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docs/index.md
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# dimal — Dimensional Analysis for Zig
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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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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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- **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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- **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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| `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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| `Tr` | Temperature | `K` |
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| `N` | Amount of Substance | `mol` |
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| `J` | Luminous Intensity | `cd` |
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---
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## Installation
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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#0.2.0
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```
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### 2. Wire it up in `build.zig`
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```zig
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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 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_app",
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.root_source_file = b.path("src/main.zig"),
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.target = target,
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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 and use
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```zig
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const dma = @import("dimal");
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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 Example: Lunar Descent
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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 std = @import("std");
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const dma = @import("dimal");
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const Tensor = dma.Tensor;
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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 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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**Output:**
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```
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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 Overview
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### Tensors
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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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```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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// Vector: N-element tensor (SIMD)
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const Vec3Meter = Tensor(f64, .{.L = 1}, .{}, &.{3});
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const v = Vec3Meter{ .data = @shuffle(f64, [_]f64{1, 2, 3}, [_]f64 undefined, [_]i32{0, 1, 2, 0, 0, 0}) };
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// Matrix: M×N tensor (SIMD-accelerated)
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const Mat3x3Velocity = Tensor(f32, .{.L = 1, .T = -1}, .{}, &.{3, 3});
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const m_vel = Mat3x3Velocity{ .data = @splat(10.0) };
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// Higher-rank tensor
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const Rank4 = Tensor(f64, .{.M = 1}, .{}, &.{2, 3, 4, 5});
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```
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### Common Operations
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| Operation | Description |
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|-----------|-------------|
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| `.add(rhs)` | Element-wise addition. Auto-converts scales. |
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| `.sub(rhs)` | Element-wise subtraction. |
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| `.mul(rhs)` | Multiply; dimensions are summed. `rhs` can be a tensor or bare number. |
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| `.div(rhs)` | Divide; dimensions are subtracted. |
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| `.contract(other, axis_a, axis_b)` | Tensor contraction: dot product, matrix multiply, or general N-D contraction. |
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| `.cross(rhs)` | Cross product (3-vectors only). Returns a 3-vector. |
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| `.length()` / `.lengthSqr()` | Euclidean length (or squared length) of a vector. Returns a scalar `T`. |
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| `.product()` | Multiply all elements. Returns a scalar with combined dimensions. |
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| `.abs()` | Element-wise absolute value. Dimensions unchanged. |
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| `.pow(exp)` | Raise to comptime exponent. Dimension exponents multiplied by `exp`. |
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| `.sqrt()` | Element-wise square root. Compile error if any dimension exponent is odd. |
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| `.to(DestType)` | Convert to another unit of the same dimension. Comptime error on mismatch. |
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| `.eq(rhs)` / `.ne(rhs)` | Element-wise equality/inequality. |
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| `.gt(rhs)` / `.gte(rhs)` | Greater-than comparisons. |
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| `.lt(rhs)` / `.lte(rhs)` | Less-than comparisons. |
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### Pre-built Types (via `dma.Base`)
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Use `.Of(T)` for base units, `.Scaled(T, scales)` for custom scales:
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```zig
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const Velocity = dma.Base.Velocity.Of(f64);
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const Kmh = dma.Base.Velocity.Scaled(f64, .{.L = .k, .T = .hour});
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const Force = dma.Base.Force.Of(f32);
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const Energy = dma.Base.Energy.Of(f64);
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```
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Also available: `Acceleration`, `Inertia`, `Pressure`, `Power`, `Area`, `Volume`, `Density`, `Frequency`, `Viscosity`, `Charge`, `Potential`, `Resistance`, `MagneticFlux`, `ThermalCapacity`, `ThermalConductivity`, and many more.
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---
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## SIMD Performance
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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.
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Run the included benchmarks to see what you get on your hardware:
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```sh
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zig build benchmark
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```
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---
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## Next Steps
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- **GPU support** — eventually, for large tensor operations. WebGPU is a target.
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- **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.
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---
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## Testing & Benchmarks
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```sh
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zig build test # Run all unit tests
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zig build benchmark # Run performance benchmarks
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```
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---
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## License
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See the repository for license details.
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## GPU support with WebGPU
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Example: https://github.com/seyhajin/webgpu-wasm-zig
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