Unit-safe computations with quantities (including money)

## Project description

The package quantity provides classes for unit-safe computations with quantities, including money.

## Defining a quantity class

A basic type of quantity is declared just by sub-classing the class Quantity:

```>>> class Length(Quantity):
...     pass
```

In addition to the new quantity class the meta-class of class Quantity creates a corresponding class for the units automatically. It can be referenced via the quantity class:

```>>> Length.Unit
<class 'quantity.quantity.LengthUnit'>
```

If the quantity has a unit which is used as a reference for defining other units, the simplest way to define it is giving a name and a symbol for it as class variables. The meta-class of class Quantity will then create a unit automatically:

```>>> class Length(Quantity):
...     refUnitName = 'Meter'
...     refUnitSymbol = 'm'
>>> Length.refUnit
Length.Unit('m')
```

Now, this unit can be given to create a quantity:

```>>> METER = Length.refUnit
>>> print(Length(15, METER))
15 m
```

Other units can be derived from the reference unit (or another unit), giving a definition by multiplying a scaling factor with that unit:

```>>> MILLIMETER = Length.Unit('mm', 'Millimeter', Decimal('0.001') * METER)
>>> MILLIMETER
Length.Unit('mm')
>>> KILOMETER = Length.Unit('km', 'Kilometer', 1000 * METER)
>>> KILOMETER
Length.Unit('km')
>>> CENTIMETER = Length.Unit('cm', 'Centimeter', 10 * MILLIMETER)
>>> CENTIMETER
Length.Unit('cm')
```

Using one unit as a reference and defining all other units by giving a scaling factor is only possible if the units have the same scale. Otherwise, units have to be instantiated via the corresponding class Unit sub-class without giving a definition.

```>>> class Temperature(Quantity):
...     pass
>>> CELSIUS = Temperature.Unit('°C', 'Degree Celsius')
>>> FAHRENHEIT = Temperature.Unit('°F', 'Degree Fahrenheit')
```

Derived types of quantities are declared by giving a definition based on more basic types of quantities:

```>>> class Volume(Quantity):
...     defineAs = Length ** 3
...     refUnitName = 'Cubic Meter'
>>> class Duration(Quantity):
...     refUnitName = 'Second'
...     refUnitSymbol = 's'
>>> class Velocity(Quantity):
...     defineAs = Length / Duration
...     refUnitName = 'Meter per Second'
```

If no symbol for the reference unit is given with the class declaration, a symbol is generated from the definition, as long as all types of quantities in that definition have a reference unit.

```>>> print(Volume.refUnit.symbol)
m³
>>> print(Velocity.refUnit.symbol)
m/s
```

## Instantiating quantities

The simplest way to create an instance of a class Quantity subclass is to call the class giving an amount and a unit. If the unit is omitted, the quantity’s reference unit is used (if one is defined).

```>>> Length(15, MILLIMETER)
Length(Decimal(15), Length.Unit(u'mm'))
```

Alternatively, the two-args infix operator ‘^’ can be used to combine an amount and a unit:

```>>> 17.5 ^ KILOMETER
Length(Decimal('17.5'), Length.Unit(u'km'))
```

Also, it’s possible to create a Quantity sub-class instance from a string representation:

```>>> Length('17.5 km')
Length(Decimal('17.5'), Length.Unit(u'km'))
```

## Unit-safe computations

A quantity can be converted to a quantity using a different unit by calling the method Quantity.convert:

```>>> l5cm = Length(Decimal(5), CENTIMETER)
>>> l5cm.convert(MILLIMETER)
Length(Decimal('50'), Length.Unit('mm'))
>>> l5cm.convert(KILOMETER)
Length(Decimal('0.00005'), Length.Unit('km'))
```

Quantities can be compared to other quantities using all comparison operators defined for numbers. Different units are taken into account automatically, as long as they are compatible, i. e. a conversion is available:

```>>> Length(27) <= Length(91)
True
>>> Length(27, METER) <= Length(91, CENTIMETER)
False
```

Quantities can be added to or subtracted from other quantities …:

```>>> Length(27) + Length(9)
Length(Decimal(36))
>>> Length(27) - Length(91)
Length(Decimal(-64))
>>> Length(27) + Length(12, CENTIMETER)
Length(Decimal('27.12'))
>>> Length(12, CENTIMETER) + Length(17, METER)
Length(Decimal('1712'), Length.Unit('cm'))
```

… as long as they are instances of the same quantity type:

```>>> Length(27) + Duration(9)
quantity.quantity.IncompatibleUnitsError: Can't add a 'Length' and a
'Duration'
```

Quantities can be multiplied or divided by scalars, preserving the unit:

```>>> 7.5 * Length(3, CENTIMETER)
Length(Decimal('22.5'), Length.Unit(u'cm'))
>>> Duration(66, MINUTE) / 11
Duration(Decimal(6), Duration.Unit(u'min'))
```

Quantities can be multiplied or divided by other quantities …:

```>>> Length(15, METER) / Duration(3, SECOND)
Velocity(Decimal(5))
```

… as long as the resulting type of quantity is defined …:

```>>> Duration(4, SECOND) * Length(7)
UndefinedResultError: Undefined result: Duration * Length
```

… or the result is a scalar:

```>>> Duration(2, MINUTE) / Duration(50, SECOND)
Decimal('2.4')
```

## Money

Money is a special type of quantity. Its unit type is known as currency.

Money differs from physical quantities mainly in two aspects:

• Money amounts are discrete. For each currency there is a smallest fraction that can not be split further.
• The relation between different currencies is not fixed, instead, it varies over time.

The sub-package quantity.money provides classes and functions to deal with these specifics.

A currency must explicitly be registered as a unit for further use. The easiest way to do this is to call the function registerCurrency. The function is backed by a database of currencies defined in ISO 4217. It takes the 3-character ISO 4217 code as parameter.

Money derives from Quantity, so all operations on quantities can also be applied to instances of Money. But because there is no fixed relation between currencies, there is no implicit conversion between money amounts of different currencies. Resulting values are always quantized to the smallest fraction defined with the currency.

A conversion factor between two currencies can be defined by using the class ExchangeRate. It is given a unit currency (aka base currency), a unit multiple, a term currency (aka price currency) and a term amount, i.e. the amount in term currency equivalent to unit multiple in unit currency.

Multiplying an amount in some currency with an exchange rate with the same currency as unit currency results in the equivalent amount in term currency. Likewise, dividing an amount in some currency with an exchange rate with the same currency as term currency results in the equivalent amount in unit currency.

As Money derives from Quantity, it can be combined with other quantities in order to define a new quantity. This is, for example, useful for defining prices per quantum.

For more details see the documentation provided with the source distribution or here.

## History

Version Changes
0.9.0 Converters raise new exception ‘UnitConversionError’ instead of returning None. Changed priority of converters: they are tried in reversed order of registration. Added ‘MoneyConverter’ (‘quantity.money.converter.py’).
0.8.1 Refactored class ‘Term’. Some bug fixes.
0.8.0 Exceptions raised by Quantity.__new__ changed to QuantityError. Added function ‘generateUnits’. Added sub-package ‘money’.
0.7.2 Prevent __dict__ from being built for subclasses of Quantity or Unit. Made ‘refUnitSymbol’ and ‘refUnitName’ read-only properties. Added class property ‘quantum’ as option to define quantized quantities. Removed ‘__version__’ from all sub-modules.
0.7.1 Added ‘install_requires’ to setup.py. Corrected unit of ‘Kelvin’ in doc and README. Added method ‘Quantity.quantize’. Enhanced method ‘Quantity.__round__’: round to quantity or unit.
0.7.0 First public release.

## Project details

This version 0.9 0.8 0.7.3 0.7.0