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. Both numerator and denominator are automatically reduced to the lowest terms.

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

[edit] Member types

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

[edit] 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
Concepts
Utilities library
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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)
Generic numeric operations
iota (C++11)
accumulate
inner_product
adjacent_difference
partial_sum

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)