A number without its unit of measure is meaningless at best and dangerous at worst. The unit
provides the context within which to interpret the value. For 'commensurate' units (units in the
same Dimension), the unit disambiguates different scalings. For example, is the length of 4.6
in feet or meters? For 'incommensurate' units, the unit limits the valid operations between units.
For example, you can't add meters and seconds.
No Naked Numbers
Software engineers (have been known to) annotate their code to identify the unit 'associated' with a number. The annotation may be in a comment:
double distance = 0.0 // in milesor it may be in the variable's name:
double distanceInMiles = 0.0;or in the documenation:
/** The distance in miles */
double distance = 0.0;None of these appoaches scales with a program's size/complexity'. The code comment is lost when code is delivered as a library, the name might be onerous to type and limit use of more convenient units and the documentation needs to be referenced or remembered. It is surely safest to pair the number with its unit.
A dimension identifies commensurate physical quantities. There is a defined set of base dimensions as: Mass (M), Length(L), Time(T), Current(I), Temperature(Θ), Intensity(J), Amount(N),
and (Planar) Angle(R). [Note Planar Angle and Spherical Angle are non-standard; we use one but
not the other]. From these base dimensions, derived dimensions can be constructed with
exponents of the bases. For example a unit for Area is L² which is 'encoded' from the base
dimensions as L with '2' and all others with '0'; a unit of Acceleration is L/T² and is 'encode' as
L with '1', T with '-2' and all others with '0'
Only units with the same dimension can be added/subtracted with one another. When units are multiplied the exponents of the base dimensions are added to produce another dimension.
For type-safe operations on units, we designate Dimension as a 'type parameter' in Unit and
Quantity type declarations. This allows a statically typed system of units (with an exception
or two)
A Unit is a defined amount of a physical quantity. Units fall into two categories based on
their dimension: 'base units' and 'derived units'.
Every Unit, base or dervied, measures a quantity in a specified Dimension. Units with the same
Dimension are related by scale+offset values. For example, a base unit 'meter' has dimension
'L'; the 'scaled unit' of 'kilometer' is 1000 meters. A base unit of 'kelvin' has dimension 'Θ';
the 'scaled unit' of 'celsius' has a scale of 1.0 and an offset of -273.15 from kelvin.
Products or Ratios of units with an offset is ill-defined.
A Quantity is a magnitude (or multitude) of a physical property. A Quantity has a Dimension
that identifies the type of the physical property; quanities with the same Dimension can be
compared with one another.
A Quantity has a value and a unit. Comparisons between quantities is performed based on
values with the same unit; unit conversion is implicit.
Quanties can be added and subtracted.
Quantities can be conditionally multiplied and divided. It is possible that the target of the
product (or division), is specified with a Dimension that is inconsistent with the product. For
example Volume = Length * Length. In such cases the result of the product is nil.
In your Package.swift file, add a dependency on SBUnits:
import PackageDescription
let package = Package (
name: "<your package>",
dependencies: [
// ...
.Package (url: "https://github.com/EBGToo/SBUnits.git", majorVersion: 1),
// ...
]
)pod 'SBUnits', '~> 0.1'$ git clone https://github.com/EBGToo/SBUnits.git SBUnitsAdd the SBUnits Xcode Project to your Xcode Workspace.