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# std::numeric_limits::digits10

From cppreference.com
< cpp‎ | types‎ | numeric limits

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.

### [edit] 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

### [edit] 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.

### [edit] See also

radix [static] | the radix or integer base used by the representation of the given type (public static member constant) [edit]
digits [static] | number of `radix` digits that can be represented without change (public static member constant) [edit]
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) [edit]
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) [edit]

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