347 lines
13 KiB
Markdown
347 lines
13 KiB
Markdown
# 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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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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> **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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## 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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- **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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---
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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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| `Tp` | 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. Fetch the dependency
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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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```
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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 dimal = b.dependency("dimal", .{}).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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.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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});
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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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```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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```
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---
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## Quick Start
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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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```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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Or use the pre-built helpers from `dma.Base`:
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```zig
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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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```
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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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```
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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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```
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---
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## API Reference
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### `Scalar(T, dims, scales)`
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| Method | Description |
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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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### `Vector(len, Q)`
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| Method | Description |
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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. |
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| `.cross(rhs)` | Cross product → `Vector(3, …)`. Vec3 only. |
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| `.abs()` | Element-wise absolute value. |
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| `.pow(exp)` | Element-wise `comptime_int` power. Dimension exponents scaled. |
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| `.sqrt()` | Element-wise square root. |
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| `.product()` | Multiply all components → `Scalar` with dimensions × `len`. |
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| `.negate()` | Negate all components. |
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| `.length()` | Euclidean length (returns `T`). |
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| `.lengthSqr()` | Sum of squared components (returns `T`). Cheaper than `length`. |
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| `.eq(rhs)` / `.ne(rhs)` | Element-wise comparison → `[len]bool`. |
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| `.gt(rhs)` / `.gte(rhs)` / `.lt(rhs)` / `.lte(rhs)` | Element-wise ordered comparisons → `[len]bool`. |
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| `.eqAll(rhs)` / `.neAll(rhs)` | Whole-vector equality / inequality → `bool`. |
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| `.eqScalar(s)` / `.neScalar(s)` | Broadcast scalar comparison → `[len]bool`. |
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| `.gtScalar(s)` / `.gteScalar(s)` / `.ltScalar(s)` / `.lteScalar(s)` | Broadcast ordered scalar comparisons → `[len]bool`. |
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| `.to(DestQ)` | Convert all components to a compatible scalar type. |
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### `dma.Base` — Pre-built quantities
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Call `.Of(T)` for base-unit scalars, `.Scaled(T, scales)` for custom scales:
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`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.
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### `Scales` — SI and Imperial Units
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| Tag | Factor (Relative to Base) | Type |
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|---|---|---|
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| `.P` ... `.f` | $10^{15}$ ... $10^{-15}$ | SI Prefixes |
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| `.min`, `.hour`, `.year` | 60, 3600, 31,536,000 | Time |
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| **`.inch`** | **0.0254** | Imperial Length (m) |
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| **`.ft`** | **0.3048** | Imperial Length (m) |
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| **`.yd`** | **0.9144** | Imperial Length (m) |
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| **`.mi`** | **1609.344** | Imperial Length (m) |
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| **`.oz`** | **28.3495231** | Imperial Mass (g) |
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| **`.lb`** | **453.59237** | Imperial Mass (g) |
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| **`.st`** | **6350.29318** | Imperial Mass (g) |
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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.
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---
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## Running Tests and Benchmarks
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```sh
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zig build test
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zig build benchmark
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```
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Benchmark results are very welcome — feel free to share yours!
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---
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## Roadmap / Known Limitations
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- SIMD acceleration for `Vector` operations.
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- Some paths may still fall back to runtime computation — optimization ongoing.
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- More test coverage.
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---
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## License
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See the repository for license details.
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