fix(determinism): own sin/cos on the world path -- same world on every CPU, 3.5% faster

On Win64, FMath::Sin/Cos resolve to CRT sinf/cosf (GenericPlatformMath.h:521/530; no platform
override), and the UCRT picks FMA3 or non-FMA3 implementations at startup by CPU. /fp:precise
closed only the compiler half, so the same build and seed could build a slightly different world
on two Windows PCs, and on Linux.

- VoxelMath::DetSin/DetCos/DetSinCos (VoxelTypes.h): fixed double-precision period reduction to
  a quarter period, then fixed float minimax polynomials; no CRT, FMath or CPU-dependent
  intrinsic. Measured max error vs sinf 5.96e-8 over the used range (|arg| <= 6.19).
- Every world-deciding FMath::Sin/Cos replaced (generator, op stacks, cave morphology, strate
  manager, content placement, strate measure); none remain in runtime code.
- Pinned test VoxelForge.Determinism.DetSinCos (golden bit patterns + error bound).
- Diagnostic start-up switch -voxel.CrtFma3=0 (Windows) forces the CRT's non-FMA3 path.
- Parse-once console switches now initialise in StartupModule on the game thread; workers only
  read them (was an unsynchronised first parse inside GetDensityAt).
- Corrected the CRC comment that claimed a CRC32 cannot give a false positive.

Proof (Codex round; orchestrator re-checked):
- Before the fix, FMA3 on vs off was identical on this Ryzen 7 5800X3D: the hole exists but was
  not observed in this world. After the fix, the canonical exports are byte-identical with
  FMA3 on and off.
- The world changed once, as expected. New canonical export SHA-256 CBB8AE18...906F (geometry
  B9EF84AC; was B3E5F4C3...377); worms region 9242C093 (was 311CA42C), walk OBJ 20CCF7BD....
  Triangle counts unchanged in every tile. Order-independent nearest-vertex distance, worms
  region: max 8.7 micrometres (the reported "11.4 m" was a line-order artefact of a line-by-line
  OBJ diff); export region max 3e-5 m.
- Capability exact: player-fit 20,830, walk-reachable 10,909, connected. TilePostReachProof,
  sealed-proof, cross-platform and strate-crossing tests pass.
- Performance, headless game path, S/M/S/M vs the committed-tip DLL: static worker 27.41 s vs
  28.44 s (-3.6%), moving 59.59 s vs 61.74 s (-3.5%); LOD0 p50/p95 not worse.

From Sol's code review (DESIGN-SOL-2026-09-15-CODE.md, section 4.1), branch sol/deterministic-math.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01TaFdXhTdYMkW1xrV6ApT6Y

Source/VoxelForge/Private/VoxelCaveMorphology.cpp

@@ -2928,7 +2928,7 @@ namespace
         const int32 MaxDownwardSearchCells = FMath::CeilToInt(
             static_cast<float>(MaxStepHeightVoxelsReal));
         const float MaxStepHeightVoxels = static_cast<float>(MaxStepHeightVoxelsReal);
-        const float MinimumWalkableNormalZ = FMath::Cos(FMath::DegreesToRadians(
+        const float MinimumWalkableNormalZ = VoxelMath::DetCos(FMath::DegreesToRadians(
             Settings.PlayerWalkableFloorAngleDegrees));
 
         TArray<float> SupportHeights;
@@ -3263,7 +3263,9 @@ namespace
             const float DirectionAngle = VoxelHash::ToFloat01(
                 VoxelHash::Mix(Site.Hash ^ 0xCAFEBABEu)) * 2.0f * PI;
             const float StretchDistance = Site.RadiusXY * 0.7f;
-            const FVector Direction(FMath::Cos(DirectionAngle), FMath::Sin(DirectionAngle), 0.0f);
+            float SinDirection = 0.0f, CosDirection = 0.0f;
+            VoxelMath::DetSinCos(SinDirection, CosDirection, DirectionAngle);
+            const FVector Direction(CosDirection, SinDirection, 0.0f);
             RoomSDF = VoxelSDF::Capsule(
                 Position,
                 Site.Center + Direction * StretchDistance,
@@ -6823,7 +6825,7 @@ void VoxelCaveMorphology::BuildChunkCache(
                 {
                     const float T = static_cast<float>(ControlIndex)
                         / static_cast<float>(WanderSegments);
-                    const float Envelope = FMath::Sin(T * PI);
+                    const float Envelope = VoxelMath::DetSin(T * PI);
                     FVector WorldControlPoint = FMath::Lerp(WorldEndA, WorldEndB, T);
                     const float RadiusBase = FMath::Lerp(RadA, RadB, T);
                     float ControlRadius = RadiusBase;
@@ -6840,7 +6842,7 @@ void VoxelCaveMorphology::BuildChunkCache(
                         // serpentine route without moving either mouth.
                         const float Side = RawSide * 0.65f + PreviousSide * 0.35f;
                         const float WindWave = bNeedsWind
-                            ? FMath::Sin(static_cast<float>(WindWaves) * PI * T)
+                            ? VoxelMath::DetSin(static_cast<float>(WindWaves) * PI * T)
                                 * WindAmplitude * Envelope
                                 * ((LedgeChoiceHash & 1u) != 0u ? 1.0f : -1.0f)
                             : 0.0f;
@@ -7364,7 +7366,9 @@ void VoxelCaveMorphology::BuildChunkCache(
                 CR.ShapeType = 2;
                 const float DirAngle = VoxelHash::ToFloat01(VoxelHash::Mix(CR.Hash ^ 0xCAFEBABEu)) * 2.0f * PI;
                 const float StretchDist = CR.RadiusXY * 0.7f;
-                const FVector Dir(FMath::Cos(DirAngle), FMath::Sin(DirAngle), 0.0f);
+                float SinDir = 0.0f, CosDir = 0.0f;
+                VoxelMath::DetSinCos(SinDir, CosDir, DirAngle);
+                const FVector Dir(CosDir, SinDir, 0.0f);
                 CR.ShapeA = CR.Center + Dir * StretchDist;
                 CR.ShapeB = CR.Center - Dir * StretchDist;
                 CR.ShapeR = FMath::Min(CR.RadiusXY * 0.6f, CR.RadiusZ);
@@ -7484,8 +7488,8 @@ void VoxelCaveMorphology::BuildChunkCache(
                 const float Angle = VoxelHash::ToFloat01(AH4) * PI;
                 const float HalfSpan = CR.RadiusXY
                     * (0.5f + VoxelHash::ToFloat01(VoxelHash::Mix(AH4)) * 0.35f);
-                const float CosA = FMath::Cos(Angle);
-                const float SinA = FMath::Sin(Angle);
+                float SinA = 0.0f, CosA = 0.0f;
+                VoxelMath::DetSinCos(SinA, CosA, Angle);
                 FCachedArch& Arch = CR.Arches[i];
                 Arch.bActive = true;
                 Arch.EndpointA = FVector(ArcCX - CosA * HalfSpan,
@@ -7517,8 +7521,7 @@ void VoxelCaveMorphology::BuildChunkCache(
                 Pinch.CenterX = PnX;
                 Pinch.CenterY = PnY;
                 Pinch.CenterZ = PnZ;
-                Pinch.CosAngle = FMath::Cos(PnAngle);
-                Pinch.SinAngle = FMath::Sin(PnAngle);
+                VoxelMath::DetSinCos(Pinch.SinAngle, Pinch.CosAngle, PnAngle);
                 Pinch.MaxExtent = FMath::Max(
                     FeatureParams.PinchLength, FeatureParams.PinchStrength) + 5.0f;
                 Pinch.HalfLength = FeatureParams.PinchLength * 0.5f;