Unit-safe computations with quantities.
"The value of a quantity is generally expressed as the product of a number and a unit. The unit is simply a particular example of the quantity concerned which is used as a reference, and the number is the ratio of the value of the quantity to the unit." (Bureau International des Poids et Mesures: The International System of Units, 8th edition, 2006)
Basic types of quantities are defined "by convention", they do not depend on other types of quantities, for example Length, Mass or Duration.
Derived types of quantities, on the opposite, are defined as products of other types of quantities raised by some exponent.
Examples:
Volume = Length ^ 3
Velocity = Length ^ 1 * Duration ^ -1
Acceleration = Length ^ 1 * Duration ^ -2
Force = Mass ^ 1 * Acceleration ^ 1
Each type of quantity may have one special unit which is used as a reference for the definition of all other units, for example Meter, Kilogram and Second. The other units are then defined by their relation to the reference unit.
If a type of quantity is derived from types of quantities that all have a reference unit, then the reference unit of that type is defined by a formula that follows the formula defining the type of quantity.
Examples:
Velocity -> Meter per Second = Meter ^ 1 * Second ^ -1
Acceleration -> Meter per Second squared = Meter ^ 1 * Second ^ -2
Force -> Newton = Kilogram ^ 1 * Meter ^ 1 * Second ^ -2
There may be different systems which define quantities, their units and the relations between these units in a different way.
This is not directly supported by this package. For each type of quantity there can be only no or exactly one reference unit. But, if you have units from different systems for the same type of quantity, you can define these units and provide mechanisms to convert between them.
The essential functionality of the package is provided by the two traits
Quantity and Unit as well as the generic struct Qty<U: Unit>.
A basic type of quantity can easily be defined using the macro
define_qty. In a future version, another macro will allow to create a
derived type of quantity based on more basic types of quantities.
The package will provide definitions of many commonly used quantities; each can be activated by a feature with a corresponding name.