17 Language support library [support]

17.3 Implementation properties [support.limits]

17.3.1 General [support.limits.general]

1
#
The headers <limits>, <climits>, and <cfloat> supply characteristics of implementation-dependent arithmetic types ([basic.fundamental]).

17.3.2 Header <version> synopsis [version.syn]

1
#
The header <version> supplies implementation-dependent information about the C++ standard library (e.g., version number and release date).
2
#
Each of the macros defined in <version> is also defined after inclusion of any member of the set of library headers indicated in the corresponding comment in this synopsis.
[Note 1:
Future revisions of C++ might replace the values of these macros with greater values.
— end note]
#define __cpp_­lib_­addressof_­constexpr 201603L // also in <memory> #define __cpp_­lib_­allocator_­traits_­is_­always_­equal 201411L // also in <memory>, <scoped_­allocator>, <string>, <deque>, <forward_­list>, <list>, <vector>, // <map>, <set>, <unordered_­map>, <unordered_­set> #define __cpp_­lib_­any 201606L // also in <any> #define __cpp_­lib_­apply 201603L // also in <tuple> #define __cpp_­lib_­array_­constexpr 201811L // also in <iterator>, <array> #define __cpp_­lib_­as_­const 201510L // also in <utility> #define __cpp_­lib_­assume_­aligned 201811L // also in <memory> #define __cpp_­lib_­atomic_­flag_­test 201907L // also in <atomic> #define __cpp_­lib_­atomic_­float 201711L // also in <atomic> #define __cpp_­lib_­atomic_­is_­always_­lock_­free 201603L // also in <atomic> #define __cpp_­lib_­atomic_­lock_­free_­type_­aliases 201907L // also in <atomic> #define __cpp_­lib_­atomic_­ref 201806L // also in <atomic> #define __cpp_­lib_­atomic_­shared_­ptr 201711L // also in <memory> #define __cpp_­lib_­atomic_­value_­initialization 201911L // also in <atomic>, <memory> #define __cpp_­lib_­atomic_­wait 201907L // also in <atomic> #define __cpp_­lib_­barrier 201907L // also in <barrier> #define __cpp_­lib_­bind_­front 201907L // also in <functional> #define __cpp_­lib_­bit_­cast 201806L // also in <bit> #define __cpp_­lib_­bitops 201907L // also in <bit> #define __cpp_­lib_­bool_­constant 201505L // also in <type_­traits> #define __cpp_­lib_­bounded_­array_­traits 201902L // also in <type_­traits> #define __cpp_­lib_­boyer_­moore_­searcher 201603L // also in <functional> #define __cpp_­lib_­byte 201603L // also in <cstddef> #define __cpp_­lib_­char8_­t 201907L // also in <atomic>, <filesystem>, <istream>, <limits>, <locale>, <ostream>, <string>, <string_­view> #define __cpp_­lib_­chrono 201907L // also in <chrono> #define __cpp_­lib_­chrono_­udls 201304L // also in <chrono> #define __cpp_­lib_­clamp 201603L // also in <algorithm> #define __cpp_­lib_­complex_­udls 201309L // also in <complex> #define __cpp_­lib_­concepts 202002L // also in <concepts> #define __cpp_­lib_­constexpr_­algorithms 201806L // also in <algorithm> #define __cpp_­lib_­constexpr_­complex 201711L // also in <complex> #define __cpp_­lib_­constexpr_­dynamic_­alloc 201907L // also in <memory> #define __cpp_­lib_­constexpr_­functional 201907L // also in <functional> #define __cpp_­lib_­constexpr_­iterator 201811L // also in <iterator> #define __cpp_­lib_­constexpr_­memory 201811L // also in <memory> #define __cpp_­lib_­constexpr_­numeric 201911L // also in <numeric> #define __cpp_­lib_­constexpr_­string 201907L // also in <string> #define __cpp_­lib_­constexpr_­string_­view 201811L // also in <string_­view> #define __cpp_­lib_­constexpr_­tuple 201811L // also in <tuple> #define __cpp_­lib_­constexpr_­utility 201811L // also in <utility> #define __cpp_­lib_­constexpr_­vector 201907L // also in <vector> #define __cpp_­lib_­coroutine 201902L // also in <coroutine> #define __cpp_­lib_­destroying_­delete 201806L // also in <new> #define __cpp_­lib_­enable_­shared_­from_­this 201603L // also in <memory> #define __cpp_­lib_­endian 201907L // also in <bit> #define __cpp_­lib_­erase_­if 202002L // also in <string>, <deque>, <forward_­list>, <list>, <vector>, <map>, <set>, <unordered_­map>, // <unordered_­set> #define __cpp_­lib_­exchange_­function 201304L // also in <utility> #define __cpp_­lib_­execution 201902L // also in <execution> #define __cpp_­lib_­filesystem 201703L // also in <filesystem> #define __cpp_­lib_­format 201907L // also in <format> #define __cpp_­lib_­gcd_­lcm 201606L // also in <numeric> #define __cpp_­lib_­generic_­associative_­lookup 201304L // also in <map>, <set> #define __cpp_­lib_­generic_­unordered_­lookup 201811L // also in <unordered_­map>, <unordered_­set> #define __cpp_­lib_­hardware_­interference_­size 201703L // also in <new> #define __cpp_­lib_­has_­unique_­object_­representations 201606L // also in <type_­traits> #define __cpp_­lib_­hypot 201603L // also in <cmath> #define __cpp_­lib_­incomplete_­container_­elements 201505L // also in <forward_­list>, <list>, <vector> #define __cpp_­lib_­int_­pow2 202002L // also in <bit> #define __cpp_­lib_­integer_­comparison_­functions 202002L // also in <utility> #define __cpp_­lib_­integer_­sequence 201304L // also in <utility> #define __cpp_­lib_­integral_­constant_­callable 201304L // also in <type_­traits> #define __cpp_­lib_­interpolate 201902L // also in <cmath>, <numeric> #define __cpp_­lib_­invoke 201411L // also in <functional> #define __cpp_­lib_­is_­aggregate 201703L // also in <type_­traits> #define __cpp_­lib_­is_­constant_­evaluated 201811L // also in <type_­traits> #define __cpp_­lib_­is_­final 201402L // also in <type_­traits> #define __cpp_­lib_­is_­invocable 201703L // also in <type_­traits> #define __cpp_­lib_­is_­layout_­compatible 201907L // also in <type_­traits> #define __cpp_­lib_­is_­nothrow_­convertible 201806L // also in <type_­traits> #define __cpp_­lib_­is_­null_­pointer 201309L // also in <type_­traits> #define __cpp_­lib_­is_­pointer_­interconvertible 201907L // also in <type_­traits> #define __cpp_­lib_­is_­swappable 201603L // also in <type_­traits> #define __cpp_­lib_­jthread 201911L // also in <stop_­token>, <thread> #define __cpp_­lib_­latch 201907L // also in <latch> #define __cpp_­lib_­launder 201606L // also in <new> #define __cpp_­lib_­list_­remove_­return_­type 201806L // also in <forward_­list>, <list> #define __cpp_­lib_­logical_­traits 201510L // also in <type_­traits> #define __cpp_­lib_­make_­from_­tuple 201606L // also in <tuple> #define __cpp_­lib_­make_­reverse_­iterator 201402L // also in <iterator> #define __cpp_­lib_­make_­unique 201304L // also in <memory> #define __cpp_­lib_­map_­try_­emplace 201411L // also in <map> #define __cpp_­lib_­math_­constants 201907L // also in <numbers> #define __cpp_­lib_­math_­special_­functions 201603L // also in <cmath> #define __cpp_­lib_­memory_­resource 201603L // also in <memory_­resource> #define __cpp_­lib_­node_­extract 201606L // also in <map>, <set>, <unordered_­map>, <unordered_­set> #define __cpp_­lib_­nonmember_­container_­access 201411L // also in <array>, <deque>, <forward_­list>, <iterator>, <list>, <map>, <regex>, <set>, <string>, // <unordered_­map>, <unordered_­set>, <vector> #define __cpp_­lib_­not_­fn 201603L // also in <functional> #define __cpp_­lib_­null_­iterators 201304L // also in <iterator> #define __cpp_­lib_­optional 201606L // also in <optional> #define __cpp_­lib_­parallel_­algorithm 201603L // also in <algorithm>, <numeric> #define __cpp_­lib_­polymorphic_­allocator 201902L // also in <memory> #define __cpp_­lib_­quoted_­string_­io 201304L // also in <iomanip> #define __cpp_­lib_­ranges 201911L // also in <algorithm>, <functional>, <iterator>, <memory>, <ranges> #define __cpp_­lib_­raw_­memory_­algorithms 201606L // also in <memory> #define __cpp_­lib_­remove_­cvref 201711L // also in <type_­traits> #define __cpp_­lib_­result_­of_­sfinae 201210L // also in <functional>, <type_­traits> #define __cpp_­lib_­robust_­nonmodifying_­seq_­ops 201304L // also in <algorithm> #define __cpp_­lib_­sample 201603L // also in <algorithm> #define __cpp_­lib_­scoped_­lock 201703L // also in <mutex> #define __cpp_­lib_­semaphore 201907L // also in <semaphore> #define __cpp_­lib_­shared_­mutex 201505L // also in <shared_­mutex> #define __cpp_­lib_­shared_­ptr_­arrays 201707L // also in <memory> #define __cpp_­lib_­shared_­ptr_­weak_­type 201606L // also in <memory> #define __cpp_­lib_­shared_­timed_­mutex 201402L // also in <shared_­mutex> #define __cpp_­lib_­shift 201806L // also in <algorithm> #define __cpp_­lib_­smart_­ptr_­for_­overwrite 202002L // also in <memory> #define __cpp_­lib_­source_­location 201907L // also in <source_­location> #define __cpp_­lib_­span 202002L // also in <span> #define __cpp_­lib_­ssize 201902L // also in <iterator> #define __cpp_­lib_­starts_­ends_­with 201711L // also in <string>, <string_­view> #define __cpp_­lib_­string_­udls 201304L // also in <string> #define __cpp_­lib_­string_­view 201803L // also in <string>, <string_­view> #define __cpp_­lib_­syncbuf 201803L // also in <syncstream> #define __cpp_­lib_­three_­way_­comparison 201907L // also in <compare> #define __cpp_­lib_­to_­address 201711L // also in <memory> #define __cpp_­lib_­to_­array 201907L // also in <array> #define __cpp_­lib_­to_­chars 201611L // also in <charconv> #define __cpp_­lib_­transformation_­trait_­aliases 201304L // also in <type_­traits> #define __cpp_­lib_­transparent_­operators 201510L // also in <memory>, <functional> #define __cpp_­lib_­tuple_­element_­t 201402L // also in <tuple> #define __cpp_­lib_­tuples_­by_­type 201304L // also in <utility>, <tuple> #define __cpp_­lib_­type_­identity 201806L // also in <type_­traits> #define __cpp_­lib_­type_­trait_­variable_­templates 201510L // also in <type_­traits> #define __cpp_­lib_­uncaught_­exceptions 201411L // also in <exception> #define __cpp_­lib_­unordered_­map_­try_­emplace 201411L // also in <unordered_­map> #define __cpp_­lib_­unwrap_­ref 201811L // also in <type_­traits> #define __cpp_­lib_­variant 201606L // also in <variant> #define __cpp_­lib_­void_­t 201411L // also in <type_­traits>

17.3.3 Header <limits> synopsis [limits.syn]

namespace std { // [fp.style], floating-point type properties enum float_round_style; enum float_denorm_style; // [numeric.limits], class template numeric_­limits template<class T> class numeric_limits; 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>; 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<char8_t>; 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>; }

17.3.4 Floating-point type properties [fp.style]

17.3.4.1 Type float_­round_­style [round.style]

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 }; }
1
#
The rounding mode for floating-point arithmetic is characterized by the values:
  • (1.1)
    round_­indeterminate if the rounding style is indeterminable
  • (1.2)
    round_­toward_­zero if the rounding style is toward zero
  • (1.3)
    round_­to_­nearest if the rounding style is to the nearest representable value
  • (1.4)
    round_­toward_­infinity if the rounding style is toward infinity
  • (1.5)
    round_­toward_­neg_­infinity if the rounding style is toward negative infinity

17.3.4.2 Type float_­denorm_­style [denorm.style]

namespace std { enum float_denorm_style { denorm_indeterminate = -1, denorm_absent = 0, denorm_present = 1 }; }
1
#
The presence or absence of subnormal numbers (variable number of exponent bits) is characterized by the values:
  • (1.1)
    denorm_­indeterminate if it cannot be determined whether or not the type allows subnormal values
  • (1.2)
    denorm_­absent if the type does not allow subnormal values
  • (1.3)
    denorm_­present if the type does allow subnormal values

17.3.5 Class template numeric_­limits [numeric.limits]

17.3.5.1 General [numeric.limits.general]

1
#
The numeric_­limits class template provides a C++ program with information about various properties of the implementation's representation of the arithmetic types.
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; }; }
2
#
For all members declared static constexpr in the numeric_­limits template, specializations shall define these values in such a way that they are usable as constant expressions.
3
#
For the numeric_­limits primary template, all data members are value-initialized and all member functions return a value-initialized object.
[Note 1:
This means all members have zero or false values unless numeric_­limits is specialized for a type.
— end note]
4
#
Specializations shall be provided for each arithmetic type, both floating-point and integer, including bool.
The member is_­specialized shall be true for all such specializations of numeric_­limits.
5
#
The value of each member of a specialization of numeric_­limits on a cv-qualified type cv T shall be equal to the value of the corresponding member of the specialization on the unqualified type T.
6
#
Non-arithmetic standard types, such as complex<T>, shall not have specializations.

17.3.5.2 numeric_­limits members [numeric.limits.members]

1
#
Each member function defined in this subclause is signal-safe.
🔗
static constexpr T min() noexcept;
2
#
Minimum finite value.189
3
#
For floating-point types with subnormal numbers, returns the minimum positive normalized value.
4
#
Meaningful for all specializations in which is_­bounded != false, or is_­bounded == false && is_­signed == false.
🔗
static constexpr T max() noexcept;
5
#
Maximum finite value.190
6
#
Meaningful for all specializations in which is_­bounded != false.
🔗
static constexpr T lowest() noexcept;
7
#
A finite value x such that there is no other finite value y where y < x.191
8
#
Meaningful for all specializations in which is_­bounded != false.
🔗
static constexpr int digits;
9
#
Number of radix digits that can be represented without change.
10
#
For integer types, the number of non-sign bits in the representation.
11
#
For floating-point types, the number of radix digits in the mantissa.192
🔗
static constexpr int digits10;
12
#
Number of base 10 digits that can be represented without change.193
13
#
Meaningful for all specializations in which is_­bounded != false.
🔗
static constexpr int max_digits10;
14
#
Number of base 10 digits required to ensure that values which differ are always differentiated.
15
#
Meaningful for all floating-point types.
🔗
static constexpr bool is_signed;
16
#
true if the type is signed.
17
#
Meaningful for all specializations.
🔗
static constexpr bool is_integer;
18
#
true if the type is integer.
19
#
Meaningful for all specializations.
🔗
static constexpr bool is_exact;
20
#
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.
21
#
Meaningful for all specializations.
🔗
static constexpr int radix;
22
#
For floating-point types, specifies the base or radix of the exponent representation (often 2).194
23
#
For integer types, specifies the base of the representation.195
24
#
Meaningful for all specializations.
🔗
static constexpr T epsilon() noexcept;
25
#
Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.196
26
#
Meaningful for all floating-point types.
🔗
static constexpr T round_error() noexcept;
27
#
Measure of the maximum rounding error.197
🔗
static constexpr int min_exponent;
28
#
Minimum negative integer such that radix raised to the power of one less than that integer is a normalized floating-point number.198
29
#
Meaningful for all floating-point types.
🔗
static constexpr int min_exponent10;
30
#
Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.199
31
#
Meaningful for all floating-point types.
🔗
static constexpr int max_exponent;
32
#
Maximum positive integer such that radix raised to the power one less than that integer is a representable finite floating-point number.200
33
#
Meaningful for all floating-point types.
🔗
static constexpr int max_exponent10;
34
#
Maximum positive integer such that 10 raised to that power is in the range of representable finite floating-point numbers.201
35
#
Meaningful for all floating-point types.
🔗
static constexpr bool has_infinity;
36
#
true if the type has a representation for positive infinity.
37
#
Meaningful for all floating-point types.
38
#
Shall be true for all specializations in which is_­iec559 != false.
🔗
static constexpr bool has_quiet_NaN;
39
#
true if the type has a representation for a quiet (non-signaling) “Not a Number”.202
40
#
Meaningful for all floating-point types.
41
#
Shall be true for all specializations in which is_­iec559 != false.
🔗
static constexpr bool has_signaling_NaN;
42
#
true if the type has a representation for a signaling “Not a Number”.203
43
#
Meaningful for all floating-point types.
44
#
Shall be true for all specializations in which is_­iec559 != false.
🔗
static constexpr float_denorm_style has_denorm;
45
#
denorm_­present if the type allows subnormal values (variable number of exponent bits)204, denorm_­absent if the type does not allow subnormal values, and denorm_­indeterminate if it is indeterminate at compile time whether the type allows subnormal values.
46
#
Meaningful for all floating-point types.
🔗
static constexpr bool has_denorm_loss;
47
#
true if loss of accuracy is detected as a denormalization loss, rather than as an inexact result.205
🔗
static constexpr T infinity() noexcept;
48
#
Representation of positive infinity, if available.206
49
#
Meaningful for all specializations for which has_­infinity != false.
Required in specializations for which is_­iec559 != false.
🔗
static constexpr T quiet_NaN() noexcept;
50
#
Representation of a quiet “Not a Number”, if available.207
51
#
Meaningful for all specializations for which has_­quiet_­NaN != false.
Required in specializations for which is_­iec559 != false.
🔗
static constexpr T signaling_NaN() noexcept;
52
#
Representation of a signaling “Not a Number”, if available.208
53
#
Meaningful for all specializations for which has_­signaling_­NaN != false.
Required in specializations for which is_­iec559 != false.
🔗
static constexpr T denorm_min() noexcept;
54
#
Minimum positive subnormal value.209
55
#
Meaningful for all floating-point types.
56
#
In specializations for which has_­denorm == false, returns the minimum positive normalized value.
🔗
static constexpr bool is_iec559;
57
#
true if and only if the type adheres to ISO/IEC/IEEE 60559.210
58
#
Meaningful for all floating-point types.
🔗
static constexpr bool is_bounded;
59
#
true if the set of values representable by the type is finite.211
[Note 1:
All fundamental types ([basic.fundamental]) are bounded.
This member would be false for arbitrary precision types.
— end note]
60
#
Meaningful for all specializations.
🔗
static constexpr bool is_modulo;
61
#
true if the type is modulo.212
A type is modulo if, for any operation involving +, -, or * on values of that type whose result would fall outside the range [min(), max()], the value returned differs from the true value by an integer multiple of max() - min() + 1.
62
#
[Example 1:
is_­modulo is false for signed integer types ([basic.fundamental]) unless an implementation, as an extension to this document, defines signed integer overflow to wrap.
— end example]
63
#
Meaningful for all specializations.
🔗
static constexpr bool traps;
64
#
true if, at the start of the program, there exists a value of the type that would cause an arithmetic operation using that value to trap.213
65
#
Meaningful for all specializations.
🔗
static constexpr bool tinyness_before;
66
#
true if tinyness is detected before rounding.214
67
#
Meaningful for all floating-point types.
🔗
static constexpr float_round_style round_style;
68
#
The rounding style for the type.215
69
#
Meaningful for all floating-point types.
Specializations for integer types shall return round_­toward_­zero.
189)
Equivalent to CHAR_­MIN, SHRT_­MIN, FLT_­MIN, DBL_­MIN, etc.
 ⮥
190)
Equivalent to CHAR_­MAX, SHRT_­MAX, FLT_­MAX, DBL_­MAX, etc.
 ⮥
191)
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.
 ⮥
192)
Equivalent to FLT_­MANT_­DIG, DBL_­MANT_­DIG, LDBL_­MANT_­DIG.
 ⮥
193)
Equivalent to FLT_­DIG, DBL_­DIG, LDBL_­DIG.
 ⮥
194)
Equivalent to FLT_­RADIX.
 ⮥
195)
Distinguishes types with bases other than 2 (e.g. BCD).
 ⮥
196)
Equivalent to FLT_­EPSILON, DBL_­EPSILON, LDBL_­EPSILON.
 ⮥
197)
Rounding error is described in LIA-1 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.
 ⮥
198)
Equivalent to FLT_­MIN_­EXP, DBL_­MIN_­EXP, LDBL_­MIN_­EXP.
 ⮥
199)
Equivalent to FLT_­MIN_­10_­EXP, DBL_­MIN_­10_­EXP, LDBL_­MIN_­10_­EXP.
 ⮥
200)
Equivalent to FLT_­MAX_­EXP, DBL_­MAX_­EXP, LDBL_­MAX_­EXP.
 ⮥
201)
Equivalent to FLT_­MAX_­10_­EXP, DBL_­MAX_­10_­EXP, LDBL_­MAX_­10_­EXP.
 ⮥
202)
Required by LIA-1.
 ⮥
203)
Required by LIA-1.
 ⮥
204)
Required by LIA-1.
 ⮥
205)
See ISO/IEC/IEEE 60559.
 ⮥
206)
Required by LIA-1.
 ⮥
207)
Required by LIA-1.
 ⮥
208)
Required by LIA-1.
 ⮥
209)
Required by LIA-1.
 ⮥
210)
ISO/IEC/IEEE 60559:2011 is the same as IEEE 754-2008.
 ⮥
211)
Required by LIA-1.
 ⮥
212)
Required by LIA-1.
 ⮥
213)
Required by LIA-1.
 ⮥
214)
Refer to ISO/IEC/IEEE 60559.
Required by LIA-1.
 ⮥
215)
Equivalent to FLT_­ROUNDS.
Required by LIA-1.
 ⮥

17.3.5.3 numeric_­limits specializations [numeric.special]

1
#
All members shall be provided for all specializations.
However, many values are only required to be meaningful under certain conditions (for example, epsilon() is only meaningful if is_­integer is false).
Any value that is not “meaningful” shall be set to 0 or false.
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[Example 1: namespace std { template<> class numeric_limits<float> { public: static constexpr bool is_specialized = true; static constexpr float min() noexcept { return 1.17549435E-38F; } static constexpr float max() noexcept { return 3.40282347E+38F; } 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; static constexpr float epsilon() noexcept { return 1.19209290E-07F; } 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; static constexpr float infinity() noexcept { return value; } static constexpr float quiet_NaN() noexcept { return value; } static constexpr float signaling_NaN() noexcept { return value; } 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 example]
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The specialization for bool shall be provided as follows: 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; } 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 bool infinity() noexcept { return 0; } static constexpr bool quiet_NaN() noexcept { return 0; } static constexpr bool signaling_NaN() noexcept { return 0; } static constexpr bool denorm_min() noexcept { return 0; } static constexpr bool is_iec559 = false; static constexpr bool is_bounded = true; 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; }; }

17.3.6 Header <climits> synopsis [climits.syn]

#define CHAR_BIT see below #define SCHAR_MIN see below #define SCHAR_MAX see below #define UCHAR_MAX see below #define CHAR_MIN see below #define CHAR_MAX see below #define MB_LEN_MAX see below #define SHRT_MIN see below #define SHRT_MAX see below #define USHRT_MAX see below #define INT_MIN see below #define INT_MAX see below #define UINT_MAX see below #define LONG_MIN see below #define LONG_MAX see below #define ULONG_MAX see below #define LLONG_MIN see below #define LLONG_MAX see below #define ULLONG_MAX see below
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The header <climits> defines all macros the same as the C standard library header <limits.h>.
[Note 1:
The types of the constants defined by macros in <climits> are not required to match the types to which the macros refer.
— end note]
See also: ISO C 5.2.4.2.1

17.3.7 Header <cfloat> synopsis [cfloat.syn]

#define FLT_ROUNDS see below #define FLT_EVAL_METHOD see below #define FLT_HAS_SUBNORM see below #define DBL_HAS_SUBNORM see below #define LDBL_HAS_SUBNORM see below #define FLT_RADIX see below #define FLT_MANT_DIG see below #define DBL_MANT_DIG see below #define LDBL_MANT_DIG see below #define FLT_DECIMAL_DIG see below #define DBL_DECIMAL_DIG see below #define LDBL_DECIMAL_DIG see below #define DECIMAL_DIG see below #define FLT_DIG see below #define DBL_DIG see below #define LDBL_DIG see below #define FLT_MIN_EXP see below #define DBL_MIN_EXP see below #define LDBL_MIN_EXP see below #define FLT_MIN_10_EXP see below #define DBL_MIN_10_EXP see below #define LDBL_MIN_10_EXP see below #define FLT_MAX_EXP see below #define DBL_MAX_EXP see below #define LDBL_MAX_EXP see below #define FLT_MAX_10_EXP see below #define DBL_MAX_10_EXP see below #define LDBL_MAX_10_EXP see below #define FLT_MAX see below #define DBL_MAX see below #define LDBL_MAX see below #define FLT_EPSILON see below #define DBL_EPSILON see below #define LDBL_EPSILON see below #define FLT_MIN see below #define DBL_MIN see below #define LDBL_MIN see below #define FLT_TRUE_MIN see below #define DBL_TRUE_MIN see below #define LDBL_TRUE_MIN see below
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The header <cfloat> defines all macros the same as the C standard library header <float.h>.
See also: ISO C 5.2.4.2.2