std::numeric_limits<T>::max_digits10
From cppreference.com
< 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 */ (C++11) | 0 |
| bool (C++11) | 0 |
| char (C++11) | 0 |
| signed char (C++11) | 0 |
| unsigned char (C++11) | 0 |
| wchar_t (C++11) | 0 |
| char8_t (C++20) | 0 |
| char16_t (C++11) | 0 |
| char32_t (C++11) | 0 |
| short (C++11) | 0 |
| unsigned short (C++11) | 0 |
| int (C++11) | 0 |
| unsigned int (C++11) | 0 |
| long (C++11) | 0 |
| unsigned long (C++11) | 0 |
| long long (C++11) | 0 |
| unsigned long long (C++11) | 0 |
| float (C++11) | FLT_DECIMAL_DIG or std::ceil(std::numeric_limits<float>::digits * std::log10(2) + 1) |
| double (C++11) | DBL_DECIMAL_DIG orstd::ceil(std::numeric_limits<double>::digits * std::log10(2) + 1) |
| long double (C++11) | 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:
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: 10.000012See also
| [static] |
the radix or integer base used by the representation of the given type (public static member constant) |
| [static] |
number of radix digits that can be represented without change (public static member constant) |
| [static] |
number of decimal digits that can be represented without change (public static member constant) |
| [static] |
one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant) |
| [static] |
one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant) |