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:

1. The label for the new unit is the label for the input unit, with the prefix symbol prepended.

2. 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
Constant	1.7_m	centi(1.7_m)	height.as<double>(centi(1.7_m))

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 $1.5\,\text{cm}$.

Anything that is not one of these kinds is rejected at the call site. (Otherwise, the unit instance overload would swallow it and produce a prefixed type that is only ill-formed when you first use it, in an error message that mentions neither the prefix nor your code.)

Applying to a Constant

A Constant carries a value as well as a unit, so applying a prefix to one scales that value. kilo(1.234_g) is a Constant for $1234\,\text{g}$. This is the main way to apply a prefix to a unit literal: see prefixed unit literals.

The prefix goes on the unit, not on the value. A unit literal such as 1.234_g is grams scaled by $1.234$, and we prefix the underlying grams: kilo(1.234_g) is labeled [(617 / 500) kg], not k[(617 / 500) g]. (The scale factor prints as a fraction because magnitudes are exact; that is independent of the prefix.)

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	$2^{10} (\approx 10^{3})$