xcharconv_ryu.h

// xcharconv_ryu.h internal header

// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception


// Copyright 2018 Ulf Adams
// Copyright (c) Microsoft Corporation. All rights reserved.

// Boost Software License - Version 1.0 - August 17th, 2003

// Permission is hereby granted, free of charge, to any person or organization
// obtaining a copy of the software and accompanying documentation covered by
// this license (the "Software") to use, reproduce, display, distribute,
// execute, and transmit the Software, and to prepare derivative works of the
// Software, and to permit third-parties to whom the Software is furnished to
// do so, all subject to the following:

// The copyright notices in the Software and this entire statement, including
// the above license grant, this restriction and the following disclaimer,
// must be included in all copies of the Software, in whole or in part, and
// all derivative works of the Software, unless such copies or derivative
// works are solely in the form of machine-executable object code generated by
// a source language processor.

// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.


#ifndef _XCHARCONV_RYU_H
#define _XCHARCONV_RYU_H
#include <yvals_core.h>
#if _STL_COMPILER_PREPROCESSOR

#if !_HAS_CXX17
#error The contents of <charconv> are only available with C++17. (Also, you should not include this internal header.)
#endif // !_HAS_CXX17

#include <cstring>
#include <type_traits>
#include <utility>
#include <xcharconv.h>
#include <xcharconv_ryu_tables.h>
#include <xutility>

#if defined(_M_X64) || defined(_M_ARM64) || defined(_M_ARM64EC) || defined(_M_HYBRID_X86_ARM64)
#define _HAS_CHARCONV_INTRINSICS 1
#else // ^^^ intrinsics available / intrinsics unavailable vvv
#define _HAS_CHARCONV_INTRINSICS 0
#endif // ^^^ intrinsics unavailable ^^^

#if _HAS_CHARCONV_INTRINSICS
#if defined(_M_ARM64) || defined(_M_ARM64EC) || defined(_M_HYBRID_X86_ARM64)
#include <intrin.h> // TRANSITION, VSO-1918426
#else // ^^^ defined(_M_ARM64) || defined(_M_ARM64EC) || defined(_M_HYBRID_X86_ARM64) / defined(_M_X64) vvv
#include _STL_INTRIN_HEADER // for _umul128(), __umulh(), and __shiftright128()
#endif // ^^^ defined(_M_X64) ^^^
#endif // ^^^ intrinsics available ^^^

#pragma pack(push, _CRT_PACKING)
#pragma warning(push, _STL_WARNING_LEVEL)
#pragma warning(disable : _STL_DISABLED_WARNINGS)
_STL_DISABLE_CLANG_WARNINGS
#pragma push_macro("new")
#undef new

_STD_BEGIN

// https://github.com/ulfjack/ryu/tree/59661c3/ryu
// (Keep the cgmanifest.json commitHash in sync.)

// clang-format off

// vvvvvvvvvv DERIVED FROM common.h vvvvvvvvvv

_NODISCARD inline uint32_t __decimalLength9(const uint32_t __v) {
  // Function precondition: __v is not a 10-digit number.
  // (f2s: 9 digits are sufficient for round-tripping.)
  // (d2fixed: We print 9-digit blocks.)
  _STL_INTERNAL_CHECK(__v < 1000000000);
  if (__v >= 100000000) { return 9; }
  if (__v >= 10000000) { return 8; }
  if (__v >= 1000000) { return 7; }
  if (__v >= 100000) { return 6; }
  if (__v >= 10000) { return 5; }
  if (__v >= 1000) { return 4; }
  if (__v >= 100) { return 3; }
  if (__v >= 10) { return 2; }
  return 1;
}

// Returns __e == 0 ? 1 : ceil(log_2(5^__e)).
_NODISCARD inline int32_t __pow5bits(const int32_t __e) {
  // This approximation works up to the point that the multiplication overflows at __e = 3529.
  // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
  // than 2^9297.
  _STL_INTERNAL_CHECK(__e >= 0);
  _STL_INTERNAL_CHECK(__e <= 3528);
  return static_cast<int32_t>(((static_cast<uint32_t>(__e) * 1217359) >> 19) + 1);
}

// Returns floor(log_10(2^__e)).
_NODISCARD inline uint32_t __log10Pow2(const int32_t __e) {
  // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
  _STL_INTERNAL_CHECK(__e >= 0);
  _STL_INTERNAL_CHECK(__e <= 1650);
  return (static_cast<uint32_t>(__e) * 78913) >> 18;
}

// Returns floor(log_10(5^__e)).
_NODISCARD inline uint32_t __log10Pow5(const int32_t __e) {
  // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
  _STL_INTERNAL_CHECK(__e >= 0);
  _STL_INTERNAL_CHECK(__e <= 2620);
  return (static_cast<uint32_t>(__e) * 732923) >> 20;
}

_NODISCARD inline uint32_t __float_to_bits(const float __f) {
  uint32_t __bits = 0;
  _CSTD memcpy(&__bits, &__f, sizeof(float));
  return __bits;
}

_NODISCARD inline uint64_t __double_to_bits(const double __d) {
  uint64_t __bits = 0;
  _CSTD memcpy(&__bits, &__d, sizeof(double));
  return __bits;
}

// ^^^^^^^^^^ DERIVED FROM common.h ^^^^^^^^^^

// vvvvvvvvvv DERIVED FROM d2s.h vvvvvvvvvv

inline constexpr int __DOUBLE_MANTISSA_BITS = 52;
inline constexpr int __DOUBLE_BIAS = 1023;

inline constexpr int __DOUBLE_POW5_INV_BITCOUNT = 122;
inline constexpr int __DOUBLE_POW5_BITCOUNT = 121;

// ^^^^^^^^^^ DERIVED FROM d2s.h ^^^^^^^^^^

// vvvvvvvvvv DERIVED FROM d2s_intrinsics.h vvvvvvvvvv

#if _HAS_CHARCONV_INTRINSICS

_NODISCARD inline uint64_t __ryu_umul128(const uint64_t __a, const uint64_t __b, uint64_t* const __productHi) {
#if defined(_M_ARM64) || defined(_M_ARM64EC) || defined(_M_HYBRID_X86_ARM64)
  *__productHi = __umulh(__a, __b);
  return __a * __b;
#else // ^^^ not native X64 / native X64 vvv
  return _umul128(__a, __b, __productHi);
#endif // defined(_M_ARM64) || defined(_M_ARM64EC) || defined(_M_HYBRID_X86_ARM64)
}

#else // ^^^ intrinsics available / intrinsics unavailable vvv

_NODISCARD __forceinline uint64_t __ryu_umul128(const uint64_t __a, const uint64_t __b, uint64_t* const __productHi) {
  // TRANSITION, VSO-634761
  // The casts here help MSVC to avoid calls to the __allmul library function.
  const uint32_t __aLo = static_cast<uint32_t>(__a);
  const uint32_t __aHi = static_cast<uint32_t>(__a >> 32);
  const uint32_t __bLo = static_cast<uint32_t>(__b);
  const uint32_t __bHi = static_cast<uint32_t>(__b >> 32);

  const uint64_t __b00 = static_cast<uint64_t>(__aLo) * __bLo;
  const uint64_t __b01 = static_cast<uint64_t>(__aLo) * __bHi;
  const uint64_t __b10 = static_cast<uint64_t>(__aHi) * __bLo;
  const uint64_t __b11 = static_cast<uint64_t>(__aHi) * __bHi;

  const uint32_t __b00Lo = static_cast<uint32_t>(__b00);
  const uint32_t __b00Hi = static_cast<uint32_t>(__b00 >> 32);

  const uint64_t __mid1 = __b10 + __b00Hi;
  const uint32_t __mid1Lo = static_cast<uint32_t>(__mid1);
  const uint32_t __mid1Hi = static_cast<uint32_t>(__mid1 >> 32);

  const uint64_t __mid2 = __b01 + __mid1Lo;
  const uint32_t __mid2Lo = static_cast<uint32_t>(__mid2);
  const uint32_t __mid2Hi = static_cast<uint32_t>(__mid2 >> 32);

  const uint64_t __pHi = __b11 + __mid1Hi + __mid2Hi;
  const uint64_t __pLo = (static_cast<uint64_t>(__mid2Lo) << 32) | __b00Lo;

  *__productHi = __pHi;
  return __pLo;
}

#endif // ^^^ intrinsics unavailable ^^^

_NODISCARD inline uint64_t __ryu_shiftright128(const uint64_t __lo, const uint64_t __hi, const uint32_t __dist) {
#if defined(_M_X64) && !defined(_M_ARM64EC)
  // For the __shiftright128 intrinsic, the shift value is always
  // modulo 64.
  // In the current implementation of the double-precision version
  // of Ryu, the shift value is always < 64.
  // (The shift value is in the range [49, 58].)
  // Check this here in case a future change requires larger shift
  // values. In this case this function needs to be adjusted.
  _STL_INTERNAL_CHECK(__dist < 64);
  return __shiftright128(__lo, __hi, static_cast<unsigned char>(__dist));
#else // ^^^ defined(_M_X64) && !defined(_M_ARM64EC) / !defined(_M_X64) || defined(_M_ARM64EC) vvv
  // We don't need to handle the case __dist >= 64 here (see above).
  _STL_INTERNAL_CHECK(__dist < 64);
#if defined(_WIN64) || defined(_M_HYBRID_X86_ARM64)
  _STL_INTERNAL_CHECK(__dist > 0);
  return (__hi << (64 - __dist)) | (__lo >> __dist);
#else // ^^^ 64-bit or _M_HYBRID_X86_ARM64 / 32-bit vvv
  // Avoid a 64-bit shift by taking advantage of the range of shift values.
  _STL_INTERNAL_CHECK(__dist >= 32);
  return (__hi << (64 - __dist)) | (static_cast<uint32_t>(__lo >> 32) >> (__dist - 32));
#endif // ^^^ 32-bit ^^^
#endif // defined(_M_X64) && !defined(_M_ARM64EC)
}


#ifndef _WIN64

// Returns the high 64 bits of the 128-bit product of __a and __b.
_NODISCARD inline uint64_t __umulh(const uint64_t __a, const uint64_t __b) {
  // Reuse the __ryu_umul128 implementation.
  // Optimizers will likely eliminate the instructions used to compute the
  // low part of the product.
  uint64_t __hi;
  (void) __ryu_umul128(__a, __b, &__hi);
  return __hi;
}

// On 32-bit platforms, compilers typically generate calls to library
// functions for 64-bit divisions, even if the divisor is a constant.
//
// TRANSITION, LLVM-37932
//
// The functions here perform division-by-constant using multiplications
// in the same way as 64-bit compilers would do.
//
// NB:
// The multipliers and shift values are the ones generated by clang x64
// for expressions like x/5, x/10, etc.

_NODISCARD inline uint64_t __div5(const uint64_t __x) {
  return __umulh(__x, 0xCCCCCCCCCCCCCCCDu) >> 2;
}

_NODISCARD inline uint64_t __div10(const uint64_t __x) {
  return __umulh(__x, 0xCCCCCCCCCCCCCCCDu) >> 3;
}

_NODISCARD inline uint64_t __div100(const uint64_t __x) {
  return __umulh(__x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
}

_NODISCARD inline uint64_t __div1e8(const uint64_t __x) {
  return __umulh(__x, 0xABCC77118461CEFDu) >> 26;
}

_NODISCARD inline uint64_t __div1e9(const uint64_t __x) {
  return __umulh(__x >> 9, 0x44B82FA09B5A53u) >> 11;
}

_NODISCARD inline uint32_t __mod1e9(const uint64_t __x) {
  // Avoid 64-bit math as much as possible.
  // Returning static_cast<uint32_t>(__x - 1000000000 * __div1e9(__x)) would
  // perform 32x64-bit multiplication and 64-bit subtraction.
  // __x and 1000000000 * __div1e9(__x) are guaranteed to differ by
  // less than 10^9, so their highest 32 bits must be identical,
  // so we can truncate both sides to uint32_t before subtracting.
  // We can also simplify static_cast<uint32_t>(1000000000 * __div1e9(__x)).
  // We can truncate before multiplying instead of after, as multiplying
  // the highest 32 bits of __div1e9(__x) can't affect the lowest 32 bits.
  return static_cast<uint32_t>(__x) - 1000000000 * static_cast<uint32_t>(__div1e9(__x));
}

#else // ^^^ 32-bit / 64-bit vvv

_NODISCARD inline uint64_t __div5(const uint64_t __x) {
  return __x / 5;
}

_NODISCARD inline uint64_t __div10(const uint64_t __x) {
  return __x / 10;
}

_NODISCARD inline uint64_t __div100(const uint64_t __x) {
  return __x / 100;
}

_NODISCARD inline uint64_t __div1e8(const uint64_t __x) {
  return __x / 100000000;
}

_NODISCARD inline uint64_t __div1e9(const uint64_t __x) {
  return __x / 1000000000;
}

_NODISCARD inline uint32_t __mod1e9(const uint64_t __x) {
  return static_cast<uint32_t>(__x - 1000000000 * __div1e9(__x));
}

#endif // ^^^ 64-bit ^^^

_NODISCARD inline uint32_t __pow5Factor(uint64_t __value) {
  uint32_t __count = 0;
  for (;;) {
    _STL_INTERNAL_CHECK(__value != 0);
    const uint64_t __q = __div5(__value);
    const uint32_t __r = static_cast<uint32_t>(__value) - 5 * static_cast<uint32_t>(__q);
    if (__r != 0) {
      break;
    }
    __value = __q;
    ++__count;
  }
  return __count;
}

// Returns true if __value is divisible by 5^__p.
_NODISCARD inline bool __multipleOfPowerOf5(const uint64_t __value, const uint32_t __p) {
  // I tried a case distinction on __p, but there was no performance difference.
  return __pow5Factor(__value) >= __p;
}

// Returns true if __value is divisible by 2^__p.
_NODISCARD inline bool __multipleOfPowerOf2(const uint64_t __value, const uint32_t __p) {
  _STL_INTERNAL_CHECK(__value != 0);
  _STL_INTERNAL_CHECK(__p < 64);
  // return __builtin_ctzll(__value) >= __p;
  return (__value & ((1ull << __p) - 1)) == 0;
}

// ^^^^^^^^^^ DERIVED FROM d2s_intrinsics.h ^^^^^^^^^^

// vvvvvvvvvv DERIVED FROM d2fixed.c vvvvvvvvvv

inline constexpr int __POW10_ADDITIONAL_BITS = 120;

#if _HAS_CHARCONV_INTRINSICS
// Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b.
_NODISCARD inline uint64_t __umul256_hi128_lo64(
  const uint64_t __aHi, const uint64_t __aLo, const uint64_t __bHi, const uint64_t __bLo) {
  uint64_t __b00Hi;
  const uint64_t __b00Lo = __ryu_umul128(__aLo, __bLo, &__b00Hi);
  uint64_t __b01Hi;
  const uint64_t __b01Lo = __ryu_umul128(__aLo, __bHi, &__b01Hi);
  uint64_t __b10Hi;
  const uint64_t __b10Lo = __ryu_umul128(__aHi, __bLo, &__b10Hi);
  uint64_t __b11Hi;
  const uint64_t __b11Lo = __ryu_umul128(__aHi, __bHi, &__b11Hi);
  (void) __b00Lo; // unused
  (void) __b11Hi; // unused
  const uint64_t __temp1Lo = __b10Lo + __b00Hi;
  const uint64_t __temp1Hi = __b10Hi + (__temp1Lo < __b10Lo);
  const uint64_t __temp2Lo = __b01Lo + __temp1Lo;
  const uint64_t __temp2Hi = __b01Hi + (__temp2Lo < __b01Lo);
  return __b11Lo + __temp1Hi + __temp2Hi;
}

_NODISCARD inline uint32_t __uint128_mod1e9(const uint64_t __vHi, const uint64_t __vLo) {
  // After multiplying, we're going to shift right by 29, then truncate to uint32_t.
  // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting.
  const uint64_t __multiplied = __umul256_hi128_lo64(__vHi, __vLo, 0x89705F4136B4A597u, 0x31680A88F8953031u);

  // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h.
  const uint32_t __shifted = static_cast<uint32_t>(__multiplied >> 29);

  return static_cast<uint32_t>(__vLo) - 1000000000 * __shifted;
}
#endif // ^^^ intrinsics available ^^^

_NODISCARD inline uint32_t __mulShift_mod1e9(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) {
  uint64_t __high0;                                               // 64
  const uint64_t __low0 = __ryu_umul128(__m, __mul[0], &__high0); // 0
  uint64_t __high1;                                               // 128
  const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64
  uint64_t __high2;                                               // 192
  const uint64_t __low2 = __ryu_umul128(__m, __mul[2], &__high2); // 128
  const uint64_t __s0low = __low0;                  // 0
  (void) __s0low; // unused
  const uint64_t __s0high = __low1 + __high0;       // 64
  const uint32_t __c1 = __s0high < __low1;
  const uint64_t __s1low = __low2 + __high1 + __c1; // 128
  const uint32_t __c2 = __s1low < __low2; // __high1 + __c1 can't overflow, so compare against __low2
  const uint64_t __s1high = __high2 + __c2;         // 192
  _STL_INTERNAL_CHECK(__j >= 128);
  _STL_INTERNAL_CHECK(__j <= 180);
#if _HAS_CHARCONV_INTRINSICS
  const uint32_t __dist = static_cast<uint32_t>(__j - 128); // __dist: [0, 52]
  const uint64_t __shiftedhigh = __s1high >> __dist;
  const uint64_t __shiftedlow = __ryu_shiftright128(__s1low, __s1high, __dist);
  return __uint128_mod1e9(__shiftedhigh, __shiftedlow);
#else // ^^^ intrinsics available / intrinsics unavailable vvv
  if (__j < 160) { // __j: [128, 160)
    const uint64_t __r0 = __mod1e9(__s1high);
    const uint64_t __r1 = __mod1e9((__r0 << 32) | (__s1low >> 32));
    const uint64_t __r2 = ((__r1 << 32) | (__s1low & 0xffffffff));
    return __mod1e9(__r2 >> (__j - 128));
  } else { // __j: [160, 192)
    const uint64_t __r0 = __mod1e9(__s1high);
    const uint64_t __r1 = ((__r0 << 32) | (__s1low >> 32));
    return __mod1e9(__r1 >> (__j - 160));
  }
#endif // ^^^ intrinsics unavailable ^^^
}

#define _WIDEN(_TYPE, _CHAR) static_cast<_TYPE>(is_same_v<_TYPE, char> ? _CHAR : L##_CHAR)

template <class _CharT>
void __append_n_digits(const uint32_t __olength, uint32_t __digits, _CharT* const __result) {
  uint32_t __i = 0;
  while (__digits >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
    const uint32_t __c = __digits - 10000 * (__digits / 10000);
#else
    const uint32_t __c = __digits % 10000;
#endif
    __digits /= 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    _CSTD memcpy(__result + __olength - __i - 2, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 4, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    __i += 4;
  }
  if (__digits >= 100) {
    const uint32_t __c = (__digits % 100) << 1;
    __digits /= 100;
    _CSTD memcpy(__result + __olength - __i - 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    __i += 2;
  }
  if (__digits >= 10) {
    const uint32_t __c = __digits << 1;
    _CSTD memcpy(__result + __olength - __i - 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
  } else {
    __result[0] = static_cast<_CharT>(_WIDEN(_CharT, '0') + __digits);
  }
}

inline void __append_d_digits(const uint32_t __olength, uint32_t __digits, char* const __result) {
  uint32_t __i = 0;
  while (__digits >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
    const uint32_t __c = __digits - 10000 * (__digits / 10000);
#else
    const uint32_t __c = __digits % 10000;
#endif
    __digits /= 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    _CSTD memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE<char> + __c0, 2);
    _CSTD memcpy(__result + __olength + 1 - __i - 4, __DIGIT_TABLE<char> + __c1, 2);
    __i += 4;
  }
  if (__digits >= 100) {
    const uint32_t __c = (__digits % 100) << 1;
    __digits /= 100;
    _CSTD memcpy(__result + __olength + 1 - __i - 2, __DIGIT_TABLE<char> + __c, 2);
    __i += 2;
  }
  if (__digits >= 10) {
    const uint32_t __c = __digits << 1;
    __result[2] = __DIGIT_TABLE<char>[__c + 1];
    __result[1] = '.';
    __result[0] = __DIGIT_TABLE<char>[__c];
  } else {
    __result[1] = '.';
    __result[0] = static_cast<char>('0' + __digits);
  }
}

template <class _CharT>
void __append_c_digits(const uint32_t __count, uint32_t __digits, _CharT* const __result) {
  uint32_t __i = 0;
  for (; __i < __count - 1; __i += 2) {
    const uint32_t __c = (__digits % 100) << 1;
    __digits /= 100;
    _CSTD memcpy(__result + __count - __i - 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
  }
  if (__i < __count) {
    const _CharT __c = static_cast<_CharT>(_WIDEN(_CharT, '0') + (__digits % 10));
    __result[__count - __i - 1] = __c;
  }
}

template <class _CharT>
void __append_nine_digits(uint32_t __digits, _CharT* const __result) {
  if (__digits == 0) {
    _STD fill_n(__result, 9, _WIDEN(_CharT, '0'));
    return;
  }

  for (uint32_t __i = 0; __i < 5; __i += 4) {
#ifdef __clang__ // TRANSITION, LLVM-38217
    const uint32_t __c = __digits - 10000 * (__digits / 10000);
#else
    const uint32_t __c = __digits % 10000;
#endif
    __digits /= 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    _CSTD memcpy(__result + 7 - __i, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + 5 - __i, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
  }
  __result[0] = static_cast<_CharT>(_WIDEN(_CharT, '0') + __digits);
}

_NODISCARD inline uint32_t __indexForExponent(const uint32_t __e) {
  return (__e + 15) / 16;
}

_NODISCARD inline uint32_t __pow10BitsForIndex(const uint32_t __idx) {
  return 16 * __idx + __POW10_ADDITIONAL_BITS;
}

_NODISCARD inline uint32_t __lengthForIndex(const uint32_t __idx) {
  // +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9
  return (__log10Pow2(16 * static_cast<int32_t>(__idx)) + 1 + 16 + 8) / 9;
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> __d2fixed_buffered_n(_CharT* _First, _CharT* const _Last, const double __d,
  const uint32_t __precision) {
  _CharT* const _Original_first = _First;

  const uint64_t __bits = __double_to_bits(__d);

  // Case distinction; exit early for the easy cases.
  if (__bits == 0) {
    const int32_t _Total_zero_length = 1 // leading zero
      + static_cast<int32_t>(__precision != 0) // possible decimal point
      + static_cast<int32_t>(__precision); // zeroes after decimal point

    if (_Last - _First < _Total_zero_length) {
      return { _Last, errc::value_too_large };
    }

    *_First++ = _WIDEN(_CharT, '0');
    if (__precision > 0) {
      *_First++ = _WIDEN(_CharT, '.');
      _STD fill_n(_First, __precision, _WIDEN(_CharT, '0'));
      _First += __precision;
    }
    return { _First, errc{} };
  }

  // Decode __bits into mantissa and exponent.
  const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1);
  const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS);

  int32_t __e2;
  uint64_t __m2;
  if (__ieeeExponent == 0) {
    __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;
    __m2 = __ieeeMantissa;
  } else {
    __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;
    __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
  }

  bool __nonzero = false;
  if (__e2 >= -52) {
    const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast<uint32_t>(__e2));
    const uint32_t __p10bits = __pow10BitsForIndex(__idx);
    const int32_t __len = static_cast<int32_t>(__lengthForIndex(__idx));
    for (int32_t __i = __len - 1; __i >= 0; --__i) {
      const uint32_t __j = __p10bits - __e2;
      // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
      // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers.
      const uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i],
        static_cast<int32_t>(__j + 8));
      if (__nonzero) {
        if (_Last - _First < 9) {
          return { _Last, errc::value_too_large };
        }
        __append_nine_digits(__digits, _First);
        _First += 9;
      } else if (__digits != 0) {
        const uint32_t __olength = __decimalLength9(__digits);
        if (_Last - _First < static_cast<ptrdiff_t>(__olength)) {
          return { _Last, errc::value_too_large };
        }
        __append_n_digits(__olength, __digits, _First);
        _First += __olength;
        __nonzero = true;
      }
    }
  }
  if (!__nonzero) {
    if (_First == _Last) {
      return { _Last, errc::value_too_large };
    }
    *_First++ = _WIDEN(_CharT, '0');
  }
  if (__precision > 0) {
    if (_First == _Last) {
      return { _Last, errc::value_too_large };
    }
    *_First++ = _WIDEN(_CharT, '.');
  }
  if (__e2 < 0) {
    const int32_t __idx = -__e2 / 16;
    const uint32_t __blocks = __precision / 9 + 1;
    // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
    int __roundUp = 0;
    uint32_t __i = 0;
    if (__blocks <= __MIN_BLOCK_2[__idx]) {
      __i = __blocks;
      if (_Last - _First < static_cast<ptrdiff_t>(__precision)) {
        return { _Last, errc::value_too_large };
      }
      _STD fill_n(_First, __precision, _WIDEN(_CharT, '0'));
      _First += __precision;
    } else if (__i < __MIN_BLOCK_2[__idx]) {
      __i = __MIN_BLOCK_2[__idx];
      if (_Last - _First < static_cast<ptrdiff_t>(9 * __i)) {
        return { _Last, errc::value_too_large };
      }
      _STD fill_n(_First, 9 * __i, _WIDEN(_CharT, '0'));
      _First += 9 * __i;
    }
    for (; __i < __blocks; ++__i) {
      const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx);
      const uint32_t __p = __POW10_OFFSET_2[__idx] + __i - __MIN_BLOCK_2[__idx];
      if (__p >= __POW10_OFFSET_2[__idx + 1]) {
        // If the remaining digits are all 0, then we might as well use memset.
        // No rounding required in this case.
        const uint32_t __fill = __precision - 9 * __i;
        if (_Last - _First < static_cast<ptrdiff_t>(__fill)) {
          return { _Last, errc::value_too_large };
        }
        _STD fill_n(_First, __fill, _WIDEN(_CharT, '0'));
        _First += __fill;
        break;
      }
      // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
      // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers.
      uint32_t __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8);
      if (__i < __blocks - 1) {
        if (_Last - _First < 9) {
          return { _Last, errc::value_too_large };
        }
        __append_nine_digits(__digits, _First);
        _First += 9;
      } else {
        const uint32_t __maximum = __precision - 9 * __i;
        uint32_t __lastDigit = 0;
        for (uint32_t __k = 0; __k < 9 - __maximum; ++__k) {
          __lastDigit = __digits % 10;
          __digits /= 10;
        }
        if (__lastDigit != 5) {
          __roundUp = __lastDigit > 5;
        } else {
          // Is m * 10^(additionalDigits + 1) / 2^(-__e2) integer?
          const int32_t __requiredTwos = -__e2 - static_cast<int32_t>(__precision) - 1;
          const bool __trailingZeros = __requiredTwos <= 0
            || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast<uint32_t>(__requiredTwos)));
          __roundUp = __trailingZeros ? 2 : 1;
        }
        if (__maximum > 0) {
          if (_Last - _First < static_cast<ptrdiff_t>(__maximum)) {
            return { _Last, errc::value_too_large };
          }
          __append_c_digits(__maximum, __digits, _First);
          _First += __maximum;
        }
        break;
      }
    }
    if (__roundUp != 0) {
      _CharT* _Round = _First;
      _CharT* _Dot = _Last;
      while (true) {
        if (_Round == _Original_first) {
          _Round[0] = _WIDEN(_CharT, '1');
          if (_Dot != _Last) {
            _Dot[0] = _WIDEN(_CharT, '0');
            _Dot[1] = _WIDEN(_CharT, '.');
          }
          if (_First == _Last) {
            return { _Last, errc::value_too_large };
          }
          *_First++ = _WIDEN(_CharT, '0');
          break;
        }
        --_Round;
        const _CharT __c = _Round[0];
        if (__c == _WIDEN(_CharT, '.')) {
          _Dot = _Round;
        } else if (__c == _WIDEN(_CharT, '9')) {
          _Round[0] = _WIDEN(_CharT, '0');
          __roundUp = 1;
        } else {
          if (__roundUp == 1 || __c % 2 != 0) {
            _Round[0] = static_cast<_CharT>(__c + 1);
          }
          break;
        }
      }
    }
  } else {
    if (_Last - _First < static_cast<ptrdiff_t>(__precision)) {
      return { _Last, errc::value_too_large };
    }
    _STD fill_n(_First, __precision, _WIDEN(_CharT, '0'));
    _First += __precision;
  }
  return { _First, errc{} };
}

_NODISCARD inline to_chars_result __d2exp_buffered_n(char* _First, char* const _Last, const double __d,
  uint32_t __precision) {
  char* const _Original_first = _First;

  const uint64_t __bits = __double_to_bits(__d);

  // Case distinction; exit early for the easy cases.
  if (__bits == 0) {
    const int32_t _Total_zero_length = 1 // leading zero
      + static_cast<int32_t>(__precision != 0) // possible decimal point
      + static_cast<int32_t>(__precision) // zeroes after decimal point
      + 4; // "e+00"
    if (_Last - _First < _Total_zero_length) {
      return { _Last, errc::value_too_large };
    }
    *_First++ = '0';
    if (__precision > 0) {
      *_First++ = '.';
      _CSTD memset(_First, '0', __precision);
      _First += __precision;
    }
    _CSTD memcpy(_First, "e+00", 4);
    _First += 4;
    return { _First, errc{} };
  }

  // Decode __bits into mantissa and exponent.
  const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1);
  const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS);

  int32_t __e2;
  uint64_t __m2;
  if (__ieeeExponent == 0) {
    __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;
    __m2 = __ieeeMantissa;
  } else {
    __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;
    __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
  }

  const bool __printDecimalPoint = __precision > 0;
  ++__precision;
  uint32_t __digits = 0;
  uint32_t __printedDigits = 0;
  uint32_t __availableDigits = 0;
  int32_t __exp = 0;
  if (__e2 >= -52) {
    const uint32_t __idx = __e2 < 0 ? 0 : __indexForExponent(static_cast<uint32_t>(__e2));
    const uint32_t __p10bits = __pow10BitsForIndex(__idx);
    const int32_t __len = static_cast<int32_t>(__lengthForIndex(__idx));
    for (int32_t __i = __len - 1; __i >= 0; --__i) {
      const uint32_t __j = __p10bits - __e2;
      // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
      // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers.
      __digits = __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT[__POW10_OFFSET[__idx] + __i],
        static_cast<int32_t>(__j + 8));
      if (__printedDigits != 0) {
        if (__printedDigits + 9 > __precision) {
          __availableDigits = 9;
          break;
        }
        if (_Last - _First < 9) {
          return { _Last, errc::value_too_large };
        }
        __append_nine_digits(__digits, _First);
        _First += 9;
        __printedDigits += 9;
      } else if (__digits != 0) {
        __availableDigits = __decimalLength9(__digits);
        __exp = __i * 9 + static_cast<int32_t>(__availableDigits) - 1;
        if (__availableDigits > __precision) {
          break;
        }
        if (__printDecimalPoint) {
          if (_Last - _First < static_cast<ptrdiff_t>(__availableDigits + 1)) {
            return { _Last, errc::value_too_large };
          }
          __append_d_digits(__availableDigits, __digits, _First);
          _First += __availableDigits + 1; // +1 for decimal point
        } else {
          if (_First == _Last) {
            return { _Last, errc::value_too_large };
          }
          *_First++ = static_cast<char>('0' + __digits);
        }
        __printedDigits = __availableDigits;
        __availableDigits = 0;
      }
    }
  }

  if (__e2 < 0 && __availableDigits == 0) {
    const int32_t __idx = -__e2 / 16;
    for (int32_t __i = __MIN_BLOCK_2[__idx]; __i < 200; ++__i) {
      const int32_t __j = __ADDITIONAL_BITS_2 + (-__e2 - 16 * __idx);
      const uint32_t __p = __POW10_OFFSET_2[__idx] + static_cast<uint32_t>(__i) - __MIN_BLOCK_2[__idx];
      // Temporary: __j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
      // a slightly faster code path in __mulShift_mod1e9. Instead, we can just increase the multipliers.
      __digits = (__p >= __POW10_OFFSET_2[__idx + 1]) ? 0 : __mulShift_mod1e9(__m2 << 8, __POW10_SPLIT_2[__p], __j + 8);
      if (__printedDigits != 0) {
        if (__printedDigits + 9 > __precision) {
          __availableDigits = 9;
          break;
        }
        if (_Last - _First < 9) {
          return { _Last, errc::value_too_large };
        }
        __append_nine_digits(__digits, _First);
        _First += 9;
        __printedDigits += 9;
      } else if (__digits != 0) {
        __availableDigits = __decimalLength9(__digits);
        __exp = -(__i + 1) * 9 + static_cast<int32_t>(__availableDigits) - 1;
        if (__availableDigits > __precision) {
          break;
        }
        if (__printDecimalPoint) {
          if (_Last - _First < static_cast<ptrdiff_t>(__availableDigits + 1)) {
            return { _Last, errc::value_too_large };
          }
          __append_d_digits(__availableDigits, __digits, _First);
          _First += __availableDigits + 1; // +1 for decimal point
        } else {
          if (_First == _Last) {
            return { _Last, errc::value_too_large };
          }
          *_First++ = static_cast<char>('0' + __digits);
        }
        __printedDigits = __availableDigits;
        __availableDigits = 0;
      }
    }
  }

  const uint32_t __maximum = __precision - __printedDigits;
  if (__availableDigits == 0) {
    __digits = 0;
  }
  uint32_t __lastDigit = 0;
  if (__availableDigits > __maximum) {
    for (uint32_t __k = 0; __k < __availableDigits - __maximum; ++__k) {
      __lastDigit = __digits % 10;
      __digits /= 10;
    }
  }
  // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
  int __roundUp = 0;
  if (__lastDigit != 5) {
    __roundUp = __lastDigit > 5;
  } else {
    // Is m * 2^__e2 * 10^(__precision + 1 - __exp) integer?
    // __precision was already increased by 1, so we don't need to write + 1 here.
    const int32_t __rexp = static_cast<int32_t>(__precision) - __exp;
    const int32_t __requiredTwos = -__e2 - __rexp;
    bool __trailingZeros = __requiredTwos <= 0
      || (__requiredTwos < 60 && __multipleOfPowerOf2(__m2, static_cast<uint32_t>(__requiredTwos)));
    if (__rexp < 0) {
      const int32_t __requiredFives = -__rexp;
      __trailingZeros = __trailingZeros && __multipleOfPowerOf5(__m2, static_cast<uint32_t>(__requiredFives));
    }
    __roundUp = __trailingZeros ? 2 : 1;
  }
  if (__printedDigits != 0) {
    if (_Last - _First < static_cast<ptrdiff_t>(__maximum)) {
      return { _Last, errc::value_too_large };
    }
    if (__digits == 0) {
      _CSTD memset(_First, '0', __maximum);
    } else {
      __append_c_digits(__maximum, __digits, _First);
    }
    _First += __maximum;
  } else {
    if (__printDecimalPoint) {
      if (_Last - _First < static_cast<ptrdiff_t>(__maximum + 1)) {
        return { _Last, errc::value_too_large };
      }
      __append_d_digits(__maximum, __digits, _First);
      _First += __maximum + 1; // +1 for decimal point
    } else {
      if (_First == _Last) {
        return { _Last, errc::value_too_large };
      }
      *_First++ = static_cast<char>('0' + __digits);
    }
  }
  if (__roundUp != 0) {
    char* _Round = _First;
    while (true) {
      if (_Round == _Original_first) {
        _Round[0] = '1';
        ++__exp;
        break;
      }
      --_Round;
      const char __c = _Round[0];
      if (__c == '.') {
        // Keep going.
      } else if (__c == '9') {
        _Round[0] = '0';
        __roundUp = 1;
      } else {
        if (__roundUp == 1 || __c % 2 != 0) {
          _Round[0] = static_cast<char>(__c + 1);
        }
        break;
      }
    }
  }

  char _Sign_character;

  if (__exp < 0) {
    _Sign_character = '-';
    __exp = -__exp;
  } else {
    _Sign_character = '+';
  }

  const int _Exponent_part_length = __exp >= 100
    ? 5 // "e+NNN"
    : 4; // "e+NN"

  if (_Last - _First < _Exponent_part_length) {
    return { _Last, errc::value_too_large };
  }

  *_First++ = 'e';
  *_First++ = _Sign_character;

  if (__exp >= 100) {
    const int32_t __c = __exp % 10;
    _CSTD memcpy(_First, __DIGIT_TABLE<char> + 2 * (__exp / 10), 2);
    _First[2] = static_cast<char>('0' + __c);
    _First += 3;
  } else {
    _CSTD memcpy(_First, __DIGIT_TABLE<char> + 2 * __exp, 2);
    _First += 2;
  }

  return { _First, errc{} };
}

// ^^^^^^^^^^ DERIVED FROM d2fixed.c ^^^^^^^^^^

// vvvvvvvvvv DERIVED FROM f2s.c vvvvvvvvvv

inline constexpr int __FLOAT_MANTISSA_BITS = 23;
inline constexpr int __FLOAT_BIAS = 127;

// This table is generated by PrintFloatLookupTable.
inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59;
inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = {
  576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u,
  472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u,
  386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u,
  316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u,
  519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u,
  425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u,
  348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u,
  570899077082383953u, 456719261665907162u, 365375409332725730u
};
inline constexpr int __FLOAT_POW5_BITCOUNT = 61;
inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = {
  1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u,
  1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u,
  1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u,
  2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u,
  1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u,
  1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u,
  1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u,
  1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u,
  1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u,
  1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u,
  2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u,
  1292469707114105741u, 1615587133892632177u, 2019483917365790221u
};

_NODISCARD inline uint32_t __pow5Factor(uint32_t __value) {
  uint32_t __count = 0;
  for (;;) {
    _STL_INTERNAL_CHECK(__value != 0);
    const uint32_t __q = __value / 5;
    const uint32_t __r = __value % 5;
    if (__r != 0) {
      break;
    }
    __value = __q;
    ++__count;
  }
  return __count;
}

// Returns true if __value is divisible by 5^__p.
_NODISCARD inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) {
  return __pow5Factor(__value) >= __p;
}

// Returns true if __value is divisible by 2^__p.
_NODISCARD inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) {
  _STL_INTERNAL_CHECK(__value != 0);
  _STL_INTERNAL_CHECK(__p < 32);
  // return __builtin_ctz(__value) >= __p;
  return (__value & ((1u << __p) - 1)) == 0;
}

_NODISCARD inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) {
  _STL_INTERNAL_CHECK(__shift > 32);

  // The casts here help MSVC to avoid calls to the __allmul library
  // function.
  const uint32_t __factorLo = static_cast<uint32_t>(__factor);
  const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32);
  const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo;
  const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi;

#ifndef _WIN64
  // On 32-bit platforms we can avoid a 64-bit shift-right since we only
  // need the upper 32 bits of the result and the shift value is > 32.
  const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32);
  uint32_t __bits1Lo = static_cast<uint32_t>(__bits1);
  uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32);
  __bits1Lo += __bits0Hi;
  __bits1Hi += (__bits1Lo < __bits0Hi);
  const int32_t __s = __shift - 32;
  return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s);
#else // ^^^ 32-bit / 64-bit vvv
  const uint64_t __sum = (__bits0 >> 32) + __bits1;
  const uint64_t __shiftedSum = __sum >> (__shift - 32);
  _STL_INTERNAL_CHECK(__shiftedSum <= UINT32_MAX);
  return static_cast<uint32_t>(__shiftedSum);
#endif // ^^^ 64-bit ^^^
}

_NODISCARD inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) {
  return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j);
}

_NODISCARD inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) {
  return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j);
}

// A floating decimal representing m * 10^e.
struct __floating_decimal_32 {
  uint32_t __mantissa;
  int32_t __exponent;
};

_NODISCARD inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
  int32_t __e2;
  uint32_t __m2;
  if (__ieeeExponent == 0) {
    // We subtract 2 so that the bounds computation has 2 additional bits.
    __e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
    __m2 = __ieeeMantissa;
  } else {
    __e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
    __m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa;
  }
  const bool __even = (__m2 & 1) == 0;
  const bool __acceptBounds = __even;

  // Step 2: Determine the interval of valid decimal representations.
  const uint32_t __mv = 4 * __m2;
  const uint32_t __mp = 4 * __m2 + 2;
  // Implicit bool -> int conversion. True is 1, false is 0.
  const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;
  const uint32_t __mm = 4 * __m2 - 1 - __mmShift;

  // Step 3: Convert to a decimal power base using 64-bit arithmetic.
  uint32_t __vr, __vp, __vm;
  int32_t __e10;
  bool __vmIsTrailingZeros = false;
  bool __vrIsTrailingZeros = false;
  uint8_t __lastRemovedDigit = 0;
  if (__e2 >= 0) {
    const uint32_t __q = __log10Pow2(__e2);
    __e10 = static_cast<int32_t>(__q);
    const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;
    const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;
    __vr = __mulPow5InvDivPow2(__mv, __q, __i);
    __vp = __mulPow5InvDivPow2(__mp, __q, __i);
    __vm = __mulPow5InvDivPow2(__mm, __q, __i);
    if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
      // We need to know one removed digit even if we are not going to loop below. We could use
      // __q = X - 1 above, except that would require 33 bits for the result, and we've found that
      // 32-bit arithmetic is faster even on 64-bit machines.
      const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1;
      __lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1,
        -__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10);
    }
    if (__q <= 9) {
      // The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well.
      // Only one of __mp, __mv, and __mm can be a multiple of 5, if any.
      if (__mv % 5 == 0) {
        __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);
      } else if (__acceptBounds) {
        __vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q);
      } else {
        __vp -= __multipleOfPowerOf5(__mp, __q);
      }
    }
  } else {
    const uint32_t __q = __log10Pow5(-__e2);
    __e10 = static_cast<int32_t>(__q) + __e2;
    const int32_t __i = -__e2 - static_cast<int32_t>(__q);
    const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT;
    int32_t __j = static_cast<int32_t>(__q) - __k;
    __vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j);
    __vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j);
    __vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j);
    if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
      __j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT);
      __lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10);
    }
    if (__q <= 1) {
      // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.
      // __mv = 4 * __m2, so it always has at least two trailing 0 bits.
      __vrIsTrailingZeros = true;
      if (__acceptBounds) {
        // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.
        __vmIsTrailingZeros = __mmShift == 1;
      } else {
        // __mp = __mv + 2, so it always has at least one trailing 0 bit.
        --__vp;
      }
    } else if (__q < 31) { // TRANSITION(ulfjack): Use a tighter bound here.
      __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);
    }
  }

  // Step 4: Find the shortest decimal representation in the interval of valid representations.
  int32_t __removed = 0;
  uint32_t _Output;
  if (__vmIsTrailingZeros || __vrIsTrailingZeros) {
    // General case, which happens rarely (~4.0%).
    while (__vp / 10 > __vm / 10) {
#ifdef __clang__ // TRANSITION, LLVM-23106
      __vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0;
#else
      __vmIsTrailingZeros &= __vm % 10 == 0;
#endif
      __vrIsTrailingZeros &= __lastRemovedDigit == 0;
      __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
      __vr /= 10;
      __vp /= 10;
      __vm /= 10;
      ++__removed;
    }
    if (__vmIsTrailingZeros) {
      while (__vm % 10 == 0) {
        __vrIsTrailingZeros &= __lastRemovedDigit == 0;
        __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
        __vr /= 10;
        __vp /= 10;
        __vm /= 10;
        ++__removed;
      }
    }
    if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {
      // Round even if the exact number is .....50..0.
      __lastRemovedDigit = 4;
    }
    // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
    _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);
  } else {
    // Specialized for the common case (~96.0%). Percentages below are relative to this.
    // Loop iterations below (approximately):
    // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
    while (__vp / 10 > __vm / 10) {
      __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
      __vr /= 10;
      __vp /= 10;
      __vm /= 10;
      ++__removed;
    }
    // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
    _Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5);
  }
  const int32_t __exp = __e10 + __removed;

  __floating_decimal_32 __fd;
  __fd.__exponent = __exp;
  __fd.__mantissa = _Output;
  return __fd;
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> _Large_integer_to_chars(_CharT* const _First, _CharT* const _Last,
  const uint32_t _Mantissa2, const int32_t _Exponent2) {

  // Print the integer _Mantissa2 * 2^_Exponent2 exactly.

  // For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.
  // In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 to shift away
  // the zeros.) The dense range of exactly representable integers has negative or zero exponents
  // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:
  // every digit is necessary to uniquely identify the value, so Ryu must print them all.

  // Positive exponents are the non-dense range of exactly representable integers.
  // This contains all of the values for which Ryu can't be used (and a few Ryu-friendly values).

  // Performance note: Long division appears to be faster than losslessly widening float to double and calling
  // __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division.

  _STL_INTERNAL_CHECK(_Exponent2 > 0);
  _STL_INTERNAL_CHECK(_Exponent2 <= 104); // because __ieeeExponent <= 254

  // Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits
  // (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits.
  // 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements.
  // We use a little-endian representation, visualized like this:

  // << left shift <<
  // most significant
  // _Data[3] _Data[2] _Data[1] _Data[0]
  //                   least significant
  //                   >> right shift >>

  constexpr uint32_t _Data_size = 4;
  uint32_t _Data[_Data_size]{};

  // _Maxidx is the index of the most significant nonzero element.
  uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1;
  _STL_INTERNAL_CHECK(_Maxidx < _Data_size);

  const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32;
  if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary
    _Data[_Maxidx] = _Mantissa2 << _Bit_shift;
  } else { // _Mantissa2's 24 bits cross an element boundary
    _Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift;
    _Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift);
  }

  // If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left
  // by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440
  uint32_t _Blocks[4];
  int32_t _Filled_blocks = 0;
  // From left to right, we're going to print:
  // _Data[0] will be [1, 10] digits.
  // Then if _Filled_blocks > 0:
  // _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks.

  if (_Maxidx != 0) { // If the integer is actually large, perform long division.
                      // Otherwise, skip to printing _Data[0].
    for (;;) {
      // Loop invariant: _Maxidx != 0 (i.e. the integer is actually large)

      const uint32_t _Most_significant_elem = _Data[_Maxidx];
      const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000;
      const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000;
      _Data[_Maxidx] = _Initial_quotient;
      uint64_t _Remainder = _Initial_remainder;

      // Process less significant elements.
      uint32_t _Idx = _Maxidx;
      do {
        --_Idx; // Initially, _Remainder is at most 10^9 - 1.

        // Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1.
        _Remainder = (_Remainder << 32) | _Data[_Idx];

        // floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless.
        const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder));

        // _Remainder is at most 10^9 - 1 again.
        // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h.
        _Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient;

        _Data[_Idx] = _Quotient;
      } while (_Idx != 0);

      // Store a 0-filled 9-digit block.
      _Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder);

      if (_Initial_quotient == 0) { // Is the large integer shrinking?
        --_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element.
        if (_Maxidx == 0) {
          break; // We've finished long division. Now we need to print _Data[0].
        }
      }
    }
  }

  _STL_INTERNAL_CHECK(_Data[0] != 0);
  for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) {
    _STL_INTERNAL_CHECK(_Data[_Idx] == 0);
  }

  const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]);
  const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks;

  if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
    return { _Last, errc::value_too_large };
  }

  _CharT* _Result = _First;

  // Print _Data[0]. While it's up to 10 digits,
  // which is more than Ryu generates, the code below can handle this.
  __append_n_digits(_Data_olength, _Data[0], _Result);
  _Result += _Data_olength;

  // Print 0-filled 9-digit blocks.
  for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) {
    __append_nine_digits(_Blocks[_Idx], _Result);
    _Result += 9;
  }

  return { _Result, errc{} };
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> __to_chars(_CharT* const _First, _CharT* const _Last, const __floating_decimal_32 __v,
  chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
  // Step 5: Print the decimal representation.
  uint32_t _Output = __v.__mantissa;
  const int32_t _Ryu_exponent = __v.__exponent;
  const uint32_t __olength = __decimalLength9(_Output);
  int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;

  if (_Fmt == chars_format{}) {
    int32_t _Lower;
    int32_t _Upper;

    if (__olength == 1) {
      // Value | Fixed   | Scientific
      // 1e-3  | "0.001" | "1e-03"
      // 1e4   | "10000" | "1e+04"
      _Lower = -3;
      _Upper = 4;
    } else {
      // Value   | Fixed       | Scientific
      // 1234e-7 | "0.0001234" | "1.234e-04"
      // 1234e5  | "123400000" | "1.234e+08"
      _Lower = -static_cast<int32_t>(__olength + 3);
      _Upper = 5;
    }

    if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {
      _Fmt = chars_format::fixed;
    } else {
      _Fmt = chars_format::scientific;
    }
  } else if (_Fmt == chars_format::general) {
    // C11 7.21.6.1 "The fprintf function"/8:
    // "Let P equal [...] 6 if the precision is omitted [...].
    // Then, if a conversion with style E would have an exponent of X:
    // - if P > X >= -4, the conversion is with style f [...].
    // - otherwise, the conversion is with style e [...]."
    if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {
      _Fmt = chars_format::fixed;
    } else {
      _Fmt = chars_format::scientific;
    }
  }

  if (_Fmt == chars_format::fixed) {
    // Example: _Output == 1729, __olength == 4

    // _Ryu_exponent | Printed  | _Whole_digits | _Total_fixed_length  | Notes
    // --------------|----------|---------------|----------------------|---------------------------------------
    //             2 | 172900   |  6            | _Whole_digits        | Ryu can't be used for printing
    //             1 | 17290    |  5            | (sometimes adjusted) | when the trimmed digits are nonzero.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //             0 | 1729     |  4            | _Whole_digits        | Unified length cases.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //            -1 | 172.9    |  3            | __olength + 1        | This case can't happen for
    //            -2 | 17.29    |  2            |                      | __olength == 1, but no additional
    //            -3 | 1.729    |  1            |                      | code is needed to avoid it.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //            -4 | 0.1729   |  0            | 2 - _Ryu_exponent    | C11 7.21.6.1 "The fprintf function"/8:
    //            -5 | 0.01729  | -1            |                      | "If a decimal-point character appears,
    //            -6 | 0.001729 | -2            |                      | at least one digit appears before it."

    const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;

    uint32_t _Total_fixed_length;
    if (_Ryu_exponent >= 0) { // cases "172900" and "1729"
      _Total_fixed_length = static_cast<uint32_t>(_Whole_digits);
      if (_Output == 1) {
        // Rounding can affect the number of digits.
        // For example, 1e11f is exactly "99999997952" which is 11 digits instead of 12.
        // We can use a lookup table to detect this and adjust the total length.
        static constexpr uint8_t _Adjustment[39] = {
          0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1 };
        _Total_fixed_length -= _Adjustment[_Ryu_exponent];
        // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.
      }
    } else if (_Whole_digits > 0) { // case "17.29"
      _Total_fixed_length = __olength + 1;
    } else { // case "0.001729"
      _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);
    }

    if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
      return { _Last, errc::value_too_large };
    }

    _CharT* _Mid;
    if (_Ryu_exponent > 0) { // case "172900"
      bool _Can_use_ryu;

      if (_Ryu_exponent > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float.
        _Can_use_ryu = false;
      } else {
        // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent
        // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)
        // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent

        // _Trailing_zero_bits is [0, 29] (aside: because 2^29 is the largest power of 2
        // with 9 decimal digits, which is float's round-trip limit.)
        // _Ryu_exponent is [1, 10].
        // Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5).
        // This adds up to [3, 62], which is well below float's maximum binary exponent 127.

        // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.

        // If that product would exceed 24 bits, then X can't be exactly represented as a float.
        // (That's not a problem for round-tripping, because X is close enough to the original float,
        // but X isn't mathematically equal to the original float.) This requires a high-precision fallback.

        // If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't
        // need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the
        // same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled).

        // (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10
        static constexpr uint32_t _Max_shifted_mantissa[11] = {
          16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 };

        unsigned long _Trailing_zero_bits;
        (void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero
        const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;
        _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];
      }

      if (!_Can_use_ryu) {
        const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
        const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
          - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization

        // Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking.
        return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
      }

      // _Can_use_ryu
      // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).
      _Mid = _First + __olength;
    } else { // cases "1729", "17.29", and "0.001729"
      // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).
      _Mid = _First + _Total_fixed_length;
    }

    while (_Output >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
      const uint32_t __c = _Output - 10000 * (_Output / 10000);
#else
      const uint32_t __c = _Output % 10000;
#endif
      _Output /= 10000;
      const uint32_t __c0 = (__c % 100) << 1;
      const uint32_t __c1 = (__c / 100) << 1;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    }
    if (_Output >= 100) {
      const uint32_t __c = (_Output % 100) << 1;
      _Output /= 100;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    }
    if (_Output >= 10) {
      const uint32_t __c = _Output << 1;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    } else {
      *--_Mid = static_cast<_CharT>(_WIDEN(_CharT, '0') + _Output);
    }

    if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu
      // Performance note: it might be more efficient to do this immediately after setting _Mid.
      _STD fill_n(_First + __olength, _Ryu_exponent, _WIDEN(_CharT, '0'));
    } else if (_Ryu_exponent == 0) { // case "1729"
      // Done!
    } else if (_Whole_digits > 0) { // case "17.29"
      // Performance note: moving digits might not be optimal.
      _CSTD memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits) * sizeof(_CharT));
      _First[_Whole_digits] = _WIDEN(_CharT, '.');
    } else { // case "0.001729"
      // Performance note: a larger memset() followed by overwriting '.' might be more efficient.
      _First[0] = _WIDEN(_CharT, '0');
      _First[1] = _WIDEN(_CharT, '.');
      _STD fill_n(_First + 2, -_Whole_digits, _WIDEN(_CharT, '0'));
    }

    return { _First + _Total_fixed_length, errc{} };
  }

  const uint32_t _Total_scientific_length =
    __olength + (__olength > 1) + 4; // digits + possible decimal point + scientific exponent
  if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {
    return { _Last, errc::value_too_large };
  }
  _CharT* const __result = _First;

  // Print the decimal digits.
  uint32_t __i = 0;
  while (_Output >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
    const uint32_t __c = _Output - 10000 * (_Output / 10000);
#else
    const uint32_t __c = _Output % 10000;
#endif
    _Output /= 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    _CSTD memcpy(__result + __olength - __i - 1, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 3, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    __i += 4;
  }
  if (_Output >= 100) {
    const uint32_t __c = (_Output % 100) << 1;
    _Output /= 100;
    _CSTD memcpy(__result + __olength - __i - 1, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    __i += 2;
  }
  if (_Output >= 10) {
    const uint32_t __c = _Output << 1;
    // We can't use memcpy here: the decimal dot goes between these two digits.
    __result[2] = __DIGIT_TABLE<_CharT>[__c + 1];
    __result[0] = __DIGIT_TABLE<_CharT>[__c];
  } else {
    __result[0] = static_cast<_CharT>(_WIDEN(_CharT, '0') + _Output);
  }

  // Print decimal point if needed.
  uint32_t __index;
  if (__olength > 1) {
    __result[1] = _WIDEN(_CharT, '.');
    __index = __olength + 1;
  } else {
    __index = 1;
  }

  // Print the exponent.
  __result[__index++] = _WIDEN(_CharT, 'e');
  if (_Scientific_exponent < 0) {
    __result[__index++] = _WIDEN(_CharT, '-');
    _Scientific_exponent = -_Scientific_exponent;
  } else {
    __result[__index++] = _WIDEN(_CharT, '+');
  }

  _CSTD memcpy(__result + __index, __DIGIT_TABLE<_CharT> + 2 * _Scientific_exponent, 2 * sizeof(_CharT));
  __index += 2;

  return { _First + _Total_scientific_length, errc{} };
}

_NODISCARD inline to_chars_result _Convert_to_chars_result(const pair<char*, errc>& _Pair) {
    return {_Pair.first, _Pair.second};
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> __f2s_buffered_n(_CharT* const _First, _CharT* const _Last, const float __f,
  const chars_format _Fmt) {

  // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
  const uint32_t __bits = __float_to_bits(__f);

  // Case distinction; exit early for the easy cases.
  if (__bits == 0) {
    if (_Fmt == chars_format::scientific) {
      if (_Last - _First < 5) {
        return { _Last, errc::value_too_large };
      }

      if constexpr (is_same_v<_CharT, char>) {
        _CSTD memcpy(_First, "0e+00", 5);
      } else {
        _CSTD memcpy(_First, L"0e+00", 5 * sizeof(wchar_t));
      }

      return { _First + 5, errc{} };
    }

    // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.
    if (_First == _Last) {
      return { _Last, errc::value_too_large };
    }

    *_First = _WIDEN(_CharT, '0');

    return { _First + 1, errc{} };
  }

  // Decode __bits into mantissa and exponent.
  const uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1);
  const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS;

  // When _Fmt == chars_format::fixed and the floating-point number is a large integer,
  // it's faster to skip Ryu and immediately print the integer exactly.
  if (_Fmt == chars_format::fixed) {
    const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
    const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
      - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization

    // Normal values are equal to _Mantissa2 * 2^_Exponent2.
    // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)

    if (_Exponent2 > 0) {
      return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
    }
  }

  const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent);
  return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent);
}

// ^^^^^^^^^^ DERIVED FROM f2s.c ^^^^^^^^^^

// vvvvvvvvvv DERIVED FROM d2s.c vvvvvvvvvv

// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
// Multiplication:
//   The 64-bit factor is variable and passed in, the 128-bit factor comes
//   from a lookup table. We know that the 64-bit factor only has 55
//   significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
//   factor only has 124 significant bits (i.e., the 4 topmost bits are
//   zeros).
// Shift:
//   In principle, the multiplication result requires 55 + 124 = 179 bits to
//   represent. However, we then shift this value to the right by __j, which is
//   at least __j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
//   bits. This means that we only need the topmost 64 significant bits of
//   the 64x128-bit multiplication.
//
// There are several ways to do this:
// 1. Best case: the compiler exposes a 128-bit type.
//    We perform two 64x64-bit multiplications, add the higher 64 bits of the
//    lower result to the higher result, and shift by __j - 64 bits.
//
//    We explicitly cast from 64-bit to 128-bit, so the compiler can tell
//    that these are only 64-bit inputs, and can map these to the best
//    possible sequence of assembly instructions.
//    x64 machines happen to have matching assembly instructions for
//    64x64-bit multiplications and 128-bit shifts.
//
// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
//    instructions mentioned in 1.
//
// 3. We only have 64x64 bit instructions that return the lower 64 bits of
//    the result, i.e., we have to use plain C.
//    Our inputs are less than the full width, so we have three options:
//    a. Ignore this fact and just implement the intrinsics manually.
//    b. Split both into 31-bit pieces, which guarantees no internal overflow,
//       but requires extra work upfront (unless we change the lookup table).
//    c. Split only the first factor into 31-bit pieces, which also guarantees
//       no internal overflow, but requires extra work since the intermediate
//       results are not perfectly aligned.
#if _HAS_CHARCONV_INTRINSICS

_NODISCARD inline uint64_t __mulShift(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) {
  // __m is maximum 55 bits
  uint64_t __high1;                                               // 128
  const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64
  uint64_t __high0;                                               // 64
  (void) __ryu_umul128(__m, __mul[0], &__high0);                  // 0
  const uint64_t __sum = __high0 + __low1;
  if (__sum < __high0) {
    ++__high1; // overflow into __high1
  }
  return __ryu_shiftright128(__sum, __high1, static_cast<uint32_t>(__j - 64));
}

_NODISCARD inline uint64_t __mulShiftAll(const uint64_t __m, const uint64_t* const __mul, const int32_t __j,
  uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) {
  *__vp = __mulShift(4 * __m + 2, __mul, __j);
  *__vm = __mulShift(4 * __m - 1 - __mmShift, __mul, __j);
  return __mulShift(4 * __m, __mul, __j);
}

#else // ^^^ intrinsics available / intrinsics unavailable vvv

_NODISCARD __forceinline uint64_t __mulShiftAll(uint64_t __m, const uint64_t* const __mul, const int32_t __j,
  uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { // TRANSITION, VSO-634761
  __m <<= 1;
  // __m is maximum 55 bits
  uint64_t __tmp;
  const uint64_t __lo = __ryu_umul128(__m, __mul[0], &__tmp);
  uint64_t __hi;
  const uint64_t __mid = __tmp + __ryu_umul128(__m, __mul[1], &__hi);
  __hi += __mid < __tmp; // overflow into __hi

  const uint64_t __lo2 = __lo + __mul[0];
  const uint64_t __mid2 = __mid + __mul[1] + (__lo2 < __lo);
  const uint64_t __hi2 = __hi + (__mid2 < __mid);
  *__vp = __ryu_shiftright128(__mid2, __hi2, static_cast<uint32_t>(__j - 64 - 1));

  if (__mmShift == 1) {
    const uint64_t __lo3 = __lo - __mul[0];
    const uint64_t __mid3 = __mid - __mul[1] - (__lo3 > __lo);
    const uint64_t __hi3 = __hi - (__mid3 > __mid);
    *__vm = __ryu_shiftright128(__mid3, __hi3, static_cast<uint32_t>(__j - 64 - 1));
  } else {
    const uint64_t __lo3 = __lo + __lo;
    const uint64_t __mid3 = __mid + __mid + (__lo3 < __lo);
    const uint64_t __hi3 = __hi + __hi + (__mid3 < __mid);
    const uint64_t __lo4 = __lo3 - __mul[0];
    const uint64_t __mid4 = __mid3 - __mul[1] - (__lo4 > __lo3);
    const uint64_t __hi4 = __hi3 - (__mid4 > __mid3);
    *__vm = __ryu_shiftright128(__mid4, __hi4, static_cast<uint32_t>(__j - 64));
  }

  return __ryu_shiftright128(__mid, __hi, static_cast<uint32_t>(__j - 64 - 1));
}

#endif // ^^^ intrinsics unavailable ^^^

_NODISCARD inline uint32_t __decimalLength17(const uint64_t __v) {
  // This is slightly faster than a loop.
  // The average output length is 16.38 digits, so we check high-to-low.
  // Function precondition: __v is not an 18, 19, or 20-digit number.
  // (17 digits are sufficient for round-tripping.)
  _STL_INTERNAL_CHECK(__v < 100000000000000000u);
  if (__v >= 10000000000000000u) { return 17; }
  if (__v >= 1000000000000000u) { return 16; }
  if (__v >= 100000000000000u) { return 15; }
  if (__v >= 10000000000000u) { return 14; }
  if (__v >= 1000000000000u) { return 13; }
  if (__v >= 100000000000u) { return 12; }
  if (__v >= 10000000000u) { return 11; }
  if (__v >= 1000000000u) { return 10; }
  if (__v >= 100000000u) { return 9; }
  if (__v >= 10000000u) { return 8; }
  if (__v >= 1000000u) { return 7; }
  if (__v >= 100000u) { return 6; }
  if (__v >= 10000u) { return 5; }
  if (__v >= 1000u) { return 4; }
  if (__v >= 100u) { return 3; }
  if (__v >= 10u) { return 2; }
  return 1;
}

// A floating decimal representing m * 10^e.
struct __floating_decimal_64 {
  uint64_t __mantissa;
  int32_t __exponent;
};

_NODISCARD inline __floating_decimal_64 __d2d(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent) {
  int32_t __e2;
  uint64_t __m2;
  if (__ieeeExponent == 0) {
    // We subtract 2 so that the bounds computation has 2 additional bits.
    __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2;
    __m2 = __ieeeMantissa;
  } else {
    __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2;
    __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
  }
  const bool __even = (__m2 & 1) == 0;
  const bool __acceptBounds = __even;

  // Step 2: Determine the interval of valid decimal representations.
  const uint64_t __mv = 4 * __m2;
  // Implicit bool -> int conversion. True is 1, false is 0.
  const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;
  // We would compute __mp and __mm like this:
  // uint64_t __mp = 4 * __m2 + 2;
  // uint64_t __mm = __mv - 1 - __mmShift;

  // Step 3: Convert to a decimal power base using 128-bit arithmetic.
  uint64_t __vr, __vp, __vm;
  int32_t __e10;
  bool __vmIsTrailingZeros = false;
  bool __vrIsTrailingZeros = false;
  if (__e2 >= 0) {
    // I tried special-casing __q == 0, but there was no effect on performance.
    // This expression is slightly faster than max(0, __log10Pow2(__e2) - 1).
    const uint32_t __q = __log10Pow2(__e2) - (__e2 > 3);
    __e10 = static_cast<int32_t>(__q);
    const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;
    const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;
    __vr = __mulShiftAll(__m2, __DOUBLE_POW5_INV_SPLIT[__q], __i, &__vp, &__vm, __mmShift);
    if (__q <= 21) {
      // This should use __q <= 22, but I think 21 is also safe. Smaller values
      // may still be safe, but it's more difficult to reason about them.
      // Only one of __mp, __mv, and __mm can be a multiple of 5, if any.
      const uint32_t __mvMod5 = static_cast<uint32_t>(__mv) - 5 * static_cast<uint32_t>(__div5(__mv));
      if (__mvMod5 == 0) {
        __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);
      } else if (__acceptBounds) {
        // Same as min(__e2 + (~__mm & 1), __pow5Factor(__mm)) >= __q
        // <=> __e2 + (~__mm & 1) >= __q && __pow5Factor(__mm) >= __q
        // <=> true && __pow5Factor(__mm) >= __q, since __e2 >= __q.
        __vmIsTrailingZeros = __multipleOfPowerOf5(__mv - 1 - __mmShift, __q);
      } else {
        // Same as min(__e2 + 1, __pow5Factor(__mp)) >= __q.
        __vp -= __multipleOfPowerOf5(__mv + 2, __q);
      }
    }
  } else {
    // This expression is slightly faster than max(0, __log10Pow5(-__e2) - 1).
    const uint32_t __q = __log10Pow5(-__e2) - (-__e2 > 1);
    __e10 = static_cast<int32_t>(__q) + __e2;
    const int32_t __i = -__e2 - static_cast<int32_t>(__q);
    const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT;
    const int32_t __j = static_cast<int32_t>(__q) - __k;
    __vr = __mulShiftAll(__m2, __DOUBLE_POW5_SPLIT[__i], __j, &__vp, &__vm, __mmShift);
    if (__q <= 1) {
      // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.
      // __mv = 4 * __m2, so it always has at least two trailing 0 bits.
      __vrIsTrailingZeros = true;
      if (__acceptBounds) {
        // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.
        __vmIsTrailingZeros = __mmShift == 1;
      } else {
        // __mp = __mv + 2, so it always has at least one trailing 0 bit.
        --__vp;
      }
    } else if (__q < 63) { // TRANSITION(ulfjack): Use a tighter bound here.
      // We need to compute min(ntz(__mv), __pow5Factor(__mv) - __e2) >= __q - 1
      // <=> ntz(__mv) >= __q - 1 && __pow5Factor(__mv) - __e2 >= __q - 1
      // <=> ntz(__mv) >= __q - 1 (__e2 is negative and -__e2 >= __q)
      // <=> (__mv & ((1 << (__q - 1)) - 1)) == 0
      // We also need to make sure that the left shift does not overflow.
      __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);
    }
  }

  // Step 4: Find the shortest decimal representation in the interval of valid representations.
  int32_t __removed = 0;
  uint8_t __lastRemovedDigit = 0;
  uint64_t _Output;
  // On average, we remove ~2 digits.
  if (__vmIsTrailingZeros || __vrIsTrailingZeros) {
    // General case, which happens rarely (~0.7%).
    for (;;) {
      const uint64_t __vpDiv10 = __div10(__vp);
      const uint64_t __vmDiv10 = __div10(__vm);
      if (__vpDiv10 <= __vmDiv10) {
        break;
      }
      const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10);
      const uint64_t __vrDiv10 = __div10(__vr);
      const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
      __vmIsTrailingZeros &= __vmMod10 == 0;
      __vrIsTrailingZeros &= __lastRemovedDigit == 0;
      __lastRemovedDigit = static_cast<uint8_t>(__vrMod10);
      __vr = __vrDiv10;
      __vp = __vpDiv10;
      __vm = __vmDiv10;
      ++__removed;
    }
    if (__vmIsTrailingZeros) {
      for (;;) {
        const uint64_t __vmDiv10 = __div10(__vm);
        const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10);
        if (__vmMod10 != 0) {
          break;
        }
        const uint64_t __vpDiv10 = __div10(__vp);
        const uint64_t __vrDiv10 = __div10(__vr);
        const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
        __vrIsTrailingZeros &= __lastRemovedDigit == 0;
        __lastRemovedDigit = static_cast<uint8_t>(__vrMod10);
        __vr = __vrDiv10;
        __vp = __vpDiv10;
        __vm = __vmDiv10;
        ++__removed;
      }
    }
    if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {
      // Round even if the exact number is .....50..0.
      __lastRemovedDigit = 4;
    }
    // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
    _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);
  } else {
    // Specialized for the common case (~99.3%). Percentages below are relative to this.
    bool __roundUp = false;
    const uint64_t __vpDiv100 = __div100(__vp);
    const uint64_t __vmDiv100 = __div100(__vm);
    if (__vpDiv100 > __vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
      const uint64_t __vrDiv100 = __div100(__vr);
      const uint32_t __vrMod100 = static_cast<uint32_t>(__vr) - 100 * static_cast<uint32_t>(__vrDiv100);
      __roundUp = __vrMod100 >= 50;
      __vr = __vrDiv100;
      __vp = __vpDiv100;
      __vm = __vmDiv100;
      __removed += 2;
    }
    // Loop iterations below (approximately), without optimization above:
    // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
    // Loop iterations below (approximately), with optimization above:
    // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
    for (;;) {
      const uint64_t __vpDiv10 = __div10(__vp);
      const uint64_t __vmDiv10 = __div10(__vm);
      if (__vpDiv10 <= __vmDiv10) {
        break;
      }
      const uint64_t __vrDiv10 = __div10(__vr);
      const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
      __roundUp = __vrMod10 >= 5;
      __vr = __vrDiv10;
      __vp = __vpDiv10;
      __vm = __vmDiv10;
      ++__removed;
    }
    // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
    _Output = __vr + (__vr == __vm || __roundUp);
  }
  const int32_t __exp = __e10 + __removed;

  __floating_decimal_64 __fd;
  __fd.__exponent = __exp;
  __fd.__mantissa = _Output;
  return __fd;
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> __to_chars(_CharT* const _First, _CharT* const _Last, const __floating_decimal_64 __v,
  chars_format _Fmt, const double __f) {
  // Step 5: Print the decimal representation.
  uint64_t _Output = __v.__mantissa;
  const int32_t _Ryu_exponent = __v.__exponent;
  const uint32_t __olength = __decimalLength17(_Output);
  int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;

  if (_Fmt == chars_format{}) {
    int32_t _Lower;
    int32_t _Upper;

    if (__olength == 1) {
      // Value | Fixed   | Scientific
      // 1e-3  | "0.001" | "1e-03"
      // 1e4   | "10000" | "1e+04"
      _Lower = -3;
      _Upper = 4;
    } else {
      // Value   | Fixed       | Scientific
      // 1234e-7 | "0.0001234" | "1.234e-04"
      // 1234e5  | "123400000" | "1.234e+08"
      _Lower = -static_cast<int32_t>(__olength + 3);
      _Upper = 5;
    }

    if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {
      _Fmt = chars_format::fixed;
    } else {
      _Fmt = chars_format::scientific;
    }
  } else if (_Fmt == chars_format::general) {
    // C11 7.21.6.1 "The fprintf function"/8:
    // "Let P equal [...] 6 if the precision is omitted [...].
    // Then, if a conversion with style E would have an exponent of X:
    // - if P > X >= -4, the conversion is with style f [...].
    // - otherwise, the conversion is with style e [...]."
    if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {
      _Fmt = chars_format::fixed;
    } else {
      _Fmt = chars_format::scientific;
    }
  }

  if (_Fmt == chars_format::fixed) {
    // Example: _Output == 1729, __olength == 4

    // _Ryu_exponent | Printed  | _Whole_digits | _Total_fixed_length  | Notes
    // --------------|----------|---------------|----------------------|---------------------------------------
    //             2 | 172900   |  6            | _Whole_digits        | Ryu can't be used for printing
    //             1 | 17290    |  5            | (sometimes adjusted) | when the trimmed digits are nonzero.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //             0 | 1729     |  4            | _Whole_digits        | Unified length cases.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //            -1 | 172.9    |  3            | __olength + 1        | This case can't happen for
    //            -2 | 17.29    |  2            |                      | __olength == 1, but no additional
    //            -3 | 1.729    |  1            |                      | code is needed to avoid it.
    // --------------|----------|---------------|----------------------|---------------------------------------
    //            -4 | 0.1729   |  0            | 2 - _Ryu_exponent    | C11 7.21.6.1 "The fprintf function"/8:
    //            -5 | 0.01729  | -1            |                      | "If a decimal-point character appears,
    //            -6 | 0.001729 | -2            |                      | at least one digit appears before it."

    const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;

    uint32_t _Total_fixed_length;
    if (_Ryu_exponent >= 0) { // cases "172900" and "1729"
      _Total_fixed_length = static_cast<uint32_t>(_Whole_digits);
      if (_Output == 1) {
        // Rounding can affect the number of digits.
        // For example, 1e23 is exactly "99999999999999991611392" which is 23 digits instead of 24.
        // We can use a lookup table to detect this and adjust the total length.
        static constexpr uint8_t _Adjustment[309] = {
          0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,
          1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,1,
          1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,1,
          1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,
          0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1,
          1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,0,
          0,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0 };
        _Total_fixed_length -= _Adjustment[_Ryu_exponent];
        // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.
      }
    } else if (_Whole_digits > 0) { // case "17.29"
      _Total_fixed_length = __olength + 1;
    } else { // case "0.001729"
      _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);
    }

    if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
      return { _Last, errc::value_too_large };
    }

    _CharT* _Mid;
    if (_Ryu_exponent > 0) { // case "172900"
      bool _Can_use_ryu;

      if (_Ryu_exponent > 22) { // 10^22 is the largest power of 10 that's exactly representable as a double.
        _Can_use_ryu = false;
      } else {
        // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent
        // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)
        // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent

        // _Trailing_zero_bits is [0, 56] (aside: because 2^56 is the largest power of 2
        // with 17 decimal digits, which is double's round-trip limit.)
        // _Ryu_exponent is [1, 22].
        // Normalization adds [2, 52] (aside: at least 2 because the pre-normalized mantissa is at least 5).
        // This adds up to [3, 130], which is well below double's maximum binary exponent 1023.

        // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.

        // If that product would exceed 53 bits, then X can't be exactly represented as a double.
        // (That's not a problem for round-tripping, because X is close enough to the original double,
        // but X isn't mathematically equal to the original double.) This requires a high-precision fallback.

        // If the product is 53 bits or smaller, then X can be exactly represented as a double (and we don't
        // need to re-synthesize it; the original double must have been X, because Ryu wouldn't produce the
        // same output for two different doubles X and Y). This allows Ryu's output to be used (zero-filled).

        // (2^53 - 1) / 5^0 (for indexing), (2^53 - 1) / 5^1, ..., (2^53 - 1) / 5^22
        static constexpr uint64_t _Max_shifted_mantissa[23] = {
          9007199254740991u, 1801439850948198u, 360287970189639u, 72057594037927u, 14411518807585u,
          2882303761517u, 576460752303u, 115292150460u, 23058430092u, 4611686018u, 922337203u, 184467440u,
          36893488u, 7378697u, 1475739u, 295147u, 59029u, 11805u, 2361u, 472u, 94u, 18u, 3u };

        unsigned long _Trailing_zero_bits;
#ifdef _WIN64
        (void) _BitScanForward64(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero
#else // ^^^ 64-bit / 32-bit vvv
        const uint32_t _Low_mantissa = static_cast<uint32_t>(__v.__mantissa);
        if (_Low_mantissa != 0) {
          (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa);
        } else {
          const uint32_t _High_mantissa = static_cast<uint32_t>(__v.__mantissa >> 32); // nonzero here
          (void) _BitScanForward(&_Trailing_zero_bits, _High_mantissa);
          _Trailing_zero_bits += 32;
        }
#endif // ^^^ 32-bit ^^^
        const uint64_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;
        _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];
      }

      if (!_Can_use_ryu) {
        // Print the integer exactly.
        // Performance note: This will redundantly perform bounds checking.
        // Performance note: This will redundantly decompose the IEEE representation.
        return __d2fixed_buffered_n(_First, _Last, __f, 0);
      }

      // _Can_use_ryu
      // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).
      _Mid = _First + __olength;
    } else { // cases "1729", "17.29", and "0.001729"
      // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).
      _Mid = _First + _Total_fixed_length;
    }

    // We prefer 32-bit operations, even on 64-bit platforms.
    // We have at most 17 digits, and uint32_t can store 9 digits.
    // If _Output doesn't fit into uint32_t, we cut off 8 digits,
    // so the rest will fit into uint32_t.
    if ((_Output >> 32) != 0) {
      // Expensive 64-bit division.
      const uint64_t __q = __div1e8(_Output);
      uint32_t __output2 = static_cast<uint32_t>(_Output - 100000000 * __q);
      _Output = __q;

      const uint32_t __c = __output2 % 10000;
      __output2 /= 10000;
      const uint32_t __d = __output2 % 10000;
      const uint32_t __c0 = (__c % 100) << 1;
      const uint32_t __c1 = (__c / 100) << 1;
      const uint32_t __d0 = (__d % 100) << 1;
      const uint32_t __d1 = (__d / 100) << 1;

      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __d0, 2 * sizeof(_CharT));
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __d1, 2 * sizeof(_CharT));
    }
    uint32_t __output2 = static_cast<uint32_t>(_Output);
    while (__output2 >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
      const uint32_t __c = __output2 - 10000 * (__output2 / 10000);
#else
      const uint32_t __c = __output2 % 10000;
#endif
      __output2 /= 10000;
      const uint32_t __c0 = (__c % 100) << 1;
      const uint32_t __c1 = (__c / 100) << 1;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    }
    if (__output2 >= 100) {
      const uint32_t __c = (__output2 % 100) << 1;
      __output2 /= 100;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    }
    if (__output2 >= 10) {
      const uint32_t __c = __output2 << 1;
      _CSTD memcpy(_Mid -= 2, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    } else {
      *--_Mid = static_cast<_CharT>(_WIDEN(_CharT, '0') + __output2);
    }

    if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu
      // Performance note: it might be more efficient to do this immediately after setting _Mid.
      _STD fill_n(_First + __olength, _Ryu_exponent, _WIDEN(_CharT, '0'));
    } else if (_Ryu_exponent == 0) { // case "1729"
      // Done!
    } else if (_Whole_digits > 0) { // case "17.29"
      // Performance note: moving digits might not be optimal.
      _CSTD memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits) * sizeof(_CharT));
      _First[_Whole_digits] = _WIDEN(_CharT, '.');
    } else { // case "0.001729"
      // Performance note: a larger memset() followed by overwriting '.' might be more efficient.
      _First[0] = _WIDEN(_CharT, '0');
      _First[1] = _WIDEN(_CharT, '.');
      _STD fill_n(_First + 2, -_Whole_digits, _WIDEN(_CharT, '0'));
    }

    return { _First + _Total_fixed_length, errc{} };
  }

  const uint32_t _Total_scientific_length = __olength + (__olength > 1) // digits + possible decimal point
    + (-100 < _Scientific_exponent && _Scientific_exponent < 100 ? 4 : 5); // + scientific exponent
  if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {
    return { _Last, errc::value_too_large };
  }
  _CharT* const __result = _First;

  // Print the decimal digits.
  uint32_t __i = 0;
  // We prefer 32-bit operations, even on 64-bit platforms.
  // We have at most 17 digits, and uint32_t can store 9 digits.
  // If _Output doesn't fit into uint32_t, we cut off 8 digits,
  // so the rest will fit into uint32_t.
  if ((_Output >> 32) != 0) {
    // Expensive 64-bit division.
    const uint64_t __q = __div1e8(_Output);
    uint32_t __output2 = static_cast<uint32_t>(_Output) - 100000000 * static_cast<uint32_t>(__q);
    _Output = __q;

    const uint32_t __c = __output2 % 10000;
    __output2 /= 10000;
    const uint32_t __d = __output2 % 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    const uint32_t __d0 = (__d % 100) << 1;
    const uint32_t __d1 = (__d / 100) << 1;
    _CSTD memcpy(__result + __olength - __i - 1, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 3, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 5, __DIGIT_TABLE<_CharT> + __d0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 7, __DIGIT_TABLE<_CharT> + __d1, 2 * sizeof(_CharT));
    __i += 8;
  }
  uint32_t __output2 = static_cast<uint32_t>(_Output);
  while (__output2 >= 10000) {
#ifdef __clang__ // TRANSITION, LLVM-38217
    const uint32_t __c = __output2 - 10000 * (__output2 / 10000);
#else
    const uint32_t __c = __output2 % 10000;
#endif
    __output2 /= 10000;
    const uint32_t __c0 = (__c % 100) << 1;
    const uint32_t __c1 = (__c / 100) << 1;
    _CSTD memcpy(__result + __olength - __i - 1, __DIGIT_TABLE<_CharT> + __c0, 2 * sizeof(_CharT));
    _CSTD memcpy(__result + __olength - __i - 3, __DIGIT_TABLE<_CharT> + __c1, 2 * sizeof(_CharT));
    __i += 4;
  }
  if (__output2 >= 100) {
    const uint32_t __c = (__output2 % 100) << 1;
    __output2 /= 100;
    _CSTD memcpy(__result + __olength - __i - 1, __DIGIT_TABLE<_CharT> + __c, 2 * sizeof(_CharT));
    __i += 2;
  }
  if (__output2 >= 10) {
    const uint32_t __c = __output2 << 1;
    // We can't use memcpy here: the decimal dot goes between these two digits.
    __result[2] = __DIGIT_TABLE<_CharT>[__c + 1];
    __result[0] = __DIGIT_TABLE<_CharT>[__c];
  } else {
    __result[0] = static_cast<_CharT>(_WIDEN(_CharT, '0') + __output2);
  }

  // Print decimal point if needed.
  uint32_t __index;
  if (__olength > 1) {
    __result[1] = _WIDEN(_CharT, '.');
    __index = __olength + 1;
  } else {
    __index = 1;
  }

  // Print the exponent.
  __result[__index++] = _WIDEN(_CharT, 'e');
  if (_Scientific_exponent < 0) {
    __result[__index++] = _WIDEN(_CharT, '-');
    _Scientific_exponent = -_Scientific_exponent;
  } else {
    __result[__index++] = _WIDEN(_CharT, '+');
  }

  if (_Scientific_exponent >= 100) {
    const int32_t __c = _Scientific_exponent % 10;
    _CSTD memcpy(__result + __index, __DIGIT_TABLE<_CharT> + 2 * (_Scientific_exponent / 10), 2 * sizeof(_CharT));
    __result[__index + 2] = static_cast<_CharT>(_WIDEN(_CharT, '0') + __c);
    __index += 3;
  } else {
    _CSTD memcpy(__result + __index, __DIGIT_TABLE<_CharT> + 2 * _Scientific_exponent, 2 * sizeof(_CharT));
    __index += 2;
  }

  return { _First + _Total_scientific_length, errc{} };
}

_NODISCARD inline bool __d2d_small_int(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent,
  __floating_decimal_64* const __v) {
  const uint64_t __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
  const int32_t __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;

  if (__e2 > 0) {
    // f = __m2 * 2^__e2 >= 2^53 is an integer.
    // Ignore this case for now.
    return false;
  }

  if (__e2 < -52) {
    // f < 1.
    return false;
  }

  // Since 2^52 <= __m2 < 2^53 and 0 <= -__e2 <= 52: 1 <= f = __m2 / 2^-__e2 < 2^53.
  // Test if the lower -__e2 bits of the significand are 0, i.e. whether the fraction is 0.
  const uint64_t __mask = (1ull << -__e2) - 1;
  const uint64_t __fraction = __m2 & __mask;
  if (__fraction != 0) {
    return false;
  }

  // f is an integer in the range [1, 2^53).
  // Note: __mantissa might contain trailing (decimal) 0's.
  // Note: since 2^53 < 10^16, there is no need to adjust __decimalLength17().
  __v->__mantissa = __m2 >> -__e2;
  __v->__exponent = 0;
  return true;
}

template <class _CharT>
_NODISCARD pair<_CharT*, errc> __d2s_buffered_n(_CharT* const _First, _CharT* const _Last, const double __f,
  const chars_format _Fmt) {

  // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
  const uint64_t __bits = __double_to_bits(__f);

  // Case distinction; exit early for the easy cases.
  if (__bits == 0) {
    if (_Fmt == chars_format::scientific) {
      if (_Last - _First < 5) {
        return { _Last, errc::value_too_large };
      }

      if constexpr (is_same_v<_CharT, char>) {
        _CSTD memcpy(_First, "0e+00", 5);
      } else {
        _CSTD memcpy(_First, L"0e+00", 5 * sizeof(wchar_t));
      }

      return { _First + 5, errc{} };
    }

    // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.
    if (_First == _Last) {
      return { _Last, errc::value_too_large };
    }

    *_First = _WIDEN(_CharT, '0');

    return { _First + 1, errc{} };
  }

  // Decode __bits into mantissa and exponent.
  const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1);
  const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS);

  if (_Fmt == chars_format::fixed) {
    // const uint64_t _Mantissa2 = __ieeeMantissa | (1ull << __DOUBLE_MANTISSA_BITS); // restore implicit bit
    const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
      - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; // bias and normalization

    // Normal values are equal to _Mantissa2 * 2^_Exponent2.
    // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)

    // For nonzero integers, _Exponent2 >= -52. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.
    // In that case, _Mantissa2 is the implicit 1 bit followed by 52 zeros, so _Exponent2 is -52 to shift away
    // the zeros.) The dense range of exactly representable integers has negative or zero exponents
    // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:
    // every digit is necessary to uniquely identify the value, so Ryu must print them all.

    // Positive exponents are the non-dense range of exactly representable integers. This contains all of the values
    // for which Ryu can't be used (and a few Ryu-friendly values). We can save time by detecting positive
    // exponents here and skipping Ryu. Calling __d2fixed_buffered_n() with precision 0 is valid for all integers
    // (so it's okay if we call it with a Ryu-friendly value).
    if (_Exponent2 > 0) {
      return __d2fixed_buffered_n(_First, _Last, __f, 0);
    }
  }

  __floating_decimal_64 __v;
  const bool __isSmallInt = __d2d_small_int(__ieeeMantissa, __ieeeExponent, &__v);
  if (__isSmallInt) {
    // For small integers in the range [1, 2^53), __v.__mantissa might contain trailing (decimal) zeros.
    // For scientific notation we need to move these zeros into the exponent.
    // (This is not needed for fixed-point notation, so it might be beneficial to trim
    // trailing zeros in __to_chars only if needed - once fixed-point notation output is implemented.)
    for (;;) {
      const uint64_t __q = __div10(__v.__mantissa);
      const uint32_t __r = static_cast<uint32_t>(__v.__mantissa) - 10 * static_cast<uint32_t>(__q);
      if (__r != 0) {
        break;
      }
      __v.__mantissa = __q;
      ++__v.__exponent;
    }
  } else {
    __v = __d2d(__ieeeMantissa, __ieeeExponent);
  }

  return __to_chars(_First, _Last, __v, _Fmt, __f);
}

// ^^^^^^^^^^ DERIVED FROM d2s.c ^^^^^^^^^^

// clang-format on

template <class _Floating>
_NODISCARD to_chars_result _Floating_to_chars_ryu(
    char* const _First, char* const _Last, const _Floating _Value, const chars_format _Fmt) noexcept {
    if constexpr (is_same_v<_Floating, float>) {
        return _Convert_to_chars_result(__f2s_buffered_n(_First, _Last, _Value, _Fmt));
    } else {
        return _Convert_to_chars_result(__d2s_buffered_n(_First, _Last, _Value, _Fmt));
    }
}

template <class _Floating>
_NODISCARD to_chars_result _Floating_to_chars_scientific_precision(
    char* const _First, char* const _Last, const _Floating _Value, int _Precision) noexcept {

    // C11 7.21.6.1 "The fprintf function"/5:
    // "A negative precision argument is taken as if the precision were omitted."
    // /8: "e,E [...] if the precision is missing, it is taken as 6"

    if (_Precision < 0) {
        _Precision = 6;
    } else if (_Precision < 1'000'000'000) {
        // _Precision is ok.
    } else {
        // Avoid integer overflow.
        // (This defensive check is slightly nonconformant; it can be carefully improved in the future.)
        return {_Last, errc::value_too_large};
    }

    return __d2exp_buffered_n(_First, _Last, _Value, static_cast<uint32_t>(_Precision));
}

template <class _Floating>
_NODISCARD to_chars_result _Floating_to_chars_fixed_precision(
    char* const _First, char* const _Last, const _Floating _Value, int _Precision) noexcept {

    // C11 7.21.6.1 "The fprintf function"/5:
    // "A negative precision argument is taken as if the precision were omitted."
    // /8: "f,F [...] If the precision is missing, it is taken as 6"

    if (_Precision < 0) {
        _Precision = 6;
    } else if (_Precision < 1'000'000'000) {
        // _Precision is ok.
    } else {
        // Avoid integer overflow.
        // (This defensive check is slightly nonconformant; it can be carefully improved in the future.)
        return {_Last, errc::value_too_large};
    }

    return _Convert_to_chars_result(__d2fixed_buffered_n(_First, _Last, _Value, static_cast<uint32_t>(_Precision)));
}

_STD_END

#undef _HAS_CHARCONV_INTRINSICS
#undef _WIDEN

#pragma pop_macro("new")
_STL_RESTORE_CLANG_WARNINGS
#pragma warning(pop)
#pragma pack(pop)

#endif // _STL_COMPILER_PREPROCESSOR
#endif // _XCHARCONV_RYU_H