std::numeric_limits<T>::digits10

 

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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 \(\small \log_{10}{radix}\)log10(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)
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)

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.

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.

See also

max_digits10 [static] (C++11)	number of decimal digits necessary to differentiate all values of this type (public static member constant)
radix [static]	the radix or integer base used by the representation of the given type (public static member constant)
digits [static]	number of radix digits that can be represented without change (public static member constant)
min_exponent [static]	one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant)
max_exponent [static]	one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant)