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
(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<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 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


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

the radix or integer base used by the representation of the given type
(public static member constant)
number of radix digits that can be represented without change
(public static member constant)
one more than the smallest negative power of the radix that is a valid normalized floating-point value
(public static member constant)
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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