std::ratio
| Defined in header <ratio>
|
||
| template< std::intmax_t Num, |
(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 std::ratio type can be reduced to the lowest terms via its type member: std::ratio<3, 6>::type is std::ratio<1, 2>.
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)
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std::ratio<1, 1000000000000000000000000> (10-24)[1]
|
zepto (since C++11)
|
std::ratio<1, 1000000000000000000000> (10-21)[1]
|
atto (since C++11)
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std::ratio<1, 1000000000000000000> (10-18)
|
femto (since C++11)
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std::ratio<1, 1000000000000000> (10-15)
|
pico (since C++11)
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std::ratio<1, 1000000000000> (10-12)
|
nano (since C++11)
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std::ratio<1, 1000000000> (10-9)
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micro (since C++11)
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std::ratio<1, 1000000> (10-6)
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milli (since C++11)
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std::ratio<1, 1000> (10-3)
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centi (since C++11)
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std::ratio<1, 100> (10-2)
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deci (since C++11)
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std::ratio<1, 10> (10-1)
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deca (since C++11)
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std::ratio<10, 1> (101)
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hecto (since C++11)
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std::ratio<100, 1> (102)
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kilo (since C++11)
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std::ratio<1000, 1> (103)
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mega (since C++11)
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std::ratio<1000000, 1> (106)
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giga (since C++11)
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std::ratio<1000000000, 1> (109)
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tera (since C++11)
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std::ratio<1000000000000, 1> (1012)
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peta (since C++11)
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std::ratio<1000000000000000, 1> (1015)
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exa (since C++11)
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std::ratio<1000000000000000000, 1> (1018)
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zetta (since C++11)
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std::ratio<1000000000000000000000, 1> (1021)[2]
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yotta (since C++11)
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std::ratio<1000000000000000000000000, 1> (1024)[2]
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ronna (since C++26)
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std::ratio<1000000000000000000000000000, 1> (1027)[2]
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quetta (since C++26)
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std::ratio<1000000000000000000000000000000, 1> (1030)[2]
|
- ↑ 1.0 1.1 1.2 1.3 These typedefs are only declared if std::intmax_t can represent the denominator.
- ↑ 2.0 2.1 2.2 2.3 These typedefs are only declared if std::intmax_t can represent the numerator.
Nested types
| Type | Definition |
type
|
std::ratio<num, den> (the rational type after reduction) |
Data members
In the definitions given below,
- sign(Denom) is -1 if Denom is negative, or 1 otherwise; and
- gcd(Num, Denom) is the greatest common divisor of std::abs(Num) and std::abs(Denom).
| Member | Definition |
| constexpr std::intmax_t num [static] |
sign(Denom) * Num / gcd(Num, Denom) (public static member constant) |
| constexpr std::intmax_t den [static] |
std::abs(Denom) / gcd(Num, Denom) (public static member constant) |
Notes
| Feature-test macro | Value | Std | Feature |
|---|---|---|---|
__cpp_lib_ratio |
202306L | (C++26) | Adding the new 2022 SI prefixes: quecto, quetta, ronto, ronna |
Example
#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 |