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std::numeric_limits

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numeric_limits
C numeric limits interface
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Defined in header <limits>
template< class T > class numeric_limits;

The std::numeric_limits class template provides a standardized way to query various properties of arithmetic types (e.g. the largest possible value for type int is std::numeric_limits<int>::max()).

This information is provided via specializations of the std::numeric_limits template. The standard library makes available specializations for all arithmetic types (only lists the specializations for cv-unqualified arithmetic types):

Defined in header <limits>
template<> class numeric_limits<bool>;
template<> class numeric_limits<char>;
template<> class numeric_limits<signed char>;
template<> class numeric_limits<unsigned char>;
template<> class numeric_limits<wchar_t>;
template<> class numeric_limits<char8_t>;
(since C++20)
template<> class numeric_limits<char16_t>;
(since C++11)
template<> class numeric_limits<char32_t>;
(since C++11)
template<> class numeric_limits<short>;
template<> class numeric_limits<unsigned short>;
template<> class numeric_limits<int>;
template<> class numeric_limits<unsigned int>;
template<> class numeric_limits<long>;
template<> class numeric_limits<unsigned long>;
template<> class numeric_limits<long long>;
(since C++11)
template<> class numeric_limits<unsigned long long>;
(since C++11)
template<> class numeric_limits<float>;
template<> class numeric_limits<double>;
template<> class numeric_limits<long double>;

The value of each member of a specialization of std::numeric_limits on a cv-qualified type cv T is equal to the value of the corresponding member of the specialization on the unqualified type T. For example, std::numeric_limits<int>::digits is equal to std::numeric_limits<const int>::digits.

Aliases of arithmetic types (such as std::size_t or std::streamsize) may also be examined with the std::numeric_limits type traits.

Non-arithmetic standard types, such as std::complex<T> or std::nullptr_t, do not have specializations.

If the implementation defines any integer-class types, specializations of std::numeric_limits must also be provided for them.

(since C++20)

Implementations may provide specializations of std::numeric_limits for implementation-specific types: e.g. GCC provides std::numeric_limits<__int128>. Non-standard libraries may add specializations for library-provided types, e.g. OpenEXR provides std::numeric_limits<half> for a 16-bit floating-point type.

Contents

[edit] Template parameters

T - a type to retrieve numeric properties for

[edit] Member constants

identifies types for which std::numeric_limits is specialized
(public static member constant) [edit]
[static]
identifies signed types
(public static member constant) [edit]
[static]
identifies integer types
(public static member constant) [edit]
[static]
identifies exact types
(public static member constant) [edit]
identifies floating-point types that can represent the special value "positive infinity"
(public static member constant) [edit]
identifies floating-point types that can represent the special value "quiet not-a-number" (NaN)
(public static member constant) [edit]
identifies floating-point types that can represent the special value "signaling not-a-number" (NaN)
(public static member constant) [edit]
[static]
identifies the denormalization style used by the floating-point type
(public static member constant) [edit]
identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result
(public static member constant) [edit]
[static]
identifies the rounding style used by the type
(public static member constant) [edit]
[static]
identifies the IEC 559/IEEE 754 floating-point types
(public static member constant) [edit]
[static]
identifies types that represent a finite set of values
(public static member constant) [edit]
[static]
identifies types that handle overflows with modulo arithmetic
(public static member constant) [edit]
[static]
number of radix digits that can be represented without change
(public static member constant) [edit]
[static]
number of decimal digits that can be represented without change
(public static member constant) [edit]
[static] (C++11)
number of decimal digits necessary to differentiate all values of this type
(public static member constant) [edit]
[static]
the radix or integer base used by the representation of the given type
(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]
the smallest negative power of ten 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]
the largest integer power of 10 that is a valid finite floating-point value
(public static member constant) [edit]
[static]
identifies types which can cause arithmetic operations to trap
(public static member constant) [edit]
identifies floating-point types that detect tinyness before rounding
(public static member constant) [edit]

[edit] Member functions

[static]
returns the smallest finite value of the given type
(public static member function) [edit]
[static] (C++11)
returns the lowest finite value of the given type
(public static member function) [edit]
[static]
returns the largest finite value of the given type
(public static member function) [edit]
[static]
returns the difference between 1.0 and the next representable value of the given floating-point type
(public static member function) [edit]
[static]
returns the maximum rounding error of the given floating-point type
(public static member function) [edit]
[static]
returns the positive infinity value of the given floating-point type
(public static member function) [edit]
[static]
returns a quiet NaN value of the given floating-point type
(public static member function) [edit]
returns a signaling NaN value of the given floating-point type
(public static member function) [edit]
[static]
returns the smallest positive subnormal value of the given floating-point type
(public static member function) [edit]

[edit] Helper classes

indicates floating-point rounding modes
(enum) [edit]
indicates floating-point denormalization modes
(enum) [edit]

[edit] Relationship with C library macro constants

Specialization
std::numeric_limits<T>
where T is
Members
min() lowest()
(C++11)
max() radix
bool false false true 2
char CHAR_MIN CHAR_MIN CHAR_MAX 2
signed char SCHAR_MIN SCHAR_MIN SCHAR_MAX 2
unsigned char 0 0 UCHAR_MAX 2
wchar_t WCHAR_MIN WCHAR_MIN WCHAR_MAX 2
char8_t 0 0 UCHAR_MAX 2
char16_t 0 0 UINT_LEAST16_MAX 2
char32_t 0 0 UINT_LEAST32_MAX 2
short SHRT_MIN SHRT_MIN SHRT_MAX 2
signed short
unsigned short 0 0 USHRT_MAX 2
int INT_MIN INT_MIN INT_MAX 2
signed int
unsigned int 0 0 UINT_MAX 2
long LONG_MIN LONG_MIN LONG_MAX 2
signed long
unsigned long 0 0 ULONG_MAX 2
long long LLONG_MIN LLONG_MIN LLONG_MAX 2
signed long long
unsigned long long 0 0 ULLONG_MAX 2
Specialization
std::numeric_limits<T>
where T is
Members
denorm_min() min() lowest()
(C++11)
max() epsilon() digits digits10
float FLT_TRUE_MIN FLT_MIN -FLT_MAX FLT_MAX FLT_EPSILON FLT_MANT_DIG FLT_DIG
double DBL_TRUE_MIN DBL_MIN -DBL_MAX DBL_MAX DBL_EPSILON DBL_MANT_DIG DBL_DIG
long double LDBL_TRUE_MIN LDBL_MIN -LDBL_MAX LDBL_MAX LDBL_EPSILON LDBL_MANT_DIG LDBL_DIG
Specialization
std::numeric_limits<T>
where T is
Members (continue)
min_exponent min_exponent10 max_exponent max_exponent10 radix
float FLT_MIN_EXP FLT_MIN_10_EXP FLT_MAX_EXP FLT_MAX_10_EXP FLT_RADIX
double DBL_MIN_EXP DBL_MIN_10_EXP DBL_MAX_EXP DBL_MAX_10_EXP FLT_RADIX
long double LDBL_MIN_EXP LDBL_MIN_10_EXP LDBL_MAX_EXP LDBL_MAX_10_EXP FLT_RADIX

[edit] Example

#include <iostream>
#include <limits>
 
int main() 
{
    std::cout << "type\t│ lowest()\t│ min()\t\t│ max()\n"
              << "bool\t│ "
              << std::numeric_limits<bool>::lowest() << "\t\t│ "
              << std::numeric_limits<bool>::min() << "\t\t│ "
              << std::numeric_limits<bool>::max() << '\n'
              << "uchar\t│ "
              << +std::numeric_limits<unsigned char>::lowest() << "\t\t│ "
              << +std::numeric_limits<unsigned char>::min() << "\t\t│ "
              << +std::numeric_limits<unsigned char>::max() << '\n'
              << "int\t│ "
              << std::numeric_limits<int>::lowest() << "\t│ "
              << std::numeric_limits<int>::min() << "\t│ "
              << std::numeric_limits<int>::max() << '\n'
              << "float\t│ "
              << std::numeric_limits<float>::lowest() << "\t│ "
              << std::numeric_limits<float>::min() << "\t│ "
              << std::numeric_limits<float>::max() << '\n'
              << "double\t│ "
              << std::numeric_limits<double>::lowest() << "\t│ "
              << std::numeric_limits<double>::min() << "\t│ "
              << std::numeric_limits<double>::max() << '\n';
}

Possible output:

type	│ lowest()	│ min()		│ max()
bool	│ 0		│ 0		│ 1
uchar	│ 0		│ 0		│ 255
int	│ -2147483648	│ -2147483648	│ 2147483647
float	│ -3.40282e+38	│ 1.17549e-38	│ 3.40282e+38
double	│ -1.79769e+308	│ 2.22507e-308	│ 1.79769e+308

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior
LWG 201 C++98 specializations for all fundamental types need to be provided excluded non-arithmetic types
LWG 559 C++98 it was unclear whether the std::numeric_limits
specialization for a cv-qualified type behaves as the same as
the corresponding specialization for the cv-unqualified type
they have the
same behavior

[edit] See also