# std::numeric_limits<T>::max_digits10

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< cpp‎ | types‎ | numeric limits

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)

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