#units #dimensional-analysis

nightly diman

Zero-cost compile-time dimensional analysis

3 releases (breaking)

0.4.0 Jan 7, 2024
0.3.0 Dec 1, 2023
0.2.0 May 27, 2023

#78 in Science

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Diman is a library for zero-cost compile time unit checking.

# #![feature(generic_const_exprs)]
use diman::si::f64::{Length, Time, Velocity};

fn get_velocity(x: Length, t: Time) -> Velocity {
    x / t

let v1 = get_velocity(Length::kilometers(36.0), Time::hours(1.0));
let v2 = get_velocity(Length::meters(10.0), Time::seconds(1.0));

assert_eq!(v1, v2);

Let's try to assign add quantities with incompatible dimensions:

use diman::si::f64::{Length, Time};

let time = Time::seconds(1.0);
let length = Length::meters(10.0);
let sum = length + time;

This results in a compiler error:

let sum = length + time;
= note: expected struct `Quantity<_, Dimension { length: 1, time: 0, mass: 0, temperature: 0, current: 0, amount_of_substance: 0, luminous_intensity: 0 }>`
        found struct `Quantity<_, Dimension { length: 0, time: 1, mass: 0, temperature: 0, current: 0, amount_of_substance: 0, luminous_intensity: 0 }>`


Diman is implemented using Rust's const generics feature. While min_const_generics has been stabilized since Rust 1.51, Diman uses more complex generic expressions and therefore requires the two currently unstable features generic_const_exprs and adt_const_params.

Moreover, Diman is in its early stages of development and APIs will change.

If you cannot use unstable Rust for your project or require a stable library, consider using uom or dimensioned, both of which do not require any experimental features and are much more mature libraries in general.


  • Invalid operations between physical quantities (adding length and time, for example) turn into compile errors.
  • Newly created quantities are automatically converted to an underlying base representation. This means that the used types are dimensions (such as Length) instead of concrete units (such as meters) which makes for more meaningful code.
  • Systems of dimensions and units can be user defined via the unit_system! macro. This gives the user complete freedom over the choice of dimensions and makes them part of the user's library, so that arbitrary new methods can be implemented on them.
  • The rational-dimensions features allows the usage of quantities and units with rational exponents.
  • f32 and f64 float storage types (behind the f32 and f64 feature gate respectively).
  • Vector storage types via glam (behind the glam-vec2, glam-vec3, glam-dvec2 and glam-dvec3 features).
  • Serialization and Deserialization via serde (behind the serde feature gate, see the official documentation for more info).
  • HDF5 support using hdf5-rs (behind the hdf5 feature gate).
  • Quantities implement the Equivalence trait so that they can be sent via MPI using mpi (behind the mpi feature gate).
  • Random quantities can be generated via rand (behind the rand feature gate, see the official documentation for more info).


Diman aims to make it as easy as possible to add compile-time unit safety to Rust code. Physical quantities are represented by the Quantity<S, D> struct, where S is the underlying storage type (f32, f64, ...) and D is the dimension of the quantity. For example, in order to represent the SI system of units, the quantity type would be defined using the unit_system! macro as follows:

#![feature(generic_const_exprs, adt_const_params)]
use diman::unit_system;

    quantity_type Quantity;
    dimension_type Dimension;

    dimension Length;
    dimension Time;
    dimension Mass;
    dimension Temperature;
    dimension Current;
    dimension AmountOfSubstance;
    dimension LuminousIntensity;

The first two statements imply that the macro should define a Quantity type, which is user-facing, and a Dimension type, which is used only internally and will surface in compiler error messages. The macro will automatically implement all the required traits and methods for the Quantity type, such that addition and subtraction of two quantities is only allowed for quantities with the same Dimension type. During multiplication of two quantities, all the entries of the two dimensions are added. See below for a more comprehensive list of the implemented methods on Quantity.

The unit_system! macro also allows defining derived dimensions and units:

#![feature(generic_const_exprs, adt_const_params)]
use diman_unit_system::unit_system;
    quantity_type Quantity;
    dimension_type Dimension;

    dimension Length;
    dimension Time;

    dimension Velocity = Length / Time;

    #[prefix(kilo, milli)]
    unit meters;

    unit seconds;

    unit hours: Time = 3600 * seconds;
    unit meters_per_second: Velocity = meters / seconds;
    unit kilometers_per_hour: Velocity = kilometers / hours;
    constant MY_FAVORITE_VELOCITY = 1000 * kilometers_per_hour;

use f64::{Length, Time, Velocity, MY_FAVORITE_VELOCITY};

fn fast_enough(x: Length, t: Time) {
    let vel = x / t;
        println!("{} m/s is definitely fast enough!", vel.in_meters_per_second());

fast_enough(Length::kilometers(100.0), Time::hours(0.3));

Here, dimension defines Quantities, which are concrete types, unit defines units, which are methods on the corresponding quantities and constant defines constants. Dimensions without a right hand side are base dimensions (such as length, time, mass, temperature, ... in the SI system of units), whereas dimensions with a right hand side are derived dimensions. The same thing holds for units - every unit is either a base unit for a given base dimension (denoted by the #[base(...)] attribute), or derived from base units and other derived units. Base units have the special property that the internal representation of the quantity will be in terms of the base unit (for example, a stored value 1.0 for a quantity with a Length dimension corresponds to meter in the above definitions). Other than this, there are no differences between base dimensions and dimensions or base units and units and they can be treated equally in user code. The macro also accepts more complex expressions such as dimension Energy = Mass (Length / Time)^2. The definitions do not have to be in any specific order.

The Quantity type

The macro will automatically implement numerical traits such as Add, Sub, Mul, and various other methods of the underlying storage type for Quantity<S, ...>. Quantity should behave just like its underlying storage type whenever possible and allowed by the dimensions. For example:

  • Addition of Quantity<Float, D> and Float is possible if and only if D is dimensionless.
  • Quantity implements the dimensionless methods of S, such as abs for dimensionless quantities.
  • It implements Deref to S if and only if D is dimensionless.
  • Debug is implemented and will print the quantity in its representation of the "closest" unit. For example Length::meters(100.0) would be debug printed as 0.1 km. If printing in a specific unit is required, conversion methods are available for each unit (such as Length::in_meters).
  • .value() provides access to the underlying storage type of a dimensionless quantity.
  • .value_unchecked() provides access to the underlying storage type for all quantities if absolutely required. This is not unit-safe since the value will depend on the unit system!
  • Similarly, new quantities can be constructed from storage types using Quantity::new_unchecked. This is also not unit-safe.

Some other, more complex operations are also allowed:

use diman::si::f64::{Length, Volume};
let x = Length::meters(3.0);
let vol = x.cubed();
assert_eq!(vol, Volume::cubic_meters(27.0))

This includes squared, cubed, sqrt, cbrt as well as powi.


Unit prefixes can automatically be generated with the #[prefix(...)] attribute for unit statements. For example

#[prefix(kilo, milli)]
unit meters;

will automatically generate the unit meters with symbol m, as well as kilometers and millimeters with symbols km and mm corresponding to 1e3 m and 1e-3 m. For simplicity, the attribute #[metric_prefixes] is provided, which will generate all metric prefixes from atto- to exa- automatically.


Unit aliases can automatically be generated with the #[alias(...)] macro. For example

unit meters;

will automatically generate a unit metres that has exactly the same definition as meters. This works with prefixes as expected (i.e. an alias is generated for every prefixed unit).

Quantity products and quotients

Sometimes, intermediate types in computations are quantities that don't really have a nice name and are also not needed too many times. Having to add a definition to the unit system for this case can be cumbersome. This is why the Product and Quotient types are provided:

use diman::si::f64::{Length, Time, Velocity, Area, Volume};
use diman::{Product, Quotient};
fn foo(l: Length, t: Time, vol: Volume) -> Product<(Length, Time, Volume)> {
    l * t * vol

fn bar(l: Length, t: Time) -> Quotient<Length, Time> {
    l / t

Rational dimensions

The rational-dimensions feature allows using quantities with rational exponents in their base dimensions, as opposed to just integer values. This allows expressing defining dimensions and units such as

dimension Sorptivity = Length Time^(-1/2);
unit meters_per_sqrt_second: Sorptivity = meters / seconds^(1/2);

and using them in the usual manner

let l = Length::micrometers(2.0);
let t = Time::milliseconds(5.0);
let sorptivity: Sorptivity = l / t.sqrt();

The unit system generated with rational-dimensions supports a superset of features of a unit system generated without them. Still, this feature should be enabled only when necessary, since the compiler errors in case of dimension mismatches will be harder to read.


Serialization and deserialization of the units is provided via serde if the serde feature gate is enabled:

use diman::si::f64::{Length, Velocity};
use serde::{Serialize, Deserialize};
#[derive(Serialize, Deserialize, Debug, PartialEq)]
struct Parameters {
    my_length: Length,
    my_vel: Velocity,

let params: Parameters = 
        my_length: 100 m
        my_vel: 10 m s^-1
    Parameters {
        my_length: Length::meters(100.0),
        my_vel: Velocity::meters_per_second(10.0),


Diman allows generating random quantities via rand if the rand feature gate is enabled:

use rand::Rng;

use diman::si::f64::Length;

let mut rng = rand::thread_rng();
for _ in 0..100 {
    let x = rng.gen_range(Length::meters(0.0)..Length::kilometers(1.0));
    assert!(Length::meters(0.0) <= x);
    assert!(x < Length::meters(1000.0));


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