std::numeric_limits<T>::digits10
static const int digits10;
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(until C++11) | |
static constexpr int digits10;
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(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 log10(radix) and rounded down.
Standard specializations
T
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value of std::numeric_limits<T>::digits10
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/* non-specialized */
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0
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bool
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0
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char
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std::numeric_limits<char>::digits * std::log10(2)
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signed char
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std::numeric_limits<signed char>::digits * std::log10(2)
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unsigned char
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std::numeric_limits<unsigned char>::digits * std::log10(2)
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wchar_t
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std::numeric_limits<wchar_t>::digits * std::log10(2)
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char8_t (since C++20)
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std::numeric_limits<char8_t>::digits * std::log10(2)
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char16_t (since C++11)
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std::numeric_limits<char16_t>::digits * std::log10(2)
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char32_t (since C++11)
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std::numeric_limits<char32_t>::digits * std::log10(2)
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short
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std::numeric_limits<short>::digits * std::log10(2)
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unsigned short
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std::numeric_limits<unsigned short>::digits * std::log10(2)
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int
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std::numeric_limits<int>::digits * std::log10(2)
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unsigned int
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std::numeric_limits<unsigned int>::digits * std::log10(2)
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long
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std::numeric_limits<long>::digits * std::log10(2)
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unsigned long
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std::numeric_limits<unsigned long>::digits * std::log10(2)
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long long (since C++11)
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std::numeric_limits<long long>::digits * std::log10(2)
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unsigned long long (since C++11)
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std::numeric_limits<unsigned long long>::digits * std::log10(2)
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float
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FLT_DIG (6 for IEEE float)
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double
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DBL_DIG (15 for IEEE double)
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long double
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LDBL_DIG (18 for 80-bit Intel long double; 33 for IEEE quadruple)
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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 (std::log10(2) ≈ 0.30103, so 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.
Example
#include <concepts>
#include <iomanip>
#include <iostream>
#include <limits>
#include <meta>
#include <string_view>
#include <type_traits>
using namespace std::literals;
template<typename T>
requires std::integral<T> or std::floating_point<T>
constexpr void digit10()
{
constexpr int w{(int)"unsigned long long"sv.size()};
std::cout << std::right << std::setw(w)
<< std::meta::display_string_of(^^T) << " : "
<< std::numeric_limits<T>::digits10 << '\n';
}
template<typename... T>
constexpr void digits10()
{
(digit10<T>(), ...);
}
int main()
{
digits10<
bool, char, signed char, unsigned char, wchar_t, char8_t, char16_t,
char32_t, short, unsigned short, int, unsigned int, long, unsigned long,
long long, unsigned long long, float, double, long double
>();
}
Possible output:
bool : 0
char : 2
signed char : 2
unsigned char : 2
wchar_t : 9
char8_t : 2
char16_t : 4
char32_t : 9
short : 4
unsigned short : 4
int : 9
unsigned int : 9
long : 18
unsigned long : 19
long long : 18
unsigned long long : 19
float : 6
double : 15
long double : 18
See also
[static] (C++11) |
number of decimal digits necessary to differentiate all values of this type (public static member constant) |
[static] |
the radix or integer base used by the representation of the given type (public static member constant) |
[static] |
number of radix digits that can be represented without change (public static member constant) |
[static] |
one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant) |
[static] |
one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant) |