std::numeric_limits<T>::max_digits10 (3) - Linux Manuals

std::numeric_limits<T>::max_digits10: std::numeric_limits<T>::max_digits10

NAME

std::numeric_limits<T>::max_digits10 - std::numeric_limits<T>::max_digits10

Synopsis

static constexpr int max_digits10 (since C++11)

The value of std::numeric_limits<T>::max_digits10 is the number of base-10 digits that are necessary to uniquely represent all distinct values of the type T, such as necessary for serialization/deserialization to text. This constant is meaningful for all floating-point types.

Standard specializations

T value of std::numeric_limits<T>::max_digits10
/* non-specialized */ 0
bool 0
char 0
signed char 0
unsigned char 0
wchar_t 0
char8_t 0
char16_t 0
char32_t 0
short 0
unsigned short 0
int 0
unsigned int 0
long 0
unsigned long 0
long long 0
unsigned long long 0
float FLT_DECIMAL_DIG or std::ceil(std::numeric_limits<float>::digits * std::log10(2) + 1)
double DBL_DECIMAL_DIG orstd::ceil(std::numeric_limits<double>::digits * std::log10(2) + 1)
long double DECIMAL_DIG or LDBL_DECIMAL_DIG orstd::ceil(std::numeric_limits<long double>::digits * std::log10(2) + 1)

Notes

Unlike most mathematical operations, the conversion of a floating-point value to text and back is exact as long as at least max_digits10 were used (9 for float, 17 for double): it is guaranteed to produce the same floating-point value, even though the intermediate text representation is not exact. It may take over a hundred decimal digits to represent the precise value of a float in decimal notation.

Example

// Run this code

  #include <limits>
  #include <sstream>
  #include <iomanip>
  #include <cmath>
  #include <iostream>

  int main()
  {
      float value = 10.0000086;

      constexpr auto digits10 = std::numeric_limits<decltype(value)>::digits10;
      constexpr auto max_digits10 = std::numeric_limits<decltype(value)>::max_digits10;
      constexpr auto submax_digits10 = max_digits10 - 1;

      std::cout
          << "float:\n"
          << " digits10 is " << digits10 << " digits" << '\n'
          << " max_digits10 is " << max_digits10 << " digits" << '\n'
          << "submax_digits10 is " << submax_digits10 << " digits" << '\n'
          << '\n';

      const auto original_precision = std::cout.precision();
      for( auto i = 0; i < 5; ++i )
      {
          std::cout
              << " max_digits10: " << std::setprecision(max_digits10) << value << '\n'
              << "submax_digits10: " << std::setprecision(submax_digits10) << value << '\n'
              << '\n';

          value = std::nextafter( value, std::numeric_limits<decltype(value)>::max() );
      }
      std::cout.precision( original_precision );

      return 0;
  }

Output:

  float:
         digits10 is 6 digits
     max_digits10 is 9 digits
  submax_digits10 is 8 digits

     max_digits10: 10.0000086
  submax_digits10: 10.000009

     max_digits10: 10.0000095
  submax_digits10: 10.00001

     max_digits10: 10.0000105
  submax_digits10: 10.00001

     max_digits10: 10.0000114
  submax_digits10: 10.000011

     max_digits10: 10.0000124
  submax_digits10: 10.000012