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%!TEX root = std.tex
\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{codeblock}
namespace std {
typedef decltype(nullptr) nullptr_t;
}
\end{codeblock}
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{codeblock}
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{codeblock}
\rSec3[numeric.limits]{Class template \tcode{numeric_limits}}
\indexlibrary{\idxcode{numeric\_limits}}%
\begin{codeblock}
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{codeblock}
\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{itemdecl}
static constexpr T min() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T max() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T lowest() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr int digits;
\end{itemdecl}
\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{itemdecl}
static constexpr int digits10;
\end{itemdecl}
\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{itemdecl}
static constexpr int max_digits10;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_signed;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_integer;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_exact;
\end{itemdecl}
\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{itemdecl}
static constexpr int radix;
\end{itemdecl}
\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{itemdecl}
static constexpr T epsilon() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T round_error() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr int min_exponent;
\end{itemdecl}
\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{itemdecl}
static constexpr int min_exponent10;
\end{itemdecl}
\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{itemdecl}
static constexpr int max_exponent;
\end{itemdecl}
\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{itemdecl}
static constexpr int max_exponent10;
\end{itemdecl}
\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{itemdecl}
static constexpr bool has_infinity;
\end{itemdecl}
\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{itemdecl}
static constexpr bool has_quiet_NaN;
\end{itemdecl}
\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{itemdecl}
static constexpr bool has_signaling_NaN;
\end{itemdecl}
\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{itemdecl}
static constexpr float_denorm_style has_denorm;
\end{itemdecl}
\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{itemdecl}
static constexpr bool has_denorm_loss;
\end{itemdecl}
\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{itemdecl}
static constexpr T infinity() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T quiet_NaN() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T signaling_NaN() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr T denorm_min() noexcept;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_iec559;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_bounded;
\end{itemdecl}
\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{itemdecl}
static constexpr bool is_modulo;
\end{itemdecl}
\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{itemdecl}
static constexpr bool traps;
\end{itemdecl}
\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{itemdecl}
static constexpr bool tinyness_before;
\end{itemdecl}
\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{itemdecl}
static constexpr float_round_style round_style;
\end{itemdecl}
\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{codeblock}
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{codeblock}
\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{codeblock}
namespace std {
enum float_denorm_style {
denorm_indeterminate = -1,
denorm_absent = 0,
denorm_present = 1
};
}
\end{codeblock}
\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{codeblock}
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{codeblock}
\exitexample
\pnum
The specialization for
\tcode{bool}
shall be provided as follows:
\indexlibrary{\idxcode{numeric_limits<bool>}}%
\begin{codeblock}
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; }