# std::numeric_limits

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Defined in header `<limits>` |  |
template< class T > class numeric_limits; |  |

The `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 `numeric_limits` template. The standard library makes available specializations for all 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>; // C++20 feature
template<> class numeric_limits<char16_t>; // C++11 feature
template<> class numeric_limits<char32_t>; // C++11 feature
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>;
template<> class numeric_limits<unsigned long long>;
template<> class numeric_limits<float>;
template<> class numeric_limits<double>;

template<> class numeric_limits<long double>;

Additionally, a specialization exists for every cv-qualified version of each arithmetic type, identical to the unqualified specialization, e.g. `std::numeric_limits<const int>`, `std::numeric_limits<volatile int>`, and `std::numeric_limits<const volatile int>` are provided and are equivalent to `std::numeric_limits<int>`.

The standard library types that are 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.

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 | Members
--- | ---
`min()` | `lowest()` (C++11) | `max()` | `epsilon()` | `digits` | `digits10` | `min_exponent` | `min_exponent10` | `max_exponent` | `max_exponent10` | `radix`
`numeric_limits<` bool`>` |  |  |  |  |  |  |  |  |  |  | 2
`numeric_limits<` char`>` | CHAR_MIN | CHAR_MIN | CHAR_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` signed char`>` | SCHAR_MIN | SCHAR_MIN | SCHAR_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` unsigned char`>` | ​0​ | ​0​ | UCHAR_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` wchar_t`>` | WCHAR_MIN | WCHAR_MIN | WCHAR_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` char8_t`>` | ​0​ | ​0​ | UCHAR_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` char16_t`>` | ​0​ | ​0​ | UINT_LEAST16_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` char32_t`>` | ​0​ | ​0​ | UINT_LEAST32_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` short`>` | SHRT_MIN | SHRT_MIN | SHRT_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` signed short`>` |  |  |  |  |  |  |
`numeric_limits<` unsigned short`>` | ​0​ | ​0​ | USHRT_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` int`>` | INT_MIN | INT_MIN | INT_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` signed int`>` |  |  |  |  |  |  |
`numeric_limits<` unsigned int`>` | ​0​ | ​0​ | UINT_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` long`>` | LONG_MIN | LONG_MIN | LONG_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` signed long`>` |  |  |  |  |  |
`numeric_limits<` unsigned long`>` | ​0​ | ​0​ | ULONG_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` long long`>` | LLONG_MIN | LLONG_MIN | LLONG_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` signed long long`>` |  |  |  |  |  |  |
`numeric_limits<` unsigned long long`>` | ​0​ | ​0​ | ULLONG_MAX |  |  |  |  |  |  |  | 2
`numeric_limits<` float`>` | FLT_MIN | - FLT_MAX | FLT_MAX | FLT_EPSILON | FLT_MANT_DIG | FLT_DIG | FLT_MIN_EXP | FLT_MIN_10_EXP | FLT_MAX_EXP | FLT_MAX_10_EXP | FLT_RADIX
`numeric_limits<` double`>` | DBL_MIN | - DBL_MAX | DBL_MAX | DBL_EPSILON | DBL_MANT_DIG | DBL_DIG | DBL_MIN_EXP | DBL_MIN_10_EXP | DBL_MAX_EXP | DBL_MAX_10_EXP | FLT_RADIX
`numeric_limits<` long double`>` | LDBL_MIN | - LDBL_MAX | LDBL_MAX | LDBL_EPSILON | LDBL_MANT_DIG | LDBL_DIG | 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\tlowest()\tmin()\t\tmax()\n\n";

        std::cout << "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';
        std::cout << "int\t"
                  << std::numeric_limits<int>::lowest() << '\t'
                  << std::numeric_limits<int>::min() << '\t'
                  << std::numeric_limits<int>::max() << '\n';
        std::cout << "float\t"
                  << std::numeric_limits<float>::lowest() << '\t'
                  << std::numeric_limits<float>::min() << '\t'
                  << std::numeric_limits<float>::max() << '\n';
        std::cout << "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()

    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

### See also

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

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