e5d3},
        {0xb10d8e1456105dad, 0x7425a83e872c5f48}, {0xdd50f1996b947518, 0xd12f124e28f7771a},
        {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa70}, {0xace73cbfdc0bfb7b, 0x636cc64d1001550c},
        {0xd8210befd30efa5a, 0x3c47f7e05401aa4f}, {0x8714a775e3e95c78, 0x65acfaec34810a72},
        {0xa8d9d1535ce3b396, 0x7f1839a741a14d0e}, {0xd31045a8341ca07c, 0x1ede48111209a051},
        {0x83ea2b892091e44d, 0x934aed0aab460433}, {0xa4e4b66b68b65d60, 0xf81da84d56178540},
        {0xce1de40642e3f4b9, 0x36251260ab9d668f}, {0x80d2ae83e9ce78f3, 0xc1d72b7c6b42601a},
        {0xa1075a24e4421730, 0xb24cf65b8612f820}, {0xc94930ae1d529cfc, 0xdee033f26797b628},
        {0xfb9b7cd9a4a7443c, 0x169840ef017da3b2}, {0x9d412e0806e88aa5, 0x8e1f289560ee864f},
        {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e3}, {0xf5b5d7ec8acb58a2, 0xae10af696774b1dc},
        {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef2a}, {0xbff610b0cc6edd3f, 0x17fd090a58d32af4},
        {0xeff394dcff8a948e, 0xddfc4b4cef07f5b1}, {0x95f83d0a1fb69cd9, 0x4abdaf101564f98f},
        {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f2}, {0xea53df5fd18d5513, 0x84c86189216dc5ee},
        {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb5}, {0xb7118682dbb66a77, 0x3fbc8c33221dc2a2},
        {0xe4d5e82392a40515, 0x0fabaf3feaa5334b}, {0x8f05b1163ba6832d, 0x29cb4d87f2a7400f},
        {0xb2c71d5bca9023f8, 0x743e20e9ef511013}, {0xdf78e4b2bd342cf6, 0x914da9246b255417},
        {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548f}, {0xae9672aba3d0c320, 0xa184ac2473b529b2},
        {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741f}, {0x8865899617fb1871, 0x7e2fa67c7a658893},
        {0xaa7eebfb9df9de8d, 0xddbb901b98feeab8}, {0xd51ea6fa85785631, 0x552a74227f3ea566},
        {0x8533285c936b35de, 0xd53a88958f872760}, {0xa67ff273b8460356, 0x8a892abaf368f138},
        {0xd01fef10a657842c, 0x2d2b7569b0432d86}, {0x8213f56a67f6b29b, 0x9c3b29620e29fc74},
        {0xa298f2c501f45f42, 0x8349f3ba91b47b90}, {0xcb3f2f7642717713, 0x241c70a936219a74},
        {0xfe0efb53d30dd4d7, 0xed238cd383aa0111}, {0x9ec95d1463e8a506, 0xf4363804324a40ab},
        {0xc67bb4597ce2ce48, 0xb143c6053edcd0d6}, {0xf81aa16fdc1b81da, 0xdd94b7868e94050b},
        {0x9b10a4e5e9913128, 0xca7cf2b4191c8327}, {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f1},
        {0xf24a01a73cf2dccf, 0xbc633b39673c8ced}, {0x976e41088617ca01, 0xd5be0503e085d814},
        {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e19}, {0xec9c459d51852ba2, 0xddf8e7d60ed1219f},
        {0x93e1ab8252f33b45, 0xcabb90e5c942b504}, {0xb8da1662e7b00a17, 0x3d6a751f3b936244},
        {0xe7109bfba19c0c9d, 0x0cc512670a783ad5}, {0x906a617d450187e2, 0x27fb2b80668b24c6},
        {0xb484f9dc9641e9da, 0xb1f9f660802dedf7}, {0xe1a63853bbd26451, 0x5e7873f8a0396974},
        {0x8d07e33455637eb2, 0xdb0b487b6423e1e9}, {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda63},
        {0xdc5c5301c56b75f7, 0x7641a140cc7810fc}, {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9e},
        {0xac2820d9623bf429, 0x546345fa9fbdcd45}, {0xd732290fbacaf133, 0xa97c177947ad4096},
        {0x867f59a9d4bed6c0, 0x49ed8eabcccc485e}, {0xa81f301449ee8c70, 0x5c68f256bfff5a75},
        {0xd226fc195c6a2f8c, 0x73832eec6fff3112}, {0x83585d8fd9c25db7, 0xc831fd53c5ff7eac},
        {0xa42e74f3d032f525, 0xba3e7ca8b77f5e56}, {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35ec},
        {0x80444b5e7aa7cf85, 0x7980d163cf5b81b4}, {0xa0555e361951c366, 0xd7e105bcc3326220},
        {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa8}, {0xfa856334878fc150, 0xb14f98f6f0feb952},
        {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d4}, {0xc3b8358109e84f07, 0x0a862f80ec4700c9},
        {0xf4a642e14c6262c8, 0xcd27bb612758c0fb}, {0x98e7e9cccfbd7dbd, 0x8038d51cb897789d},
        {0xbf21e44003acdd2c, 0xe0470a63e6bd56c4}, {0xeeea5d5004981478, 0x1858ccfce06cac75},
        {0x95527a5202df0ccb, 0x0f37801e0c43ebc9}, {0xbaa718e68396cffd, 0xd30560258f54e6bb},
        {0xe950df20247c83fd, 0x47c6b82ef32a206a}, {0x91d28b7416cdd27e, 0x4cdc331d57fa5442},
        {0xb6472e511c81471d, 0xe0133fe4adf8e953}, {0xe3d8f9e563a198e5, 0x58180fddd97723a7},
        {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7649}, {0xb201833b35d63f73, 0x2cd2cc6551e513db},
        {0xde81e40a034bcf4f, 0xf8077f7ea65e58d2}, {0x8b112e86420f6191, 0xfb04afaf27faf783},
        {0xadd57a27d29339f6, 0x79c5db9af1f9b564}, {0xd94ad8b1c7380874, 0x18375281ae7822bd},
        {0x87cec76f1c830548, 0x8f2293910d0b15b6}, {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb23},
        {0xd433179d9c8cb841, 0x5fa60692a46151ec}, {0x849feec281d7f328, 0xdbc7c41ba6bcd334},
        {0xa5c7ea73224deff3, 0x12b9b522906c0801}, {0xcf39e50feae16bef, 0xd768226b34870a01},
        {0x81842f29f2cce375, 0xe6a1158300d46641}, {0xa1e53af46f801c53, 0x60495ae3c1097fd1},
        {0xca5e89b18b602368, 0x385bb19cb14bdfc5}, {0xfcf62c1dee382c42, 0x46729e03dd9ed7b6},
        {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d2}, {0xc5a05277621be293, 0xc7098b7305241886},
        {0xf70867153aa2db38, 0xb8cbee4fc66d1ea8}};
};

#if defined(BOOST_NO_CXX17_INLINE_VARIABLES) && (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)

template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::cache_bits;
template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::min_k;
template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::max_k;
template <bool b> constexpr typename cache_holder_ieee754_binary64_impl<b>::cache_entry_type cache_holder_ieee754_binary64_impl<b>::cache[];

#endif

#if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
using cache_holder_ieee754_binary64 = cache_holder_ieee754_binary64_impl<true>;
#endif

////////////////////////////////////////////////////////////////////////////////////////
// Policies.
////////////////////////////////////////////////////////////////////////////////////////

// Forward declare the implementation class.
template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>>
struct impl;

namespace policy_impl {
// Sign policies.
namespace sign {
    struct base {};

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

        template <typename SignedSignificandBits, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void handle_sign(SignedSignificandBits, ReturnType&) noexcept {}
    };

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

        template <typename SignedSignificandBits, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void handle_sign(SignedSignificandBits s, ReturnType& r) noexcept
        {
            r.is_negative = s.is_negative();
        }
    };
}

// Trailing zero policies.
namespace trailing_zero {
    struct base {};

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

        template <typename Impl, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void on_trailing_zeros(ReturnType&) noexcept {}

        template <typename Impl, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType&) noexcept {}
    };

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

        template <typename Impl, typename ReturnType>
        BOOST_FORCEINLINE static void on_trailing_zeros(ReturnType& r) noexcept
        {
            r.exponent += Impl::remove_trailing_zeros(r.significand);
        }

        template <typename Impl, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType&) noexcept {}
    };

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

        template <typename Impl, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void on_trailing_zeros(ReturnType& r) noexcept 
        {
            r.may_have_trailing_zeros = true;
        }

        template <typename Impl, typename ReturnType>
        static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType& r) noexcept 
        {
            r.may_have_trailing_zeros = false;
        }
    };
}

// Decimal-to-binary rounding mode policies.
namespace decimal_to_binary_rounding {
    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;
            constexpr bool include_left_endpoint() const noexcept { return is_closed; }
            constexpr bool include_right_endpoint() const noexcept { return is_closed; }
        };

        struct asymmetric_boundary 
        {
            static constexpr bool is_symmetric = false;
            bool is_left_closed;
            constexpr bool include_left_endpoint() const noexcept { return is_left_closed; }
            constexpr bool include_right_endpoint() const noexcept { return !is_left_closed; }
        };

        struct closed 
        {
            static constexpr bool is_symmetric = true;
            static constexpr bool include_left_endpoint() noexcept { return true; }
            static constexpr bool include_right_endpoint() noexcept { return true; }
        };

        struct open 
        {
            static constexpr bool is_symmetric = true;
            static constexpr bool include_left_endpoint() noexcept { return false; }
            static constexpr bool include_right_endpoint() noexcept { return false; }
        };

        struct left_closed_right_open 
        {
            static constexpr bool is_symmetric = false;
            static constexpr bool include_left_endpoint() noexcept { return true; }
            static constexpr bool include_right_endpoint() noexcept { return false; }
        };

        struct right_closed_left_open 
        {
            static constexpr bool is_symmetric = false;
            static constexpr bool include_left_endpoint() noexcept { return false; }
            static constexpr bool include_right_endpoint() noexcept { return true; }
        };
    }

    template <typename T>
    struct return_type : return_type<decltype(&T::operator())>
    {};

    struct nearest_to_even : base 
    {
        using decimal_to_binary_rounding_policy = nearest_to_even;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::symmetric_boundary;
        using shorter_interval_type = interval_type::closed;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func f) noexcept
        {
            return f(nearest_to_even{});
        }
 
        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType 
        invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept
        {
            return f(s.has_even_significand_bits());
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
        {
            return f();
        }
    };

    struct nearest_to_odd : base
    {
        using decimal_to_binary_rounding_policy = nearest_to_odd;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::symmetric_boundary;
        using shorter_interval_type = interval_type::open;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
        {
            return f(nearest_to_odd{});
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept 
        {
            return f(!s.has_even_significand_bits());
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }
    };

    struct nearest_toward_plus_infinity : base
    {
        using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::asymmetric_boundary;
        using shorter_interval_type = interval_type::asymmetric_boundary;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept 
        {
            return f(nearest_toward_plus_infinity{});
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept 
        {
            return f(!s.is_negative());
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept 
        {
            return f(!s.is_negative());
        }
    };

    struct nearest_toward_minus_infinity : base 
    {
        using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::asymmetric_boundary;
        using shorter_interval_type = interval_type::asymmetric_boundary;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept 
        {
            return f(nearest_toward_minus_infinity{});
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept 
        {
            return f(s.is_negative());
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept 
        {
            return f(s.is_negative());
        }
    };

    struct nearest_toward_zero : base
    {
        using decimal_to_binary_rounding_policy = nearest_toward_zero;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::right_closed_left_open;
        using shorter_interval_type = interval_type::right_closed_left_open;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept 
        {
            return f(nearest_toward_zero{});
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }
    };

    struct nearest_away_from_zero : base
    {
        using decimal_to_binary_rounding_policy = nearest_away_from_zero;
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::left_closed_right_open;
        using shorter_interval_type = interval_type::left_closed_right_open;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept 
        {
            return f(nearest_away_from_zero{});
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }
    };

    struct nearest_always_closed
    {
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::closed;
        using shorter_interval_type = interval_type::closed;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }
    };

    struct nearest_always_open 
    {
        static constexpr auto tag = tag_t::to_nearest;
        using normal_interval_type = interval_type::open;
        using shorter_interval_type = interval_type::open;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static constexpr ReturnType
        invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept 
        {
            return f();
        }
    };

    struct nearest_to_even_static_boundary : base
    {
        using decimal_to_binary_rounding_policy = nearest_to_even_static_boundary;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept 
        {
            if (s.has_even_significand_bits())
            {
                return f(nearest_always_closed{});
            }
            else
            {
                return f(nearest_always_open{});
            }
        }
    };

    struct nearest_to_odd_static_boundary : base
    {
        using decimal_to_binary_rounding_policy = nearest_to_odd_static_boundary;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept 
        {
            if (s.has_even_significand_bits())
            {
                return f(nearest_always_open{});
            }
            else
            {
                return f(nearest_always_closed{});
            }
        }
    };
    struct nearest_toward_plus_infinity_static_boundary : base 
    {
        using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity_static_boundary;
        
        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept 
        {
            if (s.is_negative()) 
            {
                return f(nearest_toward_zero{});
            }
            else
            {
                return f(nearest_away_from_zero{});
            }
        }
    };

    struct nearest_toward_minus_infinity_static_boundary : base
    {
        using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity_static_boundary;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept 
        {
            if (s.is_negative())
            {
                return f(nearest_away_from_zero{});
            }
            else
            {
                return f(nearest_toward_zero{});
            }
        }
    };

    struct left_closed_directed 
    {
        static constexpr auto tag = tag_t::left_closed_directed;
    };
    struct right_closed_directed 
    {
        static constexpr auto tag = tag_t::right_closed_directed;
    };

    struct toward_plus_infinity : base 
    {
        using decimal_to_binary_rounding_policy = toward_plus_infinity;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s,  Func&& f) noexcept 
        {
            if (s.is_negative()) 
            {
                return f(left_closed_directed{});
            }
            else 
            {
                return f(right_closed_directed{});
            }
        }
    };

    struct toward_minus_infinity : base 
    {
        using decimal_to_binary_rounding_policy = toward_minus_infinity;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept 
        {
            if (s.is_negative())
            {
                return f(right_closed_directed{});
            }
            else
            {
                return f(left_closed_directed{});
            }
        }
    };

    struct toward_zero : base 
    {
        using decimal_to_binary_rounding_policy = toward_zero;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept 
        {
            return f(left_closed_directed{});
        }
    };

    struct away_from_zero : base
    {
        using decimal_to_binary_rounding_policy = away_from_zero;

        template <typename ReturnType, typename SignedSignificandBits, typename Func>
        BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept  
        {
            return f(right_closed_directed{});
        }
    };
}

// Binary-to-decimal rounding policies.
// (Always assumes nearest rounding modes.)
namespace binary_to_decimal_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 binary_to_decimal_rounding_policy = do_not_care;
        static constexpr auto tag = tag_t::do_not_care;

        template <typename ReturnType>
        static constexpr bool prefer_round_down(ReturnType const&) noexcept
        {
            return false;
        }
    };

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

        template <typename ReturnType>
        static constexpr bool prefer_round_down(ReturnType const& r) noexcept
        {
            return r.significand % 2 != 0;
        }
    };

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

        template <typename ReturnType>
        static constexpr bool prefer_round_down(ReturnType const& r) noexcept
        {
            return r.significand % 2 == 0;
        }
    };

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

        template <typename ReturnType>
        static constexpr bool prefer_round_down(ReturnType const&) noexcept
        {
            return false;
        }
    };

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

        template <typename ReturnType>
        static constexpr bool prefer_round_down(ReturnType const&) noexcept
        {
            return true;
        }
    };
}

// Cache policies.
namespace cache {
    struct base {};

    struct full : base 
    {
        using cache_policy = full;

        template <typename FloatFormat, typename cache_format = typename std::conditional<std::is_same<FloatFormat, ieee754_binary32>::value, 
                                                                                          cache_holder_ieee754_binary32,
                                                                                          cache_holder_ieee754_binary64>::type>
        static constexpr typename cache_format::cache_entry_type get_cache(int k) noexcept 
        {
            return cache_format::cache[std::size_t(k - cache_format::min_k)];
        }
    };
}
}

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

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

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

    BOOST_INLINE_VARIABLE constexpr auto nearest_to_even_static_boundary =
        detail::policy_impl::decimal_to_binary_rounding::nearest_to_even_static_boundary{};
    BOOST_INLINE_VARIABLE constexpr auto nearest_to_odd_static_boundary =
        detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd_static_boundary{};
    BOOST_INLINE_VARIABLE constexpr auto nearest_toward_plus_infinity_static_boundary =
        detail::policy_impl::decimal_to_binary_rounding::
            nearest_toward_plus_infinity_static_boundary{};
    BOOST_INLINE_VARIABLE constexpr auto nearest_toward_minus_infinity_static_boundary =
        detail::policy_impl::decimal_to_binary_rounding::
            nearest_toward_minus_infinity_static_boundary{};

    BOOST_INLINE_VARIABLE constexpr auto toward_plus_infinity =
        detail::policy_impl::decimal_to_binary_rounding::toward_plus_infinity{};
    BOOST_INLINE_VARIABLE constexpr auto toward_minus_infinity =
        detail::policy_impl::decimal_to_binary_rounding::toward_minus_infinity{};
    BOOST_INLINE_VARIABLE constexpr auto toward_zero =
        detail::policy_impl::decimal_to_binary_rounding::toward_zero{};
    BOOST_INLINE_VARIABLE constexpr auto away_from_zero =
        detail::policy_impl::decimal_to_binary_rounding::away_from_zero{};
}

namespace binary_to_decimal_rounding {
    BOOST_INLINE_VARIABLE constexpr auto do_not_care =
        detail::policy_impl::binary_to_decimal_rounding::do_not_care{};
    BOOST_INLINE_VARIABLE constexpr auto to_even =
        detail::policy_impl::binary_to_decimal_rounding::to_even{};
    BOOST_INLINE_VARIABLE constexpr auto to_odd =
        detail::policy_impl::binary_to_decimal_rounding::to_odd{};
    BOOST_INLINE_VARIABLE constexpr auto away_from_zero =
        detail::policy_impl::binary_to_decimal_rounding::away_from_zero{};
    BOOST_INLINE_VARIABLE constexpr auto toward_zero =
        detail::policy_impl::binary_to_decimal_rounding::toward_zero{};
}

namespace cache {
    BOOST_INLINE_VARIABLE constexpr auto full = detail::policy_impl::cache::full{};
}
} // Namespace Policy

////////////////////////////////////////////////////////////////////////////////////////
// The main algorithm.
////////////////////////////////////////////////////////////////////////////////////////

template <typename Float, typename FloatTraits>
struct impl : private FloatTraits, private FloatTraits::format 
{
    using format = typename FloatTraits::format;
    using carrier_uint = typename FloatTraits::carrier_uint;

    using FloatTraits::carrier_bits;
    using format::significand_bits;
    using format::min_exponent;
    using format::max_exponent;
    using format::exponent_bias;
    using format::decimal_digits;

    static constexpr int kappa = std::is_same<format, ieee754_binary32>::value ? 1 : 2;
    static_assert(kappa >= 1, "Kappa must be >= 1");
    // static_assert(carrier_bits >= significand_bits + 2 + log::floor_log2_pow10(kappa + 1));

    static constexpr int min_k_a = -log::floor_log10_pow2_minus_log10_4_over_3(int(max_exponent - significand_bits));
    static constexpr int min_k_b = -log::floor_log10_pow2(int(max_exponent - significand_bits)) + kappa;
    static constexpr int min_k = min_k_a < min_k_b ? min_k_a : min_k_b;
    // static_assert(min_k >= cache_holder<format>::min_k, "Min k is not in the cache");

    static constexpr int max_k_a = -log::floor_log10_pow2_minus_log10_4_over_3(int(min_exponent - significand_bits /*+ 1*/));
    static constexpr int max_k_b = -log::floor_log10_pow2(int(min_exponent - significand_bits)) + kappa;
    static constexpr int max_k = max_k_a > max_k_b ? max_k_a : max_k_b;

    using cache_format = typename std::conditional<std::is_same<format, ieee754_binary32>::value, 
                                                   cache_holder_ieee754_binary32, 
                                                   cache_holder_ieee754_binary64>::type;
    using cache_entry_type = typename cache_format::cache_entry_type;
    static constexpr auto cache_bits = cache_format::cache_bits;

    static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2;
    static BOOST_CXX14_CONSTEXPR const int case_shorter_interval_left_endpoint_upper_threshold = 3;
        //2 + log::floor_log2(compute_power(10, count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1) / 3);

    static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0;
    static BOOST_CXX14_CONSTEXPR const int case_shorter_interval_right_endpoint_upper_threshold = 3;
        //2 + log::floor_log2(compute_power(10, count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1) / 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;

    struct compute_mul_result 
    {
        carrier_uint result;
        bool is_integer;
    };

    struct compute_mul_parity_result 
    {
        bool parity;
        bool is_integer;
    };

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

    #if defined(__GNUC__) && (__GNUC__ < 5) && !defined(__clang__)
    # pragma GCC diagnostic push
    # pragma GCC diagnostic ignored "-Wmissing-field-initializers"
    #endif

    template <typename ReturnType, typename IntervalType, typename TrailingZeroPolicy,
              typename BinaryToDecimalRoundingPolicy, typename CachePolicy, typename... AdditionalArgs>
    BOOST_CHARCONV_SAFEBUFFERS static ReturnType compute_nearest_normal(carrier_uint const two_fc, const int exponent,
                                                                        AdditionalArgs... additional_args) noexcept 
    {
        //////////////////////////////////////////////////////////////////////
        // Step 1: Schubfach multiplier calculation
        //////////////////////////////////////////////////////////////////////

        ReturnType ret_value = {};
        IntervalType interval_type{additional_args...};

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

        // Compute zi and deltai.
        // 10^kappa <= deltai < 10^(kappa + 1)
        const auto deltai = compute_delta(cache, beta);
        // For the case of binary32, the result of integer check is not correct for
        // 29711844 * 2^-82
        // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
        // and 29711844 * 2^-81
        // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17,
        // and they are the unique counterexamples. However, since 29711844 is even,
        // this does not cause any problem for the endpoints calculations; it can only
        // cause a problem when we need to perform integer check for the center.
        // Fortunately, with these inputs, that branch is never executed, so we are fine.
        //const auto [zi, is_z_integer] = compute_mul((two_fc | 1) << beta, cache);
        const auto z_res = compute_mul((two_fc | 1) << beta, cache);
        const auto zi = z_res.result;
        const auto is_z_integer = z_res.is_integer;

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

        BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);
        BOOST_CXX14_CONSTEXPR auto small_divisor = compute_power(std::uint32_t(10), kappa);

        // 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.
        #ifdef BOOST_NO_CXX14_CONSTEXPR
        ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, zi);
        #else
        ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(zi);
        #endif
        
        auto r = std::uint32_t(zi - big_divisor * ret_value.significand);

        if (r < deltai)
        {
            // Exclude the right endpoint if necessary.
            if (r == 0 && (is_z_integer & !interval_type.include_right_endpoint()))
            {
                BOOST_IF_CONSTEXPR (BinaryToDecimalRoundingPolicy::tag == policy_impl::binary_to_decimal_rounding::tag_t::do_not_care)
                {
                    ret_value.significand *= 10;
                    ret_value.exponent = minus_k + kappa;
                    --ret_value.significand;
                    TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);

                    return ret_value;
                }
                else
                {
                    --ret_value.significand;
                    r = big_divisor;

                    goto small_divisor_case_label;
                }
            }
        }
        else if (r > deltai) 
        {
            goto small_divisor_case_label;
        }
        else 
        {
            // r == deltai; compare fractional parts.
            // const auto [xi_parity, x_is_integer] =
            //    compute_mul_parity(two_fc - 1, cache, beta);
            const auto x_res = compute_mul_parity(two_fc - 1, cache, beta);
            const auto xi_parity = x_res.parity;
            const auto x_is_integer = x_res.is_integer;

            if (!(xi_parity | (x_is_integer & interval_type.include_left_endpoint())))
            {
                goto small_divisor_case_label;
            }
        }
        ret_value.exponent = minus_k + kappa + 1;

        // We may need to remove trailing zeros.
        TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
        return ret_value;


        //////////////////////////////////////////////////////////////////////
        // Step 3: Find the significand with the smaller divisor
        //////////////////////////////////////////////////////////////////////

    small_divisor_case_label:
        TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
        ret_value.significand *= 10;
        ret_value.exponent = minus_k + kappa;

        BOOST_IF_CONSTEXPR (BinaryToDecimalRoundingPolicy::tag == policy_impl::binary_to_decimal_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 (!interval_type.include_right_endpoint()) 
            {
                // Is r divisible by 10^kappa?
                if (is_z_integer && div::check_divisibility_and_divide_by_pow10<kappa>(r)) 
                {
                    // 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 
        {
            auto dist = r - (deltai / 2) + (small_divisor / 2);
            const bool approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0;

            // Is dist divisible by 10^kappa?
            const bool divisible_by_small_divisor = div::check_divisibility_and_divide_by_pow10<kappa>(dist);

            // Add dist / 10^kappa to the significand.
            ret_value.significand += dist;

            if (divisible_by_small_divisor) 
            {
                // Check z^(f) >= epsilon^(f).
                // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
                // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f).
                // Since there are only 2 possibilities, we only need to care about the
                // parity. Also, zi and r should have the same parity since the divisor is
                // an even number.
                //const auto [yi_parity, is_y_integer] =
                //    compute_mul_parity(two_fc, cache, beta);
                const auto y_res = compute_mul_parity(two_fc, cache, beta);
                const auto yi_parity = y_res.parity;
                const auto is_y_integer = y_res.is_integer;

                if (yi_parity != 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 (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) & is_y_integer)
                    {
                        --ret_value.significand;
                    }
                }
            }
        }

        return ret_value;
    }

    template <typename ReturnType, typename IntervalType, typename TrailingZeroPolicy,
              typename BinaryToDecimalRoundingPolicy, typename CachePolicy, typename... AdditionalArgs>
    BOOST_CHARCONV_SAFEBUFFERS static ReturnType compute_nearest_shorter(const int exponent, AdditionalArgs... additional_args) noexcept
    {
        ReturnType ret_value = {};
        IntervalType interval_type{additional_args...};

        // Compute k and beta.
        const int minus_k = log::floor_log10_pow2_minus_log10_4_over_3(exponent);
        const int beta = exponent + log::floor_log2_pow10(-minus_k);

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

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

        // If we don't accept the right endpoint and
        // if the right endpoint is an integer, decrease it.
        if (!interval_type.include_right_endpoint() && is_right_endpoint_integer_shorter_interval(exponent)) 
        {
            --zi;
        }
        // If we don't accept the left endpoint or
        // if the left endpoint is not an integer, increase it.
        if (!interval_type.include_left_endpoint() || !is_left_endpoint_integer_shorter_interval(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::template on_trailing_zeros<impl>(ret_value);
            return ret_value;
        }

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

        // When tie occurs, choose one of them according to the rule.
        if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) &&
            exponent >= shorter_interval_tie_lower_threshold &&
            exponent <= shorter_interval_tie_upper_threshold)
        {
            --ret_value.significand;
        }
        else if (ret_value.significand < xi) 
        {
            ++ret_value.significand;
        }

        return ret_value;
    }

    #if defined(__GNUC__) && (__GNUC__ < 5) && !defined(__clang__)
    # pragma GCC diagnostic pop
    #endif

    template <class ReturnType, class TrailingZeroPolicy, class CachePolicy>
    BOOST_CHARCONV_SAFEBUFFERS static ReturnType compute_left_closed_directed(carrier_uint const two_fc, int exponent) noexcept
    {
        //////////////////////////////////////////////////////////////////////
        // Step 1: Schubfach multiplier calculation
        //////////////////////////////////////////////////////////////////////

        ReturnType ret_value;

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

        // Compute xi and deltai.
        // 10^kappa <= deltai < 10^(kappa + 1)
        const auto deltai = compute_delta(cache, beta);
        //auto [xi, is_x_integer] = compute_mul(two_fc << beta, cache);
        const auto x_res = compute_mul(two_fc << beta, cache);
        auto xi = x_res.result;
        auto is_x_integer = x_res.is_integer;

        // Deal with the unique exceptional cases
        // 29711844 * 2^-82
        // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
        // and 29711844 * 2^-81
        // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17
        // for binary32.
        BOOST_IF_CONSTEXPR (std::is_same<format, ieee754_binary32>::value)
        {
            if (exponent <= -80) 
            {
                is_x_integer = false;
            }
        }

        if (!is_x_integer)
        {
            ++xi;
        }

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

        BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);

        // 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.

        #ifdef BOOST_NO_CXX14_CONSTEXPR
        ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, xi);
        #else
        ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(xi);
        #endif

        auto r = std::uint32_t(xi - big_divisor * ret_value.significand);

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

        if (r > deltai) 
        {
            goto small_divisor_case_label;
        }
        else if (r == deltai) 
        {
            // Compare the fractional parts.
            // This branch is never taken for the exceptional cases
            // 2f_c = 29711482, e = -81
            // (6.1442649164096937243516663440523473127541365101933479309082... * 10^-18)
            // and 2f_c = 29711482, e = -80
            // (1.2288529832819387448703332688104694625508273020386695861816... * 10^-17).
            //const auto [zi_parity, is_z_integer] =
            //    compute_mul_parity(two_fc + 2, cache, beta);
            const auto z_res = compute_mul_parity(two_fc + 2, cache, beta);
            if (z_res.parity || z_res.is_integer) 
            {
                goto small_divisor_case_label;
            }
        }

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


        //////////////////////////////////////////////////////////////////////
        // Step 3: Find the significand with the smaller divisor
        //////////////////////////////////////////////////////////////////////

    small_divisor_case_label:
        ret_value.significand *= 10;
        ret_value.significand -= div::small_division_by_pow10<kappa>(r);
        ret_value.exponent = minus_k + kappa;
        TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
        return ret_value;
    }

    template <typename ReturnType, typename TrailingZeroPolicy, typename CachePolicy>
    BOOST_CHARCONV_SAFEBUFFERS static ReturnType compute_right_closed_directed(carrier_uint const two_fc, const int exponent, bool shorter_interval) noexcept
    {
        //////////////////////////////////////////////////////////////////////
        // Step 1: Schubfach multiplier calculation
        //////////////////////////////////////////////////////////////////////

        ReturnType ret_value;

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

        // Compute zi and deltai.
        // 10^kappa <= deltai < 10^(kappa + 1)
        const auto deltai = shorter_interval ? compute_delta(cache, beta - 1) : compute_delta(cache, beta);
        carrier_uint const zi = compute_mul(two_fc << beta, cache).result;


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

        BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);

        // 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.
        #ifdef BOOST_NO_CXX14_CONSTEXPR
        ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, zi);
        #else
        ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(zi);
        #endif

        const auto r = std::uint32_t(zi - big_divisor * ret_value.significand);

        if (r > deltai) 
        {
            goto small_divisor_case_label;
        }
        else if (r == deltai) 
        {
            // Compare the fractional parts.
            if (!compute_mul_parity(two_fc - (shorter_interval ? 1 : 2), cache, beta).parity) 
            {
                goto small_divisor_case_label;
            }
        }

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


        //////////////////////////////////////////////////////////////////////
        // Step 3: Find the significand with the small divisor
        //////////////////////////////////////////////////////////////////////

    small_divisor_case_label:
        ret_value.significand *= 10;
        ret_value.significand += div::small_division_by_pow10<kappa>(r);
        ret_value.exponent = minus_k + kappa;
        TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);

        return ret_value;
    }

    // Remove trailing zeros from n and return the number of zeros removed.
    BOOST_FORCEINLINE static int remove_trailing_zeros(carrier_uint& n) noexcept
    {
        if (n == 0)
        {
            return 0;
        }

        BOOST_IF_CONSTEXPR (std::is_same<format, ieee754_binary32>::value) 
        {
            constexpr auto mod_inv_5 = UINT32_C(0xcccccccd);
            constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;

            int s = 0;
            while (true)
            {
                auto q = boost::core::rotr(n * mod_inv_25, 2);
                if (q <= (std::numeric_limits<std::uint32_t>::max)() / 100)
                {
                    n = q;
                    s += 2;
                }
                else
                {
                    break;
                }
            }
            auto q = boost::core::rotr(n * mod_inv_5, 1);
            if (q <= (std::numeric_limits<std::uint32_t>::max)() / 10)
            {
                n = q;
                s |= 1;
            }

            return s;
        }
        else 
        {
            // Static assertion does not work unless if constexpr is supported
            // static_assert(std::is_same<format, ieee754_binary64>::value, "Must be a double type");

            // Divide by 10^8 and reduce to 32-bits if divisible.
            // Since ret_value.significand <= (2^53 * 1000 - 1) / 1000 < 10^16,
            // n is at most of 16 digits.

            // This magic number is ceil(2^90 / 10^8).
            constexpr auto magic_number = UINT64_C(12379400392853802749);
            auto nm = umul128(n, magic_number);

            // Is n is divisible by 10^8?
            if ((nm.high & ((std::uint64_t(1) << (90 - 64)) - 1)) == 0 &&
                nm.low < magic_number) {
                // If yes, work with the quotient.
                auto n32 = static_cast<std::uint32_t>(nm.high >> (90 - 64));

                constexpr auto mod_inv_5 = UINT32_C(0xcccccccd);
                constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;

                int s = 8;
                while (true)
                {
                    auto q = boost::core::rotr(n32 * mod_inv_25, 2);
                    if (q <= (std::numeric_limits<std::uint32_t>::max)() / 100)
                    {
                        n32 = q;
                        s += 2;
                    }
                    else 
                    {
                        break;
                    }
                }

                auto q = boost::core::rotr(n32 * mod_inv_5, 1);
                if (q <= (std::numeric_limits<std::uint32_t>::max)() / 10)
                {
                    n32 = q;
                    s |= 1;
                }

                n = n32;
                return s;
            }

            // If n is not divisible by 10^8, work with n itself.
            constexpr auto mod_inv_5 = UINT64_C(0xcccccccccccccccd);
            constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;

            int s = 0;
            while (true)
            {
                auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_25, 2));
                if (q <= (std::numeric_limits<std::uint64_t>::max)() / 100)
                {
                    n = q;
                    s += 2;
                }
                else 
                {
                    break;
                }
            }

            auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_5, 1));
            if (q <= (std::numeric_limits<std::uint64_t>::max)() / 10)
            {
                n = q;
                s |= 1;
            }

            return s;
        }
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static compute_mul_result compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept 
    {
        auto r = umul96_upper64(u, cache);
        return {carrier_uint(r >> 32), carrier_uint(r) == 0};
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static compute_mul_result compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept
    {
        auto r = umul192_upper128(u, cache);
        return {r.high, r.low == 0};
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
                                                    int beta) noexcept
    {
        return std::uint32_t(cache >> (cache_bits - 1 - beta));
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
                                                    int beta) noexcept 
    {
        return std::uint32_t(cache.high >> (carrier_bits - 1 - beta));
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
                                                        cache_entry_type const& cache,
                                                        int beta) noexcept 
    {
        auto r = umul96_lower64(two_f, cache);
        return {((r >> (64 - beta)) & 1) != 0, std::uint32_t(r >> (32 - beta)) == 0};
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
                                                        cache_entry_type const& cache,
                                                        int beta) noexcept 
    {
        auto r = umul192_lower128(two_f, cache);
        return {((r.high >> (64 - beta)) & 1) != 0, ((r.high << beta) | (r.low >> (64 - beta))) == 0};
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return carrier_uint((cache - (cache >> (significand_bits + 2))) >> (cache_bits - significand_bits - 1 - beta));
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return (cache.high - (cache.high >> (significand_bits + 2))) >> (carrier_bits - significand_bits - 1 - beta);
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return carrier_uint((cache + (cache >> (significand_bits + 1))) >> (cache_bits - significand_bits - 1 - beta));
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return (cache.high + (cache.high >> (significand_bits + 1))) >> (carrier_bits - significand_bits - 1 - beta);
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
    static constexpr carrier_uint compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return (carrier_uint(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2;
    }

    template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
    static constexpr carrier_uint compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
    {
        return ((cache.high >> (carrier_bits - significand_bits - 2 - beta)) + 1) / 2;
    }

    static constexpr bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept
    {
        return exponent >= case_shorter_interval_right_endpoint_lower_threshold &&
                exponent <= case_shorter_interval_right_endpoint_upper_threshold;
    }

    static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept 
    {
        return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
                exponent <= case_shorter_interval_left_endpoint_upper_threshold;
    }
};


////////////////////////////////////////////////////////////////////////////////////////
// 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 <typename Policy, policy_found_info info>
    struct found_policy_pair 
    {
        using policy = Policy;
        static constexpr auto found_info = info;
    };

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

        template <class FoundPolicyInfo>
        static constexpr FoundPolicyInfo get_policy_impl(FoundPolicyInfo) 
        {
            return {};
        }

        template <typename FoundPolicyInfo, typename FirstPolicy, typename... RemainingPolicies, 
                  typename std::enable_if<std::is_base_of<Base, FirstPolicy>::value && (FoundPolicyInfo::found_info == policy_found_info::not_found), bool>::type = true>
        static constexpr auto get_policy_impl(FoundPolicyInfo, FirstPolicy, RemainingPolicies... remainings) noexcept -> found_policy_pair<FirstPolicy, policy_found_info::unique>
        {
            return get_policy_impl(found_policy_pair<FirstPolicy, policy_found_info::unique>{}, remainings...);
        }

        template <typename FoundPolicyInfo, typename FirstPolicy, typename... RemainingPolicies, 
                  typename std::enable_if<std::is_base_of<Base, FirstPolicy>::value && !(FoundPolicyInfo::found_info == policy_found_info::not_found), bool>::type = true>
        static constexpr auto get_policy_impl(FoundPolicyInfo, FirstPolicy, RemainingPolicies... remainings) noexcept -> found_policy_pair<FirstPolicy, policy_found_info::repeated>
        {
            return get_policy_impl(found_policy_pair<FirstPolicy, policy_found_info::repeated>{}, remainings...);
        }

        template <typename FoundPolicyInfo, typename FirstPolicy, typename... RemainingPolicies, 
                  typename std::enable_if<!std::is_base_of<Base, FirstPolicy>::value, bool>::type = true>
        static constexpr auto get_policy_impl(FoundPolicyInfo, FirstPolicy, RemainingPolicies... remainings) noexcept -> found_policy_pair<FirstPolicy, FoundPolicyInfo::found_info>
        {
            return get_policy_impl(FoundPolicyInfo{}, remainings...);
        }

        template <typename... Policies>
        static constexpr auto get_policy(Policies... policies) -> found_policy_pair<DefaultPolicy, policy_found_info::not_found>
        {
            return get_policy_impl(found_policy_pair<DefaultPolicy, policy_found_info::not_found>{}, policies...);
        }
    };

    template <typename... BaseDefaultPairs>
    struct base_default_pair_list {};

    // Check if a given policy belongs to one of the kinds specified by the library.
    template <typename Policy>
    constexpr bool check_policy_validity(Policy, base_default_pair_list<>)
    {
        return false;
    }

    template <typename Policy, typename FirstBaseDefaultPair, typename... RemainingBaseDefaultPairs>
    constexpr bool check_policy_validity(Policy, base_default_pair_list<FirstBaseDefaultPair, RemainingBaseDefaultPairs...>) 
    {
        return std::is_base_of<typename FirstBaseDefaultPair::base, Policy>::value || 
               check_policy_validity(Policy{}, base_default_pair_list<RemainingBaseDefaultPairs...>{});
    }

    template <typename BaseDefaultPairList>
    constexpr bool check_policy_list_validity(BaseDefaultPairList)
    {
        return true;
    }

    template <typename BaseDefaultPairList, typename FirstPolicy, typename... RemainingPolicies>
    constexpr bool check_policy_list_validity(BaseDefaultPairList, FirstPolicy, RemainingPolicies... remaining_policies) 
    {
        return check_policy_validity(FirstPolicy{}, BaseDefaultPairList{}) &&
               check_policy_list_validity(BaseDefaultPairList{}, remaining_policies...);
    }

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

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

    #ifndef BOOST_CHARCONV_NO_CXX14_RETURN_TYPE_DEDUCTION

    template <bool repeated, typename... FoundPolicyPairs, typename... Policies>
    constexpr auto make_policy_holder_impl(base_default_pair_list<>, found_policy_pair_list<repeated, FoundPolicyPairs...>, Policies...) 
        -> found_policy_pair_list<repeated, FoundPolicyPairs...>
    {
        return found_policy_pair_list<repeated, FoundPolicyPairs...>{};
    }

    template <typename FirstBaseDefaultPair, typename... RemainingBaseDefaultPairs, bool repeated, 
              typename... FoundPolicyPairs, typename... Policies>
    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 || new_found_policy_pair::found_info == policy_found_info::repeated,
                                       new_found_policy_pair, FoundPolicyPairs... > {}, policies...);
    }

    template <bool repeated, typename... RawPolicies>
    constexpr auto convert_to_policy_holder(found_policy_pair_list<repeated>, RawPolicies...) -> policy_holder<RawPolicies...>
    {
        return policy_holder<RawPolicies...>{};
    }

    template <bool repeated, typename FirstFoundPolicyPair, typename... RemainingFoundPolicyPairs, typename... RawPolicies>
    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 <typename BaseDefaultPairList, typename... Policies>
    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(!policy_pair_list::repeated,
                        "jkj::dragonbox: each policy should be specified at most once");

        return convert_to_policy_holder(policy_pair_list{});
    }
    #endif
}
////////////////////////////////////////////////////////////////////////////////////////
// The interface function.
////////////////////////////////////////////////////////////////////////////////////////

#ifdef BOOST_MSVC
# pragma warning(push)
# pragma warning(disable: 4100) // Unreferenced formal parameter (interval_type_provider)
# pragma warning(disable: 4189) // Local variable is initializaed but unused (tag)
#endif

template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>, typename... Policies>
BOOST_FORCEINLINE BOOST_CHARCONV_SAFEBUFFERS auto
to_decimal(dragonbox_signed_significand_bits<Float, FloatTraits> dragonbox_signed_significand_bits,
            unsigned int exponent_bits, BOOST_ATTRIBUTE_UNUSED Policies... policies) noexcept 
            #ifdef BOOST_CHARCONV_NO_CXX14_RETURN_TYPE_DEDUCTION
            -> decimal_fp<typename FloatTraits::carrier_uint, true, false>
            #endif
{
    // Build policy holder type.
    using namespace policy_impl;
    
    #ifdef BOOST_CHARCONV_NO_CXX14_RETURN_TYPE_DEDUCTION
    // For C++11 we hardcode the policy holder
    using policy_holder = policy_holder<decimal_to_binary_rounding::nearest_to_even, binary_to_decimal_rounding::to_even, cache::full, sign::return_sign, trailing_zero::remove>;
    
    #else
    
    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<decimal_to_binary_rounding::base,
                                                    decimal_to_binary_rounding::nearest_to_even>,
                                base_default_pair<binary_to_decimal_rounding::base,
                                                    binary_to_decimal_rounding::to_even>,
                                base_default_pair<cache::base, cache::full>>{},
        policies...));
    
    #endif

    using return_type = decimal_fp<typename FloatTraits::carrier_uint, policy_holder::return_has_sign, policy_holder::report_trailing_zeros>;

    return_type ret = policy_holder::template delegate<return_type>(dragonbox_signed_significand_bits,
        [exponent_bits, dragonbox_signed_significand_bits](policy_impl::decimal_to_binary_rounding::nearest_to_even interval_type_provider) {
            using format = typename FloatTraits::format;
            constexpr auto tag = decltype(interval_type_provider)::tag;

            auto two_fc = dragonbox_signed_significand_bits.remove_sign_bit_and_shift();
            auto exponent = int(exponent_bits);

            BOOST_IF_CONSTEXPR (tag == decimal_to_binary_rounding::tag_t::to_nearest) { // NOLINT: if constexpr not always false
                // Is the input a normal number?
                if (exponent != 0) {
                    exponent += format::exponent_bias - format::significand_bits;

                    // Shorter interval case; proceed like Schubfach.
                    // One might think this condition is wrong, since when exponent_bits == 1
                    // and two_fc == 0, the interval is actually regular. However, it turns out
                    // that this seemingly wrong condition is actually fine, because the end
                    // result is anyway the same.
                    //
                    // [binary32]
                    // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38
                    // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38
                    //    fc    * 2^e = 1.175'494'35... * 10^-38
                    // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38
                    //
                    // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38.
                    // 1.175'494'3 * 10^-38 is also a correct shortest representation that will
                    // be rejected if we assume shorter interval, but 1.175'494'4 * 10^-38 is
                    // closer to the true value so it doesn't matter.
                    //
                    // [binary64]
                    // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308
                    // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308
                    //    fc    * 2^e = 2.225'073'858'507'201'38... * 10^-308
                    // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308
                    //
                    // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 *
                    // 10^-308. This is indeed of the shortest length, and it is the unique one
                    // closest to the true value among valid representations of the same length.
                    static_assert(std::is_same<format, ieee754_binary32>::value ||
                                    std::is_same<format, ieee754_binary64>::value, "Format must be IEEE754 binary 32 or 64");

                    if (two_fc == 0) {
                        return decltype(interval_type_provider)::template invoke_shorter_interval_case<return_type>(
                            dragonbox_signed_significand_bits, [exponent]() {
                                return detail::impl<Float, FloatTraits>::
                                    template compute_nearest_shorter<
                                        return_type,
                                        typename decltype(interval_type_provider)::
                                            shorter_interval_type,
                                        typename policy_holder::trailing_zero_policy,
                                        typename policy_holder::
                                            binary_to_decimal_rounding_policy,
                                        typename policy_holder::cache_policy>(
                                        exponent);
                            });
                    }

                    two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
                }
                // Is the input a subnormal number?
                else {
                    exponent = format::min_exponent - format::significand_bits;
                }

                return decltype(interval_type_provider)::template invoke_normal_interval_case<return_type>(
                    dragonbox_signed_significand_bits, [two_fc, exponent](bool additional_args) {
                        return detail::impl<Float, FloatTraits>::
                            template compute_nearest_normal<
                                return_type,
                                typename decltype(interval_type_provider)::normal_interval_type,
                                typename policy_holder::trailing_zero_policy,
                                typename policy_holder::binary_to_decimal_rounding_policy,
                                typename policy_holder::cache_policy>(two_fc, exponent, additional_args);
                    });
            }
            else BOOST_IF_CONSTEXPR (tag == decimal_to_binary_rounding::tag_t::left_closed_directed)  // NOLINT: if constexpr not always false
            {
                // Is the input a normal number?
                if (exponent != 0) {
                    exponent += format::exponent_bias - format::significand_bits;
                    two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
                }
                // Is the input a subnormal number?
                else {
                    exponent = format::min_exponent - format::significand_bits;
                }

                return detail::impl<Float>::template compute_left_closed_directed<
                    return_type, typename policy_holder::trailing_zero_policy,
                    typename policy_holder::cache_policy>(two_fc, exponent);
            }
            else 
            {
                // Assertion does not work unless if constexpr is defined
                // static_assert(tag == decimal_to_binary_rounding::tag_t::right_closed_directed, "Tag should be right_closed_direction");

                bool shorter_interval = false;

                // Is the input a normal number?
                if (exponent != 0) {
                    if (two_fc == 0 && exponent != 1) {
                        shorter_interval = true;
                    }
                    exponent += format::exponent_bias - format::significand_bits;
                    two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
                }
                // Is the input a subnormal number?
                else {
                    exponent = format::min_exponent - format::significand_bits;
                }

                return detail::impl<Float>::template compute_right_closed_directed<
                    return_type, typename policy_holder::trailing_zero_policy,
                    typename policy_holder::cache_policy>(two_fc, exponent, shorter_interval);
            }
        });

    policy_holder::handle_sign(dragonbox_signed_significand_bits, ret);
    return ret;
}

#ifdef BOOST_MSVC
# pragma warning(pop)
#endif

template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>, typename... Policies>
BOOST_FORCEINLINE BOOST_CHARCONV_SAFEBUFFERS auto to_decimal(Float x, Policies... policies) noexcept
    #ifdef BOOST_CHARCONV_NO_CXX14_RETURN_TYPE_DEDUCTION
    -> decimal_fp<typename FloatTraits::carrier_uint, true, false>
    #endif
{
    const auto br = dragonbox_float_bits<Float, FloatTraits>(x);
    const auto exponent_bits = br.extract_exponent_bits();
    const auto s = br.remove_exponent_bits(exponent_bits);

    return to_decimal<Float, FloatTraits>(s, exponent_bits, policies...);
}

namespace to_chars_detail {
    template <class Float, class FloatTraits>
    extern to_chars_result dragon_box_print_chars(typename FloatTraits::carrier_uint significand, int exponent, char* first, char* last, chars_format fmt) noexcept;

    // Avoid needless ABI overhead incurred by tag dispatch.
    template <class PolicyHolder, class Float, class FloatTraits>
    to_chars_result to_chars_n_impl(dragonbox_float_bits<Float, FloatTraits> br, char* first, char* last, chars_format fmt) noexcept
    {
        const auto exponent_bits = br.extract_exponent_bits();
        const auto s = br.remove_exponent_bits(exponent_bits);

        auto buffer = first;
        const auto buffer_size = last - first;

        if (br.is_finite(exponent_bits))
        {
            if (s.is_negative()) 
            {
                *buffer = '-';
                ++buffer;
            }
            if (br.is_nonzero()) 
            {
                auto result = to_decimal<Float, FloatTraits>(
                    s, exponent_bits, policy::sign::ignore, policy::trailing_zero::ignore,
                    typename PolicyHolder::decimal_to_binary_rounding_policy{},
                    typename PolicyHolder::binary_to_decimal_rounding_policy{},
                    typename PolicyHolder::cache_policy{});
                return to_chars_detail::dragon_box_print_chars<Float, FloatTraits>(result.significand, result.exponent, buffer, last, fmt);
            }
            else 
            {
                if (fmt != chars_format::scientific)
                {
                    std::memcpy(buffer, "0", 1); // NOLINT: Specifically not null-terminated
                    return {buffer + 1, std::errc()};
                }

                if (buffer_size >= 5)
                {
                    std::memcpy(buffer, "0e+00", 5); // NOLINT: Specifically not null-terminated
                    return {buffer + 5, std::errc()};
                }
                else
                {
                    return {last, std::errc::value_too_large};
                }
            }
        }
        else 
        {
            bool is_negative = false;
            if (s.is_negative())
            {
                *buffer = '-';
                ++buffer;
                is_negative = true;
            }

            if (s.has_all_zero_significand_bits())
            {
                if (buffer_size >= 3 + static_cast<std::ptrdiff_t>(is_negative))
                {
                    std::memcpy(buffer, "inf", 3); // NOLINT: Specifically not null-terminated
                    return {buffer + 3, std::errc()};
                }
                else
                {
                    return {last, std::errc::value_too_large};
                }
            }
            else 
            {
                // Doubles:
                // qNaN = 2251799813685248
                // sNaN = 1125899906842624
                //
                // Floats:
                // qNaN = 4194304
                // sNaN = 2097152
                //
                // use 1 for qNaN and 0 for sNaN
                int nan_type;
                BOOST_IF_CONSTEXPR (std::is_same<typename FloatTraits::format, ieee754_binary32>::value)
                {
                    if (br.extract_significand_bits() == UINT32_C(4194304))
                    {
                        nan_type = 1;
                    }
                    else
                    {
                        nan_type = 0;
                    }
                }
                else
                {
                    if (br.extract_significand_bits() == UINT64_C(2251799813685248))
                    {
                        nan_type = 1;
                    }
                    else
                    {
                        nan_type = 0;
                    }
                }

                if (nan_type == 1)
                {
                    if (!s.is_negative())
                    {
                        if (buffer_size >= 3 + static_cast<std::ptrdiff_t>(is_negative))
                        {
                            std::memcpy(buffer, "nan", 3); // NOLINT: Specifically not null-terminated
                            return {buffer + 3, std::errc()};
                        }
                        else
                        {
                            return {last, std::errc::value_too_large};
                        }
                    }
                    else
                    {
                        if (buffer_size >= 8 + static_cast<std::ptrdiff_t>(is_negative))
                        {
                            std::memcpy(buffer, "nan(ind)", 8); // NOLINT: Specifically not null-terminated
                            return {buffer + 8, std::errc()};
                        }
                        else
                        {
                            return {last, std::errc::value_too_large};
                        }
                    }
                }
                else
                {
                    if (buffer_size >= 9 + static_cast<std::ptrdiff_t>(is_negative))
                    {
                        std::memcpy(buffer, "nan(snan)", 9); // NOLINT: Specifically not null-terminated
                        return {buffer + 9, std::errc()};
                    }
                    else
                    {
                        return {last, std::errc::value_too_large};
                    }
                }
            }
        }
    }
}

// Returns the next-to-end position
template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>, typename... Policies>
to_chars_result to_chars_n(Float x, char* first, char* last, chars_format fmt, BOOST_ATTRIBUTE_UNUSED Policies... policies) noexcept
{
    using namespace policy_impl;

    #ifdef BOOST_CHARCONV_NO_CXX14_RETURN_TYPE_DEDUCTION
    // For C++11 we hardcode the policy holder
    using policy_holder = policy_holder<decimal_to_binary_rounding::nearest_to_even, binary_to_decimal_rounding::to_even, cache::full, sign::return_sign, trailing_zero::remove>;
    
    #else
    
    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<decimal_to_binary_rounding::base,
                                                    decimal_to_binary_rounding::nearest_to_even>,
                                base_default_pair<binary_to_decimal_rounding::base,
                                                    binary_to_decimal_rounding::to_even>,
                                base_default_pair<cache::base, cache::full>>{},
        policies...));
    
    #endif

    return to_chars_detail::to_chars_n_impl<policy_holder>(dragonbox_float_bits<Float, FloatTraits>(x), first, last, fmt);
}

// Null-terminate and bypass the return value of fp_to_chars_n
template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>, typename... Policies>
to_chars_result dragonbox_to_chars(Float x, char* first, char* last, chars_format fmt, Policies... policies) noexcept
{
    return to_chars_n<Float, FloatTraits>(x, first, last, fmt, policies...);
}

}}} // Namespaces

#ifdef BOOST_MSVC
# pragma warning(pop)
#endif

#endif // BOOST_CHARCONV_DETAIL_DRAGONBOX_HPP