\rSec0[language.support]{Language support library}

\rSec1[support.general]{General}

\pnum

This Clause describes the function signatures that are called

implicitly, and the types of objects generated implicitly, during the execution

of some \Cpp programs.

It also describes the headers that declare these function

signatures and define any related types.

\pnum

The following subclauses describe

common type definitions used throughout the library,

characteristics of the predefined types,

functions supporting start and termination of a \Cpp program,

support for dynamic memory management,

support for dynamic type identification,

support for exception processing, support for initializer lists,

and other runtime support,

as summarized in Table~\ref{tab:lang.sup.lib.summary}.

\begin{libsumtab}{Language support library summary}{tab:lang.sup.lib.summary}

\ref{support.types} & Types & \tcode{<cstddef>} \\ \rowsep

& & \tcode{<limits>} \\

\ref{support.limits} & Implementation properties & \tcode{<climits>} \\

& & \tcode{<cfloat>} \\ \rowsep

\ref{cstdint} & Integer types & \tcode{<cstdint>} \\ \rowsep

\ref{support.start.term} & Start and termination & \tcode{<cstdlib>} \\ \rowsep

\ref{support.dynamic} & Dynamic memory management & \tcode{<new>} \\ \rowsep

\ref{support.rtti} & Type identification & \tcode{<typeinfo>} \\ \rowsep

\ref{support.exception} & Exception handling & \tcode{<exception>} \\ \rowsep

\ref{support.initlist} & Initializer lists & \tcode{<initializer_list>} \\ \rowsep

& & \tcode{<csignal>} \\

& & \tcode{<csetjmp>} \\

& & \tcode{<cstdalign>} \\

\ref{support.runtime} & Other runtime support & \tcode{<cstdarg>} \\

& & \tcode{<cstdbool>} \\

& & \tcode{<cstdlib>} \\

& & \tcode{<ctime>} \\

\end{libsumtab}

\rSec1[support.types]{Types}

\pnum

Table~\ref{tab:support.hdr.cstddef} describes the header

\tcode{<cstddef>}.

\indexlibrary{\idxcode{NULL}}%

\indexlibrary{\idxcode{offsetof}}%

\indexlibrary{\idxcode{ptrdiff_t}}%

\indexlibrary{\idxcode{size_t}}%

\indexlibrary{\idxcode{max_align_t}}%

\indexlibrary{\idxcode{nullptr_t}}%

\begin{libsyntab3}{cstddef}{tab:support.hdr.cstddef}

\macros & \tcode{NULL} & \tcode{offsetof} \\ \rowsep

\types & \tcode{ptrdiff_t} & \tcode{size_t} \\

& \tcode{max_align_t} & \tcode{nullptr_t} \\

\end{libsyntab3}

\pnum

The contents are the same as the Standard C library header

\tcode{<stddef.h>},

with the following changes:

\pnum

The macro

\indexlibrary{\idxcode{NULL}}%

\tcode{NULL}

is an implementation-defined \Cpp null pointer constant in

\indextext{implementation-defined}%

this International Standard (\ref{conv.ptr}).\footnote{Possible definitions include

\tcode{0}

and

\tcode{0L},

but not

\tcode{(void*)0}.}

\pnum

The macro

\indexlibrary{\idxcode{offsetof}}%

\tcode{offsetof}(\textit{type},

\grammarterm{member-designator}) accepts a restricted set of \textit{type}

arguments in this International Standard. If \textit{type} is not a

standard-layout class

(Clause~\ref{class}), the results are undefined.\footnote{Note that \tcode{offsetof}

is required to work as specified even if unary

\tcode{operator\&}

is overloaded for any of the types involved.}

The expression \tcode{offsetof}(\textit{type}, \grammarterm{member-designator})

is never type-dependent~(\ref{temp.dep.expr}) and it is

value-dependent~(\ref{temp.dep.constexpr}) if and only if \textit{type} is

dependent. The result of applying the \tcode{offsetof} macro to a field that

is a static data member or a function member is undefined.

No operation invoked by the \tcode{offsetof} macro shall throw an exception and

\tcode{noexcept(offsetof(type, member-designator))} shall be \tcode{true}.

\pnum

The type \tcode{ptrdiff_t} is an

\impldef{type of \tcode{ptrdiff_t}}

signed integer type that can

hold the difference of two subscripts in an array object, as described in~\ref{expr.add}.

\pnum

The type \tcode{size_t} is an

\impldef{type of \tcode{size_t}}

unsigned integer type that is large enough

to contain the size in bytes of any object.

\pnum

\enternote

It is recommended that implementations choose types for \tcode{ptrdiff_t} and \tcode{size_t}

whose integer conversion ranks~(\ref{conv.rank}) are no greater than that of

\tcode{signed long int} unless a larger size is necessary to contain all the possible values.

\exitnote

\pnum

The type

\indexlibrary{\idxcode{max_align_t}}%

\tcode{max_align_t} is a POD type whose alignment requirement

is at least as great as that of every scalar type, and whose alignment

requirement is supported in every context.

\pnum

\indexlibrary{\idxcode{nullptr_t}}%

\tcode{nullptr_t} is defined as follows:

\begin{lstlisting}

namespace std {

typedef decltype(nullptr) nullptr_t;

}

\end{lstlisting}

The type for which \tcode{nullptr_t} is a synonym has the characteristics

described in~\ref{basic.fundamental} and~\ref{conv.ptr}. \enternote Although

\tcode{nullptr}'s address cannot be taken, the address of another

\tcode{nullptr_t} object that is an lvalue can be taken. \exitnote

\xref Alignment~(\ref{basic.align}), Sizeof~(\ref{expr.sizeof}), Additive

operators~(\ref{expr.add}), Free store~(\ref{class.free}), and ISO C~7.1.6.

\rSec1[support.limits]{Implementation properties}

\rSec2[support.limits.general]{In general}

\pnum

The headers

\tcode{<limits>}~(\ref{limits}),

\tcode{<climits>}, and

\tcode{<cfloat>}~(\ref{c.limits})

supply characteristics of implementation-dependent

arithmetic types~(\ref{basic.fundamental}).

\rSec2[limits]{Numeric limits}

\rSec3[limits.numeric]{Class template \tcode{numeric_limits}}

\pnum

The

\indexlibrary{\idxcode{numeric_limits}}%

\tcode{numeric_limits}

class template provides a \Cpp program with information about various properties of

the implementation's representation of the

arithmetic types.

\pnum

Specializations shall be provided for each

arithmetic type,

both floating point and integer, including

\tcode{bool}.

The member

\tcode{is_specialized}

shall be

\tcode{true}

for all such specializations of

\tcode{numeric_limits}.

\pnum

For all members declared

\tcode{static} \tcode{constexpr}

in the

\tcode{numeric_limits}

template, specializations shall define these values in such a way

that they are usable as

constant expressions.

\pnum

Non-arithmetic standard types, such as

\tcode{complex<T>}~(\ref{complex}), shall not have specializations.

\indextext{\idxhdr{limits}}%

\indexlibrary{\idxhdr{limits}}%

\indextext{\idxcode{numeric_limits}}%

\indexlibrary{\idxcode{numeric_limits}}%

\indexlibrary{\idxcode{float_round_style}}%

\indexlibrary{\idxcode{float_denorm_style}}%

\rSec3[limits.syn]{Header \tcode{<limits>} synopsis}

\begin{lstlisting}

namespace std {

template<class T> class numeric_limits;

enum float_round_style;

enum float_denorm_style;

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<char16_t>;

template<> class numeric_limits<char32_t>;

template<> class numeric_limits<wchar_t>;

template<> class numeric_limits<short>;

template<> class numeric_limits<int>;

template<> class numeric_limits<long>;

template<> class numeric_limits<long long>;

template<> class numeric_limits<unsigned short>;

template<> class numeric_limits<unsigned int>;

template<> class numeric_limits<unsigned long>;

template<> class numeric_limits<unsigned long long>;

template<> class numeric_limits<float>;

template<> class numeric_limits<double>;

template<> class numeric_limits<long double>;

}

\end{lstlisting}

\rSec3[numeric.limits]{Class template \tcode{numeric_limits}}

\indexlibrary{\idxcode{numeric\_limits}}%

\begin{lstlisting}

namespace std {

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 int max_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;

};

template<class T> class numeric_limits<const T>;

template<class T> class numeric_limits<volatile T>;

template<class T> class numeric_limits<const volatile T>;

}

\end{lstlisting}

\pnum

The default

\tcode{numeric_limits<T>}

template shall have all members, but with 0 or

\tcode{false}

values.

\pnum

The value of each member of a specialization of

\tcode{numeric_limits} on a \term{cv}-qualified type

\tcode{cv T} shall be equal to the value of the corresponding member of

the specialization on the unqualified type \tcode{T}.

\rSec3[numeric.limits.members]{\tcode{numeric_limits} members}

\indexlibrary{\idxcode{min}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{min}}

\begin{lstlisting}

static constexpr T min() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Minimum finite value.\footnote{Equivalent to \tcode{CHAR_MIN}, \tcode{SHRT_MIN},

\tcode{FLT_MIN}, \tcode{DBL_MIN}, etc.}

\pnum

For floating types with denormalization, returns the minimum positive

normalized value.

\pnum

Meaningful for all specializations in which

\tcode{is_bounded != false},

or

\tcode{is_bounded == false \&\& is_signed == false}.

\end{itemdescr}

\indexlibrary{\idxcode{max}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{max}}

\begin{lstlisting}

static constexpr T max() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Maximum finite value.\footnote{Equivalent to \tcode{CHAR_MAX}, \tcode{SHRT_MAX},

\tcode{FLT_MAX}, \tcode{DBL_MAX}, etc.}

\pnum

Meaningful for all specializations in which

\tcode{is_bounded != false}.

\end{itemdescr}

\indexlibrary{\idxcode{lowest}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{lowest}}

\begin{lstlisting}

static constexpr T lowest() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

A finite value \tcode{x} such that there is no other finite

value \tcode{y} where \tcode{y < x}.\footnote{\tcode{lowest()} is necessary because not all

floating-point representations have a smallest (most negative) value that is

the negative of the largest (most positive) finite value.}

\pnum

Meaningful for all specializations in which \tcode{is_bounded != false}.

\end{itemdescr}

\indexlibrary{\idxcode{digits}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{digits}}

\begin{lstlisting}

static constexpr int digits;

\end{lstlisting}

\begin{itemdescr}

\pnum

Number of

\tcode{radix}

digits that can be represented without change.

\pnum

For integer types, the number of non-sign bits in the representation.

\pnum For floating point types, the number of \tcode{radix} digits in the

mantissa.\footnote{Equivalent to \tcode{FLT_MANT_DIG}, \tcode{DBL_MANT_DIG},

\tcode{LDBL_MANT_DIG}.} \end{itemdescr}

\indexlibrary{\idxcode{digits10}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{digits10}}

\begin{lstlisting}

static constexpr int digits10;

\end{lstlisting}

\begin{itemdescr}

\pnum

Number of base 10 digits that can be represented without

change.\footnote{Equivalent to \tcode{FLT_DIG}, \tcode{DBL_DIG},

\tcode{LDBL_DIG}.}

\pnum

Meaningful for all specializations in which

\tcode{is_bounded != false}.

\end{itemdescr}

\indexlibrary{\idxcode{max_digits10}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{max_digits10}}

\begin{lstlisting}

static constexpr int max_digits10;

\end{lstlisting}

\begin{itemdescr}

\pnum

Number of base 10 digits required to ensure that values which

differ are always differentiated.

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{is_signed}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_signed}}

\begin{lstlisting}

static constexpr bool is_signed;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type is signed.

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{is_integer}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_integer}}

\begin{lstlisting}

static constexpr bool is_integer;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type is integer.

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{is_exact}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_exact}}

\begin{lstlisting}

static constexpr bool is_exact;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type uses an exact representation.

All integer types are exact, but not all exact types are integer.

For example, rational and fixed-exponent representations are exact but not integer.

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{radix}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{radix}}

\begin{lstlisting}

static constexpr int radix;

\end{lstlisting}

\begin{itemdescr}

\pnum

For floating types, specifies the base or radix of the exponent representation

(often 2).\footnote{Equivalent to \tcode{FLT_RADIX}.}

\pnum

For integer types, specifies the base of the

representation.\footnote{Distinguishes types with bases other than 2 (e.g.

BCD).}

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{epsilon}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{epsilon}}

\begin{lstlisting}

static constexpr T epsilon() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Machine epsilon: the difference between 1 and the least value greater than 1

that is representable.\footnote{Equivalent to \tcode{FLT_EPSILON}, \tcode{DBL_EPSILON}, \tcode{LDBL_EPSILON}.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{round_error}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{round_error}}

\begin{lstlisting}

static constexpr T round_error() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Measure of the maximum rounding error.\footnote{Rounding error is described in

ISO/IEC 10967-1 Language independent arithmetic - Part 1

Section 5.2.8 and

Annex A Rationale Section A.5.2.8 - Rounding constants.}

\end{itemdescr}

\indexlibrary{\idxcode{min_exponent}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{min_exponent}}

\begin{lstlisting}

static constexpr int min_exponent;

\end{lstlisting}

\begin{itemdescr}

\pnum

Minimum negative integer such that

\tcode{radix}

raised to the power of one less than that integer is a normalized floating

point number.\footnote{Equivalent to \tcode{FLT_MIN_EXP}, \tcode{DBL_MIN_EXP},

\tcode{LDBL_MIN_EXP}.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{min_exponent10}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{min_exponent10}}

\begin{lstlisting}

static constexpr int min_exponent10;

\end{lstlisting}

\begin{itemdescr}

\pnum

Minimum negative integer such that 10 raised to that power is in the range

of normalized floating point numbers.\footnote{Equivalent to

\tcode{FLT_MIN_10_EXP}, \tcode{DBL_MIN_10_EXP}, \tcode{LDBL_MIN_10_EXP}.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{max_exponent}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{max_exponent}}

\begin{lstlisting}

static constexpr int max_exponent;

\end{lstlisting}

\begin{itemdescr}

\pnum

Maximum positive integer such that

\tcode{radix}

raised to the power one less than that integer is a representable finite

floating point number.\footnote{Equivalent to \tcode{FLT_MAX_EXP},

\tcode{DBL_MAX_EXP}, \tcode{LDBL_MAX_EXP}.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{max_exponent10}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{max_exponent10}}

\begin{lstlisting}

static constexpr int max_exponent10;

\end{lstlisting}

\begin{itemdescr}

\pnum

Maximum positive integer such that 10 raised to that power is in the

range of representable finite floating point numbers.\footnote{Equivalent to

\tcode{FLT_MAX_10_EXP}, \tcode{DBL_MAX_10_EXP}, \tcode{LDBL_MAX_10_EXP}.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{has_infinity}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{has_infinity}}

\begin{lstlisting}

static constexpr bool has_infinity;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type has a representation for positive infinity.

\pnum

Meaningful for all floating point types.

\pnum

Shall be

\tcode{true}

for all specializations in which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{has_quiet_NaN}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{has_quiet_NaN}}

\begin{lstlisting}

static constexpr bool has_quiet_NaN;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type has a representation for a quiet (non-signaling) ``Not a

Number.''\footnote{Required by LIA-1.}

\pnum

Meaningful for all floating point types.

\pnum

Shall be

\tcode{true}

for all specializations in which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{has_signaling_NaN}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{has_signaling_NaN}}

\begin{lstlisting}

static constexpr bool has_signaling_NaN;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type has a representation for a signaling ``Not a Number.''\footnote{Required by LIA-1.}

\pnum

Meaningful for all floating point types.

\pnum

Shall be

\tcode{true}

for all specializations in which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{float_denorm_style}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{float_denorm_style}}

\begin{lstlisting}

static constexpr float_denorm_style has_denorm;

\end{lstlisting}

\begin{itemdescr}

\pnum

\tcode{denorm_present}

if the type allows denormalized values

(variable number of exponent bits)\footnote{Required by LIA-1.},

\tcode{denorm_absent}

if the type does not allow denormalized values,

and

\tcode{denorm_indeterminate}

if it is indeterminate at compile time whether the type allows

denormalized values.

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{has_denorm_loss}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{has_denorm_loss}}

\begin{lstlisting}

static constexpr bool has_denorm_loss;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if loss of accuracy is detected as a

denormalization loss, rather than as an inexact result.\footnote{See IEC 559.}

\end{itemdescr}

\indexlibrary{\idxcode{infinity}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{infinity}}

\begin{lstlisting}

static constexpr T infinity() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Representation of positive infinity, if available.\footnote{Required by LIA-1.}

\pnum

Meaningful for all specializations for which

\tcode{has_infinity != false}.

Required in specializations for which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{quiet_NaN}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{quiet_NaN}}

\begin{lstlisting}

static constexpr T quiet_NaN() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Representation of a quiet ``Not a Number,'' if available.\footnote{Required by LIA-1.}

\pnum

Meaningful for all specializations for which

\tcode{has_quiet_NaN != false}.

Required in specializations for which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{signaling_NaN}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{signaling_NaN}}

\begin{lstlisting}

static constexpr T signaling_NaN() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Representation of a signaling ``Not a Number,'' if available.\footnote{Required by LIA-1.}

\pnum

Meaningful for all specializations for which

\tcode{has_signaling_NaN != false}.

Required in specializations for which

\tcode{is_iec559 != false}.

\end{itemdescr}

\indexlibrary{\idxcode{denorm_min}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{denorm_min}}

\begin{lstlisting}

static constexpr T denorm_min() noexcept;

\end{lstlisting}

\begin{itemdescr}

\pnum

Minimum positive denormalized value.\footnote{Required by LIA-1.}

\pnum

Meaningful for all floating point types.

\pnum

In specializations for which

\tcode{has_denorm == false},

returns the minimum positive normalized value.

\end{itemdescr}

\indexlibrary{\idxcode{is_iec559}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_iec559}}

\begin{lstlisting}

static constexpr bool is_iec559;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if and only if the type adheres to IEC 559 standard.\footnote{International

Electrotechnical Commission standard 559 is the same as

IEEE 754.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{is_bounded}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_bounded}}

\begin{lstlisting}

static constexpr bool is_bounded;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the set of values representable by the type is finite.\footnote{Required by LIA-1.}

\enternote All fundamental types~(\ref{basic.fundamental}) are bounded. This member would be false for arbitrary

precision types.\exitnote

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{is_modulo}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{is_modulo}}

\begin{lstlisting}

static constexpr bool is_modulo;

\end{lstlisting}

\begin{itemdescr}

\pnum

True if the type is modulo.\footnote{Required by LIA-1.}

A type is modulo if, for any operation involving \tcode{+}, \tcode{-}, or

\tcode{*} on values of that type whose result would fall outside the range

\crange{min()}{max()}, the value returned differs from the true value by an

integer multiple of \tcode{max() - min() + 1}.

\pnum

On most machines, this is

\tcode{false}

for floating types,

\tcode{true}

for unsigned integers, and

\tcode{true}

for signed integers.

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{traps}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{traps}}

\begin{lstlisting}

static constexpr bool traps;

\end{lstlisting}

\begin{itemdescr}

\pnum

\tcode{true}

if, at program startup, there exists a value of the type that would cause

an arithmetic operation using that value to trap.\footnote{Required by LIA-1.}

\pnum

Meaningful for all specializations.

\end{itemdescr}

\indexlibrary{\idxcode{tinyness_before}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{tinyness_before}}

\begin{lstlisting}

static constexpr bool tinyness_before;

\end{lstlisting}

\begin{itemdescr}

\pnum

\tcode{true}

if tinyness is detected before rounding.\footnote{Refer to IEC 559.

Required by LIA-1.}

\pnum

Meaningful for all floating point types.

\end{itemdescr}

\indexlibrary{\idxcode{round_style}!\idxcode{numeric_limits}}

\indexlibrary{\idxcode{numeric_limits}!\idxcode{round_style}}

\begin{lstlisting}

static constexpr float_round_style round_style;

\end{lstlisting}

\begin{itemdescr}

\pnum

The rounding style for the type.\footnote{Equivalent to \tcode{FLT_ROUNDS}.

Required by LIA-1.}

\pnum

Meaningful for all floating point types.

Specializations for integer types shall return

\tcode{round_toward_zero}.

\end{itemdescr}

\rSec3[round.style]{Type \tcode{float_round_style}}

\indexlibrary{\idxcode{float_round_style}}%

\begin{lstlisting}

namespace std {

enum float_round_style {

round_indeterminate = -1,

round_toward_zero = 0,

round_to_nearest = 1,

round_toward_infinity = 2,

round_toward_neg_infinity = 3

};

}

\end{lstlisting}

\pnum

The rounding mode for floating point arithmetic is characterized by the

values:

\begin{itemize}

\item

\indexlibrary{\idxcode{round_indeterminate}}%

\tcode{round_indeterminate}

if the rounding style is indeterminable

\item

\indexlibrary{\idxcode{round_toward_zero}}%

\tcode{round_toward_zero}

if the rounding style is toward zero

\item

\indexlibrary{\idxcode{round_to_nearest}}%

\tcode{round_to_nearest}

if the rounding style is to the nearest representable value

\item

\indexlibrary{\idxcode{round_toward_infinity}}%

\tcode{round_toward_infinity}

if the rounding style is toward infinity

\item

\indexlibrary{\idxcode{round_toward_neg_infinity}}%

\tcode{round_toward_neg_infinity}

if the rounding style is toward negative infinity

\end{itemize}

\rSec3[denorm.style]{Type \tcode{float_denorm_style}}

\indexlibrary{\idxcode{float_denorm_style}}%

\begin{lstlisting}

namespace std {

enum float_denorm_style {

denorm_indeterminate = -1,

denorm_absent = 0,

denorm_present = 1

};

}

\end{lstlisting}

\pnum

The presence or absence of denormalization (variable number of exponent bits)

is characterized by the values:

\begin{itemize}

\item

\indexlibrary{\idxcode{denorm_indeterminate}}%

\tcode{denorm_indeterminate}

if it cannot be determined whether or not the type allows denormalized values

\item

\indexlibrary{\idxcode{denorm_absent}}%

\tcode{denorm_absent}

if the type does not allow denormalized values

\item

\indexlibrary{\idxcode{denorm_present}}%

\tcode{denorm_present}

if the type does allow denormalized values

\end{itemize}

\rSec3[numeric.special]{\tcode{numeric_limits} specializations}

\pnum

All members shall be provided for all specializations.

However, many values are only required to be meaningful under certain

conditions

(for example,

\tcode{epsilon()}

is only meaningful if

\tcode{is_integer}

is

\tcode{false}).

Any value that is not ``meaningful'' shall be set to 0 or

\tcode{false}.

\pnum

\enterexample

\begin{lstlisting}

namespace std {

template<> class numeric_limits<float> {

public:

static constexpr bool is_specialized = true;

inline static constexpr float min() noexcept { return 1.17549435E-38F; }

inline static constexpr float max() noexcept { return 3.40282347E+38F; }

inline static constexpr float lowest() noexcept { return -3.40282347E+38F; }

static constexpr int digits = 24;

static constexpr int digits10 = 6;

static constexpr int max_digits10 = 9;

static constexpr bool is_signed = true;

static constexpr bool is_integer = false;

static constexpr bool is_exact = false;

static constexpr int radix = 2;

inline static constexpr float epsilon() noexcept { return 1.19209290E-07F; }

inline static constexpr float round_error() noexcept { return 0.5F; }

static constexpr int min_exponent = -125;

static constexpr int min_exponent10 = - 37;

static constexpr int max_exponent = +128;

static constexpr int max_exponent10 = + 38;

static constexpr bool has_infinity = true;

static constexpr bool has_quiet_NaN = true;

static constexpr bool has_signaling_NaN = true;

static constexpr float_denorm_style has_denorm = denorm_absent;

static constexpr bool has_denorm_loss = false;

inline static constexpr float infinity() noexcept { return @\textit{value}@; }

inline static constexpr float quiet_NaN() noexcept { return @\textit{value}@; }

inline static constexpr float signaling_NaN() noexcept { return @\textit{value}@; }

inline static constexpr float denorm_min() noexcept { return min(); }

static constexpr bool is_iec559 = true;

static constexpr bool is_bounded = true;

static constexpr bool is_modulo = false;

static constexpr bool traps = true;

static constexpr bool tinyness_before = true;

static constexpr float_round_style round_style = round_to_nearest;

};

}

\end{lstlisting}

\exitexample

\pnum

The specialization for

\tcode{bool}

shall be provided as follows:

\indexlibrary{\idxcode{numeric_limits<bool>}}%

\begin{lstlisting}

namespace std {

template<> class numeric_limits<bool> {

public:

static constexpr bool is_specialized = true;

static constexpr bool min() noexcept { return false; }

static constexpr bool max() noexcept { return true; }

static constexpr bool lowest() noexcept { return false; }

static constexpr int digits = 1;

static constexpr int digits10 = 0;

static constexpr int max_digits10 = 0;

static constexpr bool is_signed = false;

static constexpr bool is_integer = true;

static constexpr bool is_exact = true;

static constexpr int radix = 2;

static constexpr bool epsilon() noexcept { return 0; }

static constexpr bool round_error() noexcept { return 0; }