std::ratio

Defined in header `<ratio>`
template< std::intmax_t Num, std::intmax_t Denom = 1 > class ratio;		(since C++11)

The class template std::ratio provides compile-time rational arithmetic support. Each instantiation of this template exactly represents any finite rational number as long as its numerator Num and denominator Denom are representable as compile-time constants of type std::intmax_t. In addition, Denom may not be zero and may not be equal to the most negative value.

The static data members nom and den representing the numerator and denominator are calculated by dividing Num and Denom by their greatest common divisor. However, two std::ratio with different Num or Denom are distinct types even if they represent the same rational number (after reduction). A ratio type can be reduced to the lowest terms via its type member: std::ratio<3, 6>::type is std::ratio<1, 2>.

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

Defined in header `<ratio>`
Type	Definition
`yocto`	std::ratio<1, 1000000000000000000000000>, if std::intmax_t can represent the denominator
`zepto`	std::ratio<1, 1000000000000000000000>, if std::intmax_t can represent the denominator
`atto`	std::ratio<1, 1000000000000000000>
`femto`	std::ratio<1, 1000000000000000>
`pico`	std::ratio<1, 1000000000000>
`nano`	std::ratio<1, 1000000000>
`micro`	std::ratio<1, 1000000>
`milli`	std::ratio<1, 1000>
`centi`	std::ratio<1, 100>
`deci`	std::ratio<1, 10>
`deca`	std::ratio<10, 1>
`hecto`	std::ratio<100, 1>
`kilo`	std::ratio<1000, 1>
`mega`	std::ratio<1000000, 1>
`giga`	std::ratio<1000000000, 1>
`tera`	std::ratio<1000000000000, 1>
`peta`	std::ratio<1000000000000000, 1>
`exa`	std::ratio<1000000000000000000, 1>
`zetta`	std::ratio<1000000000000000000000, 1>, if std::intmax_t can represent the numerator
`yotta`	std::ratio<1000000000000000000000000, 1>, if std::intmax_t can represent the numerator

Member types

Member type	Definition
`type`	std::ratio<num, den>

Member objects

constexpr intmax_t num [static]	constexpr value of type std::intmax_t equal to `sign(Num) * sign(Denom) * abs(Num) / gcd(Num, Denom)` (public static member constant)
constexpr intmax_t den [static]	constexpr value of type std::intmax_t equal to `abs(Denom) / gcd(Num, Denom)` (public static member constant)

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications

Common mathematical functions
Special mathematical functions
Floating-point environment (C++11)
Complex numbers
Numeric arrays
Pseudo-random number generation
Compile-time rational arithmetic (C++11)
Numeric algorithms
gcd (C++17)
lcm (C++17)
Interpolations
midpoint (C++20)
lerp (C++20)
Generic numeric operations
iota (C++11)
accumulate
inner_product
adjacent_difference
partial_sum
reduce (C++17)
transform_reduce (C++17)
inclusive_scan (C++17)
exclusive_scan (C++17)
transform_inclusive_scan (C++17)
transform_exclusive_scan (C++17)
Bit operations
bit_cast (C++20)
ispow2 (C++20)
ceil2 (C++20)
floor2 (C++20)
log2p1 (C++20)

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)