diff --git a/README.md b/README.md index 418ff16..38a94f4 100644 --- a/README.md +++ b/README.md @@ -1,53 +1,66 @@ # dimal — Dimensional Analysis for Zig -A comptime-first dimensional analysis module for Zig. If you try to add meters to seconds, **it won't compile**. That's the point. +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. -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. +If you try to add meters to seconds, it won't compile. That's the point. > **Source:** [git.bouvais.lu/adrien/zig-dimal](https://git.bouvais.lu/adrien/zig-dimal) > **Minimum Zig version:** `0.16.0` --- +## 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 -- **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. +- **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. -* **Full SI prefix & Imperial support** — `pico` through `peta`, plus common Imperial units like `inch`, `ft`, `mi`, `lb`, and `oz`. -- **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. -- **Comparison operations** — `eq`, `ne`, `gt`, `gte`, `lt`, `lte` on both `Scalar` and `Vector`, with automatic scale resolution. -- **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. -- **`abs`, `pow`, `sqrt`** — unary operations with correct dimension tracking (`pow(2)` on `L¹` → `L²`, etc.). -- **Vector geometry** — `dot` product (returns a `Scalar`), `cross` product (Vec3 only), element-wise `product` (all components multiplied). -- **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!). +- **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` | -| `Tp` | Temperature | `K` | -| `N` | Amount of Substance | `mol` | -| `J` | Luminous Intensity | `cd` | +| 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. Fetch the dependency +### 1. Add the dependency (Zig 0.14+) ```sh -zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#0.1.1 +zig fetch --save git+https://git.bouvais.lu/adrien/zig-dimal#0.2.0 ``` ### 2. Wire it up in `build.zig` @@ -57,287 +70,181 @@ const std = @import("std"); pub fn build(b: *std.Build) void { const target = b.standardTargetOptions(.{}); - const dimal = b.dependency("dimal", .{}).module("dimal"); + const optimize = b.standardOptimizeOption(.{}); + + const dimal = b.dependency("dimal", .{ + .target = target, + .optimize = optimize, + }).module("dimal"); 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, - }}, - }), + .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 in your code +### 3. Import and use ```zig const dma = @import("dimal"); -const Scalar = dma.Scalar; -const Dimensions = dma.Dimensions; -const Scales = dma.Scales; +const Tensor = dma.Tensor; +const Base = dma.Base; ``` --- -## Quick Start +## Quick Example: Lunar Descent -### Defining unit types - -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. +Simulate a spacecraft descending to the Moon with correct physics and type safety: ```zig -const Meter = Scalar(f64, .{ .L = 1 }, .{}); -const NanoMeter = Scalar(i64, .{ .L = 1 }, .{ .L = .n }); -const KiloMeter = Scalar(f64, .{ .L = 1 }, .{ .L = .k }); -const Second = Scalar(f64, .{ .T = 1 }, .{}); -const Velocity = Scalar(f64, .{ .L = 1, .T = -1 }, .{}); -const Kmh = Scalar(f64, .{ .L = 1, .T = -1 }, .{ .L = .k, .T = .hour }); +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 }); +} ``` -Or use the pre-built helpers from `dma.Base`: - -```zig -const Acceleration = dma.Base.Acceleration.Of(f64); -const KmhSpeed = dma.Base.Speed.Scaled(f64, .{ .L = .k, .T = .hour }); +**Output:** ``` - -### 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.mul(time); // → Meter -const d2 = accel.mul(time).mul(time).mul(0.5); // → Meter (bare 0.5 is dimensionless) -const dist = d1.add(d2); - -const v_final = v0.add(accel.mul(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" -``` - -#### Imperial - -```zig -const Inch = Scalar(f64, .{ .L = 1 }, .{ .L = .inch }); -const Mile = Scalar(f64, .{ .L = 1 }, .{ .L = .mi }); -const Pound = Scalar(f64, .{ .M = 1 }, .{ .M = .lb }); - -// Conversion example -const dist_m = Meter{ .value = 1609.344 }; -const dist_mi = dist_m.to(Mile); // Result: 1.0 -``` - -### Arithmetic with bare numbers - -Passing a `comptime_int`, `comptime_float`, or plain `T` to `mul` / `div` treats it as a dimensionless value. Dimensions pass through unchanged. - -```zig -const Meter = Scalar(f64, .{ .L = 1 }, .{}); -const d = Meter{ .value = 6.0 }; - -const half = d.mul(0.5); // comptime_float → still Meter -const doubled = d.mul(2); // comptime_int → still Meter -const factor: f64 = 3.0; -const tripled = d.mul(factor); // runtime f64 → still Meter -``` - -### Comparisons - -`eq`, `ne`, `gt`, `gte`, `lt`, `lte` work on any two `Scalar` values of the **same dimension**. Scales are resolved automatically before comparing. - -```zig -const Meter = Scalar(i64, .{ .L = 1 }, .{}); -const KiloMeter = Scalar(i64, .{ .L = 1 }, .{ .L = .k }); - -const m1000 = Meter{ .value = 1000 }; -const km1 = KiloMeter{ .value = 1 }; -const km2 = KiloMeter{ .value = 2 }; - -_ = m1000.eq(km1); // true — same magnitude -_ = km2.gt(m1000); // true — 2 km > 1000 m -_ = m1000.lte(km2); // true - -// Comparing with a bare number works when the scalar is dimensionless. -// Comparing incompatible dimensions is a compile error. -``` - -### Unary operations: `abs`, `pow`, `sqrt` - -```zig -const Meter = Scalar(f64, .{ .L = 1 }, .{}); -const d = Meter{ .value = -4.0 }; - -const magnitude = d.abs(); // 4.0 m — dimension unchanged -const area = d.pow(2); // 16.0 m² — dims scaled by exponent -const side = area.sqrt(); // 4.0 m — dims halved (requires even exponents) -``` - -`pow` accepts any `comptime_int` exponent and adjusts the dimension exponents accordingly. `sqrt` is a compile error unless all dimension exponents are even. - -### Working with Vectors - -Every `Scalar` type exposes a `.Vec3` alias and a generic `.Vec(n)` type accessor: - -```zig -const Vec3Meter = Meter.Vec3; // equivalent to Vector(3, Meter) - -const pos = Vec3Meter{ .data = .{ 100, 200, 300 } }; -const t = Second{ .value = 10 }; - -const vel = pos.divScalar(t); // → Vec3 of Velocity (m/s) -std.debug.print("{d}\n", .{vel}); // (10, 20, 30)m.s⁻¹ -``` - -#### Dot and cross products - -```zig -const Newton = Scalar(f32, .{ .M = 1, .L = 1, .T = -2 }, .{}); - -const r = Meter.Vec3{ .data = .{ 10.0, 0.0, 0.0 } }; -const force = Newton.Vec3{ .data = .{ 5.0, 5.0, 0.0 } }; - -// Dot product — returns a Scalar (dimensions summed) -const work = force.dot(r); // 50.0 J (M¹L²T⁻²) - -// Cross product — returns a Vec3 (dimensions summed, Vec3 only) -const torque = r.cross(force); // (0, 0, 50) N·m -``` - -#### Vector comparisons - -Element-wise comparisons return `[len]bool`. Whole-vector equality uses `eqAll` / `neAll`. A single scalar can be broadcast with the `*Scalar` variants. - -```zig -const positions = Meter.Vec3{ .data = .{ 500.0, 1200.0, 3000.0 } }; -const threshold = KiloMeter{ .value = 1.0 }; // 1 km - -const exceeded = positions.gtScalar(threshold); // [false, true, true] -const eq_each = positions.eq(positions); // [true, true, true] (element-wise) -const all_same = positions.eqAll(positions); // true (whole-vector) -``` - -#### Other Vector operations - -```zig -const v = Meter.Vec3{ .data = .{ -2.0, 3.0, -4.0 } }; - -const v_abs = v.abs(); // { 2, 3, 4 } m -const vol = v_abs.product(); // 24 m³ (dims × len) -const area = v_abs.pow(2); // { 4, 9, 16 } m² -const sides = area.sqrt(); // { 2, 3, 4 } m (element-wise sqrt) +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 Reference +## API Overview -### `Scalar(T, dims, scales)` +### Tensors -| Method | Description | -|---|---| -| `.add(rhs)` | Add two quantities of the same dimension. Auto-converts scales. | -| `.sub(rhs)` | Subtract. Auto-converts scales. | -| `.mul(rhs)` | Multiply — dimensions are **summed**. `rhs` may be a `Scalar`, `T`, `comptime_int`, or `comptime_float` (bare numbers are dimensionless). | -| `.div(rhs)` | Divide — dimensions are **subtracted**. Same `rhs` flexibility as `mul`. | -| `.abs()` | Absolute value. Dimensions and scales unchanged. | -| `.pow(exp)` | Raise to a `comptime_int` exponent. Dimension exponents are multiplied by `exp`. | -| `.sqrt()` | Square root. Compile error unless all dimension exponents are even. | -| `.eq(rhs)` / `.ne(rhs)` | Equality / inequality comparison. Scales auto-resolved. | -| `.gt(rhs)` / `.gte(rhs)` | Greater-than / greater-than-or-equal. | -| `.lt(rhs)` / `.lte(rhs)` | Less-than / less-than-or-equal. | -| `.to(DestType)` | Convert to another unit of the same dimension. Compile error on mismatch. | -| `.vec(len)` | Return a `Vector(len, Self)` with all components set to this value. | -| `.vec3()` | Shorthand for `.vec(3)`. | -| `.Vec3` | Type alias for `Vector(3, Self)`. | +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. -### `Vector(len, Q)` +```zig +// Scalar: 1-element tensor +const Meter = Tensor(f64, .{.L = 1}, .{}, &.{1}); +const m = Meter{ .data = @splat(5.0) }; -| Method | Description | -|---|---| -| `.add(rhs)` / `.sub(rhs)` | Element-wise add / subtract. | -| `.mul(rhs)` / `.div(rhs)` | Element-wise multiply / divide (both operands are Vectors). | -| `.mulScalar(s)` / `.divScalar(s)` | Scale every component by a single `Scalar`, `T`, `comptime_int`, or `comptime_float`. | -| `.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 +``` --- diff --git a/docs/index.md b/docs/index.md index 3aeb3d3..38a94f4 100644 --- a/docs/index.md +++ b/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.