// fast_float by Daniel Lemire
// fast_float by João Paulo Magalhaes
//
// with contributions from Eugene Golushkov
// with contributions from Maksim Kita
// with contributions from Marcin Wojdyr
// with contributions from Neal Richardson
// with contributions from Tim Paine
// with contributions from Fabio Pellacini
// with contributions from Lénárd Szolnoki
//
// Licensed under the Apache License, Version 2.0, or the
// MIT License at your option. This file may not be copied,
// modified, or distributed except according to those terms.
//
// MIT License Notice
//
//    MIT License
//    
//    Copyright (c) 2021 The fast_float authors
//    
//    Permission is hereby granted, free of charge, to any
//    person obtaining a copy of this software and associated
//    documentation files (the "Software"), to deal in the
//    Software without restriction, including without
//    limitation the rights to use, copy, modify, merge,
//    publish, distribute, sublicense, and/or sell copies of
//    the Software, and to permit persons to whom the Software
//    is furnished to do so, subject to the following
//    conditions:
//    
//    The above copyright notice and this permission notice
//    shall be included in all copies or substantial portions
//    of the Software.
//    
//    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 AND NONINFRINGEMENT. IN NO EVENT
//    SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
//    CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
//    OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
//    IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
//    DEALINGS IN THE SOFTWARE.
//
// Apache License (Version 2.0) Notice
//
//    Copyright 2021 The fast_float authors
//    Licensed under the Apache License, Version 2.0 (the "License");
//    you may not use this file except in compliance with the License.
//    You may obtain a copy of the License at
//    
//    http://www.apache.org/licenses/LICENSE-2.0
//    
//    Unless required by applicable law or agreed to in writing, software
//    distributed under the License is distributed on an "AS IS" BASIS,
//    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
//    See the License for the specific language governing permissions and
//

#ifndef FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H
#define FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H

#ifdef __has_include
#if __has_include(<version>)
#include <version>
#endif
#endif

// Testing for https://wg21.link/N3652, adopted in C++14
#if __cpp_constexpr >= 201304
#define FASTFLOAT_CONSTEXPR14 constexpr
#else
#define FASTFLOAT_CONSTEXPR14
#endif

#if __cpp_lib_bit_cast >= 201806L
#define FASTFLOAT_HAS_BIT_CAST 1
#else
#define FASTFLOAT_HAS_BIT_CAST 0
#endif

#if __cpp_lib_is_constant_evaluated >= 201811L
#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 1
#else
#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 0
#endif

// Testing for relevant C++20 constexpr library features
#if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED \
    && FASTFLOAT_HAS_BIT_CAST \
    && __cpp_lib_constexpr_algorithms >= 201806L /*For std::copy and std::fill*/
#define FASTFLOAT_CONSTEXPR20 constexpr
#define FASTFLOAT_IS_CONSTEXPR 1
#else
#define FASTFLOAT_CONSTEXPR20
#define FASTFLOAT_IS_CONSTEXPR 0
#endif

#endif // FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H

#ifndef FASTFLOAT_FAST_FLOAT_H
#define FASTFLOAT_FAST_FLOAT_H

#include <system_error>


namespace fast_float {
enum chars_format {
    scientific = 1<<0,
    fixed = 1<<2,
    hex = 1<<3,
    general = fixed | scientific
};


struct from_chars_result {
  const char *ptr;
  std::errc ec;
};

struct parse_options {
  constexpr explicit parse_options(chars_format fmt = chars_format::general,
                         char dot = '.')
    : format(fmt), decimal_point(dot) {}

  /** Which number formats are accepted */
  chars_format format;
  /** The character used as decimal point */
  char decimal_point;
};

/**
 * This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
 * a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
 * The resulting floating-point value is the closest floating-point values (using either float or double),
 * using the "round to even" convention for values that would otherwise fall right in-between two values.
 * That is, we provide exact parsing according to the IEEE standard.
 *
 * Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
 * parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
 * `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
 *
 * The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
 *
 * Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
 * the type `fast_float::chars_format`. It is a bitset value: we check whether
 * `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
 * to determine whether we allow the fixed point and scientific notation respectively.
 * The default is  `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
 */
template<typename T>
FASTFLOAT_CONSTEXPR20
from_chars_result from_chars(const char *first, const char *last,
                             T &value, chars_format fmt = chars_format::general)  noexcept;

/**
 * Like from_chars, but accepts an `options` argument to govern number parsing.
 */
template<typename T>
FASTFLOAT_CONSTEXPR20
from_chars_result from_chars_advanced(const char *first, const char *last,
                                      T &value, parse_options options)  noexcept;

} // namespace fast_float
#endif // FASTFLOAT_FAST_FLOAT_H

#ifndef FASTFLOAT_FLOAT_COMMON_H
#define FASTFLOAT_FLOAT_COMMON_H

#include <cfloat>
#include <cstdint>
#include <cassert>
#include <cstring>
#include <type_traits>

#if FASTFLOAT_HAS_BIT_CAST
#include <bit>
#endif

#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)   \
       || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \
       || defined(__MINGW64__)                                          \
       || defined(__s390x__)                                            \
       || (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) )
#define FASTFLOAT_64BIT 1
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86)   \
     || defined(__arm__) || defined(_M_ARM) || defined(__ppc__)   \
     || defined(__MINGW32__) || defined(__EMSCRIPTEN__))
#define FASTFLOAT_32BIT 1
#else
  // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
  // We can never tell the register width, but the SIZE_MAX is a good approximation.
  // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
  #if SIZE_MAX == 0xffff
    #error Unknown platform (16-bit, unsupported)
  #elif SIZE_MAX == 0xffffffff
    #define FASTFLOAT_32BIT 1
  #elif SIZE_MAX == 0xffffffffffffffff
    #define FASTFLOAT_64BIT 1
  #else
    #error Unknown platform (not 32-bit, not 64-bit?)
  #endif
#endif

#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
#include <intrin.h>
#endif

#if defined(_MSC_VER) && !defined(__clang__)
#define FASTFLOAT_VISUAL_STUDIO 1
#endif

#if defined __BYTE_ORDER__ && defined __ORDER_BIG_ENDIAN__
#define FASTFLOAT_IS_BIG_ENDIAN (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__)
#elif defined _WIN32
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#if defined(__APPLE__) || defined(__FreeBSD__)
#include <machine/endian.h>
#elif defined(sun) || defined(__sun)
#include <sys/byteorder.h>
#else
#ifdef __has_include
#if __has_include(<endian.h>)
#include <endian.h>
#endif //__has_include(<endian.h>)
#endif //__has_include
#endif
#
#ifndef __BYTE_ORDER__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#ifndef __ORDER_LITTLE_ENDIAN__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#define FASTFLOAT_IS_BIG_ENDIAN 1
#endif
#endif

#ifdef FASTFLOAT_VISUAL_STUDIO
#define fastfloat_really_inline __forceinline
#else
#define fastfloat_really_inline inline __attribute__((always_inline))
#endif

#ifndef FASTFLOAT_ASSERT
#define FASTFLOAT_ASSERT(x)  { ((void)(x)); }
#endif

#ifndef FASTFLOAT_DEBUG_ASSERT
#define FASTFLOAT_DEBUG_ASSERT(x) { ((void)(x)); }
#endif

// rust style `try!()` macro, or `?` operator
#define FASTFLOAT_TRY(x) { if (!(x)) return false; }

namespace fast_float {

fastfloat_really_inline constexpr bool cpp20_and_in_constexpr() {
#if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED
  return std::is_constant_evaluated();
#else
  return false;
#endif
}

// Compares two ASCII strings in a case insensitive manner.
inline FASTFLOAT_CONSTEXPR14 bool
fastfloat_strncasecmp(const char *input1, const char *input2, size_t length) {
  char running_diff{0};
  for (size_t i = 0; i < length; i++) {
    running_diff |= (input1[i] ^ input2[i]);
  }
  return (running_diff == 0) || (running_diff == 32);
}

#ifndef FLT_EVAL_METHOD
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
#endif

// a pointer and a length to a contiguous block of memory
template <typename T>
struct span {
  const T* ptr;
  size_t length;
  constexpr span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {}
  constexpr span() : ptr(nullptr), length(0) {}

  constexpr size_t len() const noexcept {
    return length;
  }

  FASTFLOAT_CONSTEXPR14 const T& operator[](size_t index) const noexcept {
    FASTFLOAT_DEBUG_ASSERT(index < length);
    return ptr[index];
  }
};

struct value128 {
  uint64_t low;
  uint64_t high;
  constexpr value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
  constexpr value128() : low(0), high(0) {}
};

/* Helper C++11 constexpr generic implementation of leading_zeroes */
fastfloat_really_inline constexpr
int leading_zeroes_generic(uint64_t input_num, int last_bit = 0) {
  return (
    ((input_num & uint64_t(0xffffffff00000000)) && (input_num >>= 32, last_bit |= 32)),
    ((input_num & uint64_t(        0xffff0000)) && (input_num >>= 16, last_bit |= 16)),
    ((input_num & uint64_t(            0xff00)) && (input_num >>=  8, last_bit |=  8)),
    ((input_num & uint64_t(              0xf0)) && (input_num >>=  4, last_bit |=  4)),
    ((input_num & uint64_t(               0xc)) && (input_num >>=  2, last_bit |=  2)),
    ((input_num & uint64_t(               0x2)) && (input_num >>=  1, last_bit |=  1)),
    63 - last_bit
  );
}

/* result might be undefined when input_num is zero */
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
int leading_zeroes(uint64_t input_num) {
  assert(input_num > 0);
  if (cpp20_and_in_constexpr()) {
    return leading_zeroes_generic(input_num);
  }
#ifdef FASTFLOAT_VISUAL_STUDIO
  #if defined(_M_X64) || defined(_M_ARM64)
  unsigned long leading_zero = 0;
  // Search the mask data from most significant bit (MSB)
  // to least significant bit (LSB) for a set bit (1).
  _BitScanReverse64(&leading_zero, input_num);
  return (int)(63 - leading_zero);
  #else
  return leading_zeroes_generic(input_num);
  #endif
#else
  return __builtin_clzll(input_num);
#endif
}

// slow emulation routine for 32-bit
fastfloat_really_inline constexpr uint64_t emulu(uint32_t x, uint32_t y) {
    return x * (uint64_t)y;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t umul128_generic(uint64_t ab, uint64_t cd, uint64_t *hi) {
  uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
  uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
  uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
  uint64_t adbc_carry = !!(adbc < ad);
  uint64_t lo = bd + (adbc << 32);
  *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
        (adbc_carry << 32) + !!(lo < bd);
  return lo;
}

#ifdef FASTFLOAT_32BIT

// slow emulation routine for 32-bit
#if !defined(__MINGW64__)
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t _umul128(uint64_t ab, uint64_t cd, uint64_t *hi) {
  return umul128_generic(ab, cd, hi);
}
#endif // !__MINGW64__

#endif // FASTFLOAT_32BIT


// compute 64-bit a*b
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
value128 full_multiplication(uint64_t a, uint64_t b) {
  if (cpp20_and_in_constexpr()) {
    value128 answer;
    answer.low = umul128_generic(a, b, &answer.high);
    return answer;
  }
  value128 answer;
#if defined(_M_ARM64) && !defined(__MINGW32__)
  // ARM64 has native support for 64-bit multiplications, no need to emulate
  // But MinGW on ARM64 doesn't have native support for 64-bit multiplications
  answer.high = __umulh(a, b);
  answer.low = a * b;
#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
  answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
#elif defined(FASTFLOAT_64BIT)
  __uint128_t r = ((__uint128_t)a) * b;
  answer.low = uint64_t(r);
  answer.high = uint64_t(r >> 64);
#else
  answer.low = umul128_generic(a, b, &answer.high);
#endif
  return answer;
}

struct adjusted_mantissa {
  uint64_t mantissa{0};
  int32_t power2{0}; // a negative value indicates an invalid result
  adjusted_mantissa() = default;
  constexpr bool operator==(const adjusted_mantissa &o) const {
    return mantissa == o.mantissa && power2 == o.power2;
  }
  constexpr bool operator!=(const adjusted_mantissa &o) const {
    return mantissa != o.mantissa || power2 != o.power2;
  }
};

// Bias so we can get the real exponent with an invalid adjusted_mantissa.
constexpr static int32_t invalid_am_bias = -0x8000;

constexpr static double powers_of_ten_double[] = {
    1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
    1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
constexpr static float powers_of_ten_float[] = {1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f,
                                                1e6f, 1e7f, 1e8f, 1e9f, 1e10f};
// used for max_mantissa_double and max_mantissa_float
constexpr uint64_t constant_55555 = 5 * 5 * 5 * 5 * 5;
// Largest integer value v so that (5**index * v) <= 1<<53.
// 0x10000000000000 == 1 << 53
constexpr static uint64_t max_mantissa_double[] = {
      0x10000000000000,
      0x10000000000000 / 5,
      0x10000000000000 / (5 * 5),
      0x10000000000000 / (5 * 5 * 5),
      0x10000000000000 / (5 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555),
      0x10000000000000 / (constant_55555 * 5),
      0x10000000000000 / (constant_55555 * 5 * 5),
      0x10000000000000 / (constant_55555 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * 5 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555),
      0x10000000000000 / (constant_55555 * constant_55555 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5),
      0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5)};
  // Largest integer value v so that (5**index * v) <= 1<<24.
  // 0x1000000 == 1<<24
  constexpr static uint64_t max_mantissa_float[] = {
      0x1000000,
      0x1000000 / 5,
      0x1000000 / (5 * 5),
      0x1000000 / (5 * 5 * 5),
      0x1000000 / (5 * 5 * 5 * 5),
      0x1000000 / (constant_55555),
      0x1000000 / (constant_55555 * 5),
      0x1000000 / (constant_55555 * 5 * 5),
      0x1000000 / (constant_55555 * 5 * 5 * 5),
      0x1000000 / (constant_55555 * 5 * 5 * 5 * 5),
      0x1000000 / (constant_55555 * constant_55555),
      0x1000000 / (constant_55555 * constant_55555 * 5)};

template <typename T> struct binary_format {
  using equiv_uint = typename std::conditional<sizeof(T) == 4, uint32_t, uint64_t>::type;

  static inline constexpr int mantissa_explicit_bits();
  static inline constexpr int minimum_exponent();
  static inline constexpr int infinite_power();
  static inline constexpr int sign_index();
  static inline constexpr int min_exponent_fast_path(); // used when fegetround() == FE_TONEAREST
  static inline constexpr int max_exponent_fast_path();
  static inline constexpr int max_exponent_round_to_even();
  static inline constexpr int min_exponent_round_to_even();
  static inline constexpr uint64_t max_mantissa_fast_path(int64_t power);
  static inline constexpr uint64_t max_mantissa_fast_path(); // used when fegetround() == FE_TONEAREST
  static inline constexpr int largest_power_of_ten();
  static inline constexpr int smallest_power_of_ten();
  static inline constexpr T exact_power_of_ten(int64_t power);
  static inline constexpr size_t max_digits();
  static inline constexpr equiv_uint exponent_mask();
  static inline constexpr equiv_uint mantissa_mask();
  static inline constexpr equiv_uint hidden_bit_mask();
};

template <> inline constexpr int binary_format<double>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return 0;
#else
  return -22;
#endif
}

template <> inline constexpr int binary_format<float>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return 0;
#else
  return -10;
#endif
}

template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
  return 52;
}
template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
  return 23;
}

template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
  return 23;
}

template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
  return 10;
}

template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
  return -4;
}

template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
  return -17;
}

template <> inline constexpr int binary_format<double>::minimum_exponent() {
  return -1023;
}
template <> inline constexpr int binary_format<float>::minimum_exponent() {
  return -127;
}

template <> inline constexpr int binary_format<double>::infinite_power() {
  return 0x7FF;
}
template <> inline constexpr int binary_format<float>::infinite_power() {
  return 0xFF;
}

template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
template <> inline constexpr int binary_format<float>::sign_index() { return 31; }

template <> inline constexpr int binary_format<double>::max_exponent_fast_path() {
  return 22;
}
template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
  return 10;
}
template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
  return uint64_t(2) << mantissa_explicit_bits();
}
template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path(int64_t power) {
  // caller is responsible to ensure that
  // power >= 0 && power <= 22
  //
  return max_mantissa_double[power];
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
  return uint64_t(2) << mantissa_explicit_bits();
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path(int64_t power) {
  // caller is responsible to ensure that
  // power >= 0 && power <= 10
  //
  return max_mantissa_float[power];
}

template <>
inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
  return powers_of_ten_double[power];
}
template <>
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {

  return powers_of_ten_float[power];
}


template <>
inline constexpr int binary_format<double>::largest_power_of_ten() {
  return 308;
}
template <>
inline constexpr int binary_format<float>::largest_power_of_ten() {
  return 38;
}

template <>
inline constexpr int binary_format<double>::smallest_power_of_ten() {
  return -342;
}
template <>
inline constexpr int binary_format<float>::smallest_power_of_ten() {
  return -65;
}

template <> inline constexpr size_t binary_format<double>::max_digits() {
  return 769;
}
template <> inline constexpr size_t binary_format<float>::max_digits() {
  return 114;
}

template <> inline constexpr binary_format<float>::equiv_uint
    binary_format<float>::exponent_mask() {
  return 0x7F800000;
}
template <> inline constexpr binary_format<double>::equiv_uint
    binary_format<double>::exponent_mask() {
  return 0x7FF0000000000000;
}

template <> inline constexpr binary_format<float>::equiv_uint
    binary_format<float>::mantissa_mask() {
  return 0x007FFFFF;
}
template <> inline constexpr binary_format<double>::equiv_uint
    binary_format<double>::mantissa_mask() {
  return 0x000FFFFFFFFFFFFF;
}

template <> inline constexpr binary_format<float>::equiv_uint
    binary_format<float>::hidden_bit_mask() {
  return 0x00800000;
}
template <> inline constexpr binary_format<double>::equiv_uint
    binary_format<double>::hidden_bit_mask() {
  return 0x0010000000000000;
}

template<typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void to_float(bool negative, adjusted_mantissa am, T &value) {
  using uint = typename binary_format<T>::equiv_uint;
  uint word = (uint)am.mantissa;
  word |= uint(am.power2) << binary_format<T>::mantissa_explicit_bits();
  word |= uint(negative) << binary_format<T>::sign_index();
#if FASTFLOAT_HAS_BIT_CAST
  value = std::bit_cast<T>(word);
#else
  ::memcpy(&value, &word, sizeof(T));
#endif
}

#if FASTFLOAT_SKIP_WHITE_SPACE // disabled by default
template <typename = void>
struct space_lut {
  static constexpr bool value[] = {
    0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
};

template <typename T>
constexpr bool space_lut<T>::value[];

inline constexpr bool is_space(uint8_t c) { return space_lut<>::value[c]; }
#endif
} // namespace fast_float

#endif

#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H

#include <cctype>
#include <cstdint>
#include <cstring>
#include <iterator>


namespace fast_float {

// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline constexpr bool is_integer(char c) noexcept {
  return c >= '0' && c <= '9';
}

fastfloat_really_inline constexpr uint64_t byteswap(uint64_t val) {
  return (val & 0xFF00000000000000) >> 56
    | (val & 0x00FF000000000000) >> 40
    | (val & 0x0000FF0000000000) >> 24
    | (val & 0x000000FF00000000) >> 8
    | (val & 0x00000000FF000000) << 8
    | (val & 0x0000000000FF0000) << 24
    | (val & 0x000000000000FF00) << 40
    | (val & 0x00000000000000FF) << 56;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t read_u64(const char *chars) {
  if (cpp20_and_in_constexpr()) {
    uint64_t val = 0;
    for(int i = 0; i < 8; ++i) {
      val |= uint64_t(*chars) << (i*8);
      ++chars;
    }
    return val;
  }
  uint64_t val;
  ::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  return val;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void write_u64(uint8_t *chars, uint64_t val) {
  if (cpp20_and_in_constexpr()) {
    for(int i = 0; i < 8; ++i) {
      *chars = uint8_t(val);
      val >>= 8;
      ++chars;
    }
    return;
  }
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  ::memcpy(chars, &val, sizeof(uint64_t));
}

// credit  @aqrit
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint32_t parse_eight_digits_unrolled(uint64_t val) {
  const uint64_t mask = 0x000000FF000000FF;
  const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
  const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
  val -= 0x3030303030303030;
  val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
  val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
  return uint32_t(val);
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
  return parse_eight_digits_unrolled(read_u64(chars));
}

// credit @aqrit
fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val)  noexcept  {
  return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
     0x8080808080808080));
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_made_of_eight_digits_fast(const char *chars)  noexcept  {
  return is_made_of_eight_digits_fast(read_u64(chars));
}

typedef span<const char> byte_span;

struct parsed_number_string {
  int64_t exponent{0};
  uint64_t mantissa{0};
  const char *lastmatch{nullptr};
  bool negative{false};
  bool valid{false};
  bool too_many_digits{false};
  // contains the range of the significant digits
  byte_span integer{};  // non-nullable
  byte_span fraction{}; // nullable
};

// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
  const chars_format fmt = options.format;
  const char decimal_point = options.decimal_point;

  parsed_number_string answer;
  answer.valid = false;
  answer.too_many_digits = false;
  answer.negative = (*p == '-');
#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
  if ((*p == '-') || (*p == '+')) {
#else
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
#endif
    ++p;
    if (p == pend) {
      return answer;
    }
    if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
      return answer;
    }
  }
  const char *const start_digits = p;

  uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)

  while ((p != pend) && is_integer(*p)) {
    // a multiplication by 10 is cheaper than an arbitrary integer
    // multiplication
    i = 10 * i +
        uint64_t(*p - '0'); // might overflow, we will handle the overflow later
    ++p;
  }
  const char *const end_of_integer_part = p;
  int64_t digit_count = int64_t(end_of_integer_part - start_digits);
  answer.integer = byte_span(start_digits, size_t(digit_count));
  int64_t exponent = 0;
  if ((p != pend) && (*p == decimal_point)) {
    ++p;
    const char* before = p;
    // can occur at most twice without overflowing, but let it occur more, since
    // for integers with many digits, digit parsing is the primary bottleneck.
    while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
      i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
      p += 8;
    }
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      ++p;
      i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
    }
    exponent = before - p;
    answer.fraction = byte_span(before, size_t(p - before));
    digit_count -= exponent;
  }
  // we must have encountered at least one integer!
  if (digit_count == 0) {
    return answer;
  }
  int64_t exp_number = 0;            // explicit exponential part
  if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
    const char * location_of_e = p;
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    if ((p == pend) || !is_integer(*p)) {
      if(!(fmt & chars_format::fixed)) {
        // We are in error.
        return answer;
      }
      // Otherwise, we will be ignoring the 'e'.
      p = location_of_e;
    } else {
      while ((p != pend) && is_integer(*p)) {
        uint8_t digit = uint8_t(*p - '0');
        if (exp_number < 0x10000000) {
          exp_number = 10 * exp_number + digit;
        }
        ++p;
      }
      if(neg_exp) { exp_number = - exp_number; }
      exponent += exp_number;
    }
  } else {
    // If it scientific and not fixed, we have to bail out.
    if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
  }
  answer.lastmatch = p;
  answer.valid = true;

  // If we frequently had to deal with long strings of digits,
  // we could extend our code by using a 128-bit integer instead
  // of a 64-bit integer. However, this is uncommon.
  //
  // We can deal with up to 19 digits.
  if (digit_count > 19) { // this is uncommon
    // It is possible that the integer had an overflow.
    // We have to handle the case where we have 0.0000somenumber.
    // We need to be mindful of the case where we only have zeroes...
    // E.g., 0.000000000...000.
    const char *start = start_digits;
    while ((start != pend) && (*start == '0' || *start == decimal_point)) {
      if(*start == '0') { digit_count --; }
      start++;
    }
    if (digit_count > 19) {
      answer.too_many_digits = true;
      // Let us start again, this time, avoiding overflows.
      // We don't need to check if is_integer, since we use the
      // pre-tokenized spans from above.
      i = 0;
      p = answer.integer.ptr;
      const char* int_end = p + answer.integer.len();
      const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
      while((i < minimal_nineteen_digit_integer) && (p != int_end)) {
        i = i * 10 + uint64_t(*p - '0');
        ++p;
      }
      if (i >= minimal_nineteen_digit_integer) { // We have a big integers
        exponent = end_of_integer_part - p + exp_number;
      } else { // We have a value with a fractional component.
          p = answer.fraction.ptr;
          const char* frac_end = p + answer.fraction.len();
          while((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
            i = i * 10 + uint64_t(*p - '0');
            ++p;
          }
          exponent = answer.fraction.ptr - p + exp_number;
      }
      // We have now corrected both exponent and i, to a truncated value
    }
  }
  answer.exponent = exponent;
  answer.mantissa = i;
  return answer;
}

} // namespace fast_float

#endif

#ifndef FASTFLOAT_FAST_TABLE_H
#define FASTFLOAT_FAST_TABLE_H

#include <cstdint>

namespace fast_float {

/**
 * When mapping numbers from decimal to binary,
 * we go from w * 10^q to m * 2^p but we have
 * 10^q = 5^q * 2^q, so effectively
 * we are trying to match
 * w * 2^q * 5^q to m * 2^p. Thus the powers of two
 * are not a concern since they can be represented
 * exactly using the binary notation, only the powers of five
 * affect the binary significand.
 */

/**
 * The smallest non-zero float (binary64) is 2^-1074.
 * We take as input numbers of the form w x 10^q where w < 2^64.
 * We have that w * 10^-343  <  2^(64-344) 5^-343 < 2^-1076.
 * However, we have that
 * (2^64-1) * 10^-342 =  (2^64-1) * 2^-342 * 5^-342 > 2^-1074.
 * Thus it is possible for a number of the form w * 10^-342 where
 * w is a 64-bit value to be a non-zero floating-point number.
 *********
 * Any number of form w * 10^309 where w>= 1 is going to be
 * infinite in binary64 so we never need to worry about powers
 * of 5 greater than 308.
 */
template <class unused = void>
struct powers_template {

constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
constexpr static uint64_t power_of_five_128[number_of_entries] = {
    0xeef453d6923bd65a,0x113faa2906a13b3f,
    0x9558b4661b6565f8,0x4ac7ca59a424c507,
    0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
    0xe95a99df8ace6f53,0xf4d82c2c107973dc,
    0x91d8a02bb6c10594,0x79071b9b8a4be869,
    0xb64ec836a47146f9,0x9748e2826cdee284,
    0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
    0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
    0xb208ef855c969f4f,0xbdbd2d335e51a935,
    0xde8b2b66b3bc4723,0xad2c788035e61382,
    0x8b16fb203055ac76,0x4c3bcb5021afcc31,
    0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
    0xd953e8624b85dd78,0xd71d6dad34a2af0d,
    0x87d4713d6f33aa6b,0x8672648c40e5ad68,
    0xa9c98d8ccb009506,0x680efdaf511f18c2,
    0xd43bf0effdc0ba48,0x212bd1b2566def2,
    0x84a57695fe98746d,0x14bb630f7604b57,
    0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
    0xcf42894a5dce35ea,0x52064cac828675b9,
    0x818995ce7aa0e1b2,0x7343efebd1940993,
    0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
    0xca66fa129f9b60a6,0xd41a26e077774ef6,
    0xfd00b897478238d0,0x8920b098955522b4,
    0x9e20735e8cb16382,0x55b46e5f5d5535b0,
    0xc5a890362fddbc62,0xeb2189f734aa831d,
    0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
    0x9a6bb0aa55653b2d,0x47b233c92125366e,
    0xc1069cd4eabe89f8,0x999ec0bb696e840a,
    0xf148440a256e2c76,0xc00670ea43ca250d,
    0x96cd2a865764dbca,0x380406926a5e5728,
    0xbc807527ed3e12bc,0xc605083704f5ecf2,
    0xeba09271e88d976b,0xf7864a44c633682e,
    0x93445b8731587ea3,0x7ab3ee6afbe0211d,
    0xb8157268fdae9e4c,0x5960ea05bad82964,
    0xe61acf033d1a45df,0x6fb92487298e33bd,
    0x8fd0c16206306bab,0xa5d3b6d479f8e056,
    0xb3c4f1ba87bc8696,0x8f48a4899877186c,
    0xe0b62e2929aba83c,0x331acdabfe94de87,
    0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
    0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
    0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
    0x892731ac9faf056e,0xbe311c083a225cd2,
    0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
    0xd64d3d9db981787d,0x92cbbccdad5b108,
    0x85f0468293f0eb4e,0x25bbf56008c58ea5,
    0xa76c582338ed2621,0xaf2af2b80af6f24e,
    0xd1476e2c07286faa,0x1af5af660db4aee1,
    0x82cca4db847945ca,0x50d98d9fc890ed4d,
    0xa37fce126597973c,0xe50ff107bab528a0,
    0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
    0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
    0x9faacf3df73609b1,0x77b191618c54e9ac,
    0xc795830d75038c1d,0xd59df5b9ef6a2417,
    0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
    0x9becce62836ac577,0x4ee367f9430aec32,
    0xc2e801fb244576d5,0x229c41f793cda73f,
    0xf3a20279ed56d48a,0x6b43527578c1110f,
    0x9845418c345644d6,0x830a13896b78aaa9,
    0xbe5691ef416bd60c,0x23cc986bc656d553,
    0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
    0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
    0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
    0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
    0x91376c36d99995be,0x23100809b9c21fa1,
    0xb58547448ffffb2d,0xabd40a0c2832a78a,
    0xe2e69915b3fff9f9,0x16c90c8f323f516c,
    0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
    0xb1442798f49ffb4a,0x99cd11cfdf41779c,
    0xdd95317f31c7fa1d,0x40405643d711d583,
    0x8a7d3eef7f1cfc52,0x482835ea666b2572,
    0xad1c8eab5ee43b66,0xda3243650005eecf,
    0xd863b256369d4a40,0x90bed43e40076a82,
    0x873e4f75e2224e68,0x5a7744a6e804a291,
    0xa90de3535aaae202,0x711515d0a205cb36,
    0xd3515c2831559a83,0xd5a5b44ca873e03,
    0x8412d9991ed58091,0xe858790afe9486c2,
    0xa5178fff668ae0b6,0x626e974dbe39a872,
    0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
    0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
    0xa139029f6a239f72,0x1c1fffc1ebc44e80,
    0xc987434744ac874e,0xa327ffb266b56220,
    0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
    0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
    0xc4ce17b399107c22,0xcb550fb4384d21d3,
    0xf6019da07f549b2b,0x7e2a53a146606a48,
    0x99c102844f94e0fb,0x2eda7444cbfc426d,
    0xc0314325637a1939,0xfa911155fefb5308,
    0xf03d93eebc589f88,0x793555ab7eba27ca,
    0x96267c7535b763b5,0x4bc1558b2f3458de,
    0xbbb01b9283253ca2,0x9eb1aaedfb016f16,
    0xea9c227723ee8bcb,0x465e15a979c1cadc,
    0x92a1958a7675175f,0xbfacd89ec191ec9,
    0xb749faed14125d36,0xcef980ec671f667b,
    0xe51c79a85916f484,0x82b7e12780e7401a,
    0x8f31cc0937ae58d2,0xd1b2ecb8b0908810,
    0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15,
    0xdfbdcece67006ac9,0x67a791e093e1d49a,
    0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0,
    0xaecc49914078536d,0x58fae9f773886e18,
    0xda7f5bf590966848,0xaf39a475506a899e,
    0x888f99797a5e012d,0x6d8406c952429603,
    0xaab37fd7d8f58178,0xc8e5087ba6d33b83,
    0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64,
    0x855c3be0a17fcd26,0x5cf2eea09a55067f,
    0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e,
    0xd0601d8efc57b08b,0xf13b94daf124da26,
    0x823c12795db6ce57,0x76c53d08d6b70858,
    0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
    0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
    0xfe5d54150b090b02,0xd3f93b35435d7c4c,
    0x9efa548d26e5a6e1,0xc47bc5014a1a6daf,
    0xc6b8e9b0709f109a,0x359ab6419ca1091b,
    0xf867241c8cc6d4c0,0xc30163d203c94b62,
    0x9b407691d7fc44f8,0x79e0de63425dcf1d,
    0xc21094364dfb5636,0x985915fc12f542e4,
    0xf294b943e17a2bc4,0x3e6f5b7b17b2939d,
    0x979cf3ca6cec5b5a,0xa705992ceecf9c42,
    0xbd8430bd08277231,0x50c6ff782a838353,
    0xece53cec4a314ebd,0xa4f8bf5635246428,
    0x940f4613ae5ed136,0x871b7795e136be99,
    0xb913179899f68584,0x28e2557b59846e3f,
    0xe757dd7ec07426e5,0x331aeada2fe589cf,
    0x9096ea6f3848984f,0x3ff0d2c85def7621,
    0xb4bca50b065abe63,0xfed077a756b53a9,
    0xe1ebce4dc7f16dfb,0xd3e8495912c62894,
    0x8d3360f09cf6e4bd,0x64712dd7abbbd95c,
    0xb080392cc4349dec,0xbd8d794d96aacfb3,
    0xdca04777f541c567,0xecf0d7a0fc5583a0,
    0x89e42caaf9491b60,0xf41686c49db57244,
    0xac5d37d5b79b6239,0x311c2875c522ced5,
    0xd77485cb25823ac7,0x7d633293366b828b,
    0x86a8d39ef77164bc,0xae5dff9c02033197,
    0xa8530886b54dbdeb,0xd9f57f830283fdfc,
    0xd267caa862a12d66,0xd072df63c324fd7b,
    0x8380dea93da4bc60,0x4247cb9e59f71e6d,
    0xa46116538d0deb78,0x52d9be85f074e608,
    0xcd795be870516656,0x67902e276c921f8b,
    0x806bd9714632dff6,0xba1cd8a3db53b6,
    0xa086cfcd97bf97f3,0x80e8a40eccd228a4,
    0xc8a883c0fdaf7df0,0x6122cd128006b2cd,
    0xfad2a4b13d1b5d6c,0x796b805720085f81,
    0x9cc3a6eec6311a63,0xcbe3303674053bb0,
    0xc3f490aa77bd60fc,0xbedbfc4411068a9c,
    0xf4f1b4d515acb93b,0xee92fb5515482d44,
    0x991711052d8bf3c5,0x751bdd152d4d1c4a,
    0xbf5cd54678eef0b6,0xd262d45a78a0635d,
    0xef340a98172aace4,0x86fb897116c87c34,
    0x9580869f0e7aac0e,0xd45d35e6ae3d4da0,
    0xbae0a846d2195712,0x8974836059cca109,
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};

template <class unused>
constexpr uint64_t powers_template<unused>::power_of_five_128[number_of_entries];

using powers = powers_template<>;

} // namespace fast_float

#endif

#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
#define FASTFLOAT_DECIMAL_TO_BINARY_H

#include <cfloat>
#include <cinttypes>
#include <cmath>
#include <cstdint>
#include <cstdlib>
#include <cstring>

namespace fast_float {

// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
// the result, with the "high" part corresponding to the most significant bits and the
// low part corresponding to the least significant bits.
//
template <int bit_precision>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
value128 compute_product_approximation(int64_t q, uint64_t w) {
  const int index = 2 * int(q - powers::smallest_power_of_five);
  // For small values of q, e.g., q in [0,27], the answer is always exact because
  // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
  // gives the exact answer.
  value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
  static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should  be in (0,64]");
  constexpr uint64_t precision_mask = (bit_precision < 64) ?
               (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
               : uint64_t(0xFFFFFFFFFFFFFFFF);
  if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with  (lower + w < lower)
    // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
    value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
    firstproduct.low += secondproduct.high;
    if(secondproduct.high > firstproduct.low) {
      firstproduct.high++;
    }
  }
  return firstproduct;
}

namespace detail {
/**
 * For q in (0,350), we have that
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to
 *   floor(p) + q
 * where
 *   p = log(5**q)/log(2) = q * log(5)/log(2)
 *
 * For negative values of q in (-400,0), we have that 
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to 
 *   -ceil(p) + q
 * where
 *   p = log(5**-q)/log(2) = -q * log(5)/log(2)
 */
  constexpr fastfloat_really_inline int32_t power(int32_t q)  noexcept  {
    return (((152170 + 65536) * q) >> 16) + 63;
  }
} // namespace detail

// create an adjusted mantissa, biased by the invalid power2
// for significant digits already multiplied by 10 ** q.
template <typename binary>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept  {
  int hilz = int(w >> 63) ^ 1;
  adjusted_mantissa answer;
  answer.mantissa = w << hilz;
  int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent();
  answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias);
  return answer;
}

// w * 10 ** q, without rounding the representation up.
// the power2 in the exponent will be adjusted by invalid_am_bias.
template <typename binary>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa compute_error(int64_t q, uint64_t w)  noexcept  {
  int lz = leading_zeroes(w);
  w <<= lz;
  value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
  return compute_error_scaled<binary>(q, product.high, lz);
}

// w * 10 ** q
// The returned value should be a valid ieee64 number that simply need to be packed.
// However, in some very rare cases, the computation will fail. In such cases, we
// return an adjusted_mantissa with a negative power of 2: the caller should recompute
// in such cases.
template <typename binary>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa compute_float(int64_t q, uint64_t w)  noexcept  {
  adjusted_mantissa answer;
  if ((w == 0) || (q < binary::smallest_power_of_ten())) {
    answer.power2 = 0;
    answer.mantissa = 0;
    // result should be zero
    return answer;
  }
  if (q > binary::largest_power_of_ten()) {
    // we want to get infinity:
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
    return answer;
  }
  // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].

  // We want the most significant bit of i to be 1. Shift if needed.
  int lz = leading_zeroes(w);
  w <<= lz;

  // The required precision is binary::mantissa_explicit_bits() + 3 because
  // 1. We need the implicit bit
  // 2. We need an extra bit for rounding purposes
  // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)

  value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
  // The computed 'product' is always sufficient.
  // Mathematical proof:
  // Noble Mushtak and Daniel Lemire, Fast Number Parsing Without Fallback (to appear)
  // See script/mushtak_lemire.py

  // The "compute_product_approximation" function can be slightly slower than a branchless approach:
  // value128 product = compute_product(q, w);
  // but in practice, we can win big with the compute_product_approximation if its additional branch
  // is easily predicted. Which is best is data specific.
  int upperbit = int(product.high >> 63);

  answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);

  answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent());
  if (answer.power2 <= 0) { // we have a subnormal?
    // Here have that answer.power2 <= 0 so -answer.power2 >= 0
    if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
      answer.power2 = 0;
      answer.mantissa = 0;
      // result should be zero
      return answer;
    }
    // next line is safe because -answer.power2 + 1 < 64
    answer.mantissa >>= -answer.power2 + 1;
    // Thankfully, we can't have both "round-to-even" and subnormals because
    // "round-to-even" only occurs for powers close to 0.
    answer.mantissa += (answer.mantissa & 1); // round up
    answer.mantissa >>= 1;
    // There is a weird scenario where we don't have a subnormal but just.
    // Suppose we start with 2.2250738585072013e-308, we end up
    // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
    // whereas 0x40000000000000 x 2^-1023-53  is normal. Now, we need to round
    // up 0x3fffffffffffff x 2^-1023-53  and once we do, we are no longer
    // subnormal, but we can only know this after rounding.
    // So we only declare a subnormal if we are smaller than the threshold.
    answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
    return answer;
  }

  // usually, we round *up*, but if we fall right in between and and we have an
  // even basis, we need to round down
  // We are only concerned with the cases where 5**q fits in single 64-bit word.
  if ((product.low <= 1) &&  (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
      ((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
    // To be in-between two floats we need that in doing
    //   answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
    // ... we dropped out only zeroes. But if this happened, then we can go back!!!
    if((answer.mantissa  << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) ==  product.high) {
      answer.mantissa &= ~uint64_t(1);          // flip it so that we do not round up
    }
  }

  answer.mantissa += (answer.mantissa & 1); // round up
  answer.mantissa >>= 1;
  if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
    answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
    answer.power2++; // undo previous addition
  }

  answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
  if (answer.power2 >= binary::infinite_power()) { // infinity
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
  }
  return answer;
}

} // namespace fast_float

#endif

#ifndef FASTFLOAT_BIGINT_H
#define FASTFLOAT_BIGINT_H

#include <algorithm>
#include <cstdint>
#include <climits>
#include <cstring>


namespace fast_float {

// the limb width: we want efficient multiplication of double the bits in
// limb, or for 64-bit limbs, at least 64-bit multiplication where we can
// extract the high and low parts efficiently. this is every 64-bit
// architecture except for sparc, which emulates 128-bit multiplication.
// we might have platforms where `CHAR_BIT` is not 8, so let's avoid
// doing `8 * sizeof(limb)`.
#if defined(FASTFLOAT_64BIT) && !defined(__sparc)
#define FASTFLOAT_64BIT_LIMB 1
typedef uint64_t limb;
constexpr size_t limb_bits = 64;
#else
#define FASTFLOAT_32BIT_LIMB
typedef uint32_t limb;
constexpr size_t limb_bits = 32;
#endif

typedef span<limb> limb_span;

// number of bits in a bigint. this needs to be at least the number
// of bits required to store the largest bigint, which is
// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or
// ~3600 bits, so we round to 4000.
constexpr size_t bigint_bits = 4000;
constexpr size_t bigint_limbs = bigint_bits / limb_bits;

// vector-like type that is allocated on the stack. the entire
// buffer is pre-allocated, and only the length changes.
template <uint16_t size>
struct stackvec {
  limb data[size];
  // we never need more than 150 limbs
  uint16_t length{0};

  stackvec() = default;
  stackvec(const stackvec &) = delete;
  stackvec &operator=(const stackvec &) = delete;
  stackvec(stackvec &&) = delete;
  stackvec &operator=(stackvec &&other) = delete;

  // create stack vector from existing limb span.
  FASTFLOAT_CONSTEXPR20 stackvec(limb_span s) {
    FASTFLOAT_ASSERT(try_extend(s));
  }

  FASTFLOAT_CONSTEXPR14 limb& operator[](size_t index) noexcept {
    FASTFLOAT_DEBUG_ASSERT(index < length);
    return data[index];
  }
  FASTFLOAT_CONSTEXPR14 const limb& operator[](size_t index) const noexcept {
    FASTFLOAT_DEBUG_ASSERT(index < length);
    return data[index];
  }
  // index from the end of the container
  FASTFLOAT_CONSTEXPR14 const limb& rindex(size_t index) const noexcept {
    FASTFLOAT_DEBUG_ASSERT(index < length);
    size_t rindex = length - index - 1;
    return data[rindex];
  }

  // set the length, without bounds checking.
  FASTFLOAT_CONSTEXPR14 void set_len(size_t len) noexcept {
    length = uint16_t(len);
  }
  constexpr size_t len() const noexcept {
    return length;
  }
  constexpr bool is_empty() const noexcept {
    return length == 0;
  }
  constexpr size_t capacity() const noexcept {
    return size;
  }
  // append item to vector, without bounds checking
  FASTFLOAT_CONSTEXPR14 void push_unchecked(limb value) noexcept {
    data[length] = value;
    length++;
  }
  // append item to vector, returning if item was added
  FASTFLOAT_CONSTEXPR14 bool try_push(limb value) noexcept {
    if (len() < capacity()) {
      push_unchecked(value);
      return true;
    } else {
      return false;
    }
  }
  // add items to the vector, from a span, without bounds checking
  FASTFLOAT_CONSTEXPR20 void extend_unchecked(limb_span s) noexcept {
    limb* ptr = data + length;
    std::copy_n(s.ptr, s.len(), ptr);
    set_len(len() + s.len());
  }
  // try to add items to the vector, returning if items were added
  FASTFLOAT_CONSTEXPR20 bool try_extend(limb_span s) noexcept {
    if (len() + s.len() <= capacity()) {
      extend_unchecked(s);
      return true;
    } else {
      return false;
    }
  }
  // resize the vector, without bounds checking
  // if the new size is longer than the vector, assign value to each
  // appended item.
  FASTFLOAT_CONSTEXPR20
  void resize_unchecked(size_t new_len, limb value) noexcept {
    if (new_len > len()) {
      size_t count = new_len - len();
      limb* first = data + len();
      limb* last = first + count;
      ::std::fill(first, last, value);
      set_len(new_len);
    } else {
      set_len(new_len);
    }
  }
  // try to resize the vector, returning if the vector was resized.
  FASTFLOAT_CONSTEXPR20 bool try_resize(size_t new_len, limb value) noexcept {
    if (new_len > capacity()) {
      return false;
    } else {
      resize_unchecked(new_len, value);
      return true;
    }
  }
  // check if any limbs are non-zero after the given index.
  // this needs to be done in reverse order, since the index
  // is relative to the most significant limbs.
  FASTFLOAT_CONSTEXPR14 bool nonzero(size_t index) const noexcept {
    while (index < len()) {
      if (rindex(index) != 0) {
        return true;
      }
      index++;
    }
    return false;
  }
  // normalize the big integer, so most-significant zero limbs are removed.
  FASTFLOAT_CONSTEXPR14 void normalize() noexcept {
    while (len() > 0 && rindex(0) == 0) {
      length--;
    }
  }
};

fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint64_t empty_hi64(bool& truncated) noexcept {
  truncated = false;
  return 0;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept {
  truncated = false;
  int shl = leading_zeroes(r0);
  return r0 << shl;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept {
  int shl = leading_zeroes(r0);
  if (shl == 0) {
    truncated = r1 != 0;
    return r0;
  } else {
    int shr = 64 - shl;
    truncated = (r1 << shl) != 0;
    return (r0 << shl) | (r1 >> shr);
  }
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept {
  return uint64_hi64(r0, truncated);
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, bool& truncated) noexcept {
  uint64_t x0 = r0;
  uint64_t x1 = r1;
  return uint64_hi64((x0 << 32) | x1, truncated);
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept {
  uint64_t x0 = r0;
  uint64_t x1 = r1;
  uint64_t x2 = r2;
  return uint64_hi64(x0, (x1 << 32) | x2, truncated);
}

// add two small integers, checking for overflow.
// we want an efficient operation. for msvc, where
// we don't have built-in intrinsics, this is still
// pretty fast.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
limb scalar_add(limb x, limb y, bool& overflow) noexcept {
  limb z;
// gcc and clang
#if defined(__has_builtin)
  #if __has_builtin(__builtin_add_overflow)
    if (!cpp20_and_in_constexpr()) {
      overflow = __builtin_add_overflow(x, y, &z);
      return z;
    }
  #endif
#endif

  // generic, this still optimizes correctly on MSVC.
  z = x + y;
  overflow = z < x;
  return z;
}

// multiply two small integers, getting both the high and low bits.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
limb scalar_mul(limb x, limb y, limb& carry) noexcept {
#ifdef FASTFLOAT_64BIT_LIMB
  #if defined(__SIZEOF_INT128__)
  // GCC and clang both define it as an extension.
  __uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry);
  carry = limb(z >> limb_bits);
  return limb(z);
  #else
  // fallback, no native 128-bit integer multiplication with carry.
  // on msvc, this optimizes identically, somehow.
  value128 z = full_multiplication(x, y);
  bool overflow;
  z.low = scalar_add(z.low, carry, overflow);
  z.high += uint64_t(overflow);  // cannot overflow
  carry = z.high;
  return z.low;
  #endif
#else
  uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry);
  carry = limb(z >> limb_bits);
  return limb(z);
#endif
}

// add scalar value to bigint starting from offset.
// used in grade school multiplication
template <uint16_t size>
inline FASTFLOAT_CONSTEXPR20
bool small_add_from(stackvec<size>& vec, limb y, size_t start) noexcept {
  size_t index = start;
  limb carry = y;
  bool overflow;
  while (carry != 0 && index < vec.len()) {
    vec[index] = scalar_add(vec[index], carry, overflow);
    carry = limb(overflow);
    index += 1;
  }
  if (carry != 0) {
    FASTFLOAT_TRY(vec.try_push(carry));
  }
  return true;
}

// add scalar value to bigint.
template <uint16_t size>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool small_add(stackvec<size>& vec, limb y) noexcept {
  return small_add_from(vec, y, 0);
}

// multiply bigint by scalar value.
template <uint16_t size>
inline FASTFLOAT_CONSTEXPR20
bool small_mul(stackvec<size>& vec, limb y) noexcept {
  limb carry = 0;
  for (size_t index = 0; index < vec.len(); index++) {
    vec[index] = scalar_mul(vec[index], y, carry);
  }
  if (carry != 0) {
    FASTFLOAT_TRY(vec.try_push(carry));
  }
  return true;
}

// add bigint to bigint starting from index.
// used in grade school multiplication
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool large_add_from(stackvec<size>& x, limb_span y, size_t start) noexcept {
  // the effective x buffer is from `xstart..x.len()`, so exit early
  // if we can't get that current range.
  if (x.len() < start || y.len() > x.len() - start) {
      FASTFLOAT_TRY(x.try_resize(y.len() + start, 0));
  }

  bool carry = false;
  for (size_t index = 0; index < y.len(); index++) {
    limb xi = x[index + start];
    limb yi = y[index];
    bool c1 = false;
    bool c2 = false;
    xi = scalar_add(xi, yi, c1);
    if (carry) {
      xi = scalar_add(xi, 1, c2);
    }
    x[index + start] = xi;
    carry = c1 | c2;
  }

  // handle overflow
  if (carry) {
    FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start));
  }
  return true;
}

// add bigint to bigint.
template <uint16_t size>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool large_add_from(stackvec<size>& x, limb_span y) noexcept {
  return large_add_from(x, y, 0);
}

// grade-school multiplication algorithm
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool long_mul(stackvec<size>& x, limb_span y) noexcept {
  limb_span xs = limb_span(x.data, x.len());
  stackvec<size> z(xs);
  limb_span zs = limb_span(z.data, z.len());

  if (y.len() != 0) {
    limb y0 = y[0];
    FASTFLOAT_TRY(small_mul(x, y0));
    for (size_t index = 1; index < y.len(); index++) {
      limb yi = y[index];
      stackvec<size> zi;
      if (yi != 0) {
        // re-use the same buffer throughout
        zi.set_len(0);
        FASTFLOAT_TRY(zi.try_extend(zs));
        FASTFLOAT_TRY(small_mul(zi, yi));
        limb_span zis = limb_span(zi.data, zi.len());
        FASTFLOAT_TRY(large_add_from(x, zis, index));
      }
    }
  }

  x.normalize();
  return true;
}

// grade-school multiplication algorithm
template <uint16_t size>
FASTFLOAT_CONSTEXPR20
bool large_mul(stackvec<size>& x, limb_span y) noexcept {
  if (y.len() == 1) {
    FASTFLOAT_TRY(small_mul(x, y[0]));
  } else {
    FASTFLOAT_TRY(long_mul(x, y));
  }
  return true;
}

template <typename = void>
struct pow5_tables {
  static constexpr uint32_t large_step = 135;
  static constexpr uint64_t small_power_of_5[] = {
    1UL, 5UL, 25UL, 125UL, 625UL, 3125UL, 15625UL, 78125UL, 390625UL,
    1953125UL, 9765625UL, 48828125UL, 244140625UL, 1220703125UL,
    6103515625UL, 30517578125UL, 152587890625UL, 762939453125UL,
    3814697265625UL, 19073486328125UL, 95367431640625UL, 476837158203125UL,
    2384185791015625UL, 11920928955078125UL, 59604644775390625UL,
    298023223876953125UL, 1490116119384765625UL, 7450580596923828125UL,
  };
#ifdef FASTFLOAT_64BIT_LIMB
  constexpr static limb large_power_of_5[] = {
    1414648277510068013UL, 9180637584431281687UL, 4539964771860779200UL,
    10482974169319127550UL, 198276706040285095UL};
#else
  constexpr static limb large_power_of_5[] = {
    4279965485U, 329373468U, 4020270615U, 2137533757U, 4287402176U,
    1057042919U, 1071430142U, 2440757623U, 381945767U, 46164893U};
#endif
};

template <typename T>
constexpr uint32_t pow5_tables<T>::large_step;

template <typename T>
constexpr uint64_t pow5_tables<T>::small_power_of_5[];

template <typename T>
constexpr limb pow5_tables<T>::large_power_of_5[];

// big integer type. implements a small subset of big integer
// arithmetic, using simple algorithms since asymptotically
// faster algorithms are slower for a small number of limbs.
// all operations assume the big-integer is normalized.
struct bigint : pow5_tables<> {
  // storage of the limbs, in little-endian order.
  stackvec<bigint_limbs> vec;

  FASTFLOAT_CONSTEXPR20 bigint(): vec() {}
  bigint(const bigint &) = delete;
  bigint &operator=(const bigint &) = delete;
  bigint(bigint &&) = delete;
  bigint &operator=(bigint &&other) = delete;

  FASTFLOAT_CONSTEXPR20 bigint(uint64_t value): vec() {
#ifdef FASTFLOAT_64BIT_LIMB
    vec.push_unchecked(value);
#else
    vec.push_unchecked(uint32_t(value));
    vec.push_unchecked(uint32_t(value >> 32));
#endif
    vec.normalize();
  }

  // get the high 64 bits from the vector, and if bits were truncated.
  // this is to get the significant digits for the float.
  FASTFLOAT_CONSTEXPR20 uint64_t hi64(bool& truncated) const noexcept {
#ifdef FASTFLOAT_64BIT_LIMB
    if (vec.len() == 0) {
      return empty_hi64(truncated);
    } else if (vec.len() == 1) {
      return uint64_hi64(vec.rindex(0), truncated);
    } else {
      uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated);
      truncated |= vec.nonzero(2);
      return result;
    }
#else
    if (vec.len() == 0) {
      return empty_hi64(truncated);
    } else if (vec.len() == 1) {
      return uint32_hi64(vec.rindex(0), truncated);
    } else if (vec.len() == 2) {
      return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated);
    } else {
      uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated);
      truncated |= vec.nonzero(3);
      return result;
    }
#endif
  }

  // compare two big integers, returning the large value.
  // assumes both are normalized. if the return value is
  // negative, other is larger, if the return value is
  // positive, this is larger, otherwise they are equal.
  // the limbs are stored in little-endian order, so we
  // must compare the limbs in ever order.
  FASTFLOAT_CONSTEXPR20 int compare(const bigint& other) const noexcept {
    if (vec.len() > other.vec.len()) {
      return 1;
    } else if (vec.len() < other.vec.len()) {
      return -1;
    } else {
      for (size_t index = vec.len(); index > 0; index--) {
        limb xi = vec[index - 1];
        limb yi = other.vec[index - 1];
        if (xi > yi) {
          return 1;
        } else if (xi < yi) {
          return -1;
        }
      }
      return 0;
    }
  }

  // shift left each limb n bits, carrying over to the new limb
  // returns true if we were able to shift all the digits.
  FASTFLOAT_CONSTEXPR20 bool shl_bits(size_t n) noexcept {
    // Internally, for each item, we shift left by n, and add the previous
    // right shifted limb-bits.
    // For example, we transform (for u8) shifted left 2, to:
    //      b10100100 b01000010
    //      b10 b10010001 b00001000
    FASTFLOAT_DEBUG_ASSERT(n != 0);
    FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8);

    size_t shl = n;
    size_t shr = limb_bits - shl;
    limb prev = 0;
    for (size_t index = 0; index < vec.len(); index++) {
      limb xi = vec[index];
      vec[index] = (xi << shl) | (prev >> shr);
      prev = xi;
    }

    limb carry = prev >> shr;
    if (carry != 0) {
      return vec.try_push(carry);
    }
    return true;
  }

  // move the limbs left by `n` limbs.
  FASTFLOAT_CONSTEXPR20 bool shl_limbs(size_t n) noexcept {
    FASTFLOAT_DEBUG_ASSERT(n != 0);
    if (n + vec.len() > vec.capacity()) {
      return false;
    } else if (!vec.is_empty()) {
      // move limbs
      limb* dst = vec.data + n;
      const limb* src = vec.data;
      std::copy_backward(src, src + vec.len(), dst + vec.len());
      // fill in empty limbs
      limb* first = vec.data;
      limb* last = first + n;
      ::std::fill(first, last, 0);
      vec.set_len(n + vec.len());
      return true;
    } else {
      return true;
    }
  }

  // move the limbs left by `n` bits.
  FASTFLOAT_CONSTEXPR20 bool shl(size_t n) noexcept {
    size_t rem = n % limb_bits;
    size_t div = n / limb_bits;
    if (rem != 0) {
      FASTFLOAT_TRY(shl_bits(rem));
    }
    if (div != 0) {
      FASTFLOAT_TRY(shl_limbs(div));
    }
    return true;
  }

  // get the number of leading zeros in the bigint.
  FASTFLOAT_CONSTEXPR20 int ctlz() const noexcept {
    if (vec.is_empty()) {
      return 0;
    } else {
#ifdef FASTFLOAT_64BIT_LIMB
      return leading_zeroes(vec.rindex(0));
#else
      // no use defining a specialized leading_zeroes for a 32-bit type.
      uint64_t r0 = vec.rindex(0);
      return leading_zeroes(r0 << 32);
#endif
    }
  }

  // get the number of bits in the bigint.
  FASTFLOAT_CONSTEXPR20 int bit_length() const noexcept {
    int lz = ctlz();
    return int(limb_bits * vec.len()) - lz;
  }

  FASTFLOAT_CONSTEXPR20 bool mul(limb y) noexcept {
    return small_mul(vec, y);
  }

  FASTFLOAT_CONSTEXPR20 bool add(limb y) noexcept {
    return small_add(vec, y);
  }

  // multiply as if by 2 raised to a power.
  FASTFLOAT_CONSTEXPR20 bool pow2(uint32_t exp) noexcept {
    return shl(exp);
  }

  // multiply as if by 5 raised to a power.
  FASTFLOAT_CONSTEXPR20 bool pow5(uint32_t exp) noexcept {
    // multiply by a power of 5
    size_t large_length = sizeof(large_power_of_5) / sizeof(limb);
    limb_span large = limb_span(large_power_of_5, large_length);
    while (exp >= large_step) {
      FASTFLOAT_TRY(large_mul(vec, large));
      exp -= large_step;
    }
#ifdef FASTFLOAT_64BIT_LIMB
    uint32_t small_step = 27;
    limb max_native = 7450580596923828125UL;
#else
    uint32_t small_step = 13;
    limb max_native = 1220703125U;
#endif
    while (exp >= small_step) {
      FASTFLOAT_TRY(small_mul(vec, max_native));
      exp -= small_step;
    }
    if (exp != 0) {
      // Work around clang bug https://godbolt.org/z/zedh7rrhc
      // This is similar to https://github.com/llvm/llvm-project/issues/47746,
      // except the workaround described there don't work here
      FASTFLOAT_TRY(
        small_mul(vec, limb(((void)small_power_of_5[0], small_power_of_5[exp])))
      );
    }

    return true;
  }

  // multiply as if by 10 raised to a power.
  FASTFLOAT_CONSTEXPR20 bool pow10(uint32_t exp) noexcept {
    FASTFLOAT_TRY(pow5(exp));
    return pow2(exp);
  }
};

} // namespace fast_float

#endif

#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H

#include <cctype>
#include <cstdint>
#include <cstring>
#include <iterator>


namespace fast_float {

// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline constexpr bool is_integer(char c) noexcept {
  return c >= '0' && c <= '9';
}

fastfloat_really_inline constexpr uint64_t byteswap(uint64_t val) {
  return (val & 0xFF00000000000000) >> 56
    | (val & 0x00FF000000000000) >> 40
    | (val & 0x0000FF0000000000) >> 24
    | (val & 0x000000FF00000000) >> 8
    | (val & 0x00000000FF000000) << 8
    | (val & 0x0000000000FF0000) << 24
    | (val & 0x000000000000FF00) << 40
    | (val & 0x00000000000000FF) << 56;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint64_t read_u64(const char *chars) {
  if (cpp20_and_in_constexpr()) {
    uint64_t val = 0;
    for(int i = 0; i < 8; ++i) {
      val |= uint64_t(*chars) << (i*8);
      ++chars;
    }
    return val;
  }
  uint64_t val;
  ::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  return val;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void write_u64(uint8_t *chars, uint64_t val) {
  if (cpp20_and_in_constexpr()) {
    for(int i = 0; i < 8; ++i) {
      *chars = uint8_t(val);
      val >>= 8;
      ++chars;
    }
    return;
  }
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  ::memcpy(chars, &val, sizeof(uint64_t));
}

// credit  @aqrit
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
uint32_t parse_eight_digits_unrolled(uint64_t val) {
  const uint64_t mask = 0x000000FF000000FF;
  const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
  const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
  val -= 0x3030303030303030;
  val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
  val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
  return uint32_t(val);
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
  return parse_eight_digits_unrolled(read_u64(chars));
}

// credit @aqrit
fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val)  noexcept  {
  return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
     0x8080808080808080));
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_made_of_eight_digits_fast(const char *chars)  noexcept  {
  return is_made_of_eight_digits_fast(read_u64(chars));
}

typedef span<const char> byte_span;

struct parsed_number_string {
  int64_t exponent{0};
  uint64_t mantissa{0};
  const char *lastmatch{nullptr};
  bool negative{false};
  bool valid{false};
  bool too_many_digits{false};
  // contains the range of the significant digits
  byte_span integer{};  // non-nullable
  byte_span fraction{}; // nullable
};

// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
  const chars_format fmt = options.format;
  const char decimal_point = options.decimal_point;

  parsed_number_string answer;
  answer.valid = false;
  answer.too_many_digits = false;
  answer.negative = (*p == '-');
#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
  if ((*p == '-') || (*p == '+')) {
#else
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
#endif
    ++p;
    if (p == pend) {
      return answer;
    }
    if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
      return answer;
    }
  }
  const char *const start_digits = p;

  uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)

  while ((p != pend) && is_integer(*p)) {
    // a multiplication by 10 is cheaper than an arbitrary integer
    // multiplication
    i = 10 * i +
        uint64_t(*p - '0'); // might overflow, we will handle the overflow later
    ++p;
  }
  const char *const end_of_integer_part = p;
  int64_t digit_count = int64_t(end_of_integer_part - start_digits);
  answer.integer = byte_span(start_digits, size_t(digit_count));
  int64_t exponent = 0;
  if ((p != pend) && (*p == decimal_point)) {
    ++p;
    const char* before = p;
    // can occur at most twice without overflowing, but let it occur more, since
    // for integers with many digits, digit parsing is the primary bottleneck.
    while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
      i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
      p += 8;
    }
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      ++p;
      i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
    }
    exponent = before - p;
    answer.fraction = byte_span(before, size_t(p - before));
    digit_count -= exponent;
  }
  // we must have encountered at least one integer!
  if (digit_count == 0) {
    return answer;
  }
  int64_t exp_number = 0;            // explicit exponential part
  if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
    const char * location_of_e = p;
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    if ((p == pend) || !is_integer(*p)) {
      if(!(fmt & chars_format::fixed)) {
        // We are in error.
        return answer;
      }
      // Otherwise, we will be ignoring the 'e'.
      p = location_of_e;
    } else {
      while ((p != pend) && is_integer(*p)) {
        uint8_t digit = uint8_t(*p - '0');
        if (exp_number < 0x10000000) {
          exp_number = 10 * exp_number + digit;
        }
        ++p;
      }
      if(neg_exp) { exp_number = - exp_number; }
      exponent += exp_number;
    }
  } else {
    // If it scientific and not fixed, we have to bail out.
    if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
  }
  answer.lastmatch = p;
  answer.valid = true;

  // If we frequently had to deal with long strings of digits,
  // we could extend our code by using a 128-bit integer instead
  // of a 64-bit integer. However, this is uncommon.
  //
  // We can deal with up to 19 digits.
  if (digit_count > 19) { // this is uncommon
    // It is possible that the integer had an overflow.
    // We have to handle the case where we have 0.0000somenumber.
    // We need to be mindful of the case where we only have zeroes...
    // E.g., 0.000000000...000.
    const char *start = start_digits;
    while ((start != pend) && (*start == '0' || *start == decimal_point)) {
      if(*start == '0') { digit_count --; }
      start++;
    }
    if (digit_count > 19) {
      answer.too_many_digits = true;
      // Let us start again, this time, avoiding overflows.
      // We don't need to check if is_integer, since we use the
      // pre-tokenized spans from above.
      i = 0;
      p = answer.integer.ptr;
      const char* int_end = p + answer.integer.len();
      const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
      while((i < minimal_nineteen_digit_integer) && (p != int_end)) {
        i = i * 10 + uint64_t(*p - '0');
        ++p;
      }
      if (i >= minimal_nineteen_digit_integer) { // We have a big integers
        exponent = end_of_integer_part - p + exp_number;
      } else { // We have a value with a fractional component.
          p = answer.fraction.ptr;
          const char* frac_end = p + answer.fraction.len();
          while((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
            i = i * 10 + uint64_t(*p - '0');
            ++p;
          }
          exponent = answer.fraction.ptr - p + exp_number;
      }
      // We have now corrected both exponent and i, to a truncated value
    }
  }
  answer.exponent = exponent;
  answer.mantissa = i;
  return answer;
}

} // namespace fast_float

#endif

#ifndef FASTFLOAT_DIGIT_COMPARISON_H
#define FASTFLOAT_DIGIT_COMPARISON_H

#include <algorithm>
#include <cstdint>
#include <cstring>
#include <iterator>


namespace fast_float {

// 1e0 to 1e19
constexpr static uint64_t powers_of_ten_uint64[] = {
    1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL,
    1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL,
    100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL,
    1000000000000000000UL, 10000000000000000000UL};

// calculate the exponent, in scientific notation, of the number.
// this algorithm is not even close to optimized, but it has no practical
// effect on performance: in order to have a faster algorithm, we'd need
// to slow down performance for faster algorithms, and this is still fast.
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
int32_t scientific_exponent(parsed_number_string& num) noexcept {
  uint64_t mantissa = num.mantissa;
  int32_t exponent = int32_t(num.exponent);
  while (mantissa >= 10000) {
    mantissa /= 10000;
    exponent += 4;
  }
  while (mantissa >= 100) {
    mantissa /= 100;
    exponent += 2;
  }
  while (mantissa >= 10) {
    mantissa /= 10;
    exponent += 1;
  }
  return exponent;
}

// this converts a native floating-point number to an extended-precision float.
template <typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa to_extended(T value) noexcept {
  using equiv_uint = typename binary_format<T>::equiv_uint;
  constexpr equiv_uint exponent_mask = binary_format<T>::exponent_mask();
  constexpr equiv_uint mantissa_mask = binary_format<T>::mantissa_mask();
  constexpr equiv_uint hidden_bit_mask = binary_format<T>::hidden_bit_mask();

  adjusted_mantissa am;
  int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
  equiv_uint bits;
#if FASTFLOAT_HAS_BIT_CAST
  bits = std::bit_cast<equiv_uint>(value);
#else
  ::memcpy(&bits, &value, sizeof(T));
#endif
  if ((bits & exponent_mask) == 0) {
    // denormal
    am.power2 = 1 - bias;
    am.mantissa = bits & mantissa_mask;
  } else {
    // normal
    am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
    am.power2 -= bias;
    am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
  }

  return am;
}

// get the extended precision value of the halfway point between b and b+u.
// we are given a native float that represents b, so we need to adjust it
// halfway between b and b+u.
template <typename T>
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa to_extended_halfway(T value) noexcept {
  adjusted_mantissa am = to_extended(value);
  am.mantissa <<= 1;
  am.mantissa += 1;
  am.power2 -= 1;
  return am;
}

// round an extended-precision float to the nearest machine float.
template <typename T, typename callback>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round(adjusted_mantissa& am, callback cb) noexcept {
  int32_t mantissa_shift = 64 - binary_format<T>::mantissa_explicit_bits() - 1;
  if (-am.power2 >= mantissa_shift) {
    // have a denormal float
    int32_t shift = -am.power2 + 1;
    cb(am, std::min<int32_t>(shift, 64));
    // check for round-up: if rounding-nearest carried us to the hidden bit.
    am.power2 = (am.mantissa < (uint64_t(1) << binary_format<T>::mantissa_explicit_bits())) ? 0 : 1;
    return;
  }

  // have a normal float, use the default shift.
  cb(am, mantissa_shift);

  // check for carry
  if (am.mantissa >= (uint64_t(2) << binary_format<T>::mantissa_explicit_bits())) {
    am.mantissa = (uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
    am.power2++;
  }

  // check for infinite: we could have carried to an infinite power
  am.mantissa &= ~(uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
  if (am.power2 >= binary_format<T>::infinite_power()) {
    am.power2 = binary_format<T>::infinite_power();
    am.mantissa = 0;
  }
}

template <typename callback>
fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
  const uint64_t mask
  = (shift == 64)
    ? UINT64_MAX
    : (uint64_t(1) << shift) - 1;
  const uint64_t halfway
  = (shift == 0)
    ? 0
    : uint64_t(1) << (shift - 1);
  uint64_t truncated_bits = am.mantissa & mask;
  bool is_above = truncated_bits > halfway;
  bool is_halfway = truncated_bits == halfway;

  // shift digits into position
  if (shift == 64) {
    am.mantissa = 0;
  } else {
    am.mantissa >>= shift;
  }
  am.power2 += shift;

  bool is_odd = (am.mantissa & 1) == 1;
  am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above));
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
  if (shift == 64) {
    am.mantissa = 0;
  } else {
    am.mantissa >>= shift;
  }
  am.power2 += shift;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void skip_zeros(const char*& first, const char* last) noexcept {
  uint64_t val;
  while (!cpp20_and_in_constexpr() && std::distance(first, last) >= 8) {
    ::memcpy(&val, first, sizeof(uint64_t));
    if (val != 0x3030303030303030) {
      break;
    }
    first += 8;
  }
  while (first != last) {
    if (*first != '0') {
      break;
    }
    first++;
  }
}

// determine if any non-zero digits were truncated.
// all characters must be valid digits.
fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_truncated(const char* first, const char* last) noexcept {
  // do 8-bit optimizations, can just compare to 8 literal 0s.
  uint64_t val;
  while (!cpp20_and_in_constexpr() && std::distance(first, last) >= 8) {
    ::memcpy(&val, first, sizeof(uint64_t));
    if (val != 0x3030303030303030) {
      return true;
    }
    first += 8;
  }
  while (first != last) {
    if (*first != '0') {
      return true;
    }
    first++;
  }
  return false;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
bool is_truncated(byte_span s) noexcept {
  return is_truncated(s.ptr, s.ptr + s.len());
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
  value = value * 100000000 + parse_eight_digits_unrolled(p);
  p += 8;
  counter += 8;
  count += 8;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR14
void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
  value = value * 10 + limb(*p - '0');
  p++;
  counter++;
  count++;
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void add_native(bigint& big, limb power, limb value) noexcept {
  big.mul(power);
  big.add(value);
}

fastfloat_really_inline FASTFLOAT_CONSTEXPR20
void round_up_bigint(bigint& big, size_t& count) noexcept {
  // need to round-up the digits, but need to avoid rounding
  // ....9999 to ...10000, which could cause a false halfway point.
  add_native(big, 10, 1);
  count++;
}

// parse the significant digits into a big integer
inline FASTFLOAT_CONSTEXPR20
void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept {
  // try to minimize the number of big integer and scalar multiplication.
  // therefore, try to parse 8 digits at a time, and multiply by the largest
  // scalar value (9 or 19 digits) for each step.
  size_t counter = 0;
  digits = 0;
  limb value = 0;
#ifdef FASTFLOAT_64BIT_LIMB
  size_t step = 19;
#else
  size_t step = 9;
#endif

  // process all integer digits.
  const char* p = num.integer.ptr;
  const char* pend = p + num.integer.len();
  skip_zeros(p, pend);
  // process all digits, in increments of step per loop
  while (p != pend) {
    while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
      parse_eight_digits(p, value, counter, digits);
    }
    while (counter < step && p != pend && digits < max_digits) {
      parse_one_digit(p, value, counter, digits);
    }
    if (digits == max_digits) {
      // add the temporary value, then check if we've truncated any digits
      add_native(result, limb(powers_of_ten_uint64[counter]), value);
      bool truncated = is_truncated(p, pend);
      if (num.fraction.ptr != nullptr) {
        truncated |= is_truncated(num.fraction);
      }
      if (truncated) {
        round_up_bigint(result, digits);
      }
      return;
    } else {
      add_native(result, limb(powers_of_ten_uint64[counter]), value);
      counter = 0;
      value = 0;
    }
  }

  // add our fraction digits, if they're available.
  if (num.fraction.ptr != nullptr) {
    p = num.fraction.ptr;
    pend = p + num.fraction.len();
    if (digits == 0) {
      skip_zeros(p, pend);
    }
    // process all digits, in increments of step per loop
    while (p != pend) {
      while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
        parse_eight_digits(p, value, counter, digits);
      }
      while (counter < step && p != pend && digits < max_digits) {
        parse_one_digit(p, value, counter, digits);
      }
      if (digits == max_digits) {
        // add the temporary value, then check if we've truncated any digits
        add_native(result, limb(powers_of_ten_uint64[counter]), value);
        bool truncated = is_truncated(p, pend);
        if (truncated) {
          round_up_bigint(result, digits);
        }
        return;
      } else {
        add_native(result, limb(powers_of_ten_uint64[counter]), value);
        counter = 0;
        value = 0;
      }
    }
  }

  if (counter != 0) {
    add_native(result, limb(powers_of_ten_uint64[counter]), value);
  }
}

template <typename T>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept {
  FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent)));
  adjusted_mantissa answer;
  bool truncated;
  answer.mantissa = bigmant.hi64(truncated);
  int bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
  answer.power2 = bigmant.bit_length() - 64 + bias;

  round<T>(answer, [truncated](adjusted_mantissa& a, int32_t shift) {
    round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool {
      return is_above || (is_halfway && truncated) || (is_odd && is_halfway);
    });
  });

  return answer;
}

// the scaling here is quite simple: we have, for the real digits `m * 10^e`,
// and for the theoretical digits `n * 2^f`. Since `e` is always negative,
// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`.
// we then need to scale by `2^(f- e)`, and then the two significant digits
// are of the same magnitude.
template <typename T>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept {
  bigint& real_digits = bigmant;
  int32_t real_exp = exponent;

  // get the value of `b`, rounded down, and get a bigint representation of b+h
  adjusted_mantissa am_b = am;
  // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type.
  round<T>(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); });
  T b;
  to_float(false, am_b, b);
  adjusted_mantissa theor = to_extended_halfway(b);
  bigint theor_digits(theor.mantissa);
  int32_t theor_exp = theor.power2;

  // scale real digits and theor digits to be same power.
  int32_t pow2_exp = theor_exp - real_exp;
  uint32_t pow5_exp = uint32_t(-real_exp);
  if (pow5_exp != 0) {
    FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp));
  }
  if (pow2_exp > 0) {
    FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp)));
  } else if (pow2_exp < 0) {
    FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp)));
  }

  // compare digits, and use it to director rounding
  int ord = real_digits.compare(theor_digits);
  adjusted_mantissa answer = am;
  round<T>(answer, [ord](adjusted_mantissa& a, int32_t shift) {
    round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool {
      (void)_;  // not needed, since we've done our comparison
      (void)__; // not needed, since we've done our comparison
      if (ord > 0) {
        return true;
      } else if (ord < 0) {
        return false;
      } else {
        return is_odd;
      }
    });
  });

  return answer;
}

// parse the significant digits as a big integer to unambiguously round the
// the significant digits. here, we are trying to determine how to round
// an extended float representation close to `b+h`, halfway between `b`
// (the float rounded-down) and `b+u`, the next positive float. this
// algorithm is always correct, and uses one of two approaches. when
// the exponent is positive relative to the significant digits (such as
// 1234), we create a big-integer representation, get the high 64-bits,
// determine if any lower bits are truncated, and use that to direct
// rounding. in case of a negative exponent relative to the significant
// digits (such as 1.2345), we create a theoretical representation of
// `b` as a big-integer type, scaled to the same binary exponent as
// the actual digits. we then compare the big integer representations
// of both, and use that to direct rounding.
template <typename T>
inline FASTFLOAT_CONSTEXPR20
adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept {
  // remove the invalid exponent bias
  am.power2 -= invalid_am_bias;

  int32_t sci_exp = scientific_exponent(num);
  size_t max_digits = binary_format<T>::max_digits();
  size_t digits = 0;
  bigint bigmant;
  parse_mantissa(bigmant, num, max_digits, digits);
  // can't underflow, since digits is at most max_digits.
  int32_t exponent = sci_exp + 1 - int32_t(digits);
  if (exponent >= 0) {
    return positive_digit_comp<T>(bigmant, exponent);
  } else {
    return negative_digit_comp<T>(bigmant, am, exponent);
  }
}

} // namespace fast_float

#endif

#ifndef FASTFLOAT_PARSE_NUMBER_H
#define FASTFLOAT_PARSE_NUMBER_H


#include <cmath>
#include <cstring>
#include <limits>
#include <system_error>

namespace fast_float {


namespace detail {
/**
 * Special case +inf, -inf, nan, infinity, -infinity.
 * The case comparisons could be made much faster given that we know that the
 * strings a null-free and fixed.
 **/
template <typename T>
from_chars_result FASTFLOAT_CONSTEXPR14
parse_infnan(const char *first, const char *last, T &value)  noexcept  {
  from_chars_result answer{};
  answer.ptr = first;
  answer.ec = std::errc(); // be optimistic
  bool minusSign = false;
  if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
      minusSign = true;
      ++first;
  }
#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default
  if (*first == '+') {
      ++first;
  }
#endif
  if (last - first >= 3) {
    if (fastfloat_strncasecmp(first, "nan", 3)) {
      answer.ptr = (first += 3);
      value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::quiet_NaN();
      // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
      if(first != last && *first == '(') {
        for(const char* ptr = first + 1; ptr != last; ++ptr) {
          if (*ptr == ')') {
            answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
            break;
          }
          else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
            break; // forbidden char, not nan(n-char-seq-opt)
        }
      }
      return answer;
    }
    if (fastfloat_strncasecmp(first, "inf", 3)) {
      if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) {
        answer.ptr = first + 8;
      } else {
        answer.ptr = first + 3;
      }
      value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
      return answer;
    }
  }
  answer.ec = std::errc::invalid_argument;
  return answer;
}

/**
 * Returns true if the floating-pointing rounding mode is to 'nearest'.
 * It is the default on most system. This function is meant to be inexpensive.
 * Credit : @mwalcott3
 */
fastfloat_really_inline bool rounds_to_nearest() noexcept {
  // https://lemire.me/blog/2020/06/26/gcc-not-nearest/
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return false;
#endif
  // See
  // A fast function to check your floating-point rounding mode
  // https://lemire.me/blog/2022/11/16/a-fast-function-to-check-your-floating-point-rounding-mode/
  //
  // This function is meant to be equivalent to :
  // prior: #include <cfenv>
  //  return fegetround() == FE_TONEAREST;
  // However, it is expected to be much faster than the fegetround()
  // function call.
  //
  // The volatile keywoard prevents the compiler from computing the function
  // at compile-time.
  // There might be other ways to prevent compile-time optimizations (e.g., asm).
  // The value does not need to be std::numeric_limits<float>::min(), any small
  // value so that 1 + x should round to 1 would do (after accounting for excess
  // precision, as in 387 instructions).
  static volatile float fmin = std::numeric_limits<float>::min();
  float fmini = fmin; // we copy it so that it gets loaded at most once.
  //
  // Explanation:
  // Only when fegetround() == FE_TONEAREST do we have that
  // fmin + 1.0f == 1.0f - fmin.
  //
  // FE_UPWARD:
  //  fmin + 1.0f > 1
  //  1.0f - fmin == 1
  //
  // FE_DOWNWARD or  FE_TOWARDZERO:
  //  fmin + 1.0f == 1
  //  1.0f - fmin < 1
  //
  // Note: This may fail to be accurate if fast-math has been
  // enabled, as rounding conventions may not apply.
  #if FASTFLOAT_VISUAL_STUDIO
  #   pragma warning(push)
  //  todo: is there a VS warning?
  //  see https://stackoverflow.com/questions/46079446/is-there-a-warning-for-floating-point-equality-checking-in-visual-studio-2013
  #elif defined(__clang__)
  #   pragma clang diagnostic push
  #   pragma clang diagnostic ignored "-Wfloat-equal"
  #elif defined(__GNUC__)
  #   pragma GCC diagnostic push
  #   pragma GCC diagnostic ignored "-Wfloat-equal"
  #endif
  return (fmini + 1.0f == 1.0f - fmini);
  #if FASTFLOAT_VISUAL_STUDIO
  #   pragma warning(pop)
  #elif defined(__clang__)
  #   pragma clang diagnostic pop
  #elif defined(__GNUC__)
  #   pragma GCC diagnostic pop
  #endif
}

} // namespace detail

template<typename T>
FASTFLOAT_CONSTEXPR20
from_chars_result from_chars(const char *first, const char *last,
                             T &value, chars_format fmt /*= chars_format::general*/)  noexcept  {
  return from_chars_advanced(first, last, value, parse_options{fmt});
}

template<typename T>
FASTFLOAT_CONSTEXPR20
from_chars_result from_chars_advanced(const char *first, const char *last,
                                      T &value, parse_options options)  noexcept  {

  static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");


  from_chars_result answer;
#if FASTFLOAT_SKIP_WHITE_SPACE  // disabled by default
  while ((first != last) && fast_float::is_space(uint8_t(*first))) {
    first++;
  }
#endif
  if (first == last) {
    answer.ec = std::errc::invalid_argument;
    answer.ptr = first;
    return answer;
  }
  parsed_number_string pns = parse_number_string(first, last, options);
  if (!pns.valid) {
    return detail::parse_infnan(first, last, value);
  }
  answer.ec = std::errc(); // be optimistic
  answer.ptr = pns.lastmatch;
  // The implementation of the Clinger's fast path is convoluted because
  // we want round-to-nearest in all cases, irrespective of the rounding mode
  // selected on the thread.
  // We proceed optimistically, assuming that detail::rounds_to_nearest() returns
  // true.
  if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && !pns.too_many_digits) {
    // Unfortunately, the conventional Clinger's fast path is only possible
    // when the system rounds to the nearest float.
    //
    // We expect the next branch to almost always be selected.
    // We could check it first (before the previous branch), but
    // there might be performance advantages at having the check
    // be last.
    if(!cpp20_and_in_constexpr() && detail::rounds_to_nearest())  {
      // We have that fegetround() == FE_TONEAREST.
      // Next is Clinger's fast path.
      if (pns.mantissa <=binary_format<T>::max_mantissa_fast_path()) {
        value = T(pns.mantissa);
        if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
        else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
        if (pns.negative) { value = -value; }
        return answer;
      }
    } else {
      // We do not have that fegetround() == FE_TONEAREST.
      // Next is a modified Clinger's fast path, inspired by Jakub Jelínek's proposal
      if (pns.exponent >= 0 && pns.mantissa <=binary_format<T>::max_mantissa_fast_path(pns.exponent)) {
#if defined(__clang__)
        // Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD
        if(pns.mantissa == 0) {
          value = pns.negative ? -0. : 0.;
          return answer;
        }
#endif
        value = T(pns.mantissa) * binary_format<T>::exact_power_of_ten(pns.exponent);
        if (pns.negative) { value = -value; }
        return answer;
      }
    }
  }
  adjusted_mantissa am = compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
  if(pns.too_many_digits && am.power2 >= 0) {
    if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
      am = compute_error<binary_format<T>>(pns.exponent, pns.mantissa);
    }
  }
  // If we called compute_float<binary_format<T>>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0),
  // then we need to go the long way around again. This is very uncommon.
  if(am.power2 < 0) { am = digit_comp<T>(pns, am); }
  to_float(pns.negative, am, value);
  // Test for over/underflow.
  if ((pns.mantissa != 0 && am.mantissa == 0 && am.power2 == 0) || am.power2 == binary_format<T>::infinite_power()) {
    answer.ec = std::errc::result_out_of_range;
  }
  return answer;
}

} // namespace fast_float

#endif

