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README.md
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README.md
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# dimal — Dimensional Analysis for Zig
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A comptime-first dimensional analysis module for Zig. If you try to add meters to seconds, **it won't compile**. That's the point.
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A dimensional analysis library for Zig with a unified `Tensor` API for scalars, vectors, matrices, and higher-dimensional data. All dimension and unit tracking happens at compile time—zero runtime overhead—and all operations use SIMD intrinsics.
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Started by 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.
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If you try to add meters to seconds, it won't compile. That's the point.
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> **Source:** [git.bouvais.lu/adrien/zig-dimal](https://git.bouvais.lu/adrien/zig-dimal)
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> **Minimum Zig version:** `0.16.0`
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---
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## Background
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Started because I needed `i128` positions for a space simulation to avoid floating-point precision loss far from the origin. Grew into a type system for tracking physical dimensions at compile time. It's been useful enough to share.
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- **Compile-time dimension checking** — catch unit mismatches before runtime.
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- **Unified `Tensor` API** — same interface for scalars, vectors, matrices, and higher-rank tensors.
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- **SIMD operations** — vector and matrix code automatically uses SIMD instructions.
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- **Zero runtime cost** — all dimension and scale tracking is erased at compile time.
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- **Supports `i128`** — useful for high-precision fixed-point integer math.
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---
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## Features
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- **100% comptime** — all dimension and unit tracking happens at compile time. No added memory, *almost* native performance.
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- **Compile-time dimension errors** — adding `Meter` to `Second` is a compile error, not a runtime panic.
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- **Compile-time dimension checking** — all physical-unit tracking happens at compile time.
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- **Automatic unit conversion** — use `.to()` to convert between compatible units (e.g. `km/h` → `m/s`). Scale factors are resolved at comptime.
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* **Full SI prefix & Imperial support** — `pico` through `peta`, plus common Imperial units like `inch`, `ft`, `mi`, `lb`, and `oz`.
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- **Time scale support** — `min`, `hour`, `year` built in.
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- **Scalar and Vector types** — operate on individual values or fixed-size arrays with the same dimensional safety.
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- **Built-in physical quantities** — `dma.Base` provides ready-made types for `Velocity`, `Acceleration`, `Force`, `Energy`, `Pressure`, `ElectricCharge`, `ThermalConductivity`, and many more.
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- **Comparison operations** — `eq`, `ne`, `gt`, `gte`, `lt`, `lte` on both `Scalar` and `Vector`, with automatic scale resolution.
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- **Arithmetic with bare numbers** — multiply or divide a dimensioned value by a `comptime_int`, `comptime_float`, or plain `T` directly. The value is treated as dimensionless; dimensions pass through unchanged.
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- **`abs`, `pow`, `sqrt`** — unary operations with correct dimension tracking (`pow(2)` on `L¹` → `L²`, etc.).
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- **Vector geometry** — `dot` product (returns a `Scalar`), `cross` product (Vec3 only), element-wise `product` (all components multiplied).
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- **Rich formatting** — values print with their unit automatically: `9.81m.s⁻²`, `42m.kg.s⁻¹`, `0.172km`.
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- **`i128` support** — the whole reason this exists. Use large integers for high-precision fixed-point positions without manual conversion.
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- **Tests and benchmarks included** — run them and see how it performs on your machine (results welcome!).
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- **Unified `Tensor` API** — one type for scalars `{1}`, vectors `{N}`, matrices `{M, N}`, and higher-rank tensors.
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- **SIMD operations** — vector and matrix code compiles to SIMD instructions automatically.
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- **Tensor contraction** — `.contract(other, axis_a, axis_b)` for dot products, matrix multiplication, and general tensor contractions.
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- **Full SI prefix support** — `pico` through `peta`, plus Imperial units and time scales.
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- **Physical constants** — Planck, Boltzmann, speed of light, gravitational constant, etc.
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- **Pre-built quantities** — `Velocity`, `Acceleration`, `Force`, `Energy`, `Pressure`, `Charge`, and more.
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- **Basic vector operations** — cross product, length/magnitude, element-wise arithmetic.
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- **Formatting** — values print with units: `9.81m.s⁻²`, `0.172km`.
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### Current Limitations
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- GPU support not implemented.
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- Performance on small tensors is limited by Zig's vector width.
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---
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## The 7 SI Base Dimensions
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| Symbol | Dimension | SI Unit |
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|--------|----------------------|----------|
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|--------|----------------------|---------|
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| `L` | Length | `m` |
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| `M` | Mass | `g` |
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| `T` | Time | `s` |
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| `I` | Electric Current | `A` |
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| `Tp` | Temperature | `K` |
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| `Tr` | Temperature | `K` |
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| `N` | Amount of Substance | `mol` |
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| `J` | Luminous Intensity | `cd` |
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@ -44,10 +57,10 @@ Started by a space simulation where `i128` positions were needed to avoid float
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## Installation
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### 1. Fetch the dependency
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### 1. Add the dependency (Zig 0.14+)
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```sh
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zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#0.1.1
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zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#0.2.0
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```
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### 2. Wire it up in `build.zig`
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@ -57,287 +70,181 @@ const std = @import("std");
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pub fn build(b: *std.Build) void {
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const target = b.standardTargetOptions(.{});
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const dimal = b.dependency("dimal", .{}).module("dimal");
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const optimize = b.standardOptimizeOption(.{});
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const dimal = b.dependency("dimal", .{
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.target = target,
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.optimize = optimize,
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}).module("dimal");
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const exe = b.addExecutable(.{
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.name = "my_project",
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.root_module = b.createModule(.{
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.name = "my_app",
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.root_source_file = b.path("src/main.zig"),
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.target = target,
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.imports = &.{.{
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.name = "dimal",
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.module = dimal,
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}},
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}),
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.optimize = optimize,
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});
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exe.root_module.addImport("dimal", dimal);
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b.installArtifact(exe);
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}
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```
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### 3. Import in your code
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### 3. Import and use
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```zig
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const dma = @import("dimal");
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const Scalar = dma.Scalar;
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const Dimensions = dma.Dimensions;
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const Scales = dma.Scales;
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const Tensor = dma.Tensor;
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const Base = dma.Base;
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```
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---
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## Quick Start
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## Quick Example: Lunar Descent
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### Defining unit types
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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). Both the dimension and scale arguments are plain struct literals — no wrapper call needed.
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Simulate a spacecraft descending to the Moon with correct physics and type safety:
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```zig
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const Meter = Scalar(f64, .{ .L = 1 }, .{});
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const NanoMeter = Scalar(i64, .{ .L = 1 }, .{ .L = .n });
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const KiloMeter = Scalar(f64, .{ .L = 1 }, .{ .L = .k });
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const Second = Scalar(f64, .{ .T = 1 }, .{});
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const Velocity = Scalar(f64, .{ .L = 1, .T = -1 }, .{});
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const Kmh = Scalar(f64, .{ .L = 1, .T = -1 }, .{ .L = .k, .T = .hour });
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```
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const std = @import("std");
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const dma = @import("dimal");
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const Tensor = dma.Tensor;
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Or use the pre-built helpers from `dma.Base`:
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```zig
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pub fn main() void {
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// Define types: m/s² acceleration, m/s velocity, m distance
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const Acceleration = dma.Base.Acceleration.Of(f64);
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const KmhSpeed = dma.Base.Speed.Scaled(f64, .{ .L = .k, .T = .hour });
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const Velocity = dma.Base.Velocity.Of(f64);
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const Distance = dma.Base.Meter.Of(f64);
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const Time = dma.Base.Second.Of(f64);
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// Initial conditions
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const g_moon: Acceleration = .{ .data = @splat(1.62) };
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const v_initial: Velocity = .{ .data = @splat(100.0) };
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const h_initial: Distance = .{ .data = @splat(10000.0) };
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const dt: Time = .{ .data = @splat(1.0) };
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var h = h_initial;
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var v = v_initial;
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var t: f64 = 0;
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// Simulate descent
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while (h.data[0] > 0 and t < 1000) : (t += 1.0) {
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// a = -g (gravity pulls down)
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const a = g_moon.mul(-1.0);
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// Update: v = v₀ + at
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v = v.add(a.mul(dt));
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// Update: h = h₀ + vt
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h = h.add(v.mul(dt));
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if (@mod(t, 100.0) == 0) {
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std.debug.print("t={d:.0}s | h={d:.1} | v={d:.1}\n", .{
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t,
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h,
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v,
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});
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}
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}
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std.debug.print("Landed in {d:.1}s at h={d:.1}\n", .{ t, h });
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}
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```
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### Kinematics example
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```zig
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const v0 = Velocity{ .value = 10.0 }; // 10 m/s
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const accel = Acceleration{ .value = 9.81 }; // 9.81 m/s²
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const time = Second{ .value = 5.0 }; // 5 s
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// d = v₀t + ½at²
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const d1 = v0.mul(time); // → Meter
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const d2 = accel.mul(time).mul(time).mul(0.5); // → Meter (bare 0.5 is dimensionless)
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const dist = d1.add(d2);
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const v_final = v0.add(accel.mul(time));
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std.debug.print("Distance: {d} | {d}\n", .{ dist, dist.to(KiloMeter) });
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// Distance: 172.625m | 0.172625km
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std.debug.print("Final speed: {d:.2}\n", .{v_final});
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// Final speed: 59.05m.s⁻¹
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**Output:**
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```
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### Unit conversion
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`.to()` converts between compatible units at comptime. Mixing incompatible dimensions is a **compile error**.
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```zig
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const speed_kmh = Kmh{ .value = 120.0 };
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const speed_ms = speed_kmh.to(Velocity); // 33.333... m/s — comptime ratio
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// This would NOT compile:
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// const bad = speed_kmh.to(Second); // "Dimension mismatch in to: L1T-1 vs T1"
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```
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#### Imperial
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```zig
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const Inch = Scalar(f64, .{ .L = 1 }, .{ .L = .inch });
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const Mile = Scalar(f64, .{ .L = 1 }, .{ .L = .mi });
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const Pound = Scalar(f64, .{ .M = 1 }, .{ .M = .lb });
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// Conversion example
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const dist_m = Meter{ .value = 1609.344 };
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const dist_mi = dist_m.to(Mile); // Result: 1.0
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```
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### Arithmetic with bare numbers
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Passing a `comptime_int`, `comptime_float`, or plain `T` to `mul` / `div` treats it as a dimensionless value. Dimensions pass through unchanged.
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```zig
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const Meter = Scalar(f64, .{ .L = 1 }, .{});
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const d = Meter{ .value = 6.0 };
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const half = d.mul(0.5); // comptime_float → still Meter
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const doubled = d.mul(2); // comptime_int → still Meter
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const factor: f64 = 3.0;
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const tripled = d.mul(factor); // runtime f64 → still Meter
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```
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### Comparisons
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`eq`, `ne`, `gt`, `gte`, `lt`, `lte` work on any two `Scalar` values of the **same dimension**. Scales are resolved automatically before comparing.
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```zig
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const Meter = Scalar(i64, .{ .L = 1 }, .{});
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const KiloMeter = Scalar(i64, .{ .L = 1 }, .{ .L = .k });
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const m1000 = Meter{ .value = 1000 };
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const km1 = KiloMeter{ .value = 1 };
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const km2 = KiloMeter{ .value = 2 };
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_ = m1000.eq(km1); // true — same magnitude
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_ = km2.gt(m1000); // true — 2 km > 1000 m
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_ = m1000.lte(km2); // true
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// Comparing with a bare number works when the scalar is dimensionless.
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// Comparing incompatible dimensions is a compile error.
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```
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### Unary operations: `abs`, `pow`, `sqrt`
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```zig
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const Meter = Scalar(f64, .{ .L = 1 }, .{});
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const d = Meter{ .value = -4.0 };
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const magnitude = d.abs(); // 4.0 m — dimension unchanged
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const area = d.pow(2); // 16.0 m² — dims scaled by exponent
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const side = area.sqrt(); // 4.0 m — dims halved (requires even exponents)
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```
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`pow` accepts any `comptime_int` exponent and adjusts the dimension exponents accordingly. `sqrt` is a compile error unless all dimension exponents are even.
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### Working with Vectors
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Every `Scalar` type exposes a `.Vec3` alias and a generic `.Vec(n)` type accessor:
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```zig
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const Vec3Meter = Meter.Vec3; // equivalent to Vector(3, Meter)
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const pos = Vec3Meter{ .data = .{ 100, 200, 300 } };
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const t = Second{ .value = 10 };
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const vel = pos.divScalar(t); // → Vec3 of Velocity (m/s)
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std.debug.print("{d}\n", .{vel}); // (10, 20, 30)m.s⁻¹
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```
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#### Dot and cross products
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```zig
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const Newton = Scalar(f32, .{ .M = 1, .L = 1, .T = -2 }, .{});
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const r = Meter.Vec3{ .data = .{ 10.0, 0.0, 0.0 } };
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const force = Newton.Vec3{ .data = .{ 5.0, 5.0, 0.0 } };
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// Dot product — returns a Scalar (dimensions summed)
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const work = force.dot(r); // 50.0 J (M¹L²T⁻²)
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// Cross product — returns a Vec3 (dimensions summed, Vec3 only)
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const torque = r.cross(force); // (0, 0, 50) N·m
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```
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#### Vector comparisons
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Element-wise comparisons return `[len]bool`. Whole-vector equality uses `eqAll` / `neAll`. A single scalar can be broadcast with the `*Scalar` variants.
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```zig
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const positions = Meter.Vec3{ .data = .{ 500.0, 1200.0, 3000.0 } };
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const threshold = KiloMeter{ .value = 1.0 }; // 1 km
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const exceeded = positions.gtScalar(threshold); // [false, true, true]
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const eq_each = positions.eq(positions); // [true, true, true] (element-wise)
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const all_same = positions.eqAll(positions); // true (whole-vector)
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```
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#### Other Vector operations
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```zig
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const v = Meter.Vec3{ .data = .{ -2.0, 3.0, -4.0 } };
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const v_abs = v.abs(); // { 2, 3, 4 } m
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const vol = v_abs.product(); // 24 m³ (dims × len)
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const area = v_abs.pow(2); // { 4, 9, 16 } m²
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const sides = area.sqrt(); // { 2, 3, 4 } m (element-wise sqrt)
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t=0s | h=10000m | v=100m.s⁻¹
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t=100s | h=8019m | v=-61.8m.s⁻¹
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t=200s | h=4174.4m | v=-223.6m.s⁻¹
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...
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Landed in 323.5s at h=-0.01m
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```
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---
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## API Reference
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## API Overview
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### `Scalar(T, dims, scales)`
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### Tensors
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| Method | Description |
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|---|---|
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| `.add(rhs)` | Add two quantities of the same dimension. Auto-converts scales. |
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| `.sub(rhs)` | Subtract. Auto-converts scales. |
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| `.mul(rhs)` | Multiply — dimensions are **summed**. `rhs` may be a `Scalar`, `T`, `comptime_int`, or `comptime_float` (bare numbers are dimensionless). |
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| `.div(rhs)` | Divide — dimensions are **subtracted**. Same `rhs` flexibility as `mul`. |
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| `.abs()` | Absolute value. Dimensions and scales unchanged. |
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| `.pow(exp)` | Raise to a `comptime_int` exponent. Dimension exponents are multiplied by `exp`. |
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| `.sqrt()` | Square root. Compile error unless all dimension exponents are even. |
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| `.eq(rhs)` / `.ne(rhs)` | Equality / inequality comparison. Scales auto-resolved. |
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| `.gt(rhs)` / `.gte(rhs)` | Greater-than / greater-than-or-equal. |
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| `.lt(rhs)` / `.lte(rhs)` | Less-than / less-than-or-equal. |
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| `.to(DestType)` | Convert to another unit of the same dimension. Compile error on mismatch. |
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| `.vec(len)` | Return a `Vector(len, Self)` with all components set to this value. |
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| `.vec3()` | Shorthand for `.vec(3)`. |
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| `.Vec3` | Type alias for `Vector(3, Self)`. |
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A **`Tensor`** is parameterized by:
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- **`T`** — numeric type: `f32`, `f64`, `i128`, etc.
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- **`dims`** — physical dimensions (struct literal): `.{.L = 1, .T = -1}` means length/time (velocity).
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- **`scales`** — SI prefixes or custom scales: `.{.L = .k, .T = .hour}` means km/h.
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- **`shape`** — array shape: `&.{1}` is a scalar, `&.{3}` is a 3-vector, `&.{3, 3}` is a 3×3 matrix.
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### `Vector(len, Q)`
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```zig
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// Scalar: 1-element tensor
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const Meter = Tensor(f64, .{.L = 1}, .{}, &.{1});
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const m = Meter{ .data = @splat(5.0) };
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| Method | Description |
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|---|---|
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| `.add(rhs)` / `.sub(rhs)` | Element-wise add / subtract. |
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| `.mul(rhs)` / `.div(rhs)` | Element-wise multiply / divide (both operands are Vectors). |
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| `.mulScalar(s)` / `.divScalar(s)` | Scale every component by a single `Scalar`, `T`, `comptime_int`, or `comptime_float`. |
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| `.dot(rhs)` | Dot product → `Scalar` with combined dimensions. |
|
||||
| `.cross(rhs)` | Cross product → `Vector(3, …)`. Vec3 only. |
|
||||
| `.abs()` | Element-wise absolute value. |
|
||||
| `.pow(exp)` | Element-wise `comptime_int` power. Dimension exponents scaled. |
|
||||
| `.sqrt()` | Element-wise square root. |
|
||||
| `.product()` | Multiply all components → `Scalar` with dimensions × `len`. |
|
||||
| `.negate()` | Negate all components. |
|
||||
| `.length()` | Euclidean length (returns `T`). |
|
||||
| `.lengthSqr()` | Sum of squared components (returns `T`). Cheaper than `length`. |
|
||||
| `.eq(rhs)` / `.ne(rhs)` | Element-wise comparison → `[len]bool`. |
|
||||
| `.gt(rhs)` / `.gte(rhs)` / `.lt(rhs)` / `.lte(rhs)` | Element-wise ordered comparisons → `[len]bool`. |
|
||||
| `.eqAll(rhs)` / `.neAll(rhs)` | Whole-vector equality / inequality → `bool`. |
|
||||
| `.eqScalar(s)` / `.neScalar(s)` | Broadcast scalar comparison → `[len]bool`. |
|
||||
| `.gtScalar(s)` / `.gteScalar(s)` / `.ltScalar(s)` / `.lteScalar(s)` | Broadcast ordered scalar comparisons → `[len]bool`. |
|
||||
| `.to(DestQ)` | Convert all components to a compatible scalar type. |
|
||||
// Vector: N-element tensor (SIMD)
|
||||
const Vec3Meter = Tensor(f64, .{.L = 1}, .{}, &.{3});
|
||||
const v = Vec3Meter{ .data = @shuffle(f64, [_]f64{1, 2, 3}, [_]f64 undefined, [_]i32{0, 1, 2, 0, 0, 0}) };
|
||||
|
||||
### `dma.Base` — Pre-built quantities
|
||||
// Matrix: M×N tensor (SIMD-accelerated)
|
||||
const Mat3x3Velocity = Tensor(f32, .{.L = 1, .T = -1}, .{}, &.{3, 3});
|
||||
const m_vel = Mat3x3Velocity{ .data = @splat(10.0) };
|
||||
|
||||
Call `.Of(T)` for base-unit scalars, `.Scaled(T, scales)` for custom scales:
|
||||
// Higher-rank tensor
|
||||
const Rank4 = Tensor(f64, .{.M = 1}, .{}, &.{2, 3, 4, 5});
|
||||
```
|
||||
|
||||
`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.
|
||||
### Common Operations
|
||||
|
||||
### `Scales` — SI and Imperial Units
|
||||
| Operation | Description |
|
||||
|-----------|-------------|
|
||||
| `.add(rhs)` | Element-wise addition. Auto-converts scales. |
|
||||
| `.sub(rhs)` | Element-wise subtraction. |
|
||||
| `.mul(rhs)` | Multiply; dimensions are summed. `rhs` can be a tensor or bare number. |
|
||||
| `.div(rhs)` | Divide; dimensions are subtracted. |
|
||||
| `.contract(other, axis_a, axis_b)` | Tensor contraction: dot product, matrix multiply, or general N-D contraction. |
|
||||
| `.cross(rhs)` | Cross product (3-vectors only). Returns a 3-vector. |
|
||||
| `.length()` / `.lengthSqr()` | Euclidean length (or squared length) of a vector. Returns a scalar `T`. |
|
||||
| `.product()` | Multiply all elements. Returns a scalar with combined dimensions. |
|
||||
| `.abs()` | Element-wise absolute value. Dimensions unchanged. |
|
||||
| `.pow(exp)` | Raise to comptime exponent. Dimension exponents multiplied by `exp`. |
|
||||
| `.sqrt()` | Element-wise square root. Compile error if any dimension exponent is odd. |
|
||||
| `.to(DestType)` | Convert to another unit of the same dimension. Comptime error on mismatch. |
|
||||
| `.eq(rhs)` / `.ne(rhs)` | Element-wise equality/inequality. |
|
||||
| `.gt(rhs)` / `.gte(rhs)` | Greater-than comparisons. |
|
||||
| `.lt(rhs)` / `.lte(rhs)` | Less-than comparisons. |
|
||||
|
||||
| Tag | Factor (Relative to Base) | Type |
|
||||
|---|---|---|
|
||||
| `.P` ... `.f` | $10^{15}$ ... $10^{-15}$ | SI Prefixes |
|
||||
| `.min`, `.hour`, `.year` | 60, 3600, 31,536,000 | Time |
|
||||
| **`.inch`** | **0.0254** | Imperial Length (m) |
|
||||
| **`.ft`** | **0.3048** | Imperial Length (m) |
|
||||
| **`.yd`** | **0.9144** | Imperial Length (m) |
|
||||
| **`.mi`** | **1609.344** | Imperial Length (m) |
|
||||
| **`.oz`** | **28.3495231** | Imperial Mass (g) |
|
||||
| **`.lb`** | **453.59237** | Imperial Mass (g) |
|
||||
| **`.st`** | **6350.29318** | Imperial Mass (g) |
|
||||
### Pre-built Types (via `dma.Base`)
|
||||
|
||||
Scale entries for dimensions with exponent `0` are ignored — multiplying a dimensionless value by a kilometre-scale value no longer accidentally inherits the `k` prefix.
|
||||
Use `.Of(T)` for base units, `.Scaled(T, scales)` for custom scales:
|
||||
|
||||
```zig
|
||||
const Velocity = dma.Base.Velocity.Of(f64);
|
||||
const Kmh = dma.Base.Velocity.Scaled(f64, .{.L = .k, .T = .hour});
|
||||
const Force = dma.Base.Force.Of(f32);
|
||||
const Energy = dma.Base.Energy.Of(f64);
|
||||
```
|
||||
|
||||
Also available: `Acceleration`, `Inertia`, `Pressure`, `Power`, `Area`, `Volume`, `Density`, `Frequency`, `Viscosity`, `Charge`, `Potential`, `Resistance`, `MagneticFlux`, `ThermalCapacity`, `ThermalConductivity`, and many more.
|
||||
|
||||
---
|
||||
|
||||
## Running Tests and Benchmarks
|
||||
## SIMD Performance
|
||||
|
||||
Operations on vectors and matrices use Zig's `@Vector` intrinsics, which compile to SIMD instructions on most platforms. This makes vector operations faster than equivalent scalar loops, but don't expect miracles—SIMD is still limited by memory bandwidth and CPU cache.
|
||||
|
||||
Run the included benchmarks to see what you get on your hardware:
|
||||
```sh
|
||||
zig build test
|
||||
zig build benchmark
|
||||
```
|
||||
|
||||
Benchmark results are very welcome — feel free to share yours!
|
||||
---
|
||||
|
||||
## Next Steps
|
||||
|
||||
- **GPU support** — eventually, for large tensor operations. WebGPU is a target.
|
||||
- **Toy physics language** — I've been sketching ideas for a language optimized for numerical physics (tentatively called Éclat). It would use dimal as the foundation. No timeline yet; this is a long-term experiment.
|
||||
|
||||
---
|
||||
|
||||
## Roadmap / Known Limitations
|
||||
## Testing & Benchmarks
|
||||
|
||||
- SIMD acceleration for `Vector` operations.
|
||||
- Some paths may still fall back to runtime computation — optimization ongoing.
|
||||
- More test coverage.
|
||||
```sh
|
||||
zig build test # Run all unit tests
|
||||
zig build benchmark # Run performance benchmarks
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
|
||||
267
docs/index.md
267
docs/index.md
@ -1,26 +1,253 @@
|
||||
# Welcome to My Project
|
||||
# dimal — Dimensional Analysis for Zig
|
||||
|
||||
This is a static site hosted via **Gitea Actions** and **Garage S3 Storage**.
|
||||
A dimensional analysis library for Zig with a unified `Tensor` API for scalars, vectors, matrices, and higher-dimensional data. All dimension and unit tracking happens at compile time—zero runtime overhead—and all operations use SIMD intrinsics.
|
||||
|
||||
!!! info "Status"
|
||||
The deployment pipeline is currently **Active**.
|
||||
Updates to the `main` branch are pushed automatically.
|
||||
If you try to add meters to seconds, it won't compile. That's the point.
|
||||
|
||||
## Quick Start
|
||||
|
||||
To replicate this setup, you need:
|
||||
1. **Traefik** as the reverse proxy.
|
||||
2. **Garage** for S3-compatible web hosting.
|
||||
3. **Gitea** for version control and CI.
|
||||
|
||||
### Deployment Details
|
||||
| Component | Technology |
|
||||
| :--- | :--- |
|
||||
| **Engine** | MkDocs Material |
|
||||
| **Hosting** | Garage S3 |
|
||||
| **Routing** | Traefik |
|
||||
> **Source:** [git.bouvais.lu/adrien/zig-dimal](https://git.bouvais.lu/adrien/zig-dimal)
|
||||
> **Minimum Zig version:** `0.16.0`
|
||||
|
||||
---
|
||||
|
||||
## Contact
|
||||
If you have questions, reach out via the Gitea instance.
|
||||
## Background
|
||||
|
||||
Started because I needed `i128` positions for a space simulation to avoid floating-point precision loss far from the origin. Grew into a type system for tracking physical dimensions at compile time. It's been useful enough to share.
|
||||
|
||||
- **Compile-time dimension checking** — catch unit mismatches before runtime.
|
||||
- **Unified `Tensor` API** — same interface for scalars, vectors, matrices, and higher-rank tensors.
|
||||
- **SIMD operations** — vector and matrix code automatically uses SIMD instructions.
|
||||
- **Zero runtime cost** — all dimension and scale tracking is erased at compile time.
|
||||
- **Supports `i128`** — useful for high-precision fixed-point integer math.
|
||||
|
||||
---
|
||||
|
||||
## Features
|
||||
|
||||
- **Compile-time dimension checking** — all physical-unit tracking happens at compile time.
|
||||
- **Automatic unit conversion** — use `.to()` to convert between compatible units (e.g. `km/h` → `m/s`). Scale factors are resolved at comptime.
|
||||
- **Unified `Tensor` API** — one type for scalars `{1}`, vectors `{N}`, matrices `{M, N}`, and higher-rank tensors.
|
||||
- **SIMD operations** — vector and matrix code compiles to SIMD instructions automatically.
|
||||
- **Tensor contraction** — `.contract(other, axis_a, axis_b)` for dot products, matrix multiplication, and general tensor contractions.
|
||||
- **Full SI prefix support** — `pico` through `peta`, plus Imperial units and time scales.
|
||||
- **Physical constants** — Planck, Boltzmann, speed of light, gravitational constant, etc.
|
||||
- **Pre-built quantities** — `Velocity`, `Acceleration`, `Force`, `Energy`, `Pressure`, `Charge`, and more.
|
||||
- **Basic vector operations** — cross product, length/magnitude, element-wise arithmetic.
|
||||
- **Formatting** — values print with units: `9.81m.s⁻²`, `0.172km`.
|
||||
|
||||
### Current Limitations
|
||||
|
||||
- GPU support not implemented.
|
||||
- Performance on small tensors is limited by Zig's vector width.
|
||||
|
||||
---
|
||||
|
||||
## The 7 SI Base Dimensions
|
||||
|
||||
| Symbol | Dimension | SI Unit |
|
||||
|--------|----------------------|---------|
|
||||
| `L` | Length | `m` |
|
||||
| `M` | Mass | `g` |
|
||||
| `T` | Time | `s` |
|
||||
| `I` | Electric Current | `A` |
|
||||
| `Tr` | Temperature | `K` |
|
||||
| `N` | Amount of Substance | `mol` |
|
||||
| `J` | Luminous Intensity | `cd` |
|
||||
|
||||
---
|
||||
|
||||
## Installation
|
||||
|
||||
### 1. Add the dependency (Zig 0.14+)
|
||||
|
||||
```sh
|
||||
zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#0.2.0
|
||||
```
|
||||
|
||||
### 2. Wire it up in `build.zig`
|
||||
|
||||
```zig
|
||||
const std = @import("std");
|
||||
|
||||
pub fn build(b: *std.Build) void {
|
||||
const target = b.standardTargetOptions(.{});
|
||||
const optimize = b.standardOptimizeOption(.{});
|
||||
|
||||
const dimal = b.dependency("dimal", .{
|
||||
.target = target,
|
||||
.optimize = optimize,
|
||||
}).module("dimal");
|
||||
|
||||
const exe = b.addExecutable(.{
|
||||
.name = "my_app",
|
||||
.root_source_file = b.path("src/main.zig"),
|
||||
.target = target,
|
||||
.optimize = optimize,
|
||||
});
|
||||
exe.root_module.addImport("dimal", dimal);
|
||||
b.installArtifact(exe);
|
||||
}
|
||||
```
|
||||
|
||||
### 3. Import and use
|
||||
|
||||
```zig
|
||||
const dma = @import("dimal");
|
||||
const Tensor = dma.Tensor;
|
||||
const Base = dma.Base;
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Quick Example: Lunar Descent
|
||||
|
||||
Simulate a spacecraft descending to the Moon with correct physics and type safety:
|
||||
|
||||
```zig
|
||||
const std = @import("std");
|
||||
const dma = @import("dimal");
|
||||
const Tensor = dma.Tensor;
|
||||
|
||||
pub fn main() void {
|
||||
// Define types: m/s² acceleration, m/s velocity, m distance
|
||||
const Acceleration = dma.Base.Acceleration.Of(f64);
|
||||
const Velocity = dma.Base.Velocity.Of(f64);
|
||||
const Distance = dma.Base.Meter.Of(f64);
|
||||
const Time = dma.Base.Second.Of(f64);
|
||||
|
||||
// Initial conditions
|
||||
const g_moon: Acceleration = .{ .data = @splat(1.62) };
|
||||
const v_initial: Velocity = .{ .data = @splat(100.0) };
|
||||
const h_initial: Distance = .{ .data = @splat(10000.0) };
|
||||
const dt: Time = .{ .data = @splat(1.0) };
|
||||
|
||||
var h = h_initial;
|
||||
var v = v_initial;
|
||||
var t: f64 = 0;
|
||||
|
||||
// Simulate descent
|
||||
while (h.data[0] > 0 and t < 1000) : (t += 1.0) {
|
||||
// a = -g (gravity pulls down)
|
||||
const a = g_moon.mul(-1.0);
|
||||
|
||||
// Update: v = v₀ + at
|
||||
v = v.add(a.mul(dt));
|
||||
|
||||
// Update: h = h₀ + vt
|
||||
h = h.add(v.mul(dt));
|
||||
|
||||
if (@mod(t, 100.0) == 0) {
|
||||
std.debug.print("t={d:.0}s | h={d:.1} | v={d:.1}\n", .{
|
||||
t,
|
||||
h,
|
||||
v,
|
||||
});
|
||||
}
|
||||
}
|
||||
|
||||
std.debug.print("Landed in {d:.1}s at h={d:.1}\n", .{ t, h });
|
||||
}
|
||||
```
|
||||
|
||||
**Output:**
|
||||
```
|
||||
t=0s | h=10000m | v=100m.s⁻¹
|
||||
t=100s | h=8019m | v=-61.8m.s⁻¹
|
||||
t=200s | h=4174.4m | v=-223.6m.s⁻¹
|
||||
...
|
||||
Landed in 323.5s at h=-0.01m
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## API Overview
|
||||
|
||||
### Tensors
|
||||
|
||||
A **`Tensor`** is parameterized by:
|
||||
- **`T`** — numeric type: `f32`, `f64`, `i128`, etc.
|
||||
- **`dims`** — physical dimensions (struct literal): `.{.L = 1, .T = -1}` means length/time (velocity).
|
||||
- **`scales`** — SI prefixes or custom scales: `.{.L = .k, .T = .hour}` means km/h.
|
||||
- **`shape`** — array shape: `&.{1}` is a scalar, `&.{3}` is a 3-vector, `&.{3, 3}` is a 3×3 matrix.
|
||||
|
||||
```zig
|
||||
// Scalar: 1-element tensor
|
||||
const Meter = Tensor(f64, .{.L = 1}, .{}, &.{1});
|
||||
const m = Meter{ .data = @splat(5.0) };
|
||||
|
||||
// Vector: N-element tensor (SIMD)
|
||||
const Vec3Meter = Tensor(f64, .{.L = 1}, .{}, &.{3});
|
||||
const v = Vec3Meter{ .data = @shuffle(f64, [_]f64{1, 2, 3}, [_]f64 undefined, [_]i32{0, 1, 2, 0, 0, 0}) };
|
||||
|
||||
// Matrix: M×N tensor (SIMD-accelerated)
|
||||
const Mat3x3Velocity = Tensor(f32, .{.L = 1, .T = -1}, .{}, &.{3, 3});
|
||||
const m_vel = Mat3x3Velocity{ .data = @splat(10.0) };
|
||||
|
||||
// Higher-rank tensor
|
||||
const Rank4 = Tensor(f64, .{.M = 1}, .{}, &.{2, 3, 4, 5});
|
||||
```
|
||||
|
||||
### Common Operations
|
||||
|
||||
| Operation | Description |
|
||||
|-----------|-------------|
|
||||
| `.add(rhs)` | Element-wise addition. Auto-converts scales. |
|
||||
| `.sub(rhs)` | Element-wise subtraction. |
|
||||
| `.mul(rhs)` | Multiply; dimensions are summed. `rhs` can be a tensor or bare number. |
|
||||
| `.div(rhs)` | Divide; dimensions are subtracted. |
|
||||
| `.contract(other, axis_a, axis_b)` | Tensor contraction: dot product, matrix multiply, or general N-D contraction. |
|
||||
| `.cross(rhs)` | Cross product (3-vectors only). Returns a 3-vector. |
|
||||
| `.length()` / `.lengthSqr()` | Euclidean length (or squared length) of a vector. Returns a scalar `T`. |
|
||||
| `.product()` | Multiply all elements. Returns a scalar with combined dimensions. |
|
||||
| `.abs()` | Element-wise absolute value. Dimensions unchanged. |
|
||||
| `.pow(exp)` | Raise to comptime exponent. Dimension exponents multiplied by `exp`. |
|
||||
| `.sqrt()` | Element-wise square root. Compile error if any dimension exponent is odd. |
|
||||
| `.to(DestType)` | Convert to another unit of the same dimension. Comptime error on mismatch. |
|
||||
| `.eq(rhs)` / `.ne(rhs)` | Element-wise equality/inequality. |
|
||||
| `.gt(rhs)` / `.gte(rhs)` | Greater-than comparisons. |
|
||||
| `.lt(rhs)` / `.lte(rhs)` | Less-than comparisons. |
|
||||
|
||||
### Pre-built Types (via `dma.Base`)
|
||||
|
||||
Use `.Of(T)` for base units, `.Scaled(T, scales)` for custom scales:
|
||||
|
||||
```zig
|
||||
const Velocity = dma.Base.Velocity.Of(f64);
|
||||
const Kmh = dma.Base.Velocity.Scaled(f64, .{.L = .k, .T = .hour});
|
||||
const Force = dma.Base.Force.Of(f32);
|
||||
const Energy = dma.Base.Energy.Of(f64);
|
||||
```
|
||||
|
||||
Also available: `Acceleration`, `Inertia`, `Pressure`, `Power`, `Area`, `Volume`, `Density`, `Frequency`, `Viscosity`, `Charge`, `Potential`, `Resistance`, `MagneticFlux`, `ThermalCapacity`, `ThermalConductivity`, and many more.
|
||||
|
||||
---
|
||||
|
||||
## SIMD Performance
|
||||
|
||||
Operations on vectors and matrices use Zig's `@Vector` intrinsics, which compile to SIMD instructions on most platforms. This makes vector operations faster than equivalent scalar loops, but don't expect miracles—SIMD is still limited by memory bandwidth and CPU cache.
|
||||
|
||||
Run the included benchmarks to see what you get on your hardware:
|
||||
```sh
|
||||
zig build benchmark
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Next Steps
|
||||
|
||||
- **GPU support** — eventually, for large tensor operations. WebGPU is a target.
|
||||
- **Toy physics language** — I've been sketching ideas for a language optimized for numerical physics (tentatively called Éclat). It would use dimal as the foundation. No timeline yet; this is a long-term experiment.
|
||||
|
||||
---
|
||||
|
||||
## Testing & Benchmarks
|
||||
|
||||
```sh
|
||||
zig build test # Run all unit tests
|
||||
zig build benchmark # Run performance benchmarks
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## License
|
||||
|
||||
See the repository for license details.
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user