fast_float.h

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// 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
 
 
// 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
 
#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) {}
 
  chars_format format;
  char decimal_point;
};
 
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
                             T &value, chars_format fmt = chars_format::general)  noexcept;
 
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
 
#include <cfloat>
#include <cstdint>
#include <cassert>
#include <cstring>
 
#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__)) \
       || defined(__EMSCRIPTEN__))
#define FASTFLOAT_64BIT
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86)   \
     || defined(__arm__) || defined(_M_ARM)                   \
     || defined(__MINGW32__))
#define FASTFLOAT_32BIT
#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
  #elif SIZE_MAX == 0xffffffffffffffff
    #define FASTFLOAT_64BIT
  #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
 
#ifdef _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) {
  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;
#ifdef _M_ARM64
  // ARM64 has native support for 64-bit multiplications, no need to emulate
  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};
 
template <typename T> struct binary_format {
  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();
  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();
  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();
};
 
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>::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>::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<float>::max_mantissa_fast_path() {
  return uint64_t(2) << mantissa_explicit_bits();
}
 
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<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
 
#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 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 ((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)) {
    // 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 {
 
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,
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        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
 
#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
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 {
  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
 
#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
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
 
#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 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 ((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)) {
    // 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 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 {
  adjusted_mantissa am;
  int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
  if (std::is_same<T, float>::value) {
    constexpr uint32_t exponent_mask = 0x7F800000;
    constexpr uint32_t mantissa_mask = 0x007FFFFF;
    constexpr uint64_t hidden_bit_mask = 0x00800000;
    uint32_t 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;
    }
  } else {
    constexpr uint64_t exponent_mask = 0x7FF0000000000000;
    constexpr uint64_t mantissa_mask = 0x000FFFFFFFFFFFFF;
    constexpr uint64_t hidden_bit_mask = 0x0010000000000000;
    uint64_t 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(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 (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 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 {
template <typename T>
from_chars_result 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 (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;
}
 
} // namespace detail
 
template<typename T>
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>
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 (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;
  // Next is Clinger's fast path.
  if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path() && !pns.too_many_digits) {
    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;
  }
  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);
  return answer;
}
 
} // namespace fast_float
 
#endif