std::ratio

 

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Compile-time rational arithmetic
Compile-time integer sequences
integer_sequence (C++14)

 

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)

 

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 both Num and Denom may not be equal to the most negative value.

The static data members num 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
quecto (C++26)	std::ratio<1, 1000000000000000000000000000000> (10-30), if std::intmax_t can represent the denominator
ronto (C++26)	std::ratio<1, 1000000000000000000000000000> (10-27), if std::intmax_t can represent the denominator
yocto	std::ratio<1, 1000000000000000000000000> (10-24), if std::intmax_t can represent the denominator
zepto	std::ratio<1, 1000000000000000000000> (10-21), if std::intmax_t can represent the denominator
atto	std::ratio<1, 1000000000000000000> (10-18)
femto	std::ratio<1, 1000000000000000> (10-15)
pico	std::ratio<1, 1000000000000> (10-12)
nano	std::ratio<1, 1000000000> (10-9)
micro	std::ratio<1, 1000000> (10-6)
milli	std::ratio<1, 1000> (10-3)
centi	std::ratio<1, 100> (10-2)
deci	std::ratio<1, 10> (10-1)
deca	std::ratio<10, 1> (101)
hecto	std::ratio<100, 1> (102)
kilo	std::ratio<1000, 1> (103)
mega	std::ratio<1000000, 1> (106)
giga	std::ratio<1000000000, 1> (109)
tera	std::ratio<1000000000000, 1> (1012)
peta	std::ratio<1000000000000000, 1> (1015)
exa	std::ratio<1000000000000000000, 1> (1018)
zetta	std::ratio<1000000000000000000000, 1> (1021), if std::intmax_t can represent the numerator
yotta	std::ratio<1000000000000000000000000, 1> (1024), if std::intmax_t can represent the numerator
ronna (C++26)	std::ratio<1000000000000000000000000000, 1> (1027), if std::intmax_t can represent the numerator
quetta (C++26)	std::ratio<1000000000000000000000000000000, 1> (1030), 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(Denom) * 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)

Example

Run this code

#include <ratio>
 
static_assert
(
    std::ratio_equal_v<std::ratio_multiply<std::femto, std::exa>, std::kilo>
);
 
int main() {}

See also

Mathematical constants (C++20)

provides several mathematical constants, such as std::numbers::e for e