Compile-time rational arithmetic (since C++11)
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.
Compile-time fractions
Defined in header <ratio> |
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(C++11) | represents exact rational fraction (class template) |
The following convenience typedefs that correspond to the SI ratios are provided by the standard library:
Defined in header <ratio> |
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| 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] |
- These typedefs are only declared if
std::intmax_tcan represent the denominator. - These typedefs are only declared if
std::intmax_tcan represent the numerator.
Compile-time rational arithmetic
Several alias templates, that perform arithmetic operations on ratio objects at compile-time are provided.
Defined in header <ratio> |
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(C++11) | adds two ratio objects at compile-time(alias template) |
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(C++11) | subtracts two ratio objects at compile-time(alias template) |
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(C++11) | multiplies two ratio objects at compile-time(alias template) |
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(C++11) | divides two ratio objects at compile-time(alias template) |
Compile-time rational comparison
Several class templates, that perform comparison operations on ratio objects at compile-time are provided.
Defined in header <ratio> |
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(C++11) | compares two ratio objects for equality at compile-time (class template) |
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(C++11) | compares two ratio objects for inequality at compile-time (class template) |
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(C++11) | compares two ratio objects for less than at compile-time (class template) |
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(C++11) | compares two ratio objects for less than or equal to at compile-time (class template) |
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(C++11) | compares two ratio objects for greater than at compile-time (class template) |
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(C++11) | compares two ratio objects for greater than or equal to at compile-time (class template) |
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