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Unitsafe computations with quantities.
What is a Quantity?
"The value of a quantity is generally expressed as the product of a number and a unit. The unit is simply a particular example of the quantity concerned which is used as a reference, and the number is the ratio of the value of the quantity to the unit." (Bureau International des Poids et Mesures: The International System of Units, 8th edition, 2006)
Basic types of quantities are defined "by convention", they do not depend on other types of quantities, for example Length, Mass or Duration.
Derived types of quantities, on the opposite, are defined as products of other types of quantities raised by some exponent.
Examples:

Volume = Length ³

Speed = Length ¹ · Duration ⁻¹

Acceleration = Length ¹ · Duration ⁻²

Force = Mass ¹ · Acceleration ¹
Each type of quantity may have one special unit which is used as a reference for the definition of all other units, for example Meter, Kilogram and Second. The other units are then defined by their relation to the reference unit.
If a type of quantity is derived from types of quantities that all have a reference unit, then the reference unit of that type is defined by a formula that follows the formula defining the type of quantity.
Examples:

Speed > Meter per Second = Meter ¹ · Second ⁻¹

Acceleration > Meter per Second squared = Meter ¹ · Second ⁻²

Force > Newton = Kilogram ¹ · Meter ¹ · Second ⁻²
"Systems of Measure"
There may be different systems which define quantities, their units and the relations between these units in a different way.
This is not directly supported by this package. For each type of quantity there can be only no or exactly one reference unit. But, if you have units from different systems for the same type of quantity, you can define these units and provide mechanisms to convert between them.
The Basics: Quantity and Unit
The essential functionality of the package is provided by the traits
Quantity
, HasRefUnit
, Unit
and LinearScaledUnit
and a macro generating
the code for concrete types of quantities.
A basic type of quantity can easily be defined using the procmacro
attribute quantity
, optionally followed by an attribute refunit
and
followed by at least one attribute unit
.
The macro generates an enum with the given units (incl. the refunit, if given)
as variants (together with an implemention of trait Unit
and, if there's a
reference unit, of trait LinearScaledUnit
), a type named after the given
struct, an implementation of trait Quantity
for this type, an implementation
of trait HasRefUnit
in case there's a reference unit, as well as
implementations of some std traits.
In addition, it creates a constant for each enum variant, thus providing a constant for each unit. This implies that the identifiers of all units over all defined quantitities have to be unique!
Example:
# use quantities::prelude::*;
#[quantity]
#[ref_unit(Kilogram, "kg", KILO)]
#[unit(Milligram, "mg", MILLI, 0.000001)]
#[unit(Carat, "ct", 0.0002)]
#[unit(Gram, "g", NONE, 0.001)]
#[unit(Ounce, "oz", 0.028349523125)]
#[unit(Pound, "lb", 0.45359237)]
#[unit(Stone, "st", 6.35029318)]
#[unit(Tonne, "t", MEGA, 1000.)]
/// The quantity of matter in a physical body.
struct Mass {}
assert_eq!(MILLIGRAM.name(), "Milligram");
assert_eq!(POUND.symbol(), "lb");
assert_eq!(TONNE.si_prefix(), Some(SIPrefix::MEGA));
assert_eq!(CARAT.scale(), Amnt!(0.0002));
In order to create a derived type of quantity based on more basic types of
quantities, an expression can be given as argument to the procmacro attribute
quantity
, specifying the quantity as product or as quotient of two base
quantities.
Instances of a derived quantity can then be build by multiplying or dividing instances of the base quantities. Instances of a quantity which is defined as a product can be divided by an instance of one of the base quantities, giving an instance of the other base quantity as result. Instances of a quantity which is defined as a quotient can be multiplied by an instance of the divisor quantity, resulting in an instance of the divident quantity.
Example:
# use quantities::prelude::*;
#[quantity]
#[ref_unit(Meter, "m", NONE, "Reference unit of quantity `Length`")]
#[unit(Centimeter, "cm", CENTI, 0.01, "0.01·m")]
#[unit(Kilometer, "km", KILO, 1000, "1000·m")]
#[unit(Mile, "mi", 1609.344, "8·fur")]
pub struct Length {}
#[quantity]
#[ref_unit(Second, "s", NONE, "Reference unit of quantity `Duration`")]
#[unit(Minute, "min", 60, "60·s")]
#[unit(Hour, "h", 3600, "60·min")]
pub struct Duration {}
#[quantity(Length * Length)]
#[ref_unit(Square_Meter, "m²", NONE, "Reference unit of quantity `Area`")]
#[unit(Square_Centimeter, "cm²", 0.00001, "cm²")]
#[unit(Square_Kilometer, "km²", MEGA, 1000000., "km²")]
pub struct Area {}
let a = Amnt!(3.) * METER;
let b = Amnt!(0.5) * KILOMETER;
let ab = a * b;
assert_eq!(ab, Amnt!(1500.) * SQUARE_METER);
let c = ab / (Amnt!(2.) * KILOMETER);
assert_eq!(c, Amnt!(0.75) * METER);
#[quantity(Length / Duration)]
#[ref_unit(Meter_per_Second, "m/s", NONE, "Reference unit of quantity `Speed`")]
#[unit(Miles_per_Hour, "mph", 0.44704, "mi/h")]
pub struct Speed {}
let l = Amnt!(150.) * MILE;
let t = Amnt!(1.2) * HOUR;
let v = l / t;
assert_eq!(v, Amnt!(125.) * MILES_PER_HOUR);
let d = v * Duration::new(Amnt!(3.), HOUR);
assert_eq!(d, Amnt!(375.) * MILE);
Type of the numerical part
The package allows to use either float
or fixedpoint decimal
values for
the numerical part of a Quantity
value.
Internally the type alias AmountT
is used. This alias can be controlled by
the optional feature fpdec
(see features).
When feature fpdec
is off (= default), AmountT
is defined as f64
on a
64bit system or as f32
on a 32bit system.
When feature fpdec
is activated, AmountT
is defined as Decimal
(imported
from crate fpdec
).
The macro Amnt!
can be used to convert float literals correctly to AmountT
depending on the configuration. This is done automatically for the scale
values of units by the procmacro quantity
described above.
Instantiating quantities
An instance of a quantity type can be created by calling the function new
,
giving an amount and a unit. Alternatively, an amount and a unit can be
multiplied.
Example:
# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let m = Mass::new(Amnt!(17.4), GRAM);
assert_eq!(m.to_string(), "17.4 g");
let m = Amnt!(17.4) * GRAM;
assert_eq!(m.to_string(), "17.4 g");
Unitsafe computations
If the quantity type has a refernce unit, a quantity instance can be converted
to a quantity instance with a different unit of the same type by calling the
method convert
.
Example:
# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Carat, "ct", 0.0002)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Mass::new(Amnt!(13.5), GRAM);
let y = x.convert(CARAT);
assert_eq!(y.to_string(), "67.5 ct");
Quantity values with the same unit can always be added or subtracted. Adding or subtracting values with different units requires the values to be convertable.
Example:
# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Amnt!(17.4) * GRAM;
let y = Amnt!(1.407) * KILOGRAM;
let z = x + y;
assert_eq!(z.amount(), Amnt!(1424.4));
assert_eq!(z.unit(), GRAM);
let z = y + x;
assert_eq!(z.to_string(), "1.4244 kg");
Quantity values can always be multiplied or divided by numerical values, preserving the unit.
Example:
# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Amnt!(7.4);
let y = Amnt!(1.7) * KILOGRAM;
let z = x * y;
assert_eq!(z.to_string(), "12.58 kg");
Commonly Used Quantities
The package provides optional modules with definitions of commonly used quantities; each can be activated by a feature with a corresponding name (see below).
Crate features
By default, only the feature std
is enabled.
Ecosystem
 std  When enabled, this will cause
quantities
to use the standard library, so that conversion to string, formatting and printing are available. When disabled, the use of cratealloc
together with a systemspecific allocator is needed to use that functionality.
Optional dependencies
 fpdec  When enabled, instead of
f64
orf32
fpdec::Decimal
is used asAmountT
(see above).
Predefined quantities
With the following features additional modules can be enabled, each providing a predefined quantity.
 mass  module [mass]  quantity Mass
 length  module [length]  quantity Length
 duration  module [duration]  quantity Duration
 area  module [area]  quantity Area
 volume  module [volume]  quantity Volume
 speed  module [speed]  quantity Speed
 acceleration  module [acceleration]  quantity Acceleration
 force  module [force]  quantity Force
 energy  module [energy]  quantity Energy
 power  module [power]  quantity Power
 frequency  module [frequency]  quantity Frequency
 datavolume  module [datavolume]  quantity DataVolume
 datathroughput  module [datathroughput]  quantity DataThroughput
 temperature  module [temperature]  quantity Temperature
Dependencies
~0.8–1.3MB
~30K SLoC