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# zig_units
# dimal — Dimensional Analysis for Zig
`zig_units` lets you attach physical units to numeric values so that dimension mismatches (like adding distance to time) become **compile errors** rather than silent bugs.
A comptime-first dimensional analysis module for Zig. If you try to add meters to seconds, **it won't compile**. That's the point.
At runtime, a `Quantity` is just its underlying numeric value — **zero memory overhead.**
Born from a space simulation where `i128` positions were needed to avoid float imprecision far from the origin, this module grew into a full physical-unit type system with zero runtime overhead.
```zig
const velocity = distance.divBy(time); // Result type: L¹T⁻¹ ✓
const error = mass.add(velocity); // COMPILE ERROR: M¹ != L¹T⁻¹
```
> **Source:** [git.bouvais.lu/adrien/zig-dimal](https://git.bouvais.lu/adrien/zig-dimal)
> **Minimum Zig version:** `0.16.0`
**Requirements:** Zig `0.16.0`
---
## Features
- **100% comptime** — all dimension and unit tracking happens at compile time. No added memory, *almost* native performance.
- **Compile-time dimension errors** — adding `Meter` to `Second` is a compile error, not a runtime panic.
- **Automatic unit conversion** — use `.to()` to convert between compatible units (e.g. `km/h` → `m/s`). Scale factors are resolved at comptime.
- **Full SI prefix support** — `pico`, `nano`, `micro`, `milli`, `centi`, `deci`, `kilo`, `mega`, `giga`, `tera`, `peta`, and more.
- **Time scale support** — `min`, `hour`, `year` built in.
- **Scalar and Vector types** — operate on individual values or fixed-size arrays with the same dimensional safety.
- **Built-in physical quantities** — `dma.Base` provides ready-made types for `Velocity`, `Acceleration`, `Force`, `Energy`, `Pressure`, `ElectricCharge`, `ThermalConductivity`, and many more.
- **Rich formatting** — values print with their unit automatically: `9.81m.s⁻²`, `42m.kg.s⁻¹`, `0.172km`.
- **`i128` support** — the whole reason this exists. Use large integers for high-precision fixed-point positions without manual conversion.
- **Tests and benchmarks included** — run them and see how it performs on your machine (results welcome!).
---
## The 7 SI Base Dimensions
| Symbol | Dimension | SI Unit |
|--------|----------------------|----------|
| `L` | Length | `m` |
| `M` | Mass | `g` |
| `T` | Time | `s` |
| `I` | Electric Current | `A` |
| `Tp` | Temperature | `K` |
| `N` | Amount of Substance | `mol` |
| `J` | Luminous Intensity | `cd` |
---
## Installation
### 1. Add as a Zig dependency
```bash
zig fetch --save https://github.com/YOUR_USERNAME/zig_units/archive/refs/heads/main.tar.gz
### 1. Fetch the dependency
```sh
zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#b9647e04266e3f395cfd26b41622b0c119a1e5be
```
### 2. Configure `build.zig`
This will add the following to your `build.zig.zon` automatically:
```zig
const zig_units = b.dependency("zig_units", .{
.target = target,
.optimize = optimize,
});
// Add to your module or executable
exe.root_module.addImport("units", zig_units.module("zig_units"));
.dependencies = .{
.dimal = .{
.url = "git+https://git.bouvais.lu/adrien/zig-dimal#b9647e04266e3f395cfd26b41622b0c119a1e5be",
.hash = "dimal-0.1.0-WNhSHvomAQAX1ISvq9ZBal-Gam6078y8hE67aC82l63V",
},
},
```
---
## Quick Start: Using Predefined Quantities
`units.Base` provides a clean way to instantiate common physical types without manually defining dimensions.
### 2. Wire it up in `build.zig`
```zig
const std = @import("std");
const units = @import("units");
pub fn main() !void {
// Instantiate types for f32 backing
const Meter = units.Base.Meter.Of(f32);
const Second = units.Base.Second.Of(f32);
const dist = Meter{ .value = 10.0 };
const time = Second{ .value = 2.0 };
pub fn build(b: *std.Build) void {
const target = b.standardTargetOptions(.{});
const dimal = b.dependency("dimal", .{}).module("dimal");
// Arithmetic is type-safe and creates the correct resulting dimension
const vel = dist.divBy(time); // Type is Velocity (L/T)
std.debug.print("Speed: {f}\n", .{vel}); // Output: 5m.s⁻¹
const exe = b.addExecutable(.{
.name = "my_project",
.root_module = b.createModule(.{
.root_source_file = b.path("src/main.zig"),
.target = target,
.imports = &.{.{
.name = "dimal",
.module = dimal,
}},
}),
});
b.installArtifact(exe);
}
```
---
### Core Arithmetic Operations
Dimensional analysis is handled entirely at compile-time. If the math doesn't make physical sense, it won't compile.
### 3. Import in your code
```zig
const M = units.Base.Meter.Of(f32);
const S = units.Base.Second.Of(f32);
const dist = M{ .value = 100.0 };
const time = S{ .value = 5.0 };
// 1. Addition & Subtraction (Must have same dimensions)
const two_dist = dist.add(dist); // 200.0m
const zero = dist.sub(dist); // 0.0m
// 2. Division (Subtracts dimension exponents)
// Result: Velocity (L¹ T⁻¹)
const vel = dist.divBy(time); // 20.0 m.s⁻¹
// 3. Multiplication (Adds dimension exponents)
// Result: Area (L²)
const area = dist.mulBy(dist); // 100.0 m²
// 4. Chained Operations
// Result: Acceleration (L¹ T⁻²)
const accel = dist.divBy(time).divBy(time); // 4.0 m.s⁻²
const dma = @import("dimal");
const Scalar = dma.Scalar;
const Dimensions = dma.Dimensions;
const Scales = dma.Scales;
```
---
## Defining Custom Quantities
## Quick Start
You aren't limited to the built-in library. You can define any physical quantity by specifying its **Dimensions**
(powers of base units) and its **Scale** (SI prefixes).
### Defining unit types
### 1. Create a custom dimension
Dimensions are defined by 7 base SI units: `L` (Length), `M` (Mass), `T` (Time), `I` (Current), `Tp` (Temp), `N` (Substance), `J` (Intensity).
A `Scalar` type is parameterized by three things: the numeric type (`f64`, `i128`, …), the dimensions (which physical quantities, and their exponents), and the scales (SI prefixes or custom time units).
```zig
const Dims = units.Dimensions;
const Scales = units.Scales;
// Frequency is T⁻¹
const FreqDims = Dims.init(.{ .T = -1 });
// Force is M¹ L¹ T⁻²
const ForceDims = Dims.init(.{ .M = 1, .L = 1, .T = -2 });
const Meter = Scalar(f64, .init(.{ .L = 1 }), .init(.{}));
const KiloMeter = Scalar(f64, .init(.{ .L = 1 }), .init(.{ .L = .k }));
const Second = Scalar(f64, .init(.{ .T = 1 }), .init(.{}));
const Velocity = Scalar(f64, .init(.{ .L = 1, .T = -1 }), .init(.{}));
const Kmh = Scalar(f64, .init(.{ .L = 1, .T = -1 }), .init(.{ .L = .k, .T = .hour }));
```
### 2. Create a custom Type
Combine a numeric type, the dimensions, and a scale.
Or use the pre-built helpers from `dma.Base`:
```zig
const Hertz = units.Quantity(f32, FreqDims, Scales.init(.{}));
// A specialized scale: Millimeters per Second Squared
const MmPerSecSq = units.Quantity(f32,
Dims.init(.{ .L = 1, .T = -2 }),
Scales.init(.{ .L = .m }) // .m = milli
);
const Acceleration = dma.Base.Acceleration.Of(f64);
const KmhSpeed = dma.Base.Speed.Scaled(f64, Scales.init(.{ .L = .k, .T = .hour }));
```
### Kinematics example
```zig
const v0 = Velocity{ .value = 10.0 }; // 10 m/s
const accel = Acceleration{ .value = 9.81 }; // 9.81 m/s²
const time = Second{ .value = 5.0 }; // 5 s
// d = v₀t + ½at²
const d1 = v0.mulBy(time); // → Meter
const d2 = accel.mulBy(time.mulBy(time)).scale(0.5); // → Meter
const dist = d1.add(d2);
const v_final = v0.add(accel.mulBy(time));
std.debug.print("Distance: {d} | {d}\n", .{ dist, dist.to(KiloMeter) });
// Distance: 172.625m | 0.172625km
std.debug.print("Final speed: {d:.2}\n", .{v_final});
// Final speed: 59.05m.s⁻¹
```
### Unit conversion
`.to()` converts between compatible units at comptime. Mixing incompatible dimensions is a **compile error**.
```zig
const speed_kmh = Kmh{ .value = 120.0 };
const speed_ms = speed_kmh.to(Velocity); // 33.333... m/s — comptime ratio
// This would NOT compile:
// const bad = speed_kmh.to(Second); // "Dimension mismatch in to: L1T-1 vs T1"
```
### Working with Vectors
Every `Scalar` type exposes a `.Vec3` and a generic `.Vec(n)`:
```zig
const Vec3Meter = Meter.Vec3; // or: Vector(3, Meter)
const pos = Vec3Meter{ .data = .{ 100, 200, 300 } };
const t = Second{ .value = 10 };
const vel = pos.divByScalar(t); // → Vec3 of Velocity (m/s)
std.debug.print("{d}\n", .{vel}); // (10, 20, 30)m.s⁻¹
```
Vectors support: `add`, `sub`, `mulBy`, `divBy`, `mulByScalar`, `divByScalar`, `negate`, `to`, `length`, `lengthSqr`.
---
## Unit Conversions
## API Reference
The library handles SI prefixes (`k`, `m`, `u`, `n`, etc.) and time aliases (`.min`, `.hour`) automatically.
When performing arithmetic between different scales, the **finer (smaller) scale wins** to preserve precision.
### `Scalar(T, dims, scales)`
```zig
const KM = units.Base.Meter.Scaled(f32, Scales.init(.{ .L = .k })); // Kilometers
const M = units.Base.Meter.Of(f32); // Meters
| Method | Description |
|---|---|
| `.add(rhs)` | Add two quantities of the same dimension. Auto-converts scales. |
| `.sub(rhs)` | Subtract. Auto-converts scales. |
| `.mulBy(rhs)` | Multiply — dimensions are **summed**. `m * s⁻¹` → `m·s⁻¹`. |
| `.divBy(rhs)` | Divide — dimensions are **subtracted**. `m / s` → `m·s⁻¹`. |
| `.to(DestType)` | Convert to another unit of the same dimension. Compile error on mismatch. |
| `.vec3()` | Wrap the value in a `Vec3` of the same type. |
| `.Vec(n)` | Get the `Vector(n, Self)` type. |
const d1 = KM{ .value = 1.2 }; // 1.2 km
const d2 = M{ .value = 300.0 }; // 300 m
### `dma.Base` — Pre-built quantities
const total = d1.add(d2); // Result is 1500.0 (Meters)
const final = total.to(KM); // Explicitly convert back to KM -> 1.5
```
A selection of what's available (call `.Of(T)` for base units, `.Scaled(T, scales)` for custom scales):
`Meter`, `Second`, `Gramm`, `Kelvin`, `ElectricCurrent`, `Speed`, `Acceleration`, `Inertia`, `Force`, `Pressure`, `Energy`, `Power`, `Area`, `Volume`, `Density`, `Frequency`, `Viscosity`, `ElectricCharge`, `ElectricPotential`, `ElectricResistance`, `MagneticFlux`, `ThermalCapacity`, `ThermalConductivity`, and more.
### `Scales` — SI prefixes
| Tag | Factor |
|---|---|
| `.P` | 10¹⁵ |
| `.T` | 10¹² |
| `.G` | 10⁹ |
| `.M` | 10⁶ |
| `.k` | 10³ |
| `.none` | 1 |
| `.c` | 10⁻² |
| `.m` | 10⁻³ |
| `.u` | 10⁻⁶ |
| `.n` | 10⁻⁹ |
| `.p` | 10⁻¹² |
| `.f` | 10⁻¹⁵ |
| `.min` | 60 |
| `.hour` | 3600 |
| `.year` | 31 536 000 |
---
## Physical Vectors (Vec3)
## Running Tests and Benchmarks
Physical quantities often come in 3D vectors (Position, Velocity, Force). Every `Quantity` type has a `.Vec3` alias built-in.
```zig
const Vec3M = units.Base.Meter.Of(f32).Vec3;
const gravity = Vec3M{ .data = .{ 0, -9.81, 0 } };
const pos = Vec3M.initDefault(0); // [0, 0, 0]
// Vectors support standard operations
const length = gravity.length(); // Returns f32: 9.81
const double = gravity.scale(2.0);
```
You can also create a Vector of any length.
Vec3 found in a Quantity is just a convenience.
```zig
const M = units.Base.Meter.Of(f32);
const Vec10M = units.QuantityVec(10, Meter);
const gravity = Vec10M.initDefault(1);
const length = gravity.length(); // Returns f32: 1.0
```
---
## High Precision & Integer Backing
While most libraries default to `f32` or `f64`, `zig_units` is mainly designed to support **large-bit integers (`i128`, `i256`)**.
This is critical for applications like **space simulations**, where floating-point numbers suffer from "jitter" or "flickering"
once you travel far from the origin. By using an `i128` with a millimeter scale, you can represent the diameter
of the observable universe with millimeter precision—something impossible with `f64`.
### Avoiding Floating-Point Jitter
```zig
// Millimeter precision using 128-bit integers
const MM = units.Base.Meter.Scaled(i128, units.Scales.init(.{ .L = .m }));
const KM = units.Base.Meter.Scaled(i128, units.Scales.init(.{ .L = .k }));
const solar_system_dist = KM{ .value = 150_000_000 }; // 150 million km
const ship_nudge = MM{ .value = 5 }; // 5 mm
// The library performs exact integer math for conversions.
// Resulting type is MM (the finer scale), maintaining perfect precision.
const new_pos = solar_system_dist.add(ship_nudge);
```
### Integer-Specific Features
* **Exact Conversions:** When converting between integer scales (e.g., `km` to `m`), the library uses fast-path native multiplication.
* **Safe Vector Lengths:** `QuantityVec.length()` includes a custom integer square root implementation, allowing you to calculate distances between coordinates without ever casting to a float.
* **Zero Drift:** Unlike floats, repeated additions and subtractions of integers never accumulate "epsilon" drift, ensuring your simulation remains deterministic.
* **Precision-First Scaling:** When operating on two different scales (e.g., adding `km` and `mm`), the result automatically adopts the finer scale (`mm`). This ensures **zero implicit data loss** during calculation. You only lose precision if you *explicitly* choose to convert back to a coarser scale using `.to()`.
---
## SI Scales Reference
| Prefix | Enum | Factor |
| :--- | :--- | :--- |
| **Kilo** | `.k` | 10³ |
| **Mega** | `.M` | 10⁶ |
| **Giga** | `.G` | 10⁹ |
| **Milli** | `.m` | 10⁻³ |
| **Micro** | `.u` | 10⁻⁶ |
| **Minute**| `.min` | 60 |
| **Hour** | `.hour`| 3,600 |
---
## API Summary
### `Quantity(T, dims, scales)`
- `.add(rhs)` / `.sub(rhs)`: Automatic scaling, requires same dimensions.
- `.mulBy(rhs)` / `.divBy(rhs)`: Composes dimensions (e.g., $L \times L = L^2$).
- `.scale(scalar)`: Multiply by a raw number (preserves dimensions).
- `.to(OtherType)`: Safely convert between scales of the same dimension.
- `.vec3()`: Create a 3D vector from a scalar.
### `Dimensions`
- `L`: Length (m)
- `M`: Mass (g)
- `T`: Time (s)
- `I`: Current (A)
- `Tp`: Temperature (K)
- `N`: Amount (mol)
- `J`: Intensity (cd)
---
## Testing & Benchmarks
`zig_units` comes with a comprehensive test suite that verifies dimensional correctness, SI prefix scaling,
and vector math accuracy across all numeric types.
### Running Tests
To run the full suite of unit tests and performance benchmarks:
```bash
```sh
zig build test
zig build benchmark
```
### Benchmarks
When you run the tests, the library also executes a performance benchmark.
This measures the cost of operations (in nanoseconds per operation) across different backing types (`i32` to `f128`) and vector lengths.
Benchmark results are very welcome — feel free to share yours!
Because all dimensional logic is resolved at **compile-time**, you will see that `Quantity` operations perform at the same speed as raw primitive math.
---
**Example Benchmark Output:**
```text
Quantity<T> benchmark — 100,000 iterations, 10 samples/cell
## Roadmap / Known Limitations
┌───────────────────┬──────┬─────────────────────┬─────────────────────┐
│ Operation │ Type │ ns / op (± delta) │ Throughput (ops/s) │
├───────────────────┼──────┼─────────────────────┼─────────────────────┤
│ add │ i32 │ 0.18 ns ±0.02 │ 5555555556 │
│ mulBy │ f64 │ 0.22 ns ±0.01 │ 4545454545 │
└───────────────────┴──────┴─────────────────────┴─────────────────────┘
```
- More operations beyond `add`, `sub`, `mulBy`, `divBy` (e.g. `pow`, `sqrt`).
- SIMD acceleration for `Vector` operations.
- Some paths may still fall back to runtime computation — optimization ongoing.
- More test coverage.
### Verification Examples
The test suite ensures that:
- **Dimension Safety:** Chained operations like `dist.divBy(time).divBy(time)` correctly result in an Acceleration type.
- **Scale Accuracy:** Adding `1km + 1mm` results exactly in `1000001mm` without truncation.
- **Formatting:** Quantities print correctly with Unicode superscripts (e.g., `9.81m.s⁻²`).
- **Vector Math:** Euclidean lengths for both floats and integers are verified against known constants.
---
## License
See the repository for license details.