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# numeric_limits

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## numeric_limits

Numeric Limits Library

- Summary
- Data Type and Member Function Indexes
- Specializations
- Synopsis
- Description
- Interface
- Member Fields and Functions
- Example
- Warning
- See Also

### Summary

A class for representing information about scalar types.

### Data Type and Member Function Indexes

(exclusive of constructors and destructors)

### Specializations

numeric_limits<float> numeric_limits<double> numeric_limits<long double> numeric_limits<short> numeric_limits<unsigned short> numeric_limits<int> numeric_limits<unsigned int> numeric_limits<long> numeric_limits<unsigned long> numeric_limits<char> numeric_limits<wchar_t> numeric_limits<unsigned char> numeric_limits<signed char> numeric_limits<bool>

### Synopsis

#include <limits> template <class T> classnumeric_limits;

### Description

** numeric_limits** is a class for representing information about scalar types. Specializations are provided for each fundamental type, both floating point and integer, including bool.

This class encapsulates information that is contained in the <climits> and <cfloat> headers, as well as providing additional information that is not contained in any existing C or C++ header.

Not all of the information provided by members is meaningful for all specializations of ** numeric_limits**. Any value which is not meaningful for a particular type is set to 0 or false.

### Interface

template <class T> class numeric_limits { public: // General -- meaningful for all specializations. static const bool is_specialized ; static T min (); static T max (); static const int radix ; static const int digits ; static const int digits10 ; static const bool is_signed ; static const bool is_integer ; static const bool is_exact ; static const bool traps ; static const bool is_modulo ; static const bool is_bounded ; // Floating point specific. static T epsilon (); static T round_error (); static const int min_exponent10 ; static const int max_exponent10 ; static const int min_exponent ; static const int max_exponent ; static const bool has_infinity ; static const bool has_quiet_NaN ; static const bool has_signaling_NaN ; static const bool is_iec559 ; static const bool has_denorm ; static const bool tinyness_before ; static const float_round_style round_style ; static T denorm_min (); static T infinity (); static T quiet_NaN (); static T signaling_NaN (); }; enum float_round_style { round_indeterminate = -1, round_toward_zero = 0, round_to_nearest = 1, round_toward_infinity = 2, round_toward_neg_infinity = 3 };

### Member Fields and Functions

static Tdenorm_min ();

Returns the minimum denormalized value. Meaningful for all floating point types. For types that do not allow denormalized values, this method must return the minimum normalized value.

static const intdigits;

Number of radix digits which can be represented without change. For built-in integer types, digits will usually be the number of non-sign bits in the representation. For floating point types, digits is the number of radix digits in the mantissa. This member is meaningful for all specializations that declare is_bounded to be true.

static const intdigits10;

Number of base 10 digits that can be represented without change. Meaningful for all specializations that declare is_bounded to be true.

static Tepsilon();

Returns the machine epsilon (the difference between 1 and the least value greater than 1 that is representable). This function is meaningful for floating point types only.

static const boolhas_denorm;

This field is true if the type allows denormalized values (variable number of exponent bits). It is meaningful for floating point types only.

static const boolhas_infinity;

This field is true if the type has a representation for positive infinity. It is meaningful for floating point types only. This field must be true for any type claiming conformance to IEC 559.

static const boolhas_quiet_NaN;

This field is true is the type has a representation for a quiet (non-signaling) "Not a Number". It is meaningful for floating point types only and must be true for any type claiming conformance to IEC 559.

static const boolhas_signaling_NaN;

This field is true if the type has a representation for a signaling "Not a Number". It is meaningful for floating point types only, and must be true for any type claiming conformance to IEC 559.

static Tinfinity();

Returns the representation of positive infinity, if available. This member function is meaningful for only those specializations that declare has_infinity to be true. Required for any type claiming conformance to IEC 559.

static const boolis_bounded;

This field is true if the set of values representable by the type is finite. All built-in C types are bounded; this member would be false for arbitrary precision types.

static const boolis_exact;

This static member field is true if the type uses an exact representation. All integer types are exact, but not vice versa. For example, rational and fixed-exponent representations are exact but not integer. This member is meaningful for all specializations.

static const boolis_iec559;

This member is true if and only if the type adheres to the IEC 559 standard. It is meaningful for floating point types only. Must be true for any type claiming conformance to IEC 559.

static const boolis_integer;

This member is true if the type is integer. This member is meaningful for all specializations.

static const boolis_modulo;

This field is true if the type is modulo. Generally, this is false for floating types, true for unsigned integers, and true for signed integers on most machines. A type is modulo if it is possible to add two positive numbers, and have a result that wraps around to a third number, which is less.

static const boolis_signed;

This member is true if the type is signed. This member is meaningful for all specializations.

static const boolis_specialized;

Indicates whether ** numeric_limits** has been specialized for type T. This flag must be true for all specializations of numeric_limits. In the default

**template, this flag must be false.**

*numeric_limits<T>*static Tmax();

Returns the maximum finite value. This function is meaningful for all specializations that declare is_bounded to be true.

static const intmax_exponent;

Maximum positive integer such that the radix raised to that power is in range. This field is meaningful for floating point types only.

static const intmax_exponent10;

Maximum positive integer such that 10 raised to that power is in range. This field is meaningful for floating point types only.

static Tmin();

Returns the minimum finite value. For floating point types with denormalization, min()must return the minimum normalized value. The minimum denormalized value is provided by denorm_min(). This function is meaningful for all specializations that declare is_bounded to be true.

static const intmin_exponent;

Minimum negative integer such that the radix raised to that power is in range. This field is meaningful for floating point types only.

static const intmin_exponent10;

Minimum negative integer such that 10 raised to that power is in range. This field is meaningful for floating point types only.

static Tquiet_NaN ();

Returns the representation of a quiet "Not a Number", if available. This function is meaningful only for those specializations that declare has_quiet_NaN to be true. This field is required for any type claiming conformance to IEC 559.

static const intradix;

For floating types, specifies the base or radix of the exponent representation (often 2). For integer types, this member must specify the base of the representation. This field is meaningful for all specializations.

static Tround_error ();

Returns the measure of the maximum rounding error. This function is meaningful for floating point types only.

static const float_round_styleround_style;

The rounding style for the type. Specializations for integer types must return round_toward_zero. This is meaningful for all floating point types.

static Tsignaling_NaN();

Returns the representation of a signaling "Not a Number", if available. This function is meaningful for only those specializations that declare has_signaling_NaN to be true. This function must be meaningful for any type claiming conformance to IEC 559.

static const booltinyness_before;

This member is true if tinyness is detected before rounding. It is meaningful for floating point types only.

static const booltraps;

This field is true if trapping is implemented for this type. The traps field is meaningful for all specializations.

### Example

// // limits.cpp // #include <limits> int main() {numeric_limits<float> float_info; if (float_info.is_specialized && float_info.has_infinity) { // get value of infinity float finfinity=float_info.infinity(); } return 0; }

### Warning

The specializations for wide chars and bool will only be available if your compiler has implemented them as real types and not simulated them with typedefs.

### See Also

IEEE Standard for Binary Floating-Point Arithmetic, 345 East 47th Street, New York, NY 10017

Language Independent Arithmetic (LIA-1)

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