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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.


[edit] 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 or std::ceil(std::numeric_limits<double>::digits * std::log10(2) + 1)
long double DECIMAL_DIG or LDBL_DECIMAL_DIG or std::ceil(std::numeric_limits<long double>::digits * std::log10(2) + 1)

[edit] 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.

[edit] Example

#include <cmath>
#include <iomanip>
#include <iostream>
#include <limits>
#include <sstream>
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)
            << "   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());


       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

[edit] See also

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