libstdc++-v3/src/c++17/fast_float/fast_float.h - gcc - Git at Google

 // 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
 //
 // 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.
 //

 #ifndef FASTFLOAT_FAST_FLOAT_H
 #define FASTFLOAT_FAST_FLOAT_H

 namespace fast_float {

 using std::chars_format;
 using std::from_chars_result;

 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>
 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>
 from_chars_result from_chars_advanced(const char *first, const char *last,
                                       T &value, parse_options options)  noexcept;

 }
 #endif // FASTFLOAT_FAST_FLOAT_H

 #ifndef FASTFLOAT_FLOAT_COMMON_H
 #define FASTFLOAT_FLOAT_COMMON_H

 #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(__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
 #include <endian.h>
 #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)  { if (!(x)) abort(); }
 #endif

 #ifndef FASTFLOAT_DEBUG_ASSERT
 #include <cassert>
 #define FASTFLOAT_DEBUG_ASSERT(x) assert(x)
 #endif

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

 namespace fast_float {

 // Compares two ASCII strings in a case insensitive manner.
 inline 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;
   span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {}
   span() : ptr(nullptr), length(0) {}

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

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

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

 /* result might be undefined when input_num is zero */
 fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
   FASTFLOAT_DEBUG_ASSERT(input_num > 0);
 #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
   int last_bit = 0;
   if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
   if(input_num & uint64_t(        0xffff0000)) input_num >>= 16, last_bit |= 16;
   if(input_num & uint64_t(            0xff00)) input_num >>=  8, last_bit |=  8;
   if(input_num & uint64_t(              0xf0)) input_num >>=  4, last_bit |=  4;
   if(input_num & uint64_t(               0xc)) input_num >>=  2, last_bit |=  2;
   if(input_num & uint64_t(               0x2)) input_num >>=  1, last_bit |=  1;
   return 63 - last_bit;
   #endif
 #else
   return __builtin_clzll(input_num);
 #endif
 }

 #ifdef FASTFLOAT_32BIT

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

 // slow emulation routine for 32-bit
 #if !defined(__MINGW64__)
 fastfloat_really_inline uint64_t _umul128(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;
 }
 #endif // !__MINGW64__

 #endif // FASTFLOAT_32BIT


 // compute 64-bit a*b
 fastfloat_really_inline value128 full_multiplication(uint64_t a,
                                                      uint64_t b) {
   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
   #error Not implemented
 #endif
   return answer;
 }

 struct adjusted_mantissa {
   uint64_t mantissa{0};
   int32_t power2{0}; // a negative value indicates an invalid result
   adjusted_mantissa() = default;
   bool operator==(const adjusted_mantissa &o) const {
     return mantissa == o.mantissa && power2 == o.power2;
   }
   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[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5,
                                                 1e6, 1e7, 1e8, 1e9, 1e10};
 // 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 void to_float(bool negative, adjusted_mantissa am, T &value) {
   uint64_t word = am.mantissa;
   word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
   word = negative
   ? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
 #if FASTFLOAT_IS_BIG_ENDIAN == 1
    if (std::is_same<T, float>::value) {
      ::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian
    } else {
      ::memcpy(&value, &word, sizeof(T));
    }
 #else
    // For little-endian systems:
    ::memcpy(&value, &word, sizeof(T));
 #endif
 }

 } // namespace fast_float

 #endif

 #ifndef FASTFLOAT_ASCII_NUMBER_H
 #define FASTFLOAT_ASCII_NUMBER_H


 namespace fast_float {

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

 fastfloat_really_inline 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 uint64_t read_u64(const char *chars) {
   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 void write_u64(uint8_t *chars, uint64_t val) {
 #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 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 uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
   return parse_eight_digits_unrolled(read_u64(chars));
 }

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

 fastfloat_really_inline 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
 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 (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
     ++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 (bool(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(!bool(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(bool(fmt & chars_format::scientific) && !bool(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

 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.
 static const uint64_t power_of_five_128[number_of_entries];
 };

 template <class unused>
 const uint64_t powers_template<unused>::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,
         0xe998d258869facd7,0x2bd1a438703fc94b,
         0x91ff83775423cc06,0x7b6306a34627ddcf,
         0xb67f6455292cbf08,0x1a3bc84c17b1d542,
         0xe41f3d6a7377eeca,0x20caba5f1d9e4a93,
         0x8e938662882af53e,0x547eb47b7282ee9c,
         0xb23867fb2a35b28d,0xe99e619a4f23aa43,
         0xdec681f9f4c31f31,0x6405fa00e2ec94d4,
         0x8b3c113c38f9f37e,0xde83bc408dd3dd04,
         0xae0b158b4738705e,0x9624ab50b148d445,
         0xd98ddaee19068c76,0x3badd624dd9b0957,
         0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6,
         0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c,
         0xd47487cc8470652b,0x7647c3200069671f,
         0x84c8d4dfd2c63f3b,0x29ecd9f40041e073,
         0xa5fb0a17c777cf09,0xf468107100525890,
         0xcf79cc9db955c2cc,0x7182148d4066eeb4,
         0x81ac1fe293d599bf,0xc6f14cd848405530,
         0xa21727db38cb002f,0xb8ada00e5a506a7c,
         0xca9cf1d206fdc03b,0xa6d90811f0e4851c,
         0xfd442e4688bd304a,0x908f4a166d1da663,
         0x9e4a9cec15763e2e,0x9a598e4e043287fe,
         0xc5dd44271ad3cdba,0x40eff1e1853f29fd,
         0xf7549530e188c128,0xd12bee59e68ef47c,
         0x9a94dd3e8cf578b9,0x82bb74f8301958ce,
         0xc13a148e3032d6e7,0xe36a52363c1faf01,
         0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1,
         0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9,
         0xbcb2b812db11a5de,0x7415d448f6b6f0e7,
         0xebdf661791d60f56,0x111b495b3464ad21,
         0x936b9fcebb25c995,0xcab10dd900beec34,
         0xb84687c269ef3bfb,0x3d5d514f40eea742,
         0xe65829b3046b0afa,0xcb4a5a3112a5112,
         0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab,
         0xb3f4e093db73a093,0x59ed216765690f56,
         0xe0f218b8d25088b8,0x306869c13ec3532c,
         0x8c974f7383725573,0x1e414218c73a13fb,
         0xafbd2350644eeacf,0xe5d1929ef90898fa,
         0xdbac6c247d62a583,0xdf45f746b74abf39,
         0x894bc396ce5da772,0x6b8bba8c328eb783,
         0xab9eb47c81f5114f,0x66ea92f3f326564,
         0xd686619ba27255a2,0xc80a537b0efefebd,
         0x8613fd0145877585,0xbd06742ce95f5f36,
         0xa798fc4196e952e7,0x2c48113823b73704,
         0xd17f3b51fca3a7a0,0xf75a15862ca504c5,
         0x82ef85133de648c4,0x9a984d73dbe722fb,
         0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba,
         0xcc963fee10b7d1b3,0x318df905079926a8,
         0xffbbcfe994e5c61f,0xfdf17746497f7052,
         0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633,
         0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0,
         0xf9bd690a1b68637b,0x3dfdce7aa3c673b0,
         0x9c1661a651213e2d,0x6bea10ca65c084e,
         0xc31bfa0fe5698db8,0x486e494fcff30a62,
         0xf3e2f893dec3f126,0x5a89dba3c3efccfa,
         0x986ddb5c6b3a76b7,0xf89629465a75e01c,
         0xbe89523386091465,0xf6bbb397f1135823,
         0xee2ba6c0678b597f,0x746aa07ded582e2c,
         0x94db483840b717ef,0xa8c2a44eb4571cdc,
         0xba121a4650e4ddeb,0x92f34d62616ce413,
         0xe896a0d7e51e1566,0x77b020baf9c81d17,
         0x915e2486ef32cd60,0xace1474dc1d122e,
         0xb5b5ada8aaff80b8,0xd819992132456ba,
         0xe3231912d5bf60e6,0x10e1fff697ed6c69,
         0x8df5efabc5979c8f,0xca8d3ffa1ef463c1,
         0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2,
         0xddd0467c64bce4a0,0xac7cb3f6d05ddbde,
         0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b,
         0xad4ab7112eb3929d,0x86c16c98d2c953c6,
         0xd89d64d57a607744,0xe871c7bf077ba8b7,
         0x87625f056c7c4a8b,0x11471cd764ad4972,
         0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf,
         0xd389b47879823479,0x4aff1d108d4ec2c3,
         0x843610cb4bf160cb,0xcedf722a585139ba,
         0xa54394fe1eedb8fe,0xc2974eb4ee658828,
         0xce947a3da6a9273e,0x733d226229feea32,
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         0x9316ff75dd87cbd8,0x9a7f12442d588f2,
         0xb7dcbf5354e9bece,0xc11ed6d538aeb2f,
         0xe5d3ef282a242e81,0x8f1668c8a86da5fa,
         0x8fa475791a569d10,0xf96e017d694487bc,
         0xb38d92d760ec4455,0x37c981dcc395a9ac,
         0xe070f78d3927556a,0x85bbe253f47b1417,
         0x8c469ab843b89562,0x93956d7478ccec8e,
         0xaf58416654a6babb,0x387ac8d1970027b2,
         0xdb2e51bfe9d0696a,0x6997b05fcc0319e,
         0x88fcf317f22241e2,0x441fece3bdf81f03,
         0xab3c2fddeeaad25a,0xd527e81cad7626c3,
         0xd60b3bd56a5586f1,0x8a71e223d8d3b074,
         0x85c7056562757456,0xf6872d5667844e49,
         0xa738c6bebb12d16c,0xb428f8ac016561db,
         0xd106f86e69d785c7,0xe13336d701beba52,
         0x82a45b450226b39c,0xecc0024661173473,
         0xa34d721642b06084,0x27f002d7f95d0190,
         0xcc20ce9bd35c78a5,0x31ec038df7b441f4,
         0xff290242c83396ce,0x7e67047175a15271,
         0x9f79a169bd203e41,0xf0062c6e984d386,
         0xc75809c42c684dd1,0x52c07b78a3e60868,
         0xf92e0c3537826145,0xa7709a56ccdf8a82,
         0x9bbcc7a142b17ccb,0x88a66076400bb691,
         0xc2abf989935ddbfe,0x6acff893d00ea435,
         0xf356f7ebf83552fe,0x583f6b8c4124d43,
         0x98165af37b2153de,0xc3727a337a8b704a,
         0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
         0xeda2ee1c7064130c,0x1162def06f79df73,
         0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
         0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
         0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
         0x910ab1d4db9914a0,0x1d9c9892400a22a2,
         0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
         0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
         0x8da471a9de737e24,0x5ceaecfed289e5d2,
         0xb10d8e1456105dad,0x7425a83e872c5f47,
         0xdd50f1996b947518,0xd12f124e28f77719,
         0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
         0xace73cbfdc0bfb7b,0x636cc64d1001550b,
         0xd8210befd30efa5a,0x3c47f7e05401aa4e,
         0x8714a775e3e95c78,0x65acfaec34810a71,
         0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
         0xd31045a8341ca07c,0x1ede48111209a050,
         0x83ea2b892091e44d,0x934aed0aab460432,
         0xa4e4b66b68b65d60,0xf81da84d5617853f,
         0xce1de40642e3f4b9,0x36251260ab9d668e,
         0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
         0xa1075a24e4421730,0xb24cf65b8612f81f,
         0xc94930ae1d529cfc,0xdee033f26797b627,
         0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
         0x9d412e0806e88aa5,0x8e1f289560ee864e,
         0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
         0xf5b5d7ec8acb58a2,0xae10af696774b1db,
         0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
         0xbff610b0cc6edd3f,0x17fd090a58d32af3,
         0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
         0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
         0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
         0xea53df5fd18d5513,0x84c86189216dc5ed,
         0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
         0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
         0xe4d5e82392a40515,0xfabaf3feaa5334a,
         0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
         0xb2c71d5bca9023f8,0x743e20e9ef511012,
         0xdf78e4b2bd342cf6,0x914da9246b255416,
         0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
         0xae9672aba3d0c320,0xa184ac2473b529b1,
         0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
         0x8865899617fb1871,0x7e2fa67c7a658892,
         0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
         0xd51ea6fa85785631,0x552a74227f3ea565,
         0x8533285c936b35de,0xd53a88958f87275f,
         0xa67ff273b8460356,0x8a892abaf368f137,
         0xd01fef10a657842c,0x2d2b7569b0432d85,
         0x8213f56a67f6b29b,0x9c3b29620e29fc73,
         0xa298f2c501f45f42,0x8349f3ba91b47b8f,
         0xcb3f2f7642717713,0x241c70a936219a73,
         0xfe0efb53d30dd4d7,0xed238cd383aa0110,
         0x9ec95d1463e8a506,0xf4363804324a40aa,
         0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
         0xf81aa16fdc1b81da,0xdd94b7868e94050a,
         0x9b10a4e5e9913128,0xca7cf2b4191c8326,
         0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
         0xf24a01a73cf2dccf,0xbc633b39673c8cec,
         0x976e41088617ca01,0xd5be0503e085d813,
         0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
         0xec9c459d51852ba2,0xddf8e7d60ed1219e,
         0x93e1ab8252f33b45,0xcabb90e5c942b503,
         0xb8da1662e7b00a17,0x3d6a751f3b936243,
         0xe7109bfba19c0c9d,0xcc512670a783ad4,
         0x906a617d450187e2,0x27fb2b80668b24c5,
         0xb484f9dc9641e9da,0xb1f9f660802dedf6,
         0xe1a63853bbd26451,0x5e7873f8a0396973,
         0x8d07e33455637eb2,0xdb0b487b6423e1e8,
         0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
         0xdc5c5301c56b75f7,0x7641a140cc7810fb,
         0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
         0xac2820d9623bf429,0x546345fa9fbdcd44,
         0xd732290fbacaf133,0xa97c177947ad4095,
         0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
         0xa81f301449ee8c70,0x5c68f256bfff5a74,
         0xd226fc195c6a2f8c,0x73832eec6fff3111,
         0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
         0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
         0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
         0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
         0xa0555e361951c366,0xd7e105bcc332621f,
         0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
         0xfa856334878fc150,0xb14f98f6f0feb951,
         0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
         0xc3b8358109e84f07,0xa862f80ec4700c8,
         0xf4a642e14c6262c8,0xcd27bb612758c0fa,
         0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
         0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
         0xeeea5d5004981478,0x1858ccfce06cac74,
         0x95527a5202df0ccb,0xf37801e0c43ebc8,
         0xbaa718e68396cffd,0xd30560258f54e6ba,
         0xe950df20247c83fd,0x47c6b82ef32a2069,
         0x91d28b7416cdd27e,0x4cdc331d57fa5441,
         0xb6472e511c81471d,0xe0133fe4adf8e952,
         0xe3d8f9e563a198e5,0x58180fddd97723a6,
         0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
 using powers = powers_template<>;

 }

 #endif

 #ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
 #define FASTFLOAT_DECIMAL_TO_BINARY_H

 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
 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
 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
 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
 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);
   if(product.low == 0xFFFFFFFFFFFFFFFF) { //  could guard it further
     // In some very rare cases, this could happen, in which case we might need a more accurate
     // computation that what we can provide cheaply. This is very, very unlikely.
     //
     const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0,
     // and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation.
     if(!inside_safe_exponent) {
       return compute_error_scaled<binary>(q, product.high, lz);
     }
   }
   // 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


 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.
   stackvec(limb_span s) {
     FASTFLOAT_ASSERT(try_extend(s));
   }

   limb& operator[](size_t index) noexcept {
     FASTFLOAT_DEBUG_ASSERT(index < length);
     return data[index];
   }
   const limb& operator[](size_t index) const noexcept {
     FASTFLOAT_DEBUG_ASSERT(index < length);
     return data[index];
   }
   // index from the end of the container
   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.
   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
   void push_unchecked(limb value) noexcept {
     data[length] = value;
     length++;
   }
   // append item to vector, returning if item was added
   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
   void extend_unchecked(limb_span s) noexcept {
     limb* ptr = data + length;
     ::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len());
     set_len(len() + s.len());
   }
   // try to add items to the vector, returning if items were added
   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.
   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.
   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.
   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.
   void normalize() noexcept {
     while (len() > 0 && rindex(0) == 0) {
       length--;
     }
   }
 };

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

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

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

 fastfloat_really_inline
 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
 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
 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)
     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
 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 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 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 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>
 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 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>
 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>
 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;
 }

 // 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 {
   // storage of the limbs, in little-endian order.
   stackvec<bigint_limbs> vec;

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

   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.
   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.
   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.
   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.
   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;
       ::memmove(dst, src, sizeof(limb) * 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.
   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.
   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.
   int bit_length() const noexcept {
     int lz = ctlz();
     return int(limb_bits * vec.len()) - lz;
   }

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

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

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

   // multiply as if by 5 raised to a power.
   bool pow5(uint32_t exp) noexcept {
     // multiply by a power of 5
     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
     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) {
       FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp])));
     }

     return true;
   }

   // multiply as if by 10 raised to a power.
   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


 namespace fast_float {

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

 fastfloat_really_inline 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 uint64_t read_u64(const char *chars) {
   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 void write_u64(uint8_t *chars, uint64_t val) {
 #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 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 uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
   return parse_eight_digits_unrolled(read_u64(chars));
 }

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

 fastfloat_really_inline 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
 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 (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
     ++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


 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 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 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;
   ::memcpy(&bits, &value, sizeof(T));
   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 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 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
 void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
   uint64_t mask;
   uint64_t halfway;
   if (shift == 64) {
     mask = UINT64_MAX;
   } else {
     mask = (uint64_t(1) << shift) - 1;
   }
   if (shift == 0) {
     halfway = 0;
   } else {
     halfway = uint64_t(1) << (shift - 1);
   }
   uint64_t truncated_bits = am.mantissa & mask;
   uint64_t is_above = truncated_bits > halfway;
   uint64_t 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 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 void skip_zeros(const char*& first, const char* last) noexcept {
   uint64_t val;
   while (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 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 (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 bool is_truncated(byte_span s) noexcept {
   return is_truncated(s.ptr, s.ptr + s.len());
 }

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

 fastfloat_really_inline 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 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 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 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<