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

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 = 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 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.

"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/:

.\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.