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std::numeric_limits::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.

Contents

[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
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)

[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 <limits>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <iostream>
 
template< typename FloatingType >
std::string to_string_scientific( FloatingType value, int precision )
{
    std::ostringstream oss;
    oss << std::scientific << std::setprecision( precision ) << value;
    return oss.str();
}
 
template< typename FloatingType >
constexpr int max_fractional_digits10()
{
    constexpr auto max_digits10 = std::numeric_limits<FloatingType>::max_digits10;
    constexpr auto one_digit10_in_integer_part = 1;
    return max_digits10 - one_digit10_in_integer_part;
}
 
template< typename FloatingType >
std::string to_string_complete( FloatingType value )
{
    return to_string_scientific( value, max_fractional_digits10<FloatingType>() );
}
 
template< typename FloatingType >
std::string to_string_incomplete( FloatingType value )
{
    return to_string_scientific( value, max_fractional_digits10<FloatingType>() - 1 );
}
 
int main()
{
    float f = 1.00000086e+01f;
 
    for( auto i = 0; i < 4; ++i )
    {
        std::cout 
            << "incomplete: " << to_string_incomplete( f ) 
            << ", complete: " << to_string_complete( f )
            << '\n';
 
        f = std::nextafter( f, std::numeric_limits<decltype(f)>::max() );
    }
}

Output:

incomplete: 1.0000009e+01, complete: 1.00000086e+01
incomplete: 1.0000010e+01, complete: 1.00000095e+01
incomplete: 1.0000010e+01, complete: 1.00000105e+01
incomplete: 1.0000011e+01, complete: 1.00000114e+01

[edit] See also

[static]
the radix or integer base used by the representation of the given type
(public static member constant) [edit]
[static]
number of radix digits that can be represented without change
(public static member constant) [edit]
[static]
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]