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`<limits>`

Include the standard header <limits> to define the template class numeric_limits. Explicit specializations of this class describe many arithmetic properties of the scalar types (other than pointers).

namespace std {
enum float_denorm_style;
enum float_round_style;
template<class Ty>
    class numeric_limits;
    };

`float_denorm_style`

enum float_denorm_style {
    denorm_indeterminate = -1,
    denorm_absent = 0,
    denorm_present = 1
    };

The enumeration describes the various methods that an implementation can choose for representing a denormalized floating-point value -- one too small to represent as a normalized value:

denorm_indeterminate -- presence or absence of denormalized forms cannot be determined at translation time
denorm_absent -- denormalized forms are absent
denorm_present -- denormalized forms are present

`float_round_style`

enum float_round_style {
    round_indeterminate = -1,
    round_toward_zero = 0,
    round_to_nearest = 1,
    round_toward_infinity = 2,
    round_toward_neg_infinity = 3
    };

The enumeration describes the various methods that an implementation can choose for rounding a floating-point value to an integer value:

round_indeterminate -- rounding method cannot be determined
round_toward_zero -- round toward zero
round_to_nearest -- round to nearest integer
round_toward_infinity -- round away from zero
round_toward_neg_infinity -- round to more negative integer

`numeric_limits`

template<class Ty>
    class numeric_limits {
public:
    static const float_denorm_style has_denorm
        = denorm_absent;
    static const bool has_denorm_loss = false;
    static const bool has_infinity = false;
    static const bool has_quiet_NaN = false;
    static const bool has_signaling_NaN = false;
    static const bool is_bounded = false;
    static const bool is_exact = false;
    static const bool is_iec559 = false;
    static const bool is_integer = false;
    static const bool is_modulo = false;
    static const bool is_signed = false;
    static const bool is_specialized = false;
    static const bool tinyness_before = false;
    static const bool traps = false;
    static const float_round_style round_style =
        round_toward_zero;
    static const int digits = 0;
    static const int digits10 = 0;
    static const int max_exponent = 0;
    static const int max_exponent10 = 0;
    static const int min_exponent = 0;
    static const int min_exponent10 = 0;
    static const int radix = 0;
    static Ty denorm_min() throw();
    static Ty epsilon() throw();
    static Ty infinity() throw();
    static Ty max() throw();
    static Ty min() throw();
    static Ty quiet_NaN() throw();
    static Ty round_error() throw();
    static Ty signaling_NaN() throw();
    };

The template class describes many arithmetic properties of its parameter type Ty. 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, and long double. For all these explicit specializations, the member is_specialized is true, and all relevant members have meaningful values. The program can supply additional explicit specializations.

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 Ty(0).

`numeric_limits::denorm_min`

static Ty denorm_min() throw();

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

`numeric_limits::digits`

static const int digits = 0;

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).

`numeric_limits::digits10`

static const int digits10 = 0;

The member stores the number of decimal digits that the type can represent without change.

`numeric_limits::epsilon`

static Ty epsilon() throw();

The function returns the difference between 1 and the smallest value greater than 1 that is representable for the type (which is the value FLT_EPSILON for type float).

`numeric_limits::has_denorm`

static const float_denorm_style has_denorm =
    denorm_absent;

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

`numeric_limits::has_denorm_loss`

static const bool has_denorm_loss = false;

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.

`numeric_limits::has_infinity`

static const bool has_infinity = false;

The member stores true for a type that has a representation for positive infinity. True if is_iec559 is true.

`numeric_limits::has_quiet_NaN`

static const bool has_quiet_NaN = false;

The member stores true for a type that has a representation for a quiet NaN, an encoding that is ``Not a Number'' which does not signal its presence in an expression. True if is_iec559 is true.

`numeric_limits::has_signaling_NaN`

static const bool has_signaling_NaN = false;

The member stores true for a type that has a representation for a signaling NaN, an encoding that is ``Not a Number'' which signals its presence in an expression by reporting an exception. True if is_iec559 is true.

`numeric_limits::infinity`

static Ty infinity() throw();

The function returns the representation of positive infinity for the type. The return value is meaningful only if has_infinity is true.

`numeric_limits::is_bounded`

static const bool is_bounded = false;

The member stores true for a type that has a bounded set of representable values (which is the case for all predefined types).

`numeric_limits::is_exact`

static const bool is_exact = false;

The member stores true for a type that has exact representations for all its values (which is the case for all predefined integer types). A fixed-point or rational representation is also considered exact, but not a floating-point representation.

`numeric_limits::is_iec559`

static const bool is_iec559 = false;

The member stores true for a type that has a representation conforming to IEC 559, an international standard for representing floating-point values (also known as IEEE 754 in the USA).

`numeric_limits::is_integer`

static const bool is_integer = false;

The member stores true for a type that has an integer representation (which is the case for all predefined integer types).

`numeric_limits::is_modulo`

static const bool is_modulo = false;

The member stores true for a type that has a modulo representation, where all results are reduced modulo some value (which is the case for all predefined unsigned integer types).

`numeric_limits::is_signed`

static const bool is_signed = false;

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).

`numeric_limits::is_specialized`

static const bool is_specialized = false;

The member stores true for a type that has an explicit specialization defined for template class numeric_limits (which is the case for all scalar types other than pointers).

`numeric_limits::max`

static Ty max() throw();

The function returns the maximum finite value for the type (which is INT_MAX for type int and FLT_MAX for type float). The return value is meaningful if is_bounded is true.

`numeric_limits::max_exponent`

static const int max_exponent = 0;

The member stores the maximum positive integer such that the type can represent as a finite value radix raised to that power (which is the value FLT_MAX_EXP for type float). Meaningful only for floating-point types.

`numeric_limits::max_exponent10`

static const int max_exponent10 = 0;

The member stores the maximum positive integer such that the type can represent as a finite value 10 raised to that power (which is the value FLT_MAX_10_EXP for type float). Meaningful only for floating-point types.

`numeric_limits::min`

static Ty min() throw();

The function returns the minimum normalized value for the type (which is INT_MIN for type int and FLT_MIN for type float). The return value is meaningful if is_bounded is true or is_bounded is false and is_signed is false.

`numeric_limits::min_exponent`

static const int min_exponent = 0;

The member stores the minimum negative integer such that the type can represent as a normalized value radix raised to that power (which is the value FLT_MIN_EXP for type float). Meaningful only for floating-point types.

`numeric_limits::min_exponent10`

static const int min_exponent10 = 0;

The member stores the minimum negative integer such that the type can represent as a normalized value 10 raised to that power (which is the value FLT_MIN_10_EXP for type float). Meaningful only for floating-point types.

`numeric_limits::quiet_NaN`

static Ty quiet_NaN() throw();

The function returns a representation of a quiet NaN for the type. The return value is meaningful only if has_quiet_NaN is true.

`numeric_limits::radix`

static const int radix = 0;

The member stores the base of the representation for the type (which 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).

`numeric_limits::round_error`

static Ty round_error() throw();

The function returns the maximum rounding error for the type.

`numeric_limits::round_style`

static const float_round_style round_style =
     round_toward_zero;

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

`numeric_limits::signaling_NaN`

static Ty signaling_NaN() throw();

The function returns a representation of a signaling NaN for the type. The return value is meaningful only if has_signaling_NaN is true.

`numeric_limits::tinyness_before`

static const bool tinyness_before = false;

The member stores true for a type that determines whether a value is ``tiny'' (too small to represent as a normalized value) before rounding, an option with IEC 559 floating-point representations that can affect some results.

`numeric_limits::traps`

static const bool traps = false;

The member stores true for a type that generates some kind of signal to report certain arithmetic exceptions.

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