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

 

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Compile-time rational arithmetic
Compile-time integer sequences
integer_sequence (C++14)

 

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 (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>
Type	Definition
quecto (since C++26)	std::ratio<1, 1000000000000000000000000000000> (10-30)
ronto (since C++26)	std::ratio<1, 1000000000000000000000000000>    (10-27)
yocto (since C++11)	std::ratio<1, 1000000000000000000000000>       (10-24)
zepto (since C++11)	std::ratio<1, 1000000000000000000000>          (10-21)
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)
yotta (since C++11)	std::ratio<1000000000000000000000000, 1>       (1024)
ronna (since C++26)	std::ratio<1000000000000000000000000000, 1>    (1027)
quetta (since C++26)	std::ratio<1000000000000000000000000000000, 1> (1030)

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)