Prefix¶

A “prefix” scales a unit by some magnitude, and prepends a prefix symbol to the unit’s label.

Applying to unit types¶

To apply a prefix to a unit type, pass that unit as a template parameter to the prefix. This results in a new unit with the following properties:

The label for the new unit is the label for the input unit, with the prefix symbol prepended.
The magnitude of the new unit is the magnitude of the input unit, scaled by the scaling factor.

Example: Centi and Meters

Centi is a prefix whose prefix symbol is c, and whose scaling factor is $1/100$ .

Meters is a unit whose symbol is m.

Therefore, Centi<Meters> is a unit whose symbol is cm, and whose magnitude is $1/100\,\text{m}$ .

Applying to instances: the “prefix applier”¶

Au uses many kinds of instances, not just types. These include QuantityMaker, QuantityPointMaker, SingularNameFor, and even instances of unit types.

Instances are naturally used as function parameters, not template parameters. Therefore, for each prefix, we provide a “prefix applier” which can be called as a function. For any of the above kinds of inputs, the prefix applier returns the same kind, but in the prefixed unit.

Let’s return to the example of Centi and Meters. The prefix applier for Centi is spelled centi: note that we use snake_case, rather than CamelCase. Here are the various ways a prefix applier can be used.

Kind of input	Example (meters)	Application	Example use
Unit instance	`Meters{}`	`centi(Meters{})`	`length.as(Centi<Meters>{})`
`QuantityMaker`	`meters`	`centi(meters)`	`centi(meters)(170)`
`QuantityPointMaker`	`meters_pt`	`centi(meters_pt)`	`centi(meters_pt)(1.5)`
`SingularNameFor`	`meter`	`centi(meter)`	`curvature.in(radians / centi(meter))`
`SymbolFor`	`m`	`centi(m)`	`constexpr auto cm = centi(m); 170 * cm`

Note again that every output here is the same kind of thing as the input. So, centi(meters_pt) is a QuantityPointMaker, and centi(meters_pt)(1.5) creates a QuantityPoint of $1.5\,\text{cm}$ .

List of supported prefixes¶

We support every SI prefix and binary prefix.

SI prefixes¶

Prefix	Prefix applier	Prefix symbol	Scaling factor
`Quetta`	`quetta`	`Q`	$10^{30}$
`Ronna`	`ronna`	`R`	$10^{27}$
`Yotta`	`yotta`	`Y`	$10^{24}$
`Zetta`	`zetta`	`Z`	$10^{21}$
`Exa`	`exa`	`E`	$10^{18}$
`Peta`	`peta`	`P`	$10^{15}$
`Tera`	`tera`	`T`	$10^{12}$
`Giga`	`giga`	`G`	$10^{9}$
`Mega`	`mega`	`M`	$10^{6}$
`Kilo`	`kilo`	`k`	$10^{3}$
`Hecto`	`hecto`	`h`	$10^{2}$
`Deka`	`deka`	`da`	$10^{1}$
`Deci`	`deci`	`d`	$10^{-1}$
`Centi`	`centi`	`c`	$10^{-2}$
`Milli`	`milli`	`m`	$10^{-3}$
`Micro`	`micro`	`u`	$10^{-6}$
`Nano`	`nano`	`n`	$10^{-9}$
`Pico`	`pico`	`p`	$10^{-12}$
`Femto`	`femto`	`f`	$10^{-15}$
`Atto`	`atto`	`a`	$10^{-18}$
`Zepto`	`zepto`	`z`	$10^{-21}$
`Yocto`	`yocto`	`y`	$10^{-24}$
`Ronto`	`ronto`	`r`	$10^{-27}$
`Quecto`	`quecto`	`q`	$10^{-30}$

Binary prefixes¶

Prefix	Prefix applier	Prefix symbol	Scaling factor
`Yobi`	`yobi`	`Yi`	$2^{80} (\approx 10^{24})$
`Zebi`	`zebi`	`Zi`	$2^{70} (\approx 10^{21})$
`Exbi`	`exbi`	`Ei`	$2^{60} (\approx 10^{18})$
`Pebi`	`pebi`	`Pi`	$2^{50} (\approx 10^{15})$
`Tebi`	`tebi`	`Ti`	$2^{40} (\approx 10^{12})$
`Gibi`	`gibi`	`Gi`	$2^{30} (\approx 10^{9})$
`Mebi`	`mebi`	`Mi`	$2^{20} (\approx 10^{6})$
`Kibi`	`kibi`	`Ki`	$2^{10} (\approx 10^{3})$