static const int digits10; | (until C++11) | |
static constexpr int digits10; | (since C++11) |
The value of std::numeric_limits<T>::digits10 is the number of base-10 digits that can be represented by the type T without change, that is, any number with this many significant decimal digits can be converted to a value of type T and back to decimal form, without change due to rounding or overflow. For base-radix types, it is the value of digits() (digits - 1 for floating-point types) multiplied by \(\small \log_{10}{radix}\)log
10(radix) and rounded down.
T | value of std::numeric_limits<T>::digits10 |
|---|---|
| /* non-specialized */ | 0 |
| bool | 0 |
| char | std::numeric_limits<char>::digits * std::log10(2) |
| signed char | std::numeric_limits<signed char>::digits * std::log10(2) |
| unsigned char | std::numeric_limits<unsigned char>::digits * std::log10(2) |
| wchar_t | std::numeric_limits<wchar_t>::digits * std::log10(2) |
| char8_t (since C++20) | std::numeric_limits<char8_t>::digits * std::log10(2) |
| char16_t (since C++11) | std::numeric_limits<char16_t>::digits * std::log10(2) |
| char32_t (since C++11) | std::numeric_limits<char32_t>::digits * std::log10(2) |
| short | std::numeric_limits<short>::digits * std::log10(2) |
| unsigned short | std::numeric_limits<unsigned short>::digits * std::log10(2) |
| int | std::numeric_limits<int>::digits * std::log10(2) |
| unsigned int | std::numeric_limits<unsigned int>::digits * std::log10(2) |
| long | std::numeric_limits<long>::digits * std::log10(2) |
| unsigned long | std::numeric_limits<unsigned long>::digits * std::log10(2) |
| long long (since C++11) | std::numeric_limits<long long>::digits * std::log10(2) |
| unsigned long long (since C++11) | std::numeric_limits<unsigned long long>::digits * std::log10(2) |
| float | FLT_DIG (6 for IEEE float) |
| double | DBL_DIG (15 for IEEE double) |
| long double | LDBL_DIG (18 for 80-bit Intel long double; 33 for IEEE quadruple) |
An 8-bit binary type can represent any two-digit decimal number exactly, but 3-digit decimal numbers 256..999 cannot be represented. The value of digits10 for an 8-bit type is 2 (8 * std::log10(2) is 2.41).
The standard 32-bit IEEE 754 floating-point type has a 24 bit fractional part (23 bits written, one implied), which may suggest that it can represent 7 digit decimals (24 * std::log10(2) is 7.22), but relative rounding errors are non-uniform and some floating-point values with 7 decimal digits do not survive conversion to 32-bit float and back: the smallest positive example is 8.589973e9, which becomes 8.589974e9 after the roundtrip. These rounding errors cannot exceed one bit in the representation, and digits10 is calculated as (24 - 1) * std::log10(2), which is 6.92. Rounding down results in the value 6.
Likewise, the 16-digit string 9007199254740993 does not survive text->double->text roundtrip, becoming 9007199254740992: the 64-bit IEEE 754 type double guarantees this roundtrip only for 15 decimal digits.
|
[static] (C++11) | number of decimal digits necessary to differentiate all values of this type (public static member constant) |
|
[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] | 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) |
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