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.
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.
#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) { 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); }
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 the radix or integer base used by the representation of the given type
radix
digits that can be represented without change
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