Compile-time rational arithmetic(since C++11)

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Metaprogramming library

Type traits

Type categories

is_void

(C++11)

is_null_pointer

(C++11)(DR*)

is_array (C++11)
is_pointer (C++11)
is_enum (C++11)
is_union (C++11)
is_class (C++11)
is_function (C++11)
is_reference (C++11)

is_object (C++11)
is_scalar (C++11)
is_compound (C++11)
is_integral (C++11)
is_floating_point (C++11)
is_fundamental (C++11)
is_arithmetic (C++11)

is_lvalue_reference

(C++11)

is_rvalue_reference

(C++11)

is_member_pointer

(C++11)

is_member_object_pointer

(C++11)

is_member_function_pointer

(C++11)

Type properties

(C++11)

(C++11)

(C++11)

(C++11)

(C++14)

(C++11)

(C++17)

(C++23)

(C++11)(deprecated in C++26)

is_trivially_copyable

(C++11)

is_standard_layout

(C++11)

is_literal_type

(C++11)(until C++20*)

is_pod

(C++11)(deprecated in C++20)

(C++11)

(C++11)

(C++20)

(C++20)

(C++23)

has_unique_object_representations

(C++17)

Type trait constants

integral_constantbool_constanttrue_typefalse_type

(C++11)(C++17)(C++11)(C++11)

Metafunctions

conjunction

(C++17)

disjunction

(C++17)

negation

(C++17)

Supported operations

is_constructibleis_trivially_constructibleis_nothrow_constructible (C++11)(C++11)(C++11)
is_default_constructibleis_trivially_default_constructibleis_nothrow_default_constructible (C++11)(C++11)(C++11)
is_copy_constructibleis_trivially_copy_constructibleis_nothrow_copy_constructible (C++11)(C++11)(C++11)
is_move_constructibleis_trivially_move_constructibleis_nothrow_move_constructible (C++11)(C++11)(C++11)
is_assignableis_trivially_assignableis_nothrow_assignable (C++11)(C++11)(C++11)

is_copy_assignableis_trivially_copy_assignableis_nothrow_copy_assignable (C++11)(C++11)(C++11)
is_move_assignableis_trivially_move_assignableis_nothrow_move_assignable (C++11)(C++11)(C++11)
is_destructibleis_trivially_destructibleis_nothrow_destructible (C++11)(C++11)(C++11)
has_virtual_destructor (C++11)
is_swappable_withis_swappableis_nothrow_swappable_withis_nothrow_swappable (C++17)(C++17)(C++17)(C++17)

Relationships and property queries

is_same (C++11)
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is_corresponding_member (C++20)
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reference_converts_from_temporary (C++23)

is_base_of (C++11)
is_virtual_base_of (C++26)
alignment_of (C++11)
rank (C++11)
extent (C++11)
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Type modifications

remove_cvremove_constremove_volatile (C++11)(C++11)(C++11)
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make_signed (C++11)
make_unsigned (C++11)

remove_reference (C++11)
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remove_pointer (C++11)
add_pointer (C++11)
remove_extent (C++11)
remove_all_extents (C++11)

Type transformations

aligned_storage (C++11)(deprecated in C++23)
aligned_union (C++11)(deprecated in C++23)
decay (C++11)
remove_cvref (C++20)
result_ofinvoke_result (C++11)(until C++20*)(C++17)

conditional (C++11)
common_type (C++11)
common_reference (C++20)
underlying_type (C++11)
type_identity (C++20)
enable_if (C++11)
void_t (C++17)

Compile-time rational arithmetic

Compile-time integer sequences

integer_sequence

(C++14)

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Compile time rational arithmetic

ratio (C++11)
Arithmetic
ratio_add (C++11)
ratio_subtract (C++11)
ratio_multiply (C++11)
ratio_divide (C++11)
Comparison
ratio_equal (C++11)
ratio_not_equal (C++11)
ratio_less (C++11)
ratio_less_equal (C++11)
ratio_greater (C++11)
ratio_greater_equal (C++11)

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The class templatestd::ratio and associated templates provide compile-time rational arithmetic support. Each instantiation of this template exactly represents any finite rational number.

[edit]Compile-time fractions

Defined in header`<ratio>`
ratio (C++11)	represents exact rational fraction (class template)[edit]

The following convenience typedefs that correspond to the SI ratios are provided by the standard library:

Defined in header`<ratio>`
Type	Definition
`quecto`(since C++26)	std::ratio<1,1000000000000000000000000000000> (10^-30)^[1]
`ronto`(since C++26)	std::ratio<1,1000000000000000000000000000> (10^-27)^[1]
`yocto`(since C++11)	std::ratio<1,1000000000000000000000000> (10^-24)^[1]
`zepto`(since C++11)	std::ratio<1,1000000000000000000000> (10^-21)^[1]
`atto`(since C++11)	std::ratio<1,1000000000000000000> (10^-18)
`femto`(since C++11)	std::ratio<1,1000000000000000> (10^-15)
`pico`(since C++11)	std::ratio<1,1000000000000> (10^-12)
`nano`(since C++11)	std::ratio<1,1000000000> (10^-9)
`micro`(since C++11)	std::ratio<1,1000000> (10^-6)
`milli`(since C++11)	std::ratio<1,1000> (10^-3)
`centi`(since C++11)	std::ratio<1,100> (10^-2)
`deci`(since C++11)	std::ratio<1,10> (10^-1)
`deca`(since C++11)	std::ratio<10,1> (10¹)
`hecto`(since C++11)	std::ratio<100,1> (10²)
`kilo`(since C++11)	std::ratio<1000,1> (10³)
`mega`(since C++11)	std::ratio<1000000,1> (10⁶)
`giga`(since C++11)	std::ratio<1000000000,1> (10⁹)
`tera`(since C++11)	std::ratio<1000000000000,1> (10¹²)
`peta`(since C++11)	std::ratio<1000000000000000,1> (10¹⁵)
`exa`(since C++11)	std::ratio<1000000000000000000,1> (10¹⁸)
`zetta`(since C++11)	std::ratio<1000000000000000000000,1> (10²¹)^[2]
`yotta`(since C++11)	std::ratio<1000000000000000000000000,1> (10²⁴)^[2]
`ronna`(since C++26)	std::ratio<1000000000000000000000000000,1> (10²⁷)^[2]
`quetta`(since C++26)	std::ratio<1000000000000000000000000000000,1> (10³⁰)^[2]

↑^1.0^1.1^1.2^1.3These typedefs are only declared ifstd::intmax_t can represent the denominator.
↑^2.0^2.1^2.2^2.3These typedefs are only declared ifstd::intmax_t can represent the numerator.

[edit]Compile-time rational arithmetic

Several alias templates, that perform arithmetic operations onratio objects at compile-time are provided.

Defined in header`<ratio>`
ratio_add (C++11)	adds two`ratio` objects at compile-time (alias template)[edit]
ratio_subtract (C++11)	subtracts two`ratio` objects at compile-time (alias template)[edit]
ratio_multiply (C++11)	multiplies two`ratio` objects at compile-time (alias template)[edit]
ratio_divide (C++11)	divides two`ratio` objects at compile-time (alias template)[edit]

[edit]Compile-time rational comparison

Several class templates, that perform comparison operations onratio objects at compile-time are provided.

Defined in header`<ratio>`
ratio_equal (C++11)	compares two`ratio` objects for equality at compile-time (class template)[edit]
ratio_not_equal (C++11)	compares two`ratio` objects for inequality at compile-time (class template)[edit]
ratio_less (C++11)	compares two`ratio` objects forless than at compile-time (class template)[edit]
ratio_less_equal (C++11)	compares two`ratio` objects forless than or equal to at compile-time (class template)[edit]
ratio_greater (C++11)	compares two`ratio` objects forgreater than at compile-time (class template)[edit]
ratio_greater_equal (C++11)	compares two`ratio` objects forgreater than or equal to at compile-time (class template)[edit]

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Compile-time rational arithmetic(since C++11)

[edit]Compile-time fractions

[edit]Compile-time rational arithmetic

[edit]Compile-time rational comparison

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