CultLib/packages/cultmath/README.md

# CultMath

CultMath is the project name. Its clean .NET package identity is
`GameCult.Math`, owned and released from the CultLib monorepo.

Clean-room math shaped for people who think in HLSL.

CultMath provides lowercase vector types, shader-style intrinsics, and native
hot-path kernels so math-heavy renderer code can move between C#, Rust, and HLSL
without turning every line into a translation exercise. It is not a
Unity.Mathematics clone. It is a small, Aquarium-born library built from public
shader semantics.

## Current Surface

- `float2`, `float3`, `float4`
- component-wise arithmetic
- scalar-to-vector splats
- every HLSL swizzle (`xyzw` and `rgba`, repeats readable, non-repeating
  masks writable) and every HLSL mixed constructor, generated by
  `tools/generate-swizzles.ps1`
- conversions to and from `System.Numerics`
- `Random`, a compact deterministic XORShift stream with scalar and vector draws
- `BatchMath` SoA kernels over `Span<float>` / `ReadOnlySpan<float>` using
  `System.Numerics.Vector<float>` when available, including radial falloff
  acceleration and semi-implicit Euler integration
- `math` intrinsics: `radians`, `degrees`, `abs`, `floor`, `ceil`, `frac`,
  `min`, `max`, `clamp`, `saturate`, `lerp`, `step`, `smoothstep`, `dot`,
  `cross`, `length`, `distance`, `normalize`, `reflect`, `csum`, `erf`,
  `erfinv` (scalar only), exponential
  `decay`/`damp`, intercept/segment helpers, Catmull-Rom, Bezier curves, and
  deterministic value-noise primitives
- `shaders/CultMath.hlsl`, a canonical HLSL mirror include for shader-side
  parity. HLSL already owns `float2`, `float3`, and `float4`; the include
  exposes `cultmath_*` functions for shared semantics HLSL does not provide.
  It includes `shaders/CultMath.Phacelle.hlsl` (MPL-2.0) and
  `shaders/CultMath.Interval.hlsl` from the same directory, so ship all three.
- interval arithmetic for culling empty space with a proof: `iv_*` functions
  over `float2(lo, hi)` (`iv_add`, `iv_mul`, `iv_exp`, `iv_smoothstep`, ...)
  and `iv_snoise_ball`/`iv_fbm_ball`, which bound `snoise` and `fbm_grad` over a
  ball, and `iv_frustum_ball`, the ball around a screen tile's rays over a depth
  segment, so one probe serves the whole tile (its radius carries its own
  float32 rounding bound). Every one returns an interval
  containing the function's value at every point of its input, so a raymarch
  can skip a segment whose `hi` is below its cutoff; `cultmath_iv_*` in HLSL.
  The bounds compose with a consumer's own analytic envelope (a height fog, a
  carved sphere): its interval over the segment proves empty space in one probe,
  and the noise ball is consulted only near the surface. See `docs/design.md`,
  "Intervals".
- `shaders/CultMath.glsl` (MIT), the same `cultmath_*` library in GLSL ES 3.00
  for WebGL2, generated from `CultMath.hlsl` (never edited by hand), and
  `shaders/CultMath.Phacelle.glsl` (MPL-2.0), generated from
  `CultMath.Phacelle.hlsl`, which holds `cultmath_phacelle` alone. GLSL has no
  `#include`: a WebGL consumer concatenates `CultMath.glsl` after its own
  `#version 300 es` line and `precision highp float; precision highp int;`
  (the library declares no precision, and its hashes need 32-bit integers),
  then `CultMath.Phacelle.glsl` only if it calls `cultmath_phacelle`, then its
  own shader source.
- `Voronoi.SampleTones`, a C# batch surface that calls the Rust
  `cultmath-core` native kernel when `cultmath_core` is available and falls back
  to the managed parity path otherwise.

## Native Core

The canonical hot-path body lives in `native/cultmath-core`. It exports a C ABI
for batch kernels such as `cultmath_apollonian_voronoi_tones`.

Runtime wrappers own syntax and integration. Rust owns optimized primitive
kernel behavior and parity fixtures.

## Example

```csharp
using CultMath;

float3 normal = math.normalize(new float3(0.25f, 1.0f, -0.1f));
float rim = math.saturate(1.0f - math.dot(normal, new float3(0.0f, 0.0f, -1.0f)));
float glow = math.smoothstep(0.2f, 1.0f, rim);
float grain = math.value_noise_bicubic(math.float2(12.0f, 3.5f));
```

```hlsl
#include "CultMath.hlsl"

float3 normal = normalize(float3(0.25, 1.0, -0.1));
float rim = cultmath_saturate(1.0 - dot(normal, float3(0.0, 0.0, -1.0)));
float glow = cultmath_smoothstep(0.2, 1.0, rim);
float grain = cultmath_value_noise_bicubic(float2(12.0, 3.5));
```

## Provenance

The small spline, damping, and pursuit helpers were promoted from Aetheria's
local `AetheriaMath` surface. The value-noise family follows public shader
literature from Inigo Quilez's noise and mini-spline articles, expressed in
CultMath names with tests instead of copied project-local helper drift.

## Build

```powershell
dotnet build packages/cultmath/src/CultMath/CultMath.csproj
dotnet test packages/cultmath/tests/CultMath.Tests/CultMath.Tests.csproj
cargo test --manifest-path packages/cultmath/native/cultmath-core/Cargo.toml
cargo build --release --manifest-path packages/cultmath/native/cultmath-core/Cargo.toml
.\packages\cultmath\scripts\build-unity-package.ps1
```

## Unity package

CultMath's Unity 2021.3 surface is the tracked precompiled package at
`packages/cultmath/unity/org.gamecult.cultmath`. Unity consumes `CultMath.dll` and the numeric
`CultMath.hlsl`; it does not compile the repository's current-language C# source
tree and does not require a consumer `csc.rsp` workaround.

```json
"org.gamecult.cultmath": "https://github.com/GameCult/CultLib.git?path=/packages/cultmath/unity/org.gamecult.cultmath"
```

The repository root is not a Unity package. Build the tracked package with
`packages/cultmath/scripts/build-unity-package.ps1`; the script fresh-builds the netstandard2.1
assembly and rejects stale binaries, missing metadata, unexpected assemblies,
or leaked C# source.

## Shader Tooling

CultMath keeps portable DXC outside git under `packages/cultmath/.tools/`:

```powershell
.\packages\cultmath\tools\get-dxc.ps1
.\packages\cultmath\tools\get-spirv-cross.ps1
.\packages\cultmath\tools\compile-hlsl-spirv.ps1 `
  -ShaderPath E:\Projects\Odin\crates\muninn-move-tracker\shaders\MoveSphereCandidate.comp.hlsl `
  -OutputPath E:\Projects\Odin\crates\muninn-move-tracker\artifacts\shader\MoveSphereCandidate.comp.spv `
  -IncludePath E:\Projects\CultLib\packages\cultmath\shaders
.\packages\cultmath\tools\compile-spirv-metal.ps1 `
  -SpirvPath E:\Projects\Odin\crates\muninn-move-tracker\artifacts\shader\MoveSphereCandidate.comp.spv `
  -OutputPath E:\Projects\Odin\crates\muninn-move-tracker\artifacts\shader\MoveSphereCandidate.comp.metal
```

DXC emits Vulkan SPIR-V with `-spirv`. `-TargetEnv vulkan1.2` is exposed by the
script, but the current Windows DXC release compiled this shader successfully
with DXC's default Vulkan target while rejecting the dotted target-env value.
The SPIR-V script applies default Vulkan register shifts for cbuffers, textures,
UAVs, and samplers so cross-compiled Metal buffers do not alias by resource
class. SPIRV-Cross emits Metal Shading Language from SPIR-V on Windows; building
an iPad-ready `.metallib` still belongs to Apple's Metal compiler on an Apple
toolchain.

## Doctrine

The goal is mechanical sympathy between CPU-side authoring, native kernels, and
GPU-side shader math. If an intrinsic exists here, it should behave like the
shader concept unless a runtime's numeric rules make that impossible. Weird
deviations get tests and documentation, not folklore.

CultMath is still not a shader generator. Projects should include
`shaders/CultMath.hlsl` directly or add that directory to their shader include
path. If a shared operation needs CPU/GPU parity, put the primitive here and
test it here before copying local math helpers into a renderer or daemon.