CultMath

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
• swizzles for common lanes
• conversions to and from System.Numerics
• 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, 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, including CultMath's safe normalize contract.
• 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

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));

#include "CultMath.hlsl"

float3 normal = cultmath_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

dotnet build CultMath.slnx
dotnet test CultMath.slnx
cargo test --manifest-path native/cultmath-core/Cargo.toml
cargo build --release --manifest-path native/cultmath-core/Cargo.toml

Shader Tooling

CultMath keeps portable DXC outside git under .tools/:

.\tools\get-dxc.ps1
.\tools\get-spirv-cross.ps1
.\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\CultMath\shaders
.\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.