std::numeric_limits<T>::digits10
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
log10(radix)
Standard specializations
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 |
Example
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
)
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
)
Likewise, the 16-digit string 9007199254740993 does not survive text->double->text roundtrip, becoming 9007199254740992
See also
|
[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) |