class template
<limits>

std::numeric_limits

template <class T> numeric_limits;
Numeric limits type
Provides information about the properties of arithmetic types (either integral or floating-point) in the specific platform for which the library compiles.

This class template is specialized for every fundamental arithmetic type, with its members describing the properties of type T. This template shall not be specialized for any other type.

Template parameters

T
A type.
If this is a fundamental arithmetic type, the members of the class describe its properties.

Template instantiations

fundamental arithmetic types
integral typesbool
char
wchar_t
signed char
short int
int
long int
unsigned char
unsigned short int
unsigned int
unsigned long int
floating point typesfloat
double
long double
For any other type, its default definition is used.
fundamental arithmetic types
integral typesbool
char
char16_t
char32_t
wchar_t
signed char
short int
int
long int
long long int
unsigned char
unsigned short int
unsigned int
unsigned long int
unsigned long long int
floating point typesfloat
double
long double
This template is also specialized for all const and/or volatile qualifications of these types, with the same values as their unqualified specializations.

For any other type, its default definition is used.

Members that produce a value of type T are member functions, while members of specific types are static member constants:

Members

membertypeproperty
is_specializedbooltrue for all arithmetic types (i.e., those for which numeric_limits is specialized).
false for all other types.
min()TMinimum finite value.
For floating types with denormalization (variable number of exponent bits): minimum positive normalized value.
Equivalent to CHAR_MIN, SCHAR_MIN, SHRT_MIN, INT_MIN, LONG_MIN, LLONG_MIN, FLT_MIN, DBL_MIN, LDBL_MIN or 0, depending on type.
max()TMaximum finite value.
Equivalent to CHAR_MAX, SCHAR_MAX, UCHAR_MAX, SHRT_MAX, USHRT_MAX, INT_MAX, UINT_MAX, LONG_MAX, ULONG_MAX, LLONG_MAX, ULLONG_MAX, UINT_LEAST16_MAX, UINT_LEAST32_MAX, FLT_MAX, DBL_MAX or LDBL_MAX, depending on type.
lowest()TMinimum finite value. (since C++11)
For integral types: the same as min().
For floating-point types: implementation-dependent; generally, the negative of max().
digitsintFor integer types: number of non-sign bits (radix base digits) in the representation.
For floating types: number of digits (in radix base) in the mantissa (equivalent to FLT_MANT_DIG, DBL_MANT_DIG or LDBL_MANT_DIG).
digits10intNumber of digits (in decimal base) that can be represented without change.
Equivalent to FLT_DIG, DBL_DIG or LDBL_DIG for floating types.
max_digits10intNumber of digits (in decimal base) required to ensure that values that differ are always differentiated.
is_signedbooltrue if type is signed.
is_integerbooltrue if type is integer.
is_exactbooltrue if type uses exact representations.
radixintFor integer types: base of the representation.
For floating types: base of the exponent of the representation (equivalent to FLT_RADIX).
epsilon()TMachine epsilon (the difference between 1 and the least value greater than 1 that is representable).
Equivalent to FLT_EPSILON, DBL_EPSILON or LDBL_EPSILON for floating types.
round_error()TMeasure of the maximum rounding error.
min_exponentintMinimum negative integer value such that radix raised to (min_exponent-1) generates a normalized floating-point number.
Equivalent to FLT_MIN_EXP, DBL_MIN_EXP or LDBL_MIN_EXP for floating types.
min_exponent10intMinimum negative integer value such that 10 raised to that power generates a normalized floating-point number.
Equivalent to FLT_MIN_10_EXP, DBL_MIN_10_EXP or LDBL_MIN_10_EXP for floating types.
max_exponentintMaximum integer value such that radix raised to (max_exponent-1) generates a representable finite floating-point number.
Equivalent to FLT_MAX_EXP, DBL_MAX_EXP or LDBL_MAX_EXP for floating types.
max_exponent10intMaximum integer value such that 10 raised to that power generates a normalized finite floating-point number.
Equivalent to FLT_MAX_10_EXP, DBL_MAX_10_EXP or LDBL_MAX_10_EXP for floating types.
has_infinitybooltrue if the type has a representation for positive infinity.
has_quiet_NaNbooltrue if the type has a representation for a quiet (non-signaling) "Not-a-Number".
has_signaling_NaNbooltrue if the type has a representation for a signaling "Not-a-Number".
has_denormfloat_denorm_styleDenormalized values (representations with a variable number of exponent bits). A type may have any of the following enum values:
denorm_absent, if it does not allow denormalized values.
denorm_present, if it allows denormalized values.
denorm_indeterminate, if indeterminate at compile time.
has_denorm_lossbooltrue if a loss of accuracy is detected as a denormalization loss, rather than an inexact result.
infinity()TRepresentation of positive infinity, if available.
quiet_NaN()TRepresentation of quiet (non-signaling) "Not-a-Number", if available.
signaling_NaN()TRepresentation of signaling "Not-a-Number", if available.
denorm_min()TMinimum positive denormalized value.
For types not allowing denormalized values: same as min().
is_iec559booltrue if the type adheres to IEC-559 / IEEE-754 standard.
An IEC-559 type always has has_infinity, has_quiet_NaN and has_signaling_NaN set to true; And infinity, quiet_NaN and signaling_NaN return some non-zero value.
is_boundedbooltrue if the set of values represented by the type is finite.
is_modulobooltrue if the type is modulo. A type is modulo if it is possible to add two positive numbers and have a result that wraps around to a third number that is less.
trapsbooltrue if trapping is implemented for the type.
tinyness_beforebooltrue if tinyness is detected before rounding.
round_stylefloat_round_styleRounding style. A type may have any of the following enum values:
round_toward_zero, if it rounds toward zero.
round_to_nearest, if it rounds to the nearest representable value.
round_toward_infinity, if it rounds toward infinity.
round_toward_neg_infinity, if it rounds toward negative infinity.
round_indeterminate, if the rounding style is indeterminable at compile time.

For all types that are not fundamental arithmetic types, the default template definition is used:
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template <class T> class numeric_limits {
public:
  static const bool is_specialized = false;
  static T min() throw();
  static T max() throw();
  static const int  digits = 0;
  static const int  digits10 = 0;
  static const bool is_signed = false;
  static const bool is_integer = false;
  static const bool is_exact = false;
  static const int radix = 0;
  static T epsilon() throw();
  static T round_error() throw();

  static const int  min_exponent = 0;
  static const int  min_exponent10 = 0;
  static const int  max_exponent = 0;
  static const int  max_exponent10 = 0;

  static const bool has_infinity = false;
  static const bool has_quiet_NaN = false;
  static const bool has_signaling_NaN = false;
  static const float_denorm_style has_denorm = denorm_absent;
  static const bool has_denorm_loss = false;
  static T infinity() throw();
  static T quiet_NaN() throw();
  static T signaling_NaN() throw();
  static T denorm_min() throw();

  static const bool is_iec559 = false;
  static const bool is_bounded = false;
  static const bool is_modulo = false;

  static const bool traps = false;
  static const bool tinyness_before = false;
  static const float_round_style round_style = round_toward_zero;
};

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template <class T> class numeric_limits {
public:
  static constexpr bool is_specialized = false;
  static constexpr T min() noexcept { return T(); }
  static constexpr T max() noexcept { return T(); }
  static constexpr T lowest() noexcept { return T(); }
  static constexpr int  digits = 0;
  static constexpr int  digits10 = 0;
  static constexpr bool is_signed = false;
  static constexpr bool is_integer = false;
  static constexpr bool is_exact = false;
  static constexpr int radix = 0;
  static constexpr T epsilon() noexcept { return T(); }
  static constexpr T round_error() noexcept { return T(); }

  static constexpr int  min_exponent = 0;
  static constexpr int  min_exponent10 = 0;
  static constexpr int  max_exponent = 0;
  static constexpr int  max_exponent10 = 0;

  static constexpr bool has_infinity = false;
  static constexpr bool has_quiet_NaN = false;
  static constexpr bool has_signaling_NaN = false;
  static constexpr float_denorm_style has_denorm = denorm_absent;
  static constexpr bool has_denorm_loss = false;
  static constexpr T infinity() noexcept { return T(); }
  static constexpr T quiet_NaN() noexcept { return T(); }
  static constexpr T signaling_NaN() noexcept { return T(); }
  static constexpr T denorm_min() noexcept { return T(); }

  static constexpr bool is_iec559 = false;
  static constexpr bool is_bounded = false;
  static constexpr bool is_modulo = false;

  static constexpr bool traps = false;
  static constexpr bool tinyness_before = false;
  static constexpr float_round_style round_style = round_toward_zero;
};


All specializations shall also provide these values as constant expressions.

Example

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// numeric_limits example
#include <iostream>     // std::cout
#include <limits>       // std::numeric_limits

int main () {
  std::cout << std::boolalpha;
  std::cout << "Minimum value for int: " << std::numeric_limits<int>::min() << '\n';
  std::cout << "Maximum value for int: " << std::numeric_limits<int>::max() << '\n';
  std::cout << "int is signed: " << std::numeric_limits<int>::is_signed << '\n';
  std::cout << "Non-sign bits in int: " << std::numeric_limits<int>::digits << '\n';
  std::cout << "int has infinity: " << std::numeric_limits<int>::has_infinity << '\n';
  return 0;
}


Possible output:

Minimum value for int: -2147483648
Maximum value for int: 2147483647
int is signed: true
Non-sign bits in int: 31
int has infinity: false

See also

<climits> (limits.h)
Sizes of integral types (header)
<cfloat> (float.h)
Characteristics of floating-point types (header)