Compile-time rational arithmetic (since C++11) (original) (raw)
Compile time rational arithmetic
The class template std::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
The following convenience typedefs that correspond to the SI ratios are provided by the standard library:
| Defined in header | |
|---|---|
| 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 1.3 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.
[edit] Compile-time rational arithmetic
Several alias templates, that perform arithmetic operations on ratio objects at compile-time are provided.
[edit] Compile-time rational comparison
Several class templates, that perform comparison operations on ratio objects at compile-time are provided.
| Defined in header | |
|---|---|
| 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 for less than at compile-time (class template) [edit] |
| ratio_less_equal(C++11) | compares two ratio objects for less than or equal to at compile-time (class template) [edit] |
| ratio_greater(C++11) | compares two ratio objects for greater than at compile-time (class template) [edit] |
| ratio_greater_equal(C++11) | compares two ratio objects for greater than or equal to at compile-time (class template) [edit] |