numeric_limits Class

The class template describes arithmetic properties of built-in numerical types.

Syntax

template <class Type>
    class numeric_limits

Parameters

Type
The fundamental element data type whose properties are being tested or queried or set. Type can also be declared const, volatile, or const volatile.

Remarks

The header defines explicit specializations for the types wchar_t, bool, char, signed char, unsigned char, short, unsigned short, int, unsigned int, long, unsigned long, float, double, long double, long long, unsigned long long, char16_t, and char32_t. For these explicit specializations, the member numeric_limits::is_specialized is true, and all relevant members have meaningful values. The program can supply additional explicit specializations. Most member functions of the class describe or test possible implementations of float.

For an arbitrary specialization, no members have meaningful values. A member object that does not have a meaningful value stores zero (or false) and a member function that does not return a meaningful value returns Type(0).

Static Functions and Constants

denorm_min Returns the smallest nonzero denormalized value.
digits Returns the number of radix digits that the type can represent without loss of precision.
digits10 Returns the number of decimal digits that the type can represent without loss of precision.
epsilon Returns the difference between 1 and the smallest value greater than 1 that the data type can represent.
has_denorm Tests whether a type allows denormalized values.
has_denorm_loss Tests whether loss of accuracy is detected as a denormalization loss rather than as an inexact result.
has_infinity Tests whether a type has a representation for positive infinity.
has_quiet_NaN Tests whether a type has a representation for a quiet not a number (NAN), which is non-signaling.
has_signaling_NaN Tests whether a type has a representation for signaling not a number (NAN).
infinity The representation for positive infinity for a type, if available.
is_bounded Tests if the set of values that a type may represent is finite.
is_exact Tests if the calculations done on a type are free of rounding errors.
is_iec559 Tests if a type conforms to IEC 559 standards.
is_integer Tests if a type has an integer representation.
is_modulo Tests if a type has a modulo representation.
is_signed Tests if a type has a signed representation.
is_specialized Tests if a type has an explicit specialization defined in the class template numeric_limits.
lowest Returns the most negative finite value.
max Returns the maximum finite value for a type.
max_digits10 Returns the number of decimal digits required to ensure that two distinct values of the type have distinct decimal representations.
max_exponent Returns the maximum positive integral exponent that the floating-point type can represent as a finite value when a base of radix is raised to that power.
max_exponent10 Returns the maximum positive integral exponent that the floating-point type can represent as a finite value when a base of ten is raised to that power.
min Returns the minimum normalized value for a type.
min_exponent Returns the maximum negative integral exponent that the floating-point type can represent as a finite value when a base of radix is raised to that power.
min_exponent10 Returns the maximum negative integral exponent that the floating-point type can represent as a finite value when a base of ten is raised to that power.
quiet_NaN Returns the representation of a quiet not a number (NAN) for the type.
radix Returns the integral base, referred to as radix, used for the representation of a type.
round_error Returns the maximum rounding error for the type.
round_style Returns a value that describes the various methods that an implementation can choose for rounding a floating-point value to an integer value.
signaling_NaN Returns the representation of a signaling not a number (NAN) for the type.
tinyness_before Tests whether a type can determine that a value is too small to represent as a normalized value before rounding it.
traps Tests whether trapping that reports on arithmetic exceptions is implemented for a type.

denorm_min

Returns the smallest nonzero denormalized value.

static constexpr Type denorm_min() throw();

Return Value

The smallest nonzero denormalized value.

Remarks

long double is the same as double for the C++ compiler.

The function returns the minimum value for the type, which is the same as min if has_denorm is not equal to denorm_present.

Example

// numeric_limits_denorm_min.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The smallest nonzero denormalized value" << endl
        << "for float objects is: "
        << numeric_limits<float>::denorm_min( ) << endl;
   cout << "The smallest nonzero denormalized value" << endl
        << "for double objects is: "
        << numeric_limits<double>::denorm_min( ) << endl;
   cout << "The smallest nonzero denormalized value" << endl
        << "for long double objects is: "
        << numeric_limits<long double>::denorm_min( ) << endl;

   // A smaller value will round to zero
   cout << numeric_limits<float>::denorm_min( )/2 <<endl;
   cout << numeric_limits<double>::denorm_min( )/2 <<endl;
   cout << numeric_limits<long double>::denorm_min( )/2 <<endl;
}
The smallest nonzero denormalized value
for float objects is: 1.4013e-045
The smallest nonzero denormalized value
for double objects is: 4.94066e-324
The smallest nonzero denormalized value
for long double objects is: 4.94066e-324
0
0
0

digits

Returns the number of radix digits that the type can represent without loss of precision.

static constexpr int digits = 0;

Return Value

The number of radix digits that the type can represent without loss of precision.

Remarks

The member stores the number of radix digits that the type can represent without change, which is the number of bits other than any sign bit for a predefined integer type, or the number of mantissa digits for a predefined floating-point type.

Example

// numeric_limits_digits_min.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << numeric_limits<float>::digits <<endl;
   cout << numeric_limits<double>::digits <<endl;
   cout << numeric_limits<long double>::digits <<endl;
   cout << numeric_limits<int>::digits <<endl;
   cout << numeric_limits<__int64>::digits <<endl;
}
24
53
53
31
63

digits10

Returns the number of decimal digits that the type can represent without loss of precision.

static constexpr int digits10 = 0;

Return Value

The number of decimal digits that the type can represent without loss of precision.

Example

// numeric_limits_digits10.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << numeric_limits<float>::digits10 <<endl;
   cout << numeric_limits<double>::digits10 <<endl;
   cout << numeric_limits<long double>::digits10 <<endl;
   cout << numeric_limits<int>::digits10 <<endl;
   cout << numeric_limits<__int64>::digits10 <<endl;
   float f = (float)99999999;
   cout.precision ( 10 );
   cout << "The float is; " << f << endl;
}
6
15
15
9
18
The float is; 100000000

epsilon

The function returns the difference between 1 and the smallest value greater than 1 that is representable for the data type.

static constexpr Type epsilon() throw();

Return Value

The difference between 1 and the smallest value greater than 1 that is representable for the data type.

Remarks

The value is FLT_EPSILON for type float. epsilon for a type is the smallest positive floating-point number N such that N + epsilon + N is representable.

Example

// numeric_limits_epsilon.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The difference between 1 and the smallest "
        << "value greater than 1" << endl
        << "for float objects is: "
        << numeric_limits<float>::epsilon( ) << endl;
   cout << "The difference between 1 and the smallest "
        << "value greater than 1" << endl
        << "for double objects is: "
        << numeric_limits<double>::epsilon( ) << endl;
   cout << "The difference between 1 and the smallest "
        << "value greater than 1" << endl
        << "for long double objects is: "
        << numeric_limits<long double>::epsilon( ) << endl;
}
The difference between 1 and the smallest value greater than 1
for float objects is: 1.19209e-007
The difference between 1 and the smallest value greater than 1
for double objects is: 2.22045e-016
The difference between 1 and the smallest value greater than 1
for long double objects is: 2.22045e-016

has_denorm

Tests whether a type allows denormalized values.

static constexpr float_denorm_style has_denorm = denorm_absent;

Return Value

An enumeration value of type constfloat_denorm_style, indicating whether the type allows denormalized values.

Remarks

The member stores denorm_present for a floating-point type that has denormalized values, effectively a variable number of exponent bits.

Example

// numeric_limits_has_denorm.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects allow denormalized values: "
        << numeric_limits<float>::has_denorm
        << endl;
   cout << "Whether double objects allow denormalized values: "
        << numeric_limits<double>::has_denorm
        << endl;
   cout << "Whether long int objects allow denormalized values: "
        << numeric_limits<long int>::has_denorm
        << endl;
}
Whether float objects allow denormalized values: 1
Whether double objects allow denormalized values: 1
Whether long int objects allow denormalized values: 0

has_denorm_loss

Tests whether loss of accuracy is detected as a denormalization loss rather than as an inexact result.

static constexpr bool has_denorm_loss = false;

Return Value

true if the loss of accuracy is detected as a denormalization loss; false if not.

Remarks

The member stores true for a type that determines whether a value has lost accuracy because it is delivered as a denormalized result (too small to represent as a normalized value) or because it is inexact (not the same as a result not subject to limitations of exponent range and precision), an option with IEC 559 floating-point representations that can affect some results.

Example

// numeric_limits_has_denorm_loss.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects can detect denormalized loss: "
        << numeric_limits<float>::has_denorm_loss
        << endl;
   cout << "Whether double objects can detect denormalized loss: "
        << numeric_limits<double>::has_denorm_loss
        << endl;
   cout << "Whether long int objects can detect denormalized loss: "
        << numeric_limits<long int>::has_denorm_loss
        << endl;
}
Whether float objects can detect denormalized loss: 1
Whether double objects can detect denormalized loss: 1
Whether long int objects can detect denormalized loss: 0

has_infinity

Tests whether a type has a representation for positive infinity.

static constexpr bool has_infinity = false;

Return Value

true if the type has a representation for positive infinity; false if not.

Remarks

The member returns true if is_iec559 is true.

Example

// numeric_limits_has_infinity.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have infinity: "
        << numeric_limits<float>::has_infinity
        << endl;
   cout << "Whether double objects have infinity: "
        << numeric_limits<double>::has_infinity
        << endl;
   cout << "Whether long int objects have infinity: "
        << numeric_limits<long int>::has_infinity
        << endl;
}
Whether float objects have infinity: 1
Whether double objects have infinity: 1
Whether long int objects have infinity: 0

has_quiet_NaN

Tests whether a type has a representation for a quiet not a number (NAN), which is nonsignaling.

static constexpr bool has_quiet_NaN = false;

Return Value

true if the type has a representation for a quiet NAN; false if not.

Remarks

A quiet NAN is an encoding for not a number, which does not signal its presence in an expression. The return value is true if is_iec559 is true.

Example

// numeric_limits_has_quiet_nan.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have quiet_NaN: "
        << numeric_limits<float>::has_quiet_NaN
        << endl;
   cout << "Whether double objects have quiet_NaN: "
        << numeric_limits<double>::has_quiet_NaN
        << endl;
   cout << "Whether long int objects have quiet_NaN: "
        << numeric_limits<long int>::has_quiet_NaN
        << endl;
}
Whether float objects have quiet_NaN: 1
Whether double objects have quiet_NaN: 1
Whether long int objects have quiet_NaN: 0

has_signaling_NaN

Tests whether a type has a representation for signaling not a number (NAN).

static constexpr bool has_signaling_NaN = false;

Return Value

true if the type has a representation for a signaling NAN; false if not.

Remarks

A signaling NAN is an encoding for not a number, which signals its presence in an expression. The return value is true if is_iec559 is true.

Example

// numeric_limits_has_signaling_nan.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have a signaling_NaN: "
        << numeric_limits<float>::has_signaling_NaN
        << endl;
   cout << "Whether double objects have a signaling_NaN: "
        << numeric_limits<double>::has_signaling_NaN
        << endl;
   cout << "Whether long int objects have a signaling_NaN: "
        << numeric_limits<long int>::has_signaling_NaN
        << endl;
}
Whether float objects have a signaling_NaN: 1
Whether double objects have a signaling_NaN: 1
Whether long int objects have a signaling_NaN: 0

infinity

The representation of positive infinity for a type, if available.

static constexpr Type infinity() throw();

Return Value

The representation of positive infinity for a type, if available.

Remarks

The return value is meaningful only if has_infinity is true.

Example

// numeric_limits_infinity.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << numeric_limits<float>::has_infinity <<endl;
   cout << numeric_limits<double>::has_infinity<<endl;
   cout << numeric_limits<long double>::has_infinity <<endl;
   cout << numeric_limits<int>::has_infinity <<endl;
   cout << numeric_limits<__int64>::has_infinity <<endl;

   cout << "The representation of infinity for type float is: "
        << numeric_limits<float>::infinity( ) <<endl;
   cout << "The representation of infinity for type double is: "
        << numeric_limits<double>::infinity( ) <<endl;
   cout << "The representation of infinity for type long double is: "
        << numeric_limits<long double>::infinity( ) <<endl;
}
1
1
1
0
0
The representation of infinity for type float is: inf
The representation of infinity for type double is: inf
The representation of infinity for type long double is: inf

is_bounded

Tests if the set of values that a type may represent is finite.

static constexpr bool is_bounded = false;

Return Value

true if the type has a bounded set of representable values; false if not.

Remarks

All predefined types have a bounded set of representable values and return true.

Example

// numeric_limits_is_bounded.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have bounded set "
        << "of representable values: "
        << numeric_limits<float>::is_bounded
        << endl;
   cout << "Whether double objects have bounded set "
        << "of representable values: "
        << numeric_limits<double>::is_bounded
        << endl;
   cout << "Whether long int objects have bounded set "
        << "of representable values: "
        << numeric_limits<long int>::is_bounded
        << endl;
   cout << "Whether unsigned char objects have bounded set "
        << "of representable values: "
        << numeric_limits<unsigned char>::is_bounded
        << endl;
}
Whether float objects have bounded set of representable values: 1
Whether double objects have bounded set of representable values: 1
Whether long int objects have bounded set of representable values: 1
Whether unsigned char objects have bounded set of representable values: 1

is_exact

Tests if the calculations done on a type are free of rounding errors.

static constexpr bool is_exact = false;

Return Value

true if the calculations are free of rounding errors; false if not.

Remarks

All predefined integer types have exact representations for their values and return false. A fixed-point or rational representation is also considered exact, but a floating-point representation is not.

Example

// numeric_limits_is_exact.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have calculations "
        << "free of rounding errors: "
        << numeric_limits<float>::is_exact
        << endl;
   cout << "Whether double objects have calculations "
        << "free of rounding errors: "
        << numeric_limits<double>::is_exact
        << endl;
   cout << "Whether long int objects have calculations "
        << "free of rounding errors: "
        << numeric_limits<long int>::is_exact
        << endl;
   cout << "Whether unsigned char objects have calculations "
        << "free of rounding errors: "
        << numeric_limits<unsigned char>::is_exact
        << endl;
}
Whether float objects have calculations free of rounding errors: 0
Whether double objects have calculations free of rounding errors: 0
Whether long int objects have calculations free of rounding errors: 1
Whether unsigned char objects have calculations free of rounding errors: 1

is_iec559

Tests if a type conforms to IEC 559 standards.

static constexpr bool is_iec559 = false;

Return Value

true if the type conforms to the IEC 559 standards; false if not.

Remarks

The IEC 559 is an international standard for representing floating-point values and is also known as IEEE 754 in the USA.

Example

// numeric_limits_is_iec559.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects conform to iec559 standards: "
        << numeric_limits<float>::is_iec559
        << endl;
   cout << "Whether double objects conform to iec559 standards: "
        << numeric_limits<double>::is_iec559
        << endl;
   cout << "Whether int objects conform to iec559 standards: "
        << numeric_limits<int>::is_iec559
        << endl;
   cout << "Whether unsigned char objects conform to iec559 standards: "
        << numeric_limits<unsigned char>::is_iec559
        << endl;
}
Whether float objects conform to iec559 standards: 1
Whether double objects conform to iec559 standards: 1
Whether int objects conform to iec559 standards: 0
Whether unsigned char objects conform to iec559 standards: 0

is_integer

Tests if a type has an integer representation.

static constexpr bool is_integer = false;

Return Value

true if the type has an integer representation; false if not.

Remarks

All predefined integer types have an integer representation.

Example

// numeric_limits_is_integer.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have an integral representation: "
        << numeric_limits<float>::is_integer
        << endl;
   cout << "Whether double objects have an integral representation: "
        << numeric_limits<double>::is_integer
        << endl;
   cout << "Whether int objects have an integral representation: "
        << numeric_limits<int>::is_integer
        << endl;
   cout << "Whether unsigned char objects have an integral representation: "
        << numeric_limits<unsigned char>::is_integer
        << endl;
}
Whether float objects have an integral representation: 0
Whether double objects have an integral representation: 0
Whether int objects have an integral representation: 1
Whether unsigned char objects have an integral representation: 1

is_modulo

Tests if a type has a modulo representation.

static constexpr bool is_modulo = false;

Return Value

true if the type has a modulo representation; false if not.

Remarks

A modulo representation is a representation where all results are reduced modulo some value. All predefined unsigned integer types have a modulo representation.

Example

// numeric_limits_is_modulo.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have a modulo representation: "
        << numeric_limits<float>::is_modulo
        << endl;
   cout << "Whether double objects have a modulo representation: "
        << numeric_limits<double>::is_modulo
        << endl;
   cout << "Whether signed char objects have a modulo representation: "
        << numeric_limits<signed char>::is_modulo
        << endl;
   cout << "Whether unsigned char objects have a modulo representation: "
        << numeric_limits<unsigned char>::is_modulo
        << endl;
}
Whether float objects have a modulo representation: 0
Whether double objects have a modulo representation: 0
Whether signed char objects have a modulo representation: 1
Whether unsigned char objects have a modulo representation: 1

is_signed

Tests if a type has a signed representation.

static constexpr bool is_signed = false;

Return Value

true if the type has a signed representation; false if not.

Remarks

The member stores true for a type that has a signed representation, which is the case for all predefined floating-point and signed integer types.

Example

// numeric_limits_is_signaled.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have a signed representation: "
        << numeric_limits<float>::is_signed
        << endl;
   cout << "Whether double objects have a signed representation: "
        << numeric_limits<double>::is_signed
        << endl;
   cout << "Whether signed char objects have a signed representation: "
        << numeric_limits<signed char>::is_signed
        << endl;
   cout << "Whether unsigned char objects have a signed representation: "
        << numeric_limits<unsigned char>::is_signed
        << endl;
}
Whether float objects have a signed representation: 1
Whether double objects have a signed representation: 1
Whether signed char objects have a signed representation: 1
Whether unsigned char objects have a signed representation: 0

is_specialized

Tests if a type has an explicit specialization defined in the class template numeric_limits.

static constexpr bool is_specialized = false;

Return Value

true if the type has an explicit specialization defined in the class template; false if not.

Remarks

All scalar types other than pointers have an explicit specialization defined for class template numeric_limits.

Example

// numeric_limits_is_specialized.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float objects have an explicit "
        << "specialization in the class: "
        << numeric_limits<float>::is_specialized
        << endl;
   cout << "Whether float* objects have an explicit "
        << "specialization in the class: "
        << numeric_limits<float*>::is_specialized
        << endl;
   cout << "Whether int objects have an explicit "
        << "specialization in the class: "
        << numeric_limits<int>::is_specialized
        << endl;
   cout << "Whether int* objects have an explicit "
        << "specialization in the class: "
        << numeric_limits<int*>::is_specialized
        << endl;
}
Whether float objects have an explicit specialization in the class: 1
Whether float* objects have an explicit specialization in the class: 0
Whether int objects have an explicit specialization in the class: 1
Whether int* objects have an explicit specialization in the class: 0

lowest

Returns the most negative finite value.

static constexpr Type lowest() throw();

Return Value

Returns the most negative finite value.

Remarks

Returns the most negative finite value for the type (which is typically min() for integer types and -max() for floating-point types). The return value is meaningful if is_bounded is true.

max

Returns the maximum finite value for a type.

static constexpr Type max() throw();

Return Value

The maximum finite value for a type.

Remarks

The maximum finite value is INT_MAX for type int and FLT_MAX for type float. The return value is meaningful if is_bounded is true.

Example

// numeric_limits_max.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main() {
   cout << "The maximum value for type float is:  "
        << numeric_limits<float>::max( )
        << endl;
   cout << "The maximum value for type double is:  "
        << numeric_limits<double>::max( )
        << endl;
   cout << "The maximum value for type int is:  "
        << numeric_limits<int>::max( )
        << endl;
   cout << "The maximum value for type short int is:  "
        << numeric_limits<short int>::max( )
        << endl;
}

max_digits10

Returns the number of decimal digits required to make sure that two distinct values of the type have distinct decimal representations.

static constexpr int max_digits10 = 0;

Return Value

Returns the number of decimal digits that are required to make sure that two distinct values of the type have distinct decimal representations.

Remarks

The member stores the number of decimal digits required to make sure that two distinct values of the type have distinct decimal representations.

max_exponent

Returns the maximum positive integral exponent that the floating-point type can represent as a finite value when a base of radix is raised to that power.

static constexpr int max_exponent = 0;

Return Value

The maximum integral radix-based exponent representable by the type.

Remarks

The member function return is meaningful only for floating-point types. The max_exponent is the value FLT_MAX_EXP for type float.

Example

// numeric_limits_max_exponent.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The maximum radix-based exponent for type float is:  "
        << numeric_limits<float>::max_exponent
        << endl;
   cout << "The maximum radix-based exponent for type double is:  "
        << numeric_limits<double>::max_exponent
        << endl;
   cout << "The maximum radix-based exponent for type long double is:  "
        << numeric_limits<long double>::max_exponent
        << endl;
}
The maximum radix-based exponent for type float is:  128
The maximum radix-based exponent for type double is:  1024
The maximum radix-based exponent for type long double is:  1024

max_exponent10

Returns the maximum positive integral exponent that the floating-point type can represent as a finite value when a base of ten is raised to that power.

static constexpr int max_exponent10 = 0;

Return Value

The maximum integral base 10 exponent representable by the type.

Remarks

The member function return is meaningful only for floating-point types. The max_exponent is the value FLT_MAX_10 for type float.

Example

// numeric_limits_max_exponent10.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The maximum base 10 exponent for type float is:  "
           << numeric_limits<float>::max_exponent10
           << endl;
   cout << "The maximum base 10 exponent for type double is:  "
           << numeric_limits<double>::max_exponent10
           << endl;
   cout << "The maximum base 10 exponent for type long double is:  "
           << numeric_limits<long double>::max_exponent10
           << endl;
}
The maximum base 10 exponent for type float is:  38
The maximum base 10 exponent for type double is:  308
The maximum base 10 exponent for type long double is:  308

min

Returns the minimum normalized value for a type.

static constexpr Type min() throw();

Return Value

The minimum normalized value for the type.

Remarks

The minimum normalized value is INT_MIN for type int and FLT_MIN for type float. The return value is meaningful if is_bounded is true or if is_signed is false.

Example

// numeric_limits_min.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The minimum value for type float is:  "
        << numeric_limits<float>::min( )
        << endl;
   cout << "The minimum value for type double is:  "
        << numeric_limits<double>::min( )
        << endl;
   cout << "The minimum value for type int is:  "
        << numeric_limits<int>::min( )
        << endl;
   cout << "The minimum value for type short int is:  "
        << numeric_limits<short int>::min( )
        << endl;
}
The minimum value for type float is:  1.17549e-038
The minimum value for type double is:  2.22507e-308
The minimum value for type int is:  -2147483648
The minimum value for type short int is:  -32768

min_exponent

Returns the maximum negative integral exponent that the floating-point type can represent as a finite value when a base of radix is raised to that power.

static constexpr int min_exponent = 0;

Return Value

The minimum integral radix-based exponent representable by the type.

Remarks

The member function is meaningful only for floating-point types. The min_exponent is the value FLT_MIN_EXP for type float.

Example

// numeric_limits_min_exponent.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The minimum radix-based exponent for type float is:  "
        << numeric_limits<float>::min_exponent
        << endl;
   cout << "The minimum radix-based exponent for type double is:  "
        << numeric_limits<double>::min_exponent
        << endl;
   cout << "The minimum radix-based exponent for type long double is:  "
         << numeric_limits<long double>::min_exponent
        << endl;
}
The minimum radix-based exponent for type float is:  -125
The minimum radix-based exponent for type double is:  -1021
The minimum radix-based exponent for type long double is:  -1021

min_exponent10

Returns the maximum negative integral exponent that the floating-point type can represent as a finite value when a base of ten is raised to that power.

static constexpr int min_exponent10 = 0;

Return Value

The minimum integral base 10 exponent representable by the type.

Remarks

The member function is meaningful only for floating-point types. The min_exponent10 is the value FLT_MIN_10_EXP for type float.

Example

// numeric_limits_min_exponent10.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The minimum base 10 exponent for type float is:  "
        << numeric_limits<float>::min_exponent10
        << endl;
   cout << "The minimum base 10 exponent for type double is:  "
        << numeric_limits<double>::min_exponent10
        << endl;
   cout << "The minimum base 10 exponent for type long double is:  "
        << numeric_limits<long double>::min_exponent10
        << endl;
}
The minimum base 10 exponent for type float is:  -37
The minimum base 10 exponent for type double is:  -307
The minimum base 10 exponent for type long double is:  -307

quiet_NaN

Returns the representation of a quiet not a number (NAN) for the type.

static constexpr Type quiet_NaN() throw();

Return Value

The representation of a quiet NAN for the type.

Remarks

The return value is meaningful only if has_quiet_NaN is true.

Example

// numeric_limits_quiet_nan.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The quiet NaN for type float is:  "
        << numeric_limits<float>::quiet_NaN( )
        << endl;
   cout << "The quiet NaN for type int is:  "
        << numeric_limits<int>::quiet_NaN( )
        << endl;
   cout << "The quiet NaN for type long double is:  "
        << numeric_limits<long double>::quiet_NaN( )
        << endl;
}
The quiet NaN for type float is:  1.#QNAN
The quiet NaN for type int is:  0
The quiet NaN for type long double is:  1.#QNAN

radix

Returns the integral base, referred to as radix, used for the representation of a type.

static constexpr int radix = 0;

Return Value

The integral base for the representation of the type.

Remarks

The base is 2 for the predefined integer types, and the base to which the exponent is raised, or FLT_RADIX, for the predefined floating-point types.

Example

// numeric_limits_radix.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The base for type float is:  "
        << numeric_limits<float>::radix
        << endl;
   cout << "The base for type int is:  "
        << numeric_limits<int>::radix
        << endl;
   cout << "The base for type long double is:  "
        << numeric_limits<long double>::radix
        << endl;
}
The base for type float is:  2
The base for type int is:  2
The base for type long double is:  2

round_error

Returns the maximum rounding error for the type.

static constexpr Type round_error() throw();

Return Value

The maximum rounding error for the type.

Example

// numeric_limits_round_error.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The maximum rounding error for type float is:  "
        << numeric_limits<float>::round_error( )
        << endl;
   cout << "The maximum rounding error for type int is:  "
        << numeric_limits<int>::round_error( )
        << endl;
   cout << "The maximum rounding error for type long double is:  "
        << numeric_limits<long double>::round_error( )
        << endl;
}
The maximum rounding error for type float is:  0.5
The maximum rounding error for type int is:  0
The maximum rounding error for type long double is:  0.5

round_style

Returns a value that describes the various methods that an implementation can choose for rounding a floating-point value to an integer value.

static constexpr float_round_style round_style = round_toward_zero;

Return Value

A value from the float_round_style enumeration that describes the rounding style.

Remarks

The member stores a value that describes the various methods that an implementation can choose for rounding a floating-point value to an integer value.

The round style is hard coded in this implementation, so even if the program starts up with a different rounding mode, that value will not change.

Example

// numeric_limits_round_style.cpp
// compile with: /EHsc
#include <iostream>
#include <float.h>
#include <limits>

using namespace std;

int main( )
{
   cout << "The rounding style for a double type is: "
        << numeric_limits<double>::round_style << endl;
   _controlfp_s(NULL,_RC_DOWN,_MCW_RC );
   cout << "The rounding style for a double type is now: "
        << numeric_limits<double>::round_style << endl;
   cout << "The rounding style for an int type is: "
        << numeric_limits<int>::round_style << endl;
}
The rounding style for a double type is: 1
The rounding style for a double type is now: 1
The rounding style for an int type is: 0

signaling_NaN

Returns the representation of a signaling not a number (NAN) for the type.

static constexpr Type signaling_NaN() throw();

Return Value

The representation of a signaling NAN for the type.

Remarks

The return value is meaningful only if has_signaling_NaN is true.

Example

// numeric_limits_signaling_nan.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "The signaling NaN for type float is:  "
        << numeric_limits<float>::signaling_NaN( )
        << endl;
   cout << "The signaling NaN for type int is:  "
        << numeric_limits<int>::signaling_NaN( )
        << endl;
   cout << "The signaling NaN for type long double is:  "
        << numeric_limits<long double>::signaling_NaN( )
        << endl;
}

tinyness_before

Tests whether a type can determine that a value is too small to represent as a normalized value before rounding it.

static constexpr bool tinyness_before = false;

Return Value

true if the type can detect tiny values before rounding; false if it cannot.

Remarks

Types that can detect tinyness were included as an option with IEC 559 floating-point representations and its implementation can affect some results.

Example

// numeric_limits_tinyness_before.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float types can detect tinyness before rounding: "
        << numeric_limits<float>::tinyness_before
        << endl;
   cout << "Whether double types can detect tinyness before rounding: "
        << numeric_limits<double>::tinyness_before
        << endl;
   cout << "Whether long int types can detect tinyness before rounding: "
        << numeric_limits<long int>::tinyness_before
        << endl;
   cout << "Whether unsigned char types can detect tinyness before rounding: "
        << numeric_limits<unsigned char>::tinyness_before
        << endl;
}
Whether float types can detect tinyness before rounding: 1
Whether double types can detect tinyness before rounding: 1
Whether long int types can detect tinyness before rounding: 0
Whether unsigned char types can detect tinyness before rounding: 0

traps

Tests whether trapping that reports on arithmetic exceptions is implemented for a type.

static constexpr bool traps = false;

Return Value

true if trapping is implemented for the type; false if it is not.

Example

// numeric_limits_traps.cpp
// compile with: /EHsc
#include <iostream>
#include <limits>

using namespace std;

int main( )
{
   cout << "Whether float types have implemented trapping: "
        << numeric_limits<float>::traps
        << endl;
   cout << "Whether double types have implemented trapping: "
        << numeric_limits<double>::traps
        << endl;
   cout << "Whether long int types have implemented trapping: "
        << numeric_limits<long int>::traps
        << endl;
   cout << "Whether unsigned char types have implemented trapping: "
        << numeric_limits<unsigned char>::traps
        << endl;
}
Whether float types have implemented trapping: 1
Whether double types have implemented trapping: 1
Whether long int types have implemented trapping: 0
Whether unsigned char types have implemented trapping: 0