NAME

std::numeric_limits::digits10 - std::numeric_limits::digits10

Synopsis

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.

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 (C++20) std::numeric_limits<char8_t>::digits * std::log10(2)
char16_t (C++11) std::numeric_limits<char16_t>::digits * std::log10(2)
char32_t (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 (C++11) std::numeric_limits<long long>::digits * std::log10(2)
unsigned long long (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

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