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Compile-time rational arithmetic (since C++11)

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Compile-time rational arithmetic
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Compile time rational arithmetic
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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

Defined in header <ratio>
(C++11)
represents exact rational fraction
(class template) [edit]

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) 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. 1.0 1.1 1.2 1.3 These typedefs are only declared if std::intmax_t can represent the denominator.
  2. 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.

Defined in header <ratio>
(C++11)
adds two ratio objects at compile-time
(alias template)[edit]
subtracts two ratio objects at compile-time
(alias template)[edit]
multiplies two ratio objects at compile-time
(alias template)[edit]
divides two ratio objects at compile-time
(alias template)[edit]

[edit] Compile-time rational comparison

Several class templates, that perform comparison operations on ratio objects at compile-time are provided.

Defined in header <ratio>
compares two ratio objects for equality at compile-time
(class template) [edit]
compares two ratio objects for inequality at compile-time
(class template) [edit]
compares two ratio objects for less than at compile-time
(class template) [edit]
compares two ratio objects for less than or equal to at compile-time
(class template) [edit]
compares two ratio objects for greater than at compile-time
(class template) [edit]
compares two ratio objects for greater than or equal to at compile-time
(class template) [edit]