Powers

Several of our monovalue types (such as units and magnitudes) can be raised to powers. This includes negative exponents (such as the inverse), and fractional exponents (such as roots).

When expressed as values (as opposed to types), we provide the same APIs for each of them.

General APIs

In what follows, x stands for an instance of the appropriate monovalue type. For example, it might be Meters{} (a unit), mag<18>() (a magnitude), or some other type.

pow<N>(x)

Raise the input x to the Nth power.

Example signature:

// T is an appropriate monovalue type (a unit, a magnitude, ...).
template<std::intmax_t N, typename T>
constexpr auto pow(T);

Result: An instance of the Nth power of the type of x.

Example

pow<3>(mag<4>()) yields mag<64>().

root<N>(x)

Take the Nth root of the input.

Example signature:

// T is an appropriate monovalue type (a unit, a magnitude, ...).
template<std::intmax_t N, typename T>
constexpr auto root(T);

Result: An instance of the Nth root of the type of x.

Example

root<2>(mag<49>()) yields mag<7>().

Helpers (inverse, squared, cubed, sqrt, cbrt)

Some powers and roots are very common. It’s useful to have shortcuts for these to make the code more readable. The following helpers are available to operate on an instance, x, of any compatible monovalue type (a unit, a magnitude, …):

Helper	Result
inverse(x)	pow<-1>(x)
squared(x)	pow<2>(x)
cubed(x)	pow<3>(x)
sqrt(x)	root<2>(x)
cbrt(x)	root<3>(x)

Type-based versions (Inverse, Squared, Cubed, Sqrt, Cbrt)

We provide type-based versions of the above helpers, to make it easier to concisely form readable type names. Here are the following helpers as applied to a unit U, and the equivalent result as expressed using more general unit power APIs.

Helper	Result
Inverse<U>	UnitPowerT<U, -1>
Squared<U>	UnitPowerT<U, 2>
Cubed<U>	UnitPowerT<U, 3>
Sqrt<U>	UnitPowerT<U, 1, 2>
Cbrt<U>	UnitPowerT<U, 1, 3>