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 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 log
10(radix) and rounded down.
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) |
char16_t | std::numeric_limits<char16_t>::digits * std::log10(2) |
char32_t | std::numeric_limits<char32_t>::digits * std::log10(2) |
short | std::numeric_limits<short>::digits * std::log10(2) |
unsigned short | std::numeric_limits<signed short>::digits * std::log10(2) |
int | std::numeric_limits<int>::digits * std::log10(2) |
unsigned int | std::numeric_limits<signed 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 | std::numeric_limits<long long>::digits * std::log10(2) |
unsigned long long | std::numeric_limits<unsigned long long>::digits * std::log10(2) |
float | FLT_DIG |
double | DBL_DIG |
long double | LDBL_DIG |
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)
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.
See 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] | 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) |
Please login to continue.