17 Language support library [support]

17.3 Implementation properties [support.limits]

17.3.1 General [support.limits.general]

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

17.3.2 Header <version> synopsis [version.syn]

The header supplies implementation-dependent information about the C++ standard library (e.g., version number and release date).

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_adaptor_iterator_pair_constructor 202106L // also in <stack>, <queue> #define __cpp_lib_addressof_constexpr 201603L // freestanding, also in <memory> #define __cpp_lib_algorithm_iterator_requirements 202207L // also in <algorithm>, <numeric>, <memory> #define __cpp_lib_allocate_at_least 202302L // also in <memory> #define __cpp_lib_allocator_traits_is_always_equal 201411L // freestanding, 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 // freestanding, also in <tuple> #define __cpp_lib_array_constexpr 201811L // also in <iterator>, <array> #define __cpp_lib_as_const 201510L // freestanding, also in <utility> #define __cpp_lib_associative_heterogeneous_erasure 202110L // also in <map>, <set>, <unordered_map>, <unordered_set> #define __cpp_lib_associative_heterogeneous_insertion 202306L // also in <map>, <set>, <unordered_map>, <unordered_set> #define __cpp_lib_assume_aligned 201811L // freestanding, also in <memory> #define __cpp_lib_atomic_flag_test 201907L // freestanding, also in <atomic> #define __cpp_lib_atomic_float 201711L // freestanding, also in <atomic> #define __cpp_lib_atomic_is_always_lock_free 201603L // freestanding, also in <atomic> #define __cpp_lib_atomic_lock_free_type_aliases 201907L // also in <atomic> #define __cpp_lib_atomic_ref 201806L // freestanding, also in <atomic> #define __cpp_lib_atomic_shared_ptr 201711L // also in <memory> #define __cpp_lib_atomic_value_initialization 201911L // freestanding, also in <atomic>, <memory> #define __cpp_lib_atomic_wait 201907L // freestanding, also in <atomic> #define __cpp_lib_barrier 202302L // also in <barrier> #define __cpp_lib_bind_back 202306L // freestanding, also in <functional> #define __cpp_lib_bind_front 202306L // freestanding, also in <functional> #define __cpp_lib_bit_cast 201806L // freestanding, also in <bit> #define __cpp_lib_bitops 201907L // freestanding, also in <bit> #define __cpp_lib_bitset 202306L // also in <bitset> #define __cpp_lib_bool_constant 201505L // freestanding, also in <type_traits> #define __cpp_lib_bounded_array_traits 201902L // freestanding, also in <type_traits> #define __cpp_lib_boyer_moore_searcher 201603L // also in <functional> #define __cpp_lib_byte 201603L // freestanding, also in <cstddef> #define __cpp_lib_byteswap 202110L // freestanding, also in <bit> #define __cpp_lib_char8_t 201907L // freestanding, also in <atomic>, <filesystem>, <istream>, <limits>, <locale>, <ostream>, <string>, // <string_view> #define __cpp_lib_chrono 202306L // also in <chrono> #define __cpp_lib_chrono_udls 201304L // also in <chrono> #define __cpp_lib_clamp 201603L // also in <algorithm> #define __cpp_lib_common_reference 202302L // also in <type_traits> #define __cpp_lib_common_reference_wrapper 202302L // also in <functional> #define __cpp_lib_complex_udls 201309L // also in <complex> #define __cpp_lib_concepts 202207L // freestanding, also in <concepts>, <compare> #define __cpp_lib_constexpr_algorithms 202306L // also in <algorithm>, <utility> #define __cpp_lib_constexpr_bitset 202207L // also in <bitset> #define __cpp_lib_constexpr_charconv 202207L // also in <charconv> #define __cpp_lib_constexpr_cmath 202306L // also in <cmath>, <cstdlib> #define __cpp_lib_constexpr_complex 202306L // also in <complex> #define __cpp_lib_constexpr_dynamic_alloc 201907L // also in <memory> #define __cpp_lib_constexpr_functional 201907L // freestanding, also in <functional> #define __cpp_lib_constexpr_iterator 201811L // freestanding, also in <iterator> #define __cpp_lib_constexpr_memory 202202L // freestanding, 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 // freestanding, also in <tuple> #define __cpp_lib_constexpr_typeinfo 202106L // freestanding, also in <typeinfo> #define __cpp_lib_constexpr_utility 201811L // freestanding, also in <utility> #define __cpp_lib_constexpr_vector 201907L // also in <vector> #define __cpp_lib_containers_ranges 202202L // also in <vector>, <list>, <forward_list>, <map>, <set>, <unordered_map>, <unordered_set>, // <deque>, <queue>, <stack>, <string> #define __cpp_lib_copyable_function 202306L // also in <functional> #define __cpp_lib_coroutine 201902L // also in <coroutine> #define __cpp_lib_debugging 202311L // freestanding, also in <debugging> #define __cpp_lib_destroying_delete 201806L // freestanding, also in <new> #define __cpp_lib_enable_shared_from_this 201603L // also in <memory> #define __cpp_lib_endian 201907L // freestanding, 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 // freestanding, also in <utility> #define __cpp_lib_execution 201902L // also in <execution> #define __cpp_lib_expected 202211L // also in <expected> #define __cpp_lib_filesystem 201703L // also in <filesystem> #define __cpp_lib_flat_map 202207L // also in <flat_map> #define __cpp_lib_flat_set 202207L // also in <flat_set> #define __cpp_lib_format 202311L // also in <format> #define __cpp_lib_format_ranges 202207L // also in <format> #define __cpp_lib_format_uchar 202311L // also in <format> #define __cpp_lib_formatters 202302L // also in <stacktrace>, <thread> #define __cpp_lib_forward_like 202207L // freestanding, also in <utility> #define __cpp_lib_freestanding_algorithm 202311L // freestanding, also in <algorithm> #define __cpp_lib_freestanding_array 202311L // freestanding, also in <array> #define __cpp_lib_freestanding_char_traits 202306L // freestanding, also in <string> #define __cpp_lib_freestanding_charconv 202306L // freestanding, also in <charconv> #define __cpp_lib_freestanding_cstdlib 202306L // freestanding, also in <cstdlib>, <cmath> #define __cpp_lib_freestanding_cstring 202311L // freestanding, also in <cstring> #define __cpp_lib_freestanding_cwchar 202306L // freestanding, also in <cwchar> #define __cpp_lib_freestanding_errc 202306L // freestanding, also in <cerrno>, <system_error> #define __cpp_lib_freestanding_expected 202311L // freestanding, also in <expected> #define __cpp_lib_freestanding_feature_test_macros 202306L // freestanding #define __cpp_lib_freestanding_functional 202306L // freestanding, also in <functional> #define __cpp_lib_freestanding_iterator 202306L // freestanding, also in <iterator> #define __cpp_lib_freestanding_mdspan 202311L // freestanding, also in <mdspan> #define __cpp_lib_freestanding_memory 202306L // freestanding, also in <memory> #define __cpp_lib_freestanding_numeric 202311L // freestanding, also in <numeric> #define __cpp_lib_freestanding_operator_new see below // freestanding, also in <new> #define __cpp_lib_freestanding_optional 202311L // freestanding, also in <optional> #define __cpp_lib_freestanding_ranges 202306L // freestanding, also in <ranges> #define __cpp_lib_freestanding_ratio 202306L // freestanding, also in <ratio> #define __cpp_lib_freestanding_string_view 202311L // freestanding, also in <string_view> #define __cpp_lib_freestanding_tuple 202306L // freestanding, also in <tuple> #define __cpp_lib_freestanding_utility 202306L // freestanding, also in <utility> #define __cpp_lib_freestanding_variant 202311L // freestanding, also in <variant> #define __cpp_lib_fstream_native_handle 202306L // also in <fstream> #define __cpp_lib_function_ref 202306L // also in <functional> #define __cpp_lib_gcd_lcm 201606L // also in <numeric> #define __cpp_lib_generator 202207L // also in <generator> #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 // freestanding, also in <new> #define __cpp_lib_has_unique_object_representations 201606L // freestanding, also in <type_traits> #define __cpp_lib_hazard_pointer 202306L // also in <hazard_pointer> #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 // freestanding, also in <bit> #define __cpp_lib_integer_comparison_functions 202002L // also in <utility> #define __cpp_lib_integer_sequence 201304L // freestanding, also in <utility> #define __cpp_lib_integral_constant_callable 201304L // freestanding, also in <type_traits> #define __cpp_lib_interpolate 201902L // also in <cmath>, <numeric> #define __cpp_lib_invoke 201411L // freestanding, also in <functional> #define __cpp_lib_invoke_r 202106L // freestanding, also in <functional> #define __cpp_lib_ios_noreplace 202207L // also in <ios> #define __cpp_lib_is_aggregate 201703L // freestanding, also in <type_traits> #define __cpp_lib_is_constant_evaluated 201811L // freestanding, also in <type_traits> #define __cpp_lib_is_final 201402L // freestanding, also in <type_traits> #define __cpp_lib_is_implicit_lifetime 202302L // also in <type_traits> #define __cpp_lib_is_invocable 201703L // freestanding, also in <type_traits> #define __cpp_lib_is_layout_compatible 201907L // freestanding, also in <type_traits> #define __cpp_lib_is_nothrow_convertible 201806L // freestanding, also in <type_traits> #define __cpp_lib_is_null_pointer 201309L // freestanding, also in <type_traits> #define __cpp_lib_is_pointer_interconvertible 201907L // freestanding, also in <type_traits> #define __cpp_lib_is_scoped_enum 202011L // freestanding, also in <type_traits> #define __cpp_lib_is_swappable 201603L // freestanding, also in <type_traits> #define __cpp_lib_is_within_lifetime 202306L // 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 // freestanding, also in <new> #define __cpp_lib_linalg 202311L // also in <linalg> #define __cpp_lib_list_remove_return_type 201806L // also in <forward_list>, <list> #define __cpp_lib_logical_traits 201510L // freestanding, also in <type_traits> #define __cpp_lib_make_from_tuple 201606L // freestanding, also in <tuple> #define __cpp_lib_make_reverse_iterator 201402L // freestanding, 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_mdspan 202207L // also in <mdspan> #define __cpp_lib_memory_resource 201603L // also in <memory_resource> #define __cpp_lib_modules 202207L // freestanding #define __cpp_lib_move_iterator_concept 202207L // freestanding, also in <iterator> #define __cpp_lib_move_only_function 202110L // also in <functional> #define __cpp_lib_node_extract 201606L // also in <map>, <set>, <unordered_map>, <unordered_set> #define __cpp_lib_nonmember_container_access 201411L // freestanding, also in <array>, <deque>, <forward_list>, <iterator>, <list>, <map>, <regex>, <set>, // <string>, <unordered_map>, <unordered_set>, <vector> #define __cpp_lib_not_fn 202306L // freestanding, also in <functional> #define __cpp_lib_null_iterators 201304L // freestanding, also in <iterator> #define __cpp_lib_optional 202110L // also in <optional> #define __cpp_lib_out_ptr 202311L // freestanding, also in <memory> #define __cpp_lib_parallel_algorithm 201603L // also in <algorithm>, <numeric> #define __cpp_lib_polymorphic_allocator 201902L // also in <memory_resource> #define __cpp_lib_print 202207L // also in <print>, <ostream> #define __cpp_lib_quoted_string_io 201304L // also in <iomanip> #define __cpp_lib_ranges 202302L // also in <algorithm>, <functional>, <iterator>, <memory>, <ranges> #define __cpp_lib_ranges_as_const 202311L // freestanding, also in <ranges> #define __cpp_lib_ranges_as_rvalue 202207L // freestanding, also in <ranges> #define __cpp_lib_ranges_cartesian_product 202207L // freestanding, also in <ranges> #define __cpp_lib_ranges_chunk 202202L // freestanding, also in <ranges> #define __cpp_lib_ranges_chunk_by 202202L // freestanding, also in <ranges> #define __cpp_lib_ranges_contains 202207L // also in <algorithm> #define __cpp_lib_ranges_enumerate 202302L // also in <ranges>, <version> #define __cpp_lib_ranges_find_last 202207L // also in <algorithm> #define __cpp_lib_ranges_fold 202207L // also in <algorithm> #define __cpp_lib_ranges_iota 202202L // also in <numeric> #define __cpp_lib_ranges_join_with 202202L // freestanding, also in <ranges> #define __cpp_lib_ranges_repeat 202207L // freestanding, also in <ranges> #define __cpp_lib_ranges_slide 202202L // freestanding, also in <ranges> #define __cpp_lib_ranges_starts_ends_with 202106L // also in <algorithm> #define __cpp_lib_ranges_stride 202207L // freestanding, also in <ranges> #define __cpp_lib_ranges_to_container 202202L // freestanding, also in <ranges> #define __cpp_lib_ranges_zip 202110L // freestanding, also in <ranges>, <tuple>, <utility> #define __cpp_lib_ratio 202306L // also in <ratio> #define __cpp_lib_raw_memory_algorithms 201606L // also in <memory> #define __cpp_lib_rcu 202306L // also in <rcu> #define __cpp_lib_reference_from_temporary 202202L // freestanding, also in <type_traits> #define __cpp_lib_remove_cvref 201711L // freestanding, also in <type_traits> #define __cpp_lib_result_of_sfinae 201210L // freestanding, 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_saturation_arithmetic 202311L // also in <numeric> #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 202202L // also in <algorithm> #define __cpp_lib_smart_ptr_for_overwrite 202002L // also in <memory> #define __cpp_lib_smart_ptr_owner_equality 202306L // also in <memory> #define __cpp_lib_source_location 201907L // freestanding, also in <source_location> #define __cpp_lib_span 202311L // freestanding, also in <span> #define __cpp_lib_span_initializer_list 202311L // also in <span> #define __cpp_lib_spanstream 202106L // also in <spanstream> #define __cpp_lib_ssize 201902L // freestanding, also in <iterator> #define __cpp_lib_sstream_from_string_view 202306L // also in <sstream> #define __cpp_lib_stacktrace 202011L // also in <stacktrace> #define __cpp_lib_start_lifetime_as 202207L // freestanding, also in <memory> #define __cpp_lib_starts_ends_with 201711L // also in <string>, <string_view> #define __cpp_lib_stdatomic_h 202011L // also in <stdatomic.h> #define __cpp_lib_string_contains 202011L // also in <string>, <string_view> #define __cpp_lib_string_resize_and_overwrite 202110L // also in <string> #define __cpp_lib_string_udls 201304L // also in <string> #define __cpp_lib_string_view 201803L // also in <string>, <string_view> #define __cpp_lib_submdspan 202306L // also in <mdspan> #define __cpp_lib_syncbuf 201803L // also in <syncstream> #define __cpp_lib_text_encoding 202306L // also in <text_encoding> #define __cpp_lib_three_way_comparison 201907L // freestanding, also in <compare> #define __cpp_lib_to_address 201711L // freestanding, also in <memory> #define __cpp_lib_to_array 201907L // also in <array> #define __cpp_lib_to_chars 202306L // also in <charconv> #define __cpp_lib_to_string 202306L // also in <string> #define __cpp_lib_to_underlying 202102L // freestanding, also in <utility> #define __cpp_lib_transformation_trait_aliases 201304L // freestanding, also in <type_traits> #define __cpp_lib_transparent_operators 201510L // freestanding, also in <memory>, <functional> #define __cpp_lib_tuple_element_t 201402L // freestanding, also in <tuple> #define __cpp_lib_tuple_like 202311L // also in <utility>, <tuple>, <map>, <unordered_map> #define __cpp_lib_tuples_by_type 201304L // freestanding, also in <utility>, <tuple> #define __cpp_lib_type_identity 201806L // freestanding, also in <type_traits> #define __cpp_lib_type_trait_variable_templates 201510L // freestanding, also in <type_traits> #define __cpp_lib_uncaught_exceptions 201411L // freestanding, also in <exception> #define __cpp_lib_unordered_map_try_emplace 201411L // also in <unordered_map> #define __cpp_lib_unreachable 202202L // freestanding, also in <utility> #define __cpp_lib_unwrap_ref 201811L // freestanding, also in <type_traits> #define __cpp_lib_variant 202306L // also in <variant> #define __cpp_lib_void_t 201411L // freestanding, also in <type_traits>

The macro __cpp_lib_freestanding_operator_new is defined to the integer literal 202306L if all the default versions of the replaceable global allocation functions meet the requirements of a hosted implementation, and to the integer literal 0 otherwise ([new.delete]).

Recommended practice: Freestanding implementations should only define a macro from <version> if the implementation provides the corresponding facility in its entirety.

17.3.3 Header <limits> synopsis [limits.syn]

// all freestanding namespace std { // [round.style], enumeration float_round_style enum float_round_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 Enum 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 }; }

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

17.3.5 Class template numeric_limits [numeric.limits]

17.3.5.1 General [numeric.limits.general]

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 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; }; }

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.

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]

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.

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.

Non-arithmetic standard types, such as complex<T>, shall not have specializations.

17.3.5.2 numeric_limits members [numeric.limits.members]

Each member function defined in this subclause is signal-safe .

🔗

static constexpr T min() noexcept;

Minimum finite value.169

For floating-point types with subnormal numbers, returns the minimum positive normalized value.

Meaningful for all specializations in which is_bounded != false, or is_bounded == false && is_signed == false.

🔗

static constexpr T max() noexcept;

Maximum finite value.170

Meaningful for all specializations in which is_bounded != false.

🔗

static constexpr T lowest() noexcept;

A finite value x such that there is no other finite value y where y < x.171

Meaningful for all specializations in which is_bounded != false.

🔗

static constexpr int digits;

Number of radix digits that can be represented without change.

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

For floating-point types, the number of radix digits in the significand.172

🔗

static constexpr int digits10;

Number of base 10 digits that can be represented without change.173

Meaningful for all specializations in which is_bounded != false.

🔗

static constexpr int max_digits10;

Number of base 10 digits required to ensure that values which differ are always differentiated.

Meaningful for all floating-point types.

🔗

static constexpr bool is_signed;

true if the type is signed.

Meaningful for all specializations.

🔗

static constexpr bool is_integer;

true if the type is integer.

Meaningful for all specializations.

🔗

static constexpr bool is_exact;

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.

Meaningful for all specializations.

🔗

static constexpr int radix;

For floating-point types, specifies the base or radix of the exponent representation (often 2).174

For integer types, specifies the base of the representation.175

Meaningful for all specializations.

🔗

static constexpr T epsilon() noexcept;

Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.176

Meaningful for all floating-point types.

🔗

static constexpr T round_error() noexcept;

Measure of the maximum rounding error.177

🔗

static constexpr int  min_exponent;

Minimum negative integer such that radix raised to the power of one less than that integer is a normalized floating-point number.178

Meaningful for all floating-point types.

🔗

static constexpr int  min_exponent10;

Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.179

Meaningful for all floating-point types.

🔗

static constexpr int  max_exponent;

Maximum positive integer such that radix raised to the power one less than that integer is a representable finite floating-point number.180

Meaningful for all floating-point types.

🔗

static constexpr int  max_exponent10;

Maximum positive integer such that 10 raised to that power is in the range of representable finite floating-point numbers.181

Meaningful for all floating-point types.

🔗

static constexpr bool has_infinity;

true if the type has a representation for positive infinity.

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

🔗

static constexpr bool has_quiet_NaN;

true if the type has a representation for a quiet (non-signaling) “Not a Number”.182

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

🔗

static constexpr bool has_signaling_NaN;

true if the type has a representation for a signaling “Not a Number”.183

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

🔗

static constexpr T infinity() noexcept;

Representation of positive infinity, if available.184

Meaningful for all specializations for which has_infinity != false.

Required in specializations for which is_iec559 != false.

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static constexpr T quiet_NaN() noexcept;

Representation of a quiet “Not a Number”, if available.185

Meaningful for all specializations for which has_quiet_NaN != false.

Required in specializations for which is_iec559 != false.

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static constexpr T signaling_NaN() noexcept;

Representation of a signaling “Not a Number”, if available.186

Meaningful for all specializations for which has_signaling_NaN != false.

Required in specializations for which is_iec559 != false.

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static constexpr T denorm_min() noexcept;

Minimum positive subnormal value, if available.187

Otherwise, minimum positive normalized value.

Meaningful for all floating-point types.

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static constexpr bool is_iec559;

true if and only if the type adheres to ISO/IEC/IEEE 60559.188

[Note 1:

The value is true for any of the types float16_t, float32_t, float64_t, or float128_t, if present ([basic.extended.fp]).

— end note]

Meaningful for all floating-point types.

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static constexpr bool is_bounded;

true if the set of values representable by the type is finite.189

[Note 2:

All fundamental types ([basic.fundamental]) are bounded.

This member would be false for arbitrary precision types.

— end note]

Meaningful for all specializations.

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static constexpr bool is_modulo;

true if the type is modulo.190

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.

[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]

Meaningful for all specializations.

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static constexpr bool traps;

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.191

Meaningful for all specializations.

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static constexpr bool tinyness_before;

true if tinyness is detected before rounding.192

Meaningful for all floating-point types.

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static constexpr float_round_style round_style;

The rounding style for the type.193

Meaningful for all floating-point types.

Specializations for integer types shall return round_toward_zero.

169)169)

Equivalent to CHAR_MIN, SHRT_MIN, FLT_MIN, DBL_MIN, etc.

170)170)

Equivalent to CHAR_MAX, SHRT_MAX, FLT_MAX, DBL_MAX, etc.

171)171)

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.

172)172)

Equivalent to FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG.

173)173)

Equivalent to FLT_DIG, DBL_DIG, LDBL_DIG.

174)174)

Equivalent to FLT_RADIX.

175)175)

Distinguishes types with bases other than 2 (e.g., BCD).

176)176)

Equivalent to FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON.

177)177)

Rounding error is described in LIA-1 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.

178)178)

Equivalent to FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP.

179)179)

Equivalent to FLT_MIN_10_EXP, DBL_MIN_10_EXP, LDBL_MIN_10_EXP.

180)180)

Equivalent to FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP.

181)181)

Equivalent to FLT_MAX_10_EXP, DBL_MAX_10_EXP, LDBL_MAX_10_EXP.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

ISO/IEC/IEEE 60559:2020 is the same as IEEE 754-2019.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Refer to ISO/IEC/IEEE 60559.

Required by LIA-1.

193)193)

Equivalent to FLT_ROUNDS.

Required by LIA-1.

17.3.5.3 numeric_limits specializations [numeric.special]

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.

[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 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]

The specialization for bool shall be provided as follows:

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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 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]

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// all freestanding #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

The header <climits> defines all macros the same as the C standard library header <limits.h>.

[Note 1:

Except for CHAR_BIT and MB_LEN_MAX, a macro referring to an integer type T defines a constant whose type is the promoted type of T ([conv.prom]).

— end note]

17.3.7 Header <cfloat> synopsis [cfloat.syn]

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// all freestanding #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

The header <cfloat> defines all macros the same as the C standard library header <float.h>.