Compile-time rational arithmetic

C++

Language

Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

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)

Filesystem library (C++17)

Technical Specifications

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

floor2 (C++20)

log2p1 (C++20)

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.

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

Compile-time rational arithmetic

Several alias 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 (alias template)
ratio_subtract (C++11)	subtracts two ratio objects at compile-time (alias template)
ratio_multiply (C++11)	multiplies two ratio objects at compile-time (alias template)
ratio_divide (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>
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)