Physical Units
A library for working with values that have physical units in a simple sound way
§Base Units
Any SI unit can be represented as the powers of the seven SI base units that multiply to construct it.
| Name | Symbol | Quantity |
|---|---|---|
| kilogram | kg | mass |
| meter | m | distance |
| second | s | time |
| mole | mol | amount |
| ampere | A | current |
| kelvin | K | temperature |
| candela | cd | luminosity |
For example, 1 newton (1 N) is equal to one kilogram meter per second squared (1 kg⋅m/s²),
which can be represented a (1, 1, -2, 0, 0, 0, 0) where each value corresponds to the exponent
of an SI base unit. This is how the BaseUnit type represents units.
§Derived Units
In addition to the base units, there are also SI derived units which can be useful for talking about common combinations of base units.
| Name | Symbol | Quantity | SI Base Units |
|---|---|---|---|
| hertz | Hz | frequency | s⁻¹ |
| newton | N | force, weight | kg⋅m⋅s⁻² |
| pascal | Pa | pressure, stress | kg⋅m⁻¹⋅s⁻² |
| joule | J | energy, work, heat | kg⋅m²⋅s⁻² |
| watt | W | power, radiant flux | kg⋅m²⋅s⁻³ |
| coulomb | C | electrical charge | s⋅A |
| volt | V | voltage, electrical potential difference | kg⋅m²⋅s⁻³⋅A⁻¹ |
| farad | F | electrical capacitance | kg⁻¹⋅m⁻2⋅s³⋅A² |
| ohm | Ω | electrical resistance | kg⋅m²⋅s⁻³⋅A⁻² |
| siemens | S | electrical conductance | kg⁻¹⋅m⁻²⋅s³⋅A² |
| weber | Wb | magnetic flux | kg⋅m²⋅s⁻²⋅A⁻¹ |
| tesla | T | magnetic induction | kg⋅s⁻²⋅A⁻¹ |
| henry | H | electrical inductance | kg⋅m²⋅s⁻²⋅A⁻² |
| lux | lx | illuminance | cd⋅m⁻² |
| becquerel | Bq | radioactivity | s⁻¹ |
| gray | Gy | absorbed dose (of ionizing radiation) | m²⋅s⁻² |
| sievert | Sv | equivalent dose (of ionizing radiation) | m²⋅s⁻² |
| katal | kat | catalytic activity | s⁻¹⋅mol |
(based on Wikipedia: SI derived unit - Special names)
These units can all be represented in BaseUnit as powers of SI base units,
but the derived module also provides a representation that keeps track
of specifically which base and derived units were specified.
Units represented this way are encoded using 7 base exponents
and 18 additional exponents for the derived units!
This is NOT a minimal encoding of the unit information but
the redundancy allows us to distinguish between "N" and "kg⋅m/s²".
§Arithmetic
Both BaseValue and DerivedValue support basic arithmetic including addition, subtraction, multiplication, and division.
- Addition and subtraction require the values to have the same units and if they are, not produces a
UnitMismatcherror. - Multiplication and division don't require the values to have the same units and infers the correct units for the resulting value.
§Comparison
All of the types (BaseUnit, BaseValue, DerivedUnit, DerivedValue) support comparison
and, in the case of the derived ones, perform the necessary conversions to check that they are equal
even if the representations differ.
§Limitations
The exponent for each unit is an 8-bit signed integer (i8) which can
encode values in the range -128..128 (inclusive..exclusive).
This means that fractional unit exponents can't be represented and
if you attempt to multiply or divide BaseUnit, BaseValue, DerivedUnit, or DerivedValue
such that any unit exponent leaves this range, you will get a runtime panic.
§Simplifying
The DerivedUnit type implements a simplify() function that attempts to express
the unit in terms of the fewest exponents using a naive greedy algorithm
which applies identities which reduce the sum of absolute exponents.
§Formatting
All of the unit types have a pretty-printed Display implementation.
The Display implementation operates at the level of abstraction of the unit type it's for.
BaseUnit-"kg⋅m/s²"DerivedUnit-"N"OR"kg⋅m/s²"(depending on how it was constructed)
They also have a Debug implementation that uses the full names of units and doesn't use / or parenthesis.
BaseUnit-"BaseUnit(kilogram⋅meter⋅second⁻²)"DerivedUnit-"DerivedUnit(newton)"OR"DerivedUnit(kilogram⋅meter⋅second⁻²)"
§Parsing
TODO: Implement and document parsing for each unit representation
§Read-eval-print-loop (REPL)
TODO: Implement and document a simple REPL for evaluating expressions with units
§Inspiration
Inspired by the video Seven Dimensions: Why mass is a vector (and so is everything else) (kind of), which proposes treating units as a vector space and applying linear algebra concepts to it.