# std::numeric_limits

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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.

### Template parameters

T | - | a type to retrieve numeric properties for

### Member constants

is_specialized [static] | identifies types for which std::numeric_limits is specialized (public static member constant)
is_signed [static] | identifies signed types (public static member constant)
is_integer [static] | identifies integer types (public static member constant)
is_exact [static] | identifies exact types (public static member constant)
has_infinity [static] | identifies floating-point types that can represent the special value "positive infinity" (public static member constant)
has_quiet_NaN [static] | identifies floating-point types that can represent the special value "quiet not-a-number" (NaN) (public static member constant)
has_signaling_NaN [static] | identifies floating-point types that can represent the special value "signaling not-a-number" (NaN) (public static member constant)
has_denorm [static] | identifies the denormalization style used by the floating-point type (public static member constant)
has_denorm_loss [static] | identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result (public static member constant)
round_style [static] | identifies the rounding style used by the type (public static member constant)
is_iec559 [static] | identifies the IEC 559/IEEE 754 floating-point types (public static member constant)
is_bounded [static] | identifies types that represent a finite set of values (public static member constant)
is_modulo [static] | identifies types that handle overflows with modulo arithmetic (public static member constant)
digits [static] | number of `radix` digits that can be represented without change (public static member constant)
digits10 [static] | number of decimal digits that can be represented without change (public static member constant)
max_digits10 [static] (C++11) | number of decimal digits necessary to differentiate all values of this type (public static member constant)
radix [static] | the radix or integer base used by the representation of the given type (public static member constant)
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)
min_exponent10 [static] | the smallest negative power of ten that is a valid normalized floating-point value (public static member constant)
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)
max_exponent10 [static] | the largest integer power of 10 that is a valid finite floating-point value (public static member constant)
traps [static] | identifies types which can cause arithmetic operations to trap (public static member constant)
tinyness_before [static] | identifies floating-point types that detect tinyness before rounding (public static member constant)

### Member functions

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

### Helper classes

float_round_style | indicates floating-point rounding modes (enum)
float_denorm_style | indicates floating-point denormalization modes (enum)

### 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

### Example

Run this code

    #include <limits>
    #include <iostream>

    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

### 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

### See also

- Fixed width integer types
- Arithmetic types
- C++ type system overview
- Type support (basic types, RTTI, type traits)
- C numeric limits interface

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