Namespaces
Variants
Views
Actions

std::numeric_limits<T>::max_digits10

From cppreference.com
 
 
 
Type support
Basic types
Fundamental types
Fixed width integer types (C++11)
Numeric limits
C numeric limits interface
Runtime type information
Type traits
Type categories
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
Type properties
(C++11)
(C++11)
(C++14)
(C++11)
(C++11)(until C++20)
(C++11)(deprecated in C++20)
(C++11)
Type trait constants
Metafunctions
(C++17)
Constant evaluation context
Supported operations
Relationships and property queries
Type modifications
(C++11)(C++11)(C++11)
Type transformations
(C++11)
(C++11)
(C++17)
(C++11)(until C++20)(C++17)
 
 
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
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)

[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>
 
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

[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]