# DefUnit

DefUnit provides a pair of macros that allow you to quickly create a module that
defines a set of core units for its users to work with. The macros
create documentation attributes, conversion operators and type specs that allow
Dialyzer to detect most incompatible assignments at compile time.

DefUnit adds almost no run-time overhead to your code. The values you work with
are everyday floats.

#### Example

Create the file _units.ex_:

defmodule Unit do

  use DefUnit
  @doc_from_operator """
  Convert from other units to core units used for calculations.

  @doc_to_operator """
  Convert from core units used for calculations to other units.
  # Units we do our calculations in
  DefUnit.core  "m",        :m,     "SI length"
  DefUnit.core  "kg",       :kg,    "SI mass"
  DefUnit.core  "s",        :s,     "Time"
  DefUnit.core  "m^2",      :m2,    "SI area"
  DefUnit.core  "ms^{-1}",  :ms,    "SI velocity"
  DefUnit.core  "ms^{-2}",  :ms2,   "SI acceleration"
  DefUnit.core  "kgm^{-3}", :kgm3,  "SI density"
  # Units we convert to and from core units
  DefUnit.other "feet",     :feet,    0.3048,   :m,   "FPS length and altitude"
  DefUnit.other "kmh^{-1}", :kmh,     0.27777,  :ms,  "Kilometres per hour"
  DefUnit.other "mph",      :mph,     0.44704,  :ms,  "Imperial velocity"
  DefUnit.other "knots",    :knots,   0.514444, :ms,  "Nautical miles per hour"


Note this isn't an SI vs Imperial units thing - kmh is an SI unit, but it's not the
unit we're choosing to work in, which is metres per second.

Now in iex:

  iex>import Unit
  iex> 65 <~ :knots
  iex> 60 <~ :mph
  iex> 100 <~ :kmh

All these values are converted to their equivalent 'core' representation, in this
example metres per second. Conversely:

  iex> 33.43886 ~> :knots
  iex> 10 ~> :mph
  iex> 10 ~> :kmh

The values are assumed to be in 'core' representation and are converted to their
corresponding 'other' unit. The idea of separating units into 'core' and 'other' may
seem arbitrary, but the idea is that the code using the Unit module is easier to
write and reason about if it is working with a consistent set of core units of the 
developer's choosing.

The operators can also be used to convert between 'other' types in a readable way:

  iex> 100 <~ :kmh ~> :mph

You can read the above as 'convert 100 from kmh to mph'. But what is this?

  iex> 100 <~ :kg ~> :mph

Apparently 100 kilograms is 224 miles per hour right? It is worth repeating:

_>>> DefUnit does not provide run time type checking <<<_

If you really want runtime type checking you should look at 
[Unit Fun]( However if you're interested in
using [Dialyzer]( with the type specs
created by the DefUnit macros to do static analysis, read on.

#### Using Types

Assume we're writing a library of aerodynamics functions. Aerospace uses a mix of units
from FPS, navigation and SI unit systems, and you really don't want to mess up your units
(see [Mars Climate Orbiter](

defmodule Aero do

  @doc "pressure in standard atmosphere at `alt` feet"
  @spec p(Unit.feet) :: Unit.kgm3
  def p(alt) do
    8.0e-19 * :math.pow(alt, 4)  \
    - 4.0e-14 * :math.pow(alt, 3) \
    + 1.0e-09 * :math.pow(alt, 2) \
    - 4.0e-05 * alt \
    + 1.225
  @doc "acceleration due to gravity"
  @spec g() :: Unit.ms2
  def g() do
  @doc "stall speed given aircraft weight, wing area, max lift and altitude"
  @spec vs(, Unit.m2, float, Unit.feet) ::
  def vs(m, s, cl_max, alt \\ 0.0) do
    :math.sqrt((2.0 * m * g()) / (p(alt) * s * cl_max))

The units defined in the Unit module are available to use in specs for our
aerodynamics functions. If you were calling your library and wanted to be clear
about the units you were using you can write:

piper_archer_stall_speed_kts = vs(1157 <~ :kg, 15.8 <~ :m2, 2.1, 0 <~ :feet) ~> :knots

However if you mistakenly write:

piper_archer_stall_speed_kts = vs(1157 <~ :kg, 15.8 <~ :m2, 2.1, 0 <~ :feet) ~> :kg

nothing will happen... unless you run Dialyzer*, in which case you'll
get a response similar to this:

$ mix dialyzer
Starting Dialyzer
...stuff ommitted
aero.ex:118: The call 'Elixir.Unit':'~>'(float(),'kg') will never return since
the success typing is (number(),'feet' | 'kmh' | 'knots') -> float() and the
contract is 
    ; (ms(),'knots') -> knots()
    ; (ms(),'mph') -> mph()
    ; (ms(),'kmh') -> kmh()
    ; (m(),'feet') -> feet()
 done in 0m1.36s
done (warnings were emitted)

\* Perhaps using the [dialyxir]( mix plugin