Compile-time rational arithmetic

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C++ Standard Library
Language Utilities library Strings library Containers library Algorithms library Iterators library Numerics library Input/output library Localizations library Regular expressions library (C++11) Atomic operations library (C++11) Thread support library (C++11)
Numerics library
Common mathematical functions Floating-point environment Complex numbers Numeric arrays Pseudo-random number generation Compile-time rational arithmetic (C++11) Generic numeric operations iota (C++11) accumulate inner_product adjacent_difference partial_sum
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)

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>
ratio	represents exact rational fraction (class template)

Several convenience typedefs that correspond to the SI ratios are provided by the standard library:

Defined in header <ratio>
Type	Definition
yocto	std::ratio<1, 1000000000000000000000000>, if std::intmax_t can represent the denominator
zepto	std::ratio<1, 1000000000000000000000>, if std::intmax_t can represent the denominator
atto	std::ratio<1, 1000000000000000000>
femto	std::ratio<1, 1000000000000000>
pico	std::ratio<1, 1000000000000>
nano	std::ratio<1, 1000000000>
micro	std::ratio<1, 1000000>
milli	std::ratio<1, 1000>
centi	std::ratio<1, 100>
deci	std::ratio<1, 10>
deca	std::ratio<10, 1>
hecto	std::ratio<100, 1>
kilo	std::ratio<1000, 1>
mega	std::ratio<1000000, 1>
giga	std::ratio<1000000000, 1>
tera	std::ratio<1000000000000, 1>
peta	std::ratio<1000000000000000, 1>
exa	std::ratio<1000000000000000000, 1>
zetta	std::ratio<1000000000000000000000, 1>, if std::intmax_t can represent the numerator
yotta	std::ratio<1000000000000000000000000, 1>, if std::intmax_t can represent the numerator

[edit] Compile-time rational arithmetic

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

Defined in header <ratio>
ratio_add (C++11)	adds two ratio objects at compile-time (class template)
ratio_subtract (C++11)	subtracts two ratio objects at compile-time (class template)
ratio_multiply (C++11)	multiplies two ratio objects at compile-time (class template)
ratio_divide (C++11)	divides two ratio objects at compile-time (class template)

[edit] Compile-time rational comparison

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

Defined in header <ratio>
ratio_equal (C++11)	compares two ratio objects for equality at compile-time (class template)
ratio_not_equal (C++11)	compares two ratio objects for inequality at compile-time (class template)
ratio_less (C++11)	compares two ratio objects for less than at compile-time (class template)
ratio_less_equal (C++11)	compares two ratio objects for less than or equal to at compile-time (class template)
ratio_greater (C++11)	compares two ratio objects for greater than at compile-time (class template)
ratio_greater_equal (C++11)	compares two ratio objects for greater than or equal to at compile-time (class template)