std::numeric_limits::max_digits10 (3) Linux Manual Page
std::numeric_limits<T>::max_digits10 – std::numeric_limits<T>::max_digits10
Synopsis
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 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);
return 0;
}
Output:
See also
radix the radix or integer base used by the representation of the given type
[static]
digits number of radix digits that can be represented without change
[static]
digits10 number of decimal digits that can be represented without change
[static]
min_exponent one more than the smallest negative power of the radix that is a valid normalized floating-point value
[static]
max_exponent one more than the largest integer power of the radix that is a valid finite floating-point value
[static]