json.hpp

                }

                bool prefix_required = true;
                if (use_type and not j.m_value.array->empty())
                {
                    assert(use_count);
                    const CharType first_prefix = ubjson_prefix(j.front());
                    const bool same_prefix = std::all_of(j.begin() + 1, j.end(),
                                                         [this, first_prefix](const BasicJsonType & v)
                    {
                        return ubjson_prefix(v) == first_prefix;
                    });

                    if (same_prefix)
                    {
                        prefix_required = false;
                        oa->write_character(static_cast<CharType>('$'));
                        oa->write_character(first_prefix);
                    }
                }

                if (use_count)
                {
                    oa->write_character(static_cast<CharType>('#'));
                    write_number_with_ubjson_prefix(j.m_value.array->size(), true);
                }

                for (const auto& el : *j.m_value.array)
                {
                    write_ubjson(el, use_count, use_type, prefix_required);
                }

                if (not use_count)
                {
                    oa->write_character(static_cast<CharType>(']'));
                }

                break;
            }

            case value_t::object:
            {
                if (add_prefix)
                {
                    oa->write_character(static_cast<CharType>('{'));
                }

                bool prefix_required = true;
                if (use_type and not j.m_value.object->empty())
                {
                    assert(use_count);
                    const CharType first_prefix = ubjson_prefix(j.front());
                    const bool same_prefix = std::all_of(j.begin(), j.end(),
                                                         [this, first_prefix](const BasicJsonType & v)
                    {
                        return ubjson_prefix(v) == first_prefix;
                    });

                    if (same_prefix)
                    {
                        prefix_required = false;
                        oa->write_character(static_cast<CharType>('$'));
                        oa->write_character(first_prefix);
                    }
                }

                if (use_count)
                {
                    oa->write_character(static_cast<CharType>('#'));
                    write_number_with_ubjson_prefix(j.m_value.object->size(), true);
                }

                for (const auto& el : *j.m_value.object)
                {
                    write_number_with_ubjson_prefix(el.first.size(), true);
                    oa->write_characters(
                        reinterpret_cast<const CharType*>(el.first.c_str()),
                        el.first.size());
                    write_ubjson(el.second, use_count, use_type, prefix_required);
                }

                if (not use_count)
                {
                    oa->write_character(static_cast<CharType>('}'));
                }

                break;
            }

            default:
                break;
        }
    }

  private:
    /*
    @brief write a number to output input

    @param[in] n number of type @a NumberType
    @tparam NumberType the type of the number

    @note This function needs to respect the system's endianess, because bytes
          in CBOR, MessagePack, and UBJSON are stored in network order (big
          endian) and therefore need reordering on little endian systems.
    */
    template<typename NumberType>
    void write_number(const NumberType n)
    {
        // step 1: write number to array of length NumberType
        std::array<CharType, sizeof(NumberType)> vec;
        std::memcpy(vec.data(), &n, sizeof(NumberType));

        // step 2: write array to output (with possible reordering)
        if (is_little_endian)
        {
            // reverse byte order prior to conversion if necessary
            std::reverse(vec.begin(), vec.end());
        }

        oa->write_characters(vec.data(), sizeof(NumberType));
    }

    // UBJSON: write number (floating point)
    template<typename NumberType, typename std::enable_if<
                 std::is_floating_point<NumberType>::value, int>::type = 0>
    void write_number_with_ubjson_prefix(const NumberType n,
                                         const bool add_prefix)
    {
        if (add_prefix)
        {
            oa->write_character(get_ubjson_float_prefix(n));
        }
        write_number(n);
    }

    // UBJSON: write number (unsigned integer)
    template<typename NumberType, typename std::enable_if<
                 std::is_unsigned<NumberType>::value, int>::type = 0>
    void write_number_with_ubjson_prefix(const NumberType n,
                                         const bool add_prefix)
    {
        if (n <= static_cast<uint64_t>((std::numeric_limits<int8_t>::max)()))
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('i'));  // int8
            }
            write_number(static_cast<uint8_t>(n));
        }
        else if (n <= (std::numeric_limits<uint8_t>::max)())
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('U'));  // uint8
            }
            write_number(static_cast<uint8_t>(n));
        }
        else if (n <= static_cast<uint64_t>((std::numeric_limits<int16_t>::max)()))
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('I'));  // int16
            }
            write_number(static_cast<int16_t>(n));
        }
        else if (n <= static_cast<uint64_t>((std::numeric_limits<int32_t>::max)()))
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('l'));  // int32
            }
            write_number(static_cast<int32_t>(n));
        }
        else if (n <= static_cast<uint64_t>((std::numeric_limits<int64_t>::max)()))
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('L'));  // int64
            }
            write_number(static_cast<int64_t>(n));
        }
        else
        {
            JSON_THROW(out_of_range::create(407, "number overflow serializing " + std::to_string(n)));
        }
    }

    // UBJSON: write number (signed integer)
    template<typename NumberType, typename std::enable_if<
                 std::is_signed<NumberType>::value and
                 not std::is_floating_point<NumberType>::value, int>::type = 0>
    void write_number_with_ubjson_prefix(const NumberType n,
                                         const bool add_prefix)
    {
        if ((std::numeric_limits<int8_t>::min)() <= n and n <= (std::numeric_limits<int8_t>::max)())
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('i'));  // int8
            }
            write_number(static_cast<int8_t>(n));
        }
        else if (static_cast<int64_t>((std::numeric_limits<uint8_t>::min)()) <= n and n <= static_cast<int64_t>((std::numeric_limits<uint8_t>::max)()))
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('U'));  // uint8
            }
            write_number(static_cast<uint8_t>(n));
        }
        else if ((std::numeric_limits<int16_t>::min)() <= n and n <= (std::numeric_limits<int16_t>::max)())
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('I'));  // int16
            }
            write_number(static_cast<int16_t>(n));
        }
        else if ((std::numeric_limits<int32_t>::min)() <= n and n <= (std::numeric_limits<int32_t>::max)())
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('l'));  // int32
            }
            write_number(static_cast<int32_t>(n));
        }
        else if ((std::numeric_limits<int64_t>::min)() <= n and n <= (std::numeric_limits<int64_t>::max)())
        {
            if (add_prefix)
            {
                oa->write_character(static_cast<CharType>('L'));  // int64
            }
            write_number(static_cast<int64_t>(n));
        }
        // LCOV_EXCL_START
        else
        {
            JSON_THROW(out_of_range::create(407, "number overflow serializing " + std::to_string(n)));
        }
        // LCOV_EXCL_STOP
    }

    /*!
    @brief determine the type prefix of container values

    @note This function does not need to be 100% accurate when it comes to
          integer limits. In case a number exceeds the limits of int64_t,
          this will be detected by a later call to function
          write_number_with_ubjson_prefix. Therefore, we return 'L' for any
          value that does not fit the previous limits.
    */
    CharType ubjson_prefix(const BasicJsonType& j) const noexcept
    {
        switch (j.type())
        {
            case value_t::null:
                return 'Z';

            case value_t::boolean:
                return j.m_value.boolean ? 'T' : 'F';

            case value_t::number_integer:
            {
                if ((std::numeric_limits<int8_t>::min)() <= j.m_value.number_integer and j.m_value.number_integer <= (std::numeric_limits<int8_t>::max)())
                {
                    return 'i';
                }
                else if ((std::numeric_limits<uint8_t>::min)() <= j.m_value.number_integer and j.m_value.number_integer <= (std::numeric_limits<uint8_t>::max)())
                {
                    return 'U';
                }
                else if ((std::numeric_limits<int16_t>::min)() <= j.m_value.number_integer and j.m_value.number_integer <= (std::numeric_limits<int16_t>::max)())
                {
                    return 'I';
                }
                else if ((std::numeric_limits<int32_t>::min)() <= j.m_value.number_integer and j.m_value.number_integer <= (std::numeric_limits<int32_t>::max)())
                {
                    return 'l';
                }
                else  // no check and assume int64_t (see note above)
                {
                    return 'L';
                }
            }

            case value_t::number_unsigned:
            {
                if (j.m_value.number_unsigned <= (std::numeric_limits<int8_t>::max)())
                {
                    return 'i';
                }
                else if (j.m_value.number_unsigned <= (std::numeric_limits<uint8_t>::max)())
                {
                    return 'U';
                }
                else if (j.m_value.number_unsigned <= (std::numeric_limits<int16_t>::max)())
                {
                    return 'I';
                }
                else if (j.m_value.number_unsigned <= (std::numeric_limits<int32_t>::max)())
                {
                    return 'l';
                }
                else  // no check and assume int64_t (see note above)
                {
                    return 'L';
                }
            }

            case value_t::number_float:
                return get_ubjson_float_prefix(j.m_value.number_float);

            case value_t::string:
                return 'S';

            case value_t::array:
                return '[';

            case value_t::object:
                return '{';

            default:  // discarded values
                return 'N';
        }
    }

    static constexpr CharType get_cbor_float_prefix(float)
    {
        return static_cast<CharType>(0xFA);  // Single-Precision Float
    }

    static constexpr CharType get_cbor_float_prefix(double)
    {
        return static_cast<CharType>(0xFB);  // Double-Precision Float
    }

    static constexpr CharType get_msgpack_float_prefix(float)
    {
        return static_cast<CharType>(0xCA);  // float 32
    }

    static constexpr CharType get_msgpack_float_prefix(double)
    {
        return static_cast<CharType>(0xCB);  // float 64
    }

    static constexpr CharType get_ubjson_float_prefix(float)
    {
        return 'd';  // float 32
    }

    static constexpr CharType get_ubjson_float_prefix(double)
    {
        return 'D';  // float 64
    }

  private:
    /// whether we can assume little endianess
    const bool is_little_endian = binary_reader<BasicJsonType>::little_endianess();

    /// the output
    output_adapter_t<CharType> oa = nullptr;
};
}
}

// #include <nlohmann/detail/output/serializer.hpp>


#include <algorithm> // reverse, remove, fill, find, none_of
#include <array> // array
#include <cassert> // assert
#include <ciso646> // and, or
#include <clocale> // localeconv, lconv
#include <cmath> // labs, isfinite, isnan, signbit
#include <cstddef> // size_t, ptrdiff_t
#include <cstdint> // uint8_t
#include <cstdio> // snprintf
#include <limits> // numeric_limits
#include <string> // string
#include <type_traits> // is_same

// #include <nlohmann/detail/exceptions.hpp>

// #include <nlohmann/detail/conversions/to_chars.hpp>


#include <cassert> // assert
#include <ciso646> // or, and, not
#include <cmath>   // signbit, isfinite
#include <cstdint> // intN_t, uintN_t
#include <cstring> // memcpy, memmove

namespace nlohmann
{
namespace detail
{

/*!
@brief implements the Grisu2 algorithm for binary to decimal floating-point
conversion.

This implementation is a slightly modified version of the reference
implementation which may be obtained from
http://florian.loitsch.com/publications (bench.tar.gz).

The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.

For a detailed description of the algorithm see:

[1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with
    Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming
    Language Design and Implementation, PLDI 2010
[2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
    Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language
    Design and Implementation, PLDI 1996
*/
namespace dtoa_impl
{

template <typename Target, typename Source>
Target reinterpret_bits(const Source source)
{
    static_assert(sizeof(Target) == sizeof(Source), "size mismatch");

    Target target;
    std::memcpy(&target, &source, sizeof(Source));
    return target;
}

struct diyfp // f * 2^e
{
    static constexpr int kPrecision = 64; // = q

    uint64_t f;
    int e;

    constexpr diyfp() noexcept : f(0), e(0) {}
    constexpr diyfp(uint64_t f_, int e_) noexcept : f(f_), e(e_) {}

    /*!
    @brief returns x - y
    @pre x.e == y.e and x.f >= y.f
    */
    static diyfp sub(const diyfp& x, const diyfp& y) noexcept
    {
        assert(x.e == y.e);
        assert(x.f >= y.f);

        return diyfp(x.f - y.f, x.e);
    }

    /*!
    @brief returns x * y
    @note The result is rounded. (Only the upper q bits are returned.)
    */
    static diyfp mul(const diyfp& x, const diyfp& y) noexcept
    {
        static_assert(kPrecision == 64, "internal error");

        // Computes:
        //  f = round((x.f * y.f) / 2^q)
        //  e = x.e + y.e + q

        // Emulate the 64-bit * 64-bit multiplication:
        //
        // p = u * v
        //   = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
        //   = (u_lo v_lo         ) + 2^32 ((u_lo v_hi         ) + (u_hi v_lo         )) + 2^64 (u_hi v_hi         )
        //   = (p0                ) + 2^32 ((p1                ) + (p2                )) + 2^64 (p3                )
        //   = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3                )
        //   = (p0_lo             ) + 2^32 (p0_hi + p1_lo + p2_lo                      ) + 2^64 (p1_hi + p2_hi + p3)
        //   = (p0_lo             ) + 2^32 (Q                                          ) + 2^64 (H                 )
        //   = (p0_lo             ) + 2^32 (Q_lo + 2^32 Q_hi                           ) + 2^64 (H                 )
        //
        // (Since Q might be larger than 2^32 - 1)
        //
        //   = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
        //
        // (Q_hi + H does not overflow a 64-bit int)
        //
        //   = p_lo + 2^64 p_hi

        const uint64_t u_lo = x.f & 0xFFFFFFFF;
        const uint64_t u_hi = x.f >> 32;
        const uint64_t v_lo = y.f & 0xFFFFFFFF;
        const uint64_t v_hi = y.f >> 32;

        const uint64_t p0 = u_lo * v_lo;
        const uint64_t p1 = u_lo * v_hi;
        const uint64_t p2 = u_hi * v_lo;
        const uint64_t p3 = u_hi * v_hi;

        const uint64_t p0_hi = p0 >> 32;
        const uint64_t p1_lo = p1 & 0xFFFFFFFF;
        const uint64_t p1_hi = p1 >> 32;
        const uint64_t p2_lo = p2 & 0xFFFFFFFF;
        const uint64_t p2_hi = p2 >> 32;

        uint64_t Q = p0_hi + p1_lo + p2_lo;

        // The full product might now be computed as
        //
        // p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
        // p_lo = p0_lo + (Q << 32)
        //
        // But in this particular case here, the full p_lo is not required.
        // Effectively we only need to add the highest bit in p_lo to p_hi (and
        // Q_hi + 1 does not overflow).

        Q += uint64_t{1} << (64 - 32 - 1); // round, ties up

        const uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32);

        return diyfp(h, x.e + y.e + 64);
    }

    /*!
    @brief normalize x such that the significand is >= 2^(q-1)
    @pre x.f != 0
    */
    static diyfp normalize(diyfp x) noexcept
    {
        assert(x.f != 0);

        while ((x.f >> 63) == 0)
        {
            x.f <<= 1;
            x.e--;
        }

        return x;
    }

    /*!
    @brief normalize x such that the result has the exponent E
    @pre e >= x.e and the upper e - x.e bits of x.f must be zero.
    */
    static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept
    {
        const int delta = x.e - target_exponent;

        assert(delta >= 0);
        assert(((x.f << delta) >> delta) == x.f);

        return diyfp(x.f << delta, target_exponent);
    }
};

struct boundaries
{
    diyfp w;
    diyfp minus;
    diyfp plus;
};

/*!
Compute the (normalized) diyfp representing the input number 'value' and its
boundaries.

@pre value must be finite and positive
*/
template <typename FloatType>
boundaries compute_boundaries(FloatType value)
{
    assert(std::isfinite(value));
    assert(value > 0);

    // Convert the IEEE representation into a diyfp.
    //
    // If v is denormal:
    //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))
    // If v is normalized:
    //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))

    static_assert(std::numeric_limits<FloatType>::is_iec559,
                  "internal error: dtoa_short requires an IEEE-754 floating-point implementation");

    constexpr int      kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
    constexpr int      kBias      = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
    constexpr int      kMinExp    = 1 - kBias;
    constexpr uint64_t kHiddenBit = uint64_t{1} << (kPrecision - 1); // = 2^(p-1)

    using bits_type = typename std::conditional< kPrecision == 24, uint32_t, uint64_t >::type;

    const uint64_t bits = reinterpret_bits<bits_type>(value);
    const uint64_t E = bits >> (kPrecision - 1);
    const uint64_t F = bits & (kHiddenBit - 1);

    const bool is_denormal = (E == 0);
    const diyfp v = is_denormal
                    ? diyfp(F, kMinExp)
                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);

    // Compute the boundaries m- and m+ of the floating-point value
    // v = f * 2^e.
    //
    // Determine v- and v+, the floating-point predecessor and successor if v,
    // respectively.
    //
    //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)
    //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)
    //
    //      v+ = v + 2^e
    //
    // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
    // between m- and m+ round to v, regardless of how the input rounding
    // algorithm breaks ties.
    //
    //      ---+-------------+-------------+-------------+-------------+---  (A)
    //         v-            m-            v             m+            v+
    //
    //      -----------------+------+------+-------------+-------------+---  (B)
    //                       v-     m-     v             m+            v+

    const bool lower_boundary_is_closer = (F == 0 and E > 1);
    const diyfp m_plus = diyfp(2 * v.f + 1, v.e - 1);
    const diyfp m_minus = lower_boundary_is_closer
                          ? diyfp(4 * v.f - 1, v.e - 2)  // (B)
                          : diyfp(2 * v.f - 1, v.e - 1); // (A)

    // Determine the normalized w+ = m+.
    const diyfp w_plus = diyfp::normalize(m_plus);

    // Determine w- = m- such that e_(w-) = e_(w+).
    const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);

    return {diyfp::normalize(v), w_minus, w_plus};
}

// Given normalized diyfp w, Grisu needs to find a (normalized) cached
// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
// within a certain range [alpha, gamma] (Definition 3.2 from [1])
//
//      alpha <= e = e_c + e_w + q <= gamma
//
// or
//
//      f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q
//                          <= f_c * f_w * 2^gamma
//
// Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies
//
//      2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma
//
// or
//
//      2^(q - 2 + alpha) <= c * w < 2^(q + gamma)
//
// The choice of (alpha,gamma) determines the size of the table and the form of
// the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well
// in practice:
//
// The idea is to cut the number c * w = f * 2^e into two parts, which can be
// processed independently: An integral part p1, and a fractional part p2:
//
//      f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e
//              = (f div 2^-e) + (f mod 2^-e) * 2^e
//              = p1 + p2 * 2^e
//
// The conversion of p1 into decimal form requires a series of divisions and
// modulos by (a power of) 10. These operations are faster for 32-bit than for
// 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be
// achieved by choosing
//
//      -e >= 32   or   e <= -32 := gamma
//
// In order to convert the fractional part
//
//      p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...
//
// into decimal form, the fraction is repeatedly multiplied by 10 and the digits
// d[-i] are extracted in order:
//
//      (10 * p2) div 2^-e = d[-1]
//      (10 * p2) mod 2^-e = d[-2] / 10^1 + ...
//
// The multiplication by 10 must not overflow. It is sufficient to choose
//
//      10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.
//
// Since p2 = f mod 2^-e < 2^-e,
//
//      -e <= 60   or   e >= -60 := alpha

constexpr int kAlpha = -60;
constexpr int kGamma = -32;

struct cached_power // c = f * 2^e ~= 10^k
{
    uint64_t f;
    int e;
    int k;
};

/*!
For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached
power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c
satisfies (Definition 3.2 from [1])

     alpha <= e_c + e + q <= gamma.
*/
inline cached_power get_cached_power_for_binary_exponent(int e)
{
    // Now
    //
    //      alpha <= e_c + e + q <= gamma                                    (1)
    //      ==> f_c * 2^alpha <= c * 2^e * 2^q
    //
    // and since the c's are normalized, 2^(q-1) <= f_c,
    //
    //      ==> 2^(q - 1 + alpha) <= c * 2^(e + q)
    //      ==> 2^(alpha - e - 1) <= c
    //
    // If c were an exakt power of ten, i.e. c = 10^k, one may determine k as
    //
    //      k = ceil( log_10( 2^(alpha - e - 1) ) )
    //        = ceil( (alpha - e - 1) * log_10(2) )
    //
    // From the paper:
    // "In theory the result of the procedure could be wrong since c is rounded,
    //  and the computation itself is approximated [...]. In practice, however,
    //  this simple function is sufficient."
    //
    // For IEEE double precision floating-point numbers converted into
    // normalized diyfp's w = f * 2^e, with q = 64,
    //
    //      e >= -1022      (min IEEE exponent)
    //           -52        (p - 1)
    //           -52        (p - 1, possibly normalize denormal IEEE numbers)
    //           -11        (normalize the diyfp)
    //         = -1137
    //
    // and
    //
    //      e <= +1023      (max IEEE exponent)
    //           -52        (p - 1)
    //           -11        (normalize the diyfp)
    //         = 960
    //
    // This binary exponent range [-1137,960] results in a decimal exponent
    // range [-307,324]. One does not need to store a cached power for each
    // k in this range. For each such k it suffices to find a cached power
    // such that the exponent of the product lies in [alpha,gamma].
    // This implies that the difference of the decimal exponents of adjacent
    // table entries must be less than or equal to
    //
    //      floor( (gamma - alpha) * log_10(2) ) = 8.
    //
    // (A smaller distance gamma-alpha would require a larger table.)

    // NB:
    // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.

    constexpr int kCachedPowersSize = 79;
    constexpr int kCachedPowersMinDecExp = -300;
    constexpr int kCachedPowersDecStep = 8;

    static constexpr cached_power kCachedPowers[] =
    {
        { 0xAB70FE17C79AC6CA, -1060, -300 },
        { 0xFF77B1FCBEBCDC4F, -1034, -292 },
        { 0xBE5691EF416BD60C, -1007, -284 },
        { 0x8DD01FAD907FFC3C,  -980, -276 },
        { 0xD3515C2831559A83,  -954, -268 },
        { 0x9D71AC8FADA6C9B5,  -927, -260 },
        { 0xEA9C227723EE8BCB,  -901, -252 },
        { 0xAECC49914078536D,  -874, -244 },
        { 0x823C12795DB6CE57,  -847, -236 },
        { 0xC21094364DFB5637,  -821, -228 },
        { 0x9096EA6F3848984F,  -794, -220 },
        { 0xD77485CB25823AC7,  -768, -212 },
        { 0xA086CFCD97BF97F4,  -741, -204 },
        { 0xEF340A98172AACE5,  -715, -196 },
        { 0xB23867FB2A35B28E,  -688, -188 },
        { 0x84C8D4DFD2C63F3B,  -661, -180 },
        { 0xC5DD44271AD3CDBA,  -635, -172 },
        { 0x936B9FCEBB25C996,  -608, -164 },
        { 0xDBAC6C247D62A584,  -582, -156 },
        { 0xA3AB66580D5FDAF6,  -555, -148 },
        { 0xF3E2F893DEC3F126,  -529, -140 },
        { 0xB5B5ADA8AAFF80B8,  -502, -132 },
        { 0x87625F056C7C4A8B,  -475, -124 },
        { 0xC9BCFF6034C13053,  -449, -116 },
        { 0x964E858C91BA2655,  -422, -108 },
        { 0xDFF9772470297EBD,  -396, -100 },
        { 0xA6DFBD9FB8E5B88F,  -369,  -92 },
        { 0xF8A95FCF88747D94,  -343,  -84 },
        { 0xB94470938FA89BCF,  -316,  -76 },
        { 0x8A08F0F8BF0F156B,  -289,  -68 },
        { 0xCDB02555653131B6,  -263,  -60 },
        { 0x993FE2C6D07B7FAC,  -236,  -52 },
        { 0xE45C10C42A2B3B06,  -210,  -44 },
        { 0xAA242499697392D3,  -183,  -36 },
        { 0xFD87B5F28300CA0E,  -157,  -28 },
        { 0xBCE5086492111AEB,  -130,  -20 },
        { 0x8CBCCC096F5088CC,  -103,  -12 },
        { 0xD1B71758E219652C,   -77,   -4 },
        { 0x9C40000000000000,   -50,    4 },
        { 0xE8D4A51000000000,   -24,   12 },
        { 0xAD78EBC5AC620000,     3,   20 },
        { 0x813F3978F8940984,    30,   28 },
        { 0xC097CE7BC90715B3,    56,   36 },
        { 0x8F7E32CE7BEA5C70,    83,   44 },
        { 0xD5D238A4ABE98068,   109,   52 },
        { 0x9F4F2726179A2245,   136,   60 },
        { 0xED63A231D4C4FB27,   162,   68 },
        { 0xB0DE65388CC8ADA8,   189,   76 },
        { 0x83C7088E1AAB65DB,   216,   84 },
        { 0xC45D1DF942711D9A,   242,   92 },
        { 0x924D692CA61BE758,   269,  100 },
        { 0xDA01EE641A708DEA,   295,  108 },
        { 0xA26DA3999AEF774A,   322,  116 },
        { 0xF209787BB47D6B85,   348,  124 },
        { 0xB454E4A179DD1877,   375,  132 },
        { 0x865B86925B9BC5C2,   402,  140 },
        { 0xC83553C5C8965D3D,   428,  148 },
        { 0x952AB45CFA97A0B3,   455,  156 },
        { 0xDE469FBD99A05FE3,   481,  164 },
        { 0xA59BC234DB398C25,   508,  172 },
        { 0xF6C69A72A3989F5C,   534,  180 },
        { 0xB7DCBF5354E9BECE,   561,  188 },
        { 0x88FCF317F22241E2,   588,  196 },
        { 0xCC20CE9BD35C78A5,   614,  204 },
        { 0x98165AF37B2153DF,   641,  212 },
        { 0xE2A0B5DC971F303A,   667,  220 },
        { 0xA8D9D1535CE3B396,   694,  228 },
        { 0xFB9B7CD9A4A7443C,   720,  236 },
        { 0xBB764C4CA7A44410,   747,  244 },
        { 0x8BAB8EEFB6409C1A,   774,  252 },
        { 0xD01FEF10A657842C,   800,  260 },
        { 0x9B10A4E5E9913129,   827,  268 },
        { 0xE7109BFBA19C0C9D,   853,  276 },
        { 0xAC2820D9623BF429,   880,  284 },
        { 0x80444B5E7AA7CF85,   907,  292 },
        { 0xBF21E44003ACDD2D,   933,  300 },
        { 0x8E679C2F5E44FF8F,   960,  308 },
        { 0xD433179D9C8CB841,   986,  316 },
        { 0x9E19DB92B4E31BA9,  1013,  324 },
    };

    // This computation gives exactly the same results for k as
    //      k = ceil((kAlpha - e - 1) * 0.30102999566398114)
    // for |e| <= 1500, but doesn't require floating-point operations.
    // NB: log_10(2) ~= 78913 / 2^18
    assert(e >= -1500);
    assert(e <=  1500);
    const int f = kAlpha - e - 1;
    const int k = (f * 78913) / (1 << 18) + (f > 0);

    const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
    assert(index >= 0);
    assert(index < kCachedPowersSize);
    static_cast<void>(kCachedPowersSize); // Fix warning.

    const cached_power cached = kCachedPowers[index];
    assert(kAlpha <= cached.e + e + 64);
    assert(kGamma >= cached.e + e + 64);

    return cached;
}

/*!
For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
For n == 0, returns 1 and sets pow10 := 1.
*/
inline int find_largest_pow10(const uint32_t n, uint32_t& pow10)
{
    // LCOV_EXCL_START
    if (n >= 1000000000)
    {
        pow10 = 1000000000;
        return 10;
    }
    // LCOV_EXCL_STOP
    else if (n >= 100000000)
    {
        pow10 = 100000000;
        return  9;
    }
    else if (n >= 10000000)
    {
        pow10 = 10000000;
        return  8;
    }
    else if (n >= 1000000)
    {
        pow10 = 1000000;
        return  7;
    }
    else if (n >= 100000)
    {
        pow10 = 100000;
        return  6;
    }
    else if (n >= 10000)
    {
        pow10 = 10000;
        return  5;
    }
    else if (n >= 1000)
    {
        pow10 = 1000;
        return  4;
    }
    else if (n >= 100)
    {
        pow10 = 100;
        return  3;
    }
    else if (n >= 10)
    {
        pow10 = 10;
        return  2;
    }
    else
    {
        pow10 = 1;
        return 1;
    }
}

inline void grisu2_round(char* buf, int len, uint64_t dist, uint64_t delta,
                         uint64_t rest, uint64_t ten_k)
{
    assert(len >= 1);
    assert(dist <= delta);
    assert(rest <= delta);
    assert(ten_k > 0);

    //               <--------------------------- delta ---->
    //                                  <---- dist --------->
    // --------------[------------------+-------------------]--------------
    //               M-                 w                   M+
    //
    //                                  ten_k
    //                                <------>
    //                                       <---- rest ---->
    // --------------[------------------+----+--------------]--------------
    //                                  w    V
    //                                       = buf * 10^k
    //
    // ten_k represents a unit-in-the-last-place in the decimal representation
    // stored in buf.
    // Decrement buf by ten_k while this takes buf closer to w.

    // The tests are written in this order to avoid overflow in unsigned
    // integer arithmetic.

    while (rest < dist
            and delta - rest >= ten_k
            and (rest + ten_k < dist or dist - rest > rest + ten_k - dist))
    {
        assert(buf[len - 1] != '0');
        buf[len - 1]--;
        rest += ten_k;
    }
}

/*!
Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
*/
inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,
                             diyfp M_minus, diyfp w, diyfp M_plus)
{
    static_assert(kAlpha >= -60, "internal error");
    static_assert(kGamma <= -32, "internal error");

    // Generates the digits (and the exponent) of a decimal floating-point
    // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
    // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
    //
    //               <--------------------------- delta ---->
    //                                  <---- dist --------->
    // --------------[------------------+-------------------]--------------
    //               M-                 w                   M+
    //
    // Grisu2 generates the digits of M+ from left to right and stops as soon as
    // V is in [M-,M+].

    assert(M_plus.e >= kAlpha);
    assert(M_plus.e <= kGamma);

    uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
    uint64_t dist  = diyfp::sub(M_plus, w      ).f; // (significand of (M+ - w ), implicit exponent is e)

    // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
    //
    //      M+ = f * 2^e
    //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
    //         = ((p1        ) * 2^-e + (p2        )) * 2^e
    //         = p1 + p2 * 2^e

    const diyfp one(uint64_t{1} << -M_plus.e, M_plus.e);

    uint32_t p1 = static_cast<uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
    uint64_t p2 = M_plus.f & (one.f - 1);                    // p2 = f mod 2^-e

    // 1)