std::numeric_limits<T>::max_digits10

 

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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 (since C++20)	​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);
}

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

See also

radix [static]	the radix or integer base used by the representation of the given type (public static member constant)
digits [static]	number of radix digits that can be represented without change (public static member constant)
digits10 [static]	number of decimal digits that can be represented without change (public static member constant)
min_exponent [static]	one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant)
max_exponent [static]	one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant)