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std::numeric_limits::digits10

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Template:ddcl list begin <tr class="t-dcl ">

<td >
static const int digits10
</td>

<td class="t-dcl-nopad"> </td> <td > (until C++11) </td> </tr> <tr class="t-dcl ">

<td >
static constexpr int digits10
</td>

<td class="t-dcl-nopad"> </td> <td > (since C++11) </td> </tr> Template:ddcl list end

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) [edit]
[static]
number of radix digits that can be represented without change
(public static member constant) [edit]
one more than the smallest negative power of the radix that is a valid normalized floating-point value
(public static member constant) [edit]
one more than the largest integer power of the radix that is a valid finite floating-point value
(public static member constant) [edit]