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+# zig_units
+
+**Compile-time dimensional analysis for Zig.**
+
+`zig_units` lets you attach physical units to numeric values so that
+dimension mismatches become *compile errors* rather than silent bugs.
+At runtime a `Quantity` is nothing but a single number — zero overhead.
+
+```
+velocity = distance / time   →  L¹T⁻¹  ✓
+force    = mass + velocity   →  compile error: M¹ ≠ L¹T⁻¹
+```
+
+Requires **Zig 0.16** or later.
+
+---
+
+## Features
+
+- Seven SI base dimensions (`L M T I Tp N J`)
+- Full SI prefix support (`P T G M k h da d c m u n p f`)
+- Custom time aliases (`.min`, `.hour`, `.year`)
+- Automatic scale conversion on add/sub (finer unit wins)
+- `Quantity(T, dims, scales)` — scalar, any numeric backing type
+- `QuantityVec3` — three-component vector with the same guarantees
+- Unicode superscript formatting (`9.81m.s⁻²`)
+- Integer-safe square root for `Vec3.length()`
+- All dimension tracking happens at `comptime` — no runtime cost
+
+---
+
+## Installation
+
+### Add as a Zig dependency
+
+```bash
+zig fetch --save https://github.com/YOUR_USERNAME/zig_units/archive/refs/heads/main.tar.gz
+```
+
+This adds an entry to your `build.zig.zon`.  Then wire it up in your
+`build.zig`:
+
+```zig
+const zig_units = b.dependency("zig_units", .{
+    .target  = target,
+    .optimize = optimize,
+});
+my_module.addImport("zig_units", zig_units.module("zig_units"));
+```
+
+### Local path (monorepo / development)
+
+```zig
+// build.zig.zon
+.dependencies = .{
+    .zig_units = .{ .path = "../zig_units" },
+},
+```
+
+---
+
+## Quick start
+
+```zig
+const units     = @import("zig_units");
+const Quantity  = units.Quantity;
+const Dims      = units.Dimensions;
+const Scales    = units.Scales;
+
+// Define named unit types
+const Meter    = Quantity(f32, Dims.init(.{ .L = 1 }),           Scales.init(.{}));
+const KiloMeter= Quantity(f32, Dims.init(.{ .L = 1 }),           Scales.init(.{ .L = .k }));
+const Second   = Quantity(f32, Dims.init(.{ .T = 1 }),           Scales.init(.{}));
+const MPerSec  = Quantity(f32, Dims.init(.{ .L = 1, .T = -1 }), Scales.init(.{}));
+
+const dist = Meter{ .value = 100.0 };
+const t    = Second{ .value = 5.0 };
+
+// Dimension is tracked automatically — vel has type L¹T⁻¹
+const vel = dist.divBy(t);
+
+// Convert to an explicit type (same dims required, compile error otherwise)
+const vel2 = vel.to(MPerSec);
+
+// Cross-scale addition: km + m → result in metres (finer scale)
+const km  = KiloMeter{ .value = 1.0 };
+const sum = km.add(dist);   // 1100 m
+```
+
+---
+
+## API reference
+
+### `Quantity(T, dims, scales)`
+
+| Member | Kind | Description |
+|---|---|---|
+| `value` | field | The raw numeric value |
+| `ValueType` | comptime | Alias for `T` |
+| `dims` | comptime | The `Dimensions` of this type |
+| `scales` | comptime | The `Scales` of this type |
+| `Vec3` | comptime | The matching `QuantityVec3` type |
+| `add(rhs)` | fn | Same-dimension addition, finer scale |
+| `sub(rhs)` | fn | Same-dimension subtraction, finer scale |
+| `mulBy(rhs)` | fn | Multiplication, dims are added |
+| `divBy(rhs)` | fn | Division, dims are subtracted |
+| `scale(s: T)` | fn | Dimensionless scalar multiply |
+| `to(Dest)` | fn | Convert to another `Quantity` type (same dims) |
+| `vec3()` | fn | Broadcast scalar to a `Vec3` |
+| `format(writer)` | fn | Print `value + unit string` |
+
+### `QuantityVec3`
+
+Obtained via `SomeQuantity.Vec3`.
+
+| Member | Kind | Description |
+|---|---|---|
+| `x, y, z` | fields | The three components |
+| `zero` | comptime | `(0, 0, 0)` |
+| `one` | comptime | `(1, 1, 1)` |
+| `initDefault(v)` | fn | Broadcast scalar to all components |
+| `add(rhs)` | fn | Component-wise addition |
+| `sub(rhs)` | fn | Component-wise subtraction |
+| `mulBy(rhs)` | fn | Component-wise element-wise multiply |
+| `divBy(rhs)` | fn | Component-wise element-wise divide |
+| `mulByScalar(q)` | fn | Multiply by a scalar `Quantity` |
+| `divByScalar(q)` | fn | Divide by a scalar `Quantity` |
+| `scale(s: T)` | fn | Dimensionless scalar multiply |
+| `negate()` | fn | Negate all components |
+| `to(DestQ)` | fn | Convert to another vector quantity type |
+| `lengthSqr()` | fn | Squared Euclidean length (no sqrt) |
+| `length()` | fn | Euclidean length (integer-safe) |
+| `format(writer)` | fn | Print `(x, y, z) + unit string` |
+
+### `Dimensions`
+
+A comptime struct storing a signed exponent per SI base dimension.
+
+```zig
+const Dims = @import("zig_units").Dimensions;
+
+// Acceleration: L¹ T⁻²
+const accel_dims = Dims.init(.{ .L = 1, .T = -2 });
+```
+
+| Function | Description |
+|---|---|
+| `init(struct_literal)` | Create from named exponents; unset dims default to 0 |
+| `initFill(val: i8)` | Set all exponents to `val` |
+| `get(dim)` | Read a single exponent |
+| `set(dim, val)` | Write a single exponent |
+| `add(a, b)` | Component-wise sum (for `mulBy`) |
+| `sub(a, b)` | Component-wise difference (for `divBy`) |
+| `eql(a, b)` | Equality check |
+| `str()` | Comptime human-readable string, e.g. `"L1T-2"` |
+
+### `Scales`
+
+A comptime struct storing a `UnitScale` per SI base dimension.
+
+```zig
+const Scales = @import("zig_units").Scales;
+
+// Kilometres per nanosecond
+const spd_scales = Scales.init(.{ .L = .k, .T = .n });
+```
+
+| `UnitScale` variant | Factor |
+|---|---|
+| `.P` | ×10¹⁵ |
+| `.T` | ×10¹² |
+| `.G` | ×10⁹ |
+| `.M` | ×10⁶ |
+| `.k` | ×10³ |
+| `.h` | ×10² |
+| `.da` | ×10¹ |
+| `.none` | ×1 |
+| `.d` | ×10⁻¹ |
+| `.c` | ×10⁻² |
+| `.m` | ×10⁻³ |
+| `.u` | ×10⁻⁶ |
+| `.n` | ×10⁻⁹ |
+| `.p` | ×10⁻¹² |
+| `.f` | ×10⁻¹⁵ |
+| `.min` | ×60 (seconds) |
+| `.hour` | ×3 600 |
+| `.year` | ×31 536 000 |
+
+---
+
+## Examples
+
+### Kinematics
+
+```zig
+const Meter  = Quantity(f64, Dims.init(.{ .L = 1 }),           Scales.init(.{}));
+const Second = Quantity(f64, Dims.init(.{ .T = 1 }),           Scales.init(.{}));
+
+const pos  = Meter{ .value = 200.0 };
+const time = Second{ .value = 8.0 };
+
+const vel  = pos.divBy(time);        // L¹T⁻¹  — 25 m/s
+const accel = vel.divBy(time);       // L¹T⁻²  — 3.125 m/s²
+```
+
+### Cross-scale addition
+
+```zig
+const KM = Quantity(i64, Dims.init(.{ .L = 1 }), Scales.init(.{ .L = .k }));
+const M  = Quantity(i64, Dims.init(.{ .L = 1 }), Scales.init(.{}));
+
+const a = KM{ .value = 2 };   // 2 km
+const b = M{ .value = 500 };  // 500 m
+
+const sum = a.add(b);          // result scale = metres (finer) → 2500 m
+```
+
+### Time conversion
+
+```zig
+const Hour   = Quantity(i64, Dims.init(.{ .T = 1 }), Scales.init(.{ .T = .hour }));
+const Minute = Quantity(i64, Dims.init(.{ .T = 1 }), Scales.init(.{ .T = .min  }));
+const Second = Quantity(i64, Dims.init(.{ .T = 1 }), Scales.init(.{}));
+
+const h   = Hour{ .value = 2 };
+const min = h.to(Minute);     // 120
+const sec = min.to(Second);   // 7200
+```
+
+### Vec3 velocity
+
+```zig
+const Meter  = Quantity(f32, Dims.init(.{ .L = 1 }), Scales.init(.{}));
+const Second = Quantity(f32, Dims.init(.{ .T = 1 }), Scales.init(.{}));
+
+const pos  = Meter.Vec3{ .x = 30.0, .y = 60.0, .z = 90.0 };
+const time = Second{ .value = 3.0 };
+
+const vel  = pos.divByScalar(time);   // Vec3 with dims L¹T⁻¹
+const dist = vel.length();            // Euclidean length
+```
+
+### Dimension mismatch — compile error
+
+```zig
+const Meter  = Quantity(f32, Dims.init(.{ .L = 1 }), Scales.init(.{}));
+const Second = Quantity(f32, Dims.init(.{ .T = 1 }), Scales.init(.{}));
+
+const d = Meter{ .value = 5.0 };
+const t = Second{ .value = 2.0 };
+
+// This will NOT compile:
+const bad = d.add(t);  // error: Dimension mismatch in add: L1 vs T1
+```
+
+---
+
+## Running the tests
+
+```bash
+zig build test
+```
+
+The test suite covers scalar and vector arithmetic, cross-scale operations,
+conversion chains, negative values, formatting, and an optional benchmark
+(`"Comprehensive Benchmark: All Ops × All Types"`).
+
+---
+
+## Project layout
+
+```
+zig_units/
+├── build.zig          # Build script; exposes the "zig_units" module
+├── build.zig.zon      # Package manifest
+├── src/
+│   ├── main.zig       # Quantity, QuantityVec3, tests
+│   ├── Dimensions.zig # SI base dimensions + comptime arithmetic
+│   ├── Scales.zig     # SI prefixes + scale helpers
+│   └── helper.zig     # Internal utilities (isInt, printSuperscript)
+└── README.md
+```
+
+---
+
+## Design notes
+
+**Why comptime parameters?**  Zig's `comptime` means the compiler can
+evaluate all dimension arithmetic before any machine code is generated.
+Two quantities with mismatched dimensions simply fail to compile —
+there is no runtime overhead and no need for exception handling.
+
+**Scale selection on arithmetic.**  When two operands have different
+scales (e.g. km and m), `zig_units` automatically picks the finer
+(smaller-factor) scale for the result.  This prevents silent precision
+loss at the cost of an automatic rescaling of both operands.
+
+**Integer backing types.**  Division uses an `f64` intermediate and
+rounds back to the integer type.  For best accuracy, prefer `f32`/`f64`
+for quantities that will be divided frequently.
+
+---
+
+## License
+
+MIT — see `LICENSE` for details.