0a5f4bf571
Seven values change: four snoise(float3) in HlslSemanticsTests and three snoise(float2) in MathTests (the 2D (0,0) golden is 0 either way). Regenerated from the code after the continuity probe passed. The tests no longer claim to match Unity.Mathematics, whose snoise keeps the old constants. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
526 lines
20 KiB
C#
526 lines
20 KiB
C#
using CultMath;
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using Xunit;
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namespace CultMath.Tests;
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public sealed class MathTests
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{
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[Fact]
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public void FracMatchesShaderStylePositiveAndNegativeValues()
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{
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Assert.Equal(0.25f, math.frac(1.25f));
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Assert.Equal(0.75f, math.frac(-1.25f));
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}
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// Expected values come from a Python transcription of the paper's pcg3d/pcg4d (JCGT 9(3) 2020, p. 32) and
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// O'Neill's pcg_output_rxs_m_xs_32_32 with PCG_DEFAULT_MULTIPLIER_32/INCREMENT_32, independent of this code.
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[Fact]
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public void PcgHashesMatchReferenceTranscription()
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{
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static int3 U3(uint x, uint y, uint z) => new((int)x, (int)y, (int)z);
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static int4 U4(uint x, uint y, uint z, uint w) => new((int)x, (int)y, (int)z, (int)w);
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Assert.Equal(0x07BB2FE2u, math.pcg(0u));
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Assert.Equal(0xA8BEEA3Cu, math.pcg(1u));
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Assert.Equal(0x995312E1u, math.pcg(0x12345678u));
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Assert.Equal(0xE62A4902u, math.pcg(0xFFFFFFFFu));
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Assert.Equal(U3(0x9BAFD7C6u, 0xA8E88A6Bu, 0x3F15482Cu), math.pcg3d(new int3(0, 0, 0)));
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Assert.Equal(U3(0xFA9F79A6u, 0x48F2F44Cu, 0x596F5AB1u), math.pcg3d(new int3(1, 2, 3)));
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Assert.Equal(U3(0x67DCF282u, 0x49E87E17u, 0x10018917u), math.pcg3d(U3(0xFFFFFFFFu, 0x80000000u, 0x7FFFFFFFu)));
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Assert.Equal(U4(0x0F02F829u, 0x2D568769u, 0x32B0C43Bu, 0xD32548EAu), math.pcg4d(new int4(0, 0, 0, 0)));
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Assert.Equal(U4(0x3622CD16u, 0xF11471D8u, 0xE1109B3Fu, 0x02B94C2Fu), math.pcg4d(new int4(1, 2, 3, 4)));
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Assert.Equal(U4(0x72180037u, 0x81D493E6u, 0xD9BA7226u, 0x14C9ABA7u), math.pcg4d(U4(0xFFFFFFFFu, 0x80000000u, 0x7FFFFFFFu, 0xDEADBEEFu)));
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Assert.Equal(U3(0xA7B40FEEu, 0x9B70DFC0u, 0x3106C2C5u), math.pcg3d(new float3(1.5f, -2.25f, 1e7f)));
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Assert.Equal(U3(0x5A09E5C6u, 0x53EC0DABu, 0x4BE4A1ECu), math.pcg3d(new float2(3.0f, 4.0f)));
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Assert.Equal(U4(0x1849E380u, 0xF199DEE0u, 0x6C6B4934u, 0x34AF16DFu),
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math.pcg4d(new float4(-0.0f, BitConverter.Int32BitsToSingle(0x7FC00000), 0.5f, 1e-7f)));
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}
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[Fact]
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public void Pcg3dSeparatesAPositionGrid()
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{
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// A single 32-bit component is subject to birthday collisions (x has one here); the full output is distinct.
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var hashes = new HashSet<int3>();
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for (var i = 0; i < 100; i++)
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for (var j = 0; j < 100; j++)
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hashes.Add(math.pcg3d(new float2(i * 0.5f - 25.0f, j * 0.5f - 25.0f)));
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Assert.Equal(10000, hashes.Count);
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}
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[Fact]
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public void VectorOperationsAreComponentWise()
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{
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var value = new float3(1.0f, 2.0f, 3.0f) * new float3(4.0f, 5.0f, 6.0f);
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Assert.Equal(new float3(4.0f, 10.0f, 18.0f), value);
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}
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[Fact]
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public void VectorConstructorsAcceptLowerDimensionVectors()
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{
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Assert.Equal(new int2(1, 2), math.int2(1, 2));
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Assert.Equal(new float2(1.0f, 2.0f), math.float2(1.0f, 2.0f));
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Assert.Equal(new float3(1.0f, 1.0f, 1.0f), math.float3(1.0f));
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Assert.Equal(new float4(1.0f, 2.0f, 3.0f, 4.0f), math.float4(new float3(1.0f, 2.0f, 3.0f), 4.0f));
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Assert.Equal(new float3(1.0f, 2.0f, 3.0f), new float3(new float2(1.0f, 2.0f), 3.0f));
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Assert.Equal(new float4(1.0f, 2.0f, 3.0f, 4.0f), new float4(new float2(1.0f, 2.0f), 3.0f, 4.0f));
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Assert.Equal(new float4(1.0f, 2.0f, 3.0f, 4.0f), new float4(new float3(1.0f, 2.0f, 3.0f), 4.0f));
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}
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[Fact]
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public void VectorsExposeCommonSwizzles()
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{
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Assert.Equal(new float3(2.0f, 3.0f, 1.0f), new float3(1.0f, 2.0f, 3.0f).yzx);
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Assert.Equal(new float3(3.0f, 2.0f, 1.0f), new float3(1.0f, 2.0f, 3.0f).zyx);
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Assert.Equal(new float2(3.0f, 2.0f), new float3(1.0f, 2.0f, 3.0f).zy);
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Assert.Equal(new float3(1.0f, 2.0f, 4.0f), new float4(1.0f, 2.0f, 3.0f, 4.0f).xyw);
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Assert.Equal(new float3(2.0f, 3.0f, 1.0f), new float4(1.0f, 2.0f, 3.0f, 4.0f).yzx);
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Assert.Equal(new float4(1.0f, 2.0f, 3.0f, 4.0f), new float4(1.0f, new float3(2.0f, 3.0f, 4.0f)));
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Assert.Equal(new float4(1.0f, 2.0f, 3.0f, 4.0f), math.float4(1.0f, new float3(2.0f, 3.0f, 4.0f)));
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}
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[Fact]
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public void VectorsSupportUnityStyleFieldAndSwizzleMutation()
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{
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var position = new float3(1.0f, 2.0f, 3.0f);
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position.y = 5.0f;
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position.xz = new float2(8.0f, 13.0f);
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Assert.Equal(new float3(8.0f, 5.0f, 13.0f), position);
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var bounds = new float4(1.0f, 2.0f, 3.0f, 4.0f);
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bounds.xy = new float2(-1.0f, -2.0f);
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Assert.Equal(new float4(-1.0f, -2.0f, 3.0f, 4.0f), bounds);
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}
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[Fact]
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public void DoubleVectorsSupportDampedMath()
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{
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var value = new double3(1.0, 2.0, 3.0);
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value.xy = new double2(5.0, 8.0);
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Assert.Equal(new double3(5.0, 8.0, 3.0), value);
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Assert.Equal(new double2(Math.Exp(-2.0), Math.Exp(-4.0)), math.exp(new double2(-2.0, -4.0)));
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Assert.Equal(new double3(2.0, 4.0, 6.0), math.lerp(new double3(0.0, 0.0, 0.0), new double3(4.0, 8.0, 12.0), new double3(0.5, 0.5, 0.5)));
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}
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[Fact]
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public void Int2SupportsGridArithmeticAndFloatPromotion()
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{
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var cell = new int2(2, 3);
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Assert.Equal(new int2(3, 5), cell + new int2(1, 2));
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Assert.Equal(new int2(4, 6), cell * new int2(2, 2));
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Assert.Equal(3, cell[1]);
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float2 promoted = cell;
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Assert.Equal(new float2(2.0f, 3.0f), promoted);
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}
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[Fact]
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public void Bool2SupportsHullGridStyleStorage()
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{
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bool2 conductivity = true;
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conductivity.y = false;
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Assert.True(conductivity.x);
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Assert.False(conductivity[1]);
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Assert.Equal(new bool2(false, true), math.bool2(false, true));
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}
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[Fact]
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public void QuaternionLookRotationProducesUnitOrientation()
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{
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var rotation = quaternion.LookRotation(new float3(0.0f, 0.0f, 1.0f), new float3(0.0f, 1.0f, 0.0f));
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Assert.Equal(quaternion.identity, rotation);
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Assert.Equal(1.0f, math.length((float4)quaternion.LookRotation(new float3(1.0f, 0.0f, 0.0f), new float3(0.0f, 1.0f, 0.0f))), precision: 5);
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}
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[Fact]
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public void RandomUsesStableXorShift32Sequence()
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{
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var a = new Random(1234);
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var b = new Random(1234);
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Assert.Equal(332584831u, a.NextUInt());
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Assert.Equal(1855942593u, a.NextUInt());
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Assert.Equal(4018585650u, a.NextUInt());
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Assert.Equal(3348358578u, a.NextUInt());
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Assert.Equal(332584831u, b.NextUInt());
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}
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[Fact]
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public void RandomProvidesDeterministicPortableSampling()
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{
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var a = new Random(1234);
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var b = new Random(1234);
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Assert.Equal(a.NextUInt(), b.NextUInt());
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Assert.Equal(a.NextFloat(), b.NextFloat());
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var bounded = a.NextFloat(-2.0f, 4.0f);
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Assert.True(bounded >= -2.0f && bounded < 4.0f);
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var direction = a.NextFloat2Direction();
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Assert.Equal(1.0f, math.length(direction), precision: 5);
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var point = a.NextFloat3(new float3(-1.0f, -2.0f, -3.0f), new float3(1.0f, 2.0f, 3.0f));
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Assert.True(point.x >= -1.0f && point.x < 1.0f);
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Assert.True(point.y >= -2.0f && point.y < 2.0f);
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Assert.True(point.z >= -3.0f && point.z < 3.0f);
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}
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[Fact]
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public void NormalizeProducesUnitLength()
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{
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var value = math.normalize(new float3(3.0f, 4.0f, 0.0f));
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Assert.Equal(1.0f, math.length(value), precision: 5);
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}
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[Fact]
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public void SmoothstepUsesHermiteRamp()
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{
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Assert.Equal(0.0f, math.smoothstep(0.0f, 1.0f, -1.0f));
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Assert.Equal(0.5f, math.smoothstep(0.0f, 1.0f, 0.5f), precision: 5);
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Assert.Equal(1.0f, math.smoothstep(0.0f, 1.0f, 2.0f));
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Assert.Equal(0.5f, math.smootherstep(0.5f), precision: 5);
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}
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[Fact]
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public void TrigIntrinsicsUseRadians()
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{
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Assert.Equal(1.0f, math.sin(math.HALF_PI), precision: 5);
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Assert.Equal(-1.0f, math.cos(math.PI), precision: 5);
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Assert.Equal(1.0f, math.tan(math.PI * 0.25f), precision: 5);
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Assert.Equal(math.HALF_PI, math.atan2(1.0f, 0.0f), precision: 5);
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Assert.Equal(2, math.min(2, 5));
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Assert.Equal(5, math.max(2, 5));
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Assert.True(math.isinf(float.PositiveInfinity));
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}
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[Fact]
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public void SignIsComponentWiseForSimulationVectors()
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{
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Assert.Equal(-1, math.sign(-12.0f));
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Assert.Equal(0, math.sign(0.0f));
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Assert.Equal(1, math.sign(12.0f));
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Assert.Equal(new int3(-1, 0, 1), math.sign(new float3(-2.0f, 0.0f, 4.0f)));
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}
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[Fact]
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public void RotateTurnsFloat2CounterClockwiseInRadians()
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{
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var rotated = math.rotate(new float2(1.0f, 0.0f), math.HALF_PI);
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Assert.Equal(0.0f, rotated.x, precision: 5);
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Assert.Equal(1.0f, rotated.y, precision: 5);
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var rotatedDegrees = math.rotate_degrees(new float2(0.0f, 1.0f), 90.0f);
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Assert.Equal(-1.0f, rotatedDegrees.x, precision: 5);
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Assert.Equal(0.0f, rotatedDegrees.y, precision: 5);
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}
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[Fact]
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public void AetheriaPrimitivesRemainSmallAndDeterministic()
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{
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Assert.Equal(6.0f, math.csum(new float3(1.0f, 2.0f, 3.0f)));
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Assert.Equal(0.25f, math.unlerp(10.0f, 30.0f, 15.0f));
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Assert.Equal(new float2(0.25f, 0.75f), math.unlerp(new float2(10.0f, 10.0f), new float2(30.0f, 30.0f), new float2(15.0f, 25.0f)));
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Assert.Equal(MathF.Exp(-2.0f), math.decay(1.0f, 2.0f, 1.0f), precision: 5);
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Assert.Equal(1.0f - MathF.Exp(-2.0f), math.damp(0.0f, 1.0f, 2.0f, 1.0f), precision: 5);
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Assert.Equal(15.0f, math.catmullrom(0.0f, 10.0f, 20.0f, 30.0f, 0.5f), precision: 5);
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Assert.Equal(0.25f, math.quadratic_bezier(0.0f, 0.0f, 1.0f, 0.5f), precision: 5);
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Assert.Equal(0.5f, math.cubic_bezier(0.0f, 0.0f, 1.0f, 1.0f, 0.5f), precision: 5);
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}
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[Fact]
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public void SegmentDistanceReportsClosestPoint()
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{
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var distance = math.distance_to_segment(new float2(2.0f, 3.0f), new float2(0.0f, 0.0f), new float2(4.0f, 0.0f), out var closest);
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Assert.Equal(3.0f, distance, precision: 5);
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Assert.Equal(new float2(2.0f, 0.0f), closest);
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}
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[Fact]
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public void RectNormalizesAndDerivesFromMinMax()
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{
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var bounds = new rect(8.0f, 6.0f, 2.0f, -2.0f);
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Assert.Equal(new float2(2.0f, -2.0f), bounds.min);
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Assert.Equal(new float2(8.0f, 6.0f), bounds.max);
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Assert.Equal(new float2(6.0f, 8.0f), bounds.size);
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Assert.Equal(new float2(5.0f, 2.0f), bounds.center);
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Assert.Equal(48.0f, bounds.area);
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}
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[Fact]
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public void RectContainmentIncludesBoundary()
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{
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var bounds = new rect(-2.0f, -1.0f, 4.0f, 3.0f);
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Assert.True(bounds.Contains(new float2(-2.0f, -1.0f)));
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Assert.True(bounds.Contains(new float2(4.0f, 3.0f)));
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Assert.True(bounds.Contains(new rect(-1.0f, 0.0f, 1.0f, 2.0f)));
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Assert.False(bounds.Contains(new float2(4.001f, 3.0f)));
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}
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[Fact]
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public void RectIntersectionTreatsTouchingEdgesAsContact()
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{
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var left = new rect(0.0f, 0.0f, 4.0f, 4.0f);
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var touching = new rect(4.0f, 1.0f, 8.0f, 3.0f);
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var separate = new rect(4.001f, 1.0f, 8.0f, 3.0f);
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Assert.True(left.Intersects(touching));
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Assert.Equal(0.0f, left.Intersection(touching).area);
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Assert.False(left.Intersects(separate));
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}
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[Fact]
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public void FirstOrderInterceptSolvesSimpleClosingTarget()
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{
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var time = math.first_order_intercept_time(
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2.0f,
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new float3(10.0f, 0.0f, 0.0f),
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new float3(-1.0f, 0.0f, 0.0f));
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Assert.Equal(10.0f / 3.0f, time, precision: 5);
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}
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[Fact]
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public void ValueNoiseIsDeterministicAndSmoothAtCellCorners()
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{
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var position = new float2(12.25f, -4.5f);
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Assert.Equal(math.value_noise(position), math.value_noise(position));
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Assert.Equal(math.hash(new float2(3.0f, 5.0f)), math.value_noise(new float2(3.0f, 5.0f)), precision: 5);
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var bicubic = math.value_noise_bicubic(position);
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Assert.True(bicubic > -0.25f && bicubic < 1.25f);
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}
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[Theory]
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[InlineData(0.0f, 0.0f, 0.0f)]
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[InlineData(0.25f, -0.5f, 0.225074813f)]
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[InlineData(12.25f, -4.5f, -0.388599217f)]
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[InlineData(536.5106f, 536.5106f, 0.538390875f)]
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public void SimplexNoiseMatchesGoldenValues(float x, float y, float expected)
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{
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Assert.Equal(expected, math.snoise(new float2(x, y)), precision: 6);
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}
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[Fact]
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public void VoronoiBatchProducesToneMappedColors()
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{
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var xs = new[] { 0.0f, 24.0f, 96.0f };
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var ys = new[] { 0.0f, 36.0f, 144.0f };
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var tones = new[] { CultMathTone.Background, CultMathTone.Header, CultMathTone.Body };
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var spans = new[] { 1920.0f, 8.0f, 8.0f };
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var colors = new Color32[xs.Length];
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Voronoi.SampleTones(xs, ys, tones, spans, 1080.0f, 12, colors);
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Assert.NotEqual(new Color32(), colors[0]);
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Assert.True(colors[1].r > colors[1].g);
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Assert.True(colors[2].r > 120 && colors[2].g > 120 && colors[2].b > 120);
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}
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[Fact]
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public void BatchRadialFalloffAccelerationMatchesScalarContract()
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{
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var xs = new[] { 0.0f, 5.0f, 10.0f };
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var ys = new[] { 0.0f, 0.0f, 0.0f };
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var ax = new float[xs.Length];
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var ay = new float[xs.Length];
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BatchMath.AddRadialFalloffAcceleration2D(xs, ys, 10.0f, 0.0f, 10.0f, 20.0f, ax, ay);
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Assert.True(BatchMath.LaneCount >= 4);
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Assert.Equal(5.0f, ax[0], precision: 5);
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Assert.Equal(7.5f, ax[1], precision: 5);
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Assert.Equal(0.0f, ax[2], precision: 5);
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Assert.Equal(0.0f, ay[0], precision: 5);
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}
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[Fact]
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public void BatchEulerIntegrationHonorsDynamicMask()
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{
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var dynamicMask = new[] { 1.0f, 0.0f };
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var px = new[] { 0.0f, 0.0f };
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var py = new[] { 0.0f, 0.0f };
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var vx = new[] { 1.0f, 1.0f };
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var vy = new[] { 0.0f, 0.0f };
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var ax = new[] { 2.0f, 2.0f };
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var ay = new[] { 0.0f, 4.0f };
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BatchMath.IntegrateSemiImplicitEuler2D(0.5f, dynamicMask, px, py, vx, vy, ax, ay);
|
|
|
|
Assert.Equal(2.0f, vx[0], precision: 5);
|
|
Assert.Equal(1.0f, px[0], precision: 5);
|
|
Assert.Equal(1.0f, vx[1], precision: 5);
|
|
Assert.Equal(0.0f, px[1], precision: 5);
|
|
Assert.Equal(0.0f, py[1], precision: 5);
|
|
}
|
|
|
|
// Tabulated to 16 significant figures (Abramowitz & Stegun table 7.1 lineage / standard erf tables).
|
|
[Theory]
|
|
[InlineData(0.0f, 0.0)]
|
|
[InlineData(0.5f, 0.5204998778130465)]
|
|
[InlineData(-0.5f, -0.5204998778130465)]
|
|
[InlineData(1.0f, 0.8427007929497149)]
|
|
[InlineData(-1.0f, -0.8427007929497149)]
|
|
[InlineData(2.0f, 0.9953222650189527)]
|
|
[InlineData(-2.0f, -0.9953222650189527)]
|
|
[InlineData(3.0f, 0.9999779095030014)]
|
|
[InlineData(-3.0f, -0.9999779095030014)]
|
|
public void ErfMatchesReferenceValues(float x, double expected)
|
|
{
|
|
Assert.True(
|
|
Math.Abs(math.erf(x) - expected) <= 2e-6,
|
|
$"erf({x}) = {math.erf(x)}, expected {expected}");
|
|
}
|
|
|
|
[Fact]
|
|
public void ErfIsOdd()
|
|
{
|
|
for (var i = -30; i <= 30; i++)
|
|
{
|
|
var x = i / 10.0f;
|
|
Assert.Equal(-math.erf(x), math.erf(-x));
|
|
}
|
|
}
|
|
|
|
[Fact]
|
|
public void ErfApproachesItsLimitsOfPlusMinusOne()
|
|
{
|
|
Assert.Equal(1.0f, math.erf(6.0f));
|
|
Assert.Equal(1.0f, math.erf(20.0f));
|
|
Assert.Equal(-1.0f, math.erf(-6.0f));
|
|
Assert.Equal(-1.0f, math.erf(-20.0f));
|
|
}
|
|
|
|
[Fact]
|
|
public void ErfinvInvertsErf()
|
|
{
|
|
for (var i = -999; i <= 999; i++)
|
|
{
|
|
var y = i / 1000.0f;
|
|
var x = math.erfinv(y);
|
|
var roundTrip = math.erf(x);
|
|
Assert.True(
|
|
MathF.Abs(roundTrip - y) < 1e-5f,
|
|
$"erf(erfinv({y})) = {roundTrip}");
|
|
}
|
|
}
|
|
|
|
// Reference values from bisecting the platform's double-precision erf (Python's math.erf,
|
|
// glibc-backed), not this package's own erf, to 200 iterations over [-6, 6] -- effectively
|
|
// exact at float precision. This is what ErfinvInvertsErf cannot be: a check against this
|
|
// package's own erf only proves the two functions agree with each other, not that either is
|
|
// numerically correct. Soul measured the round-trip test alone to be blind to a coefficient
|
|
// change that degraded erfinv's worst error 300-400x (5.0e-7 to 2.0e-4).
|
|
[Theory]
|
|
// Expected values are computed for the actual float32-rounded input (e.g. the literal
|
|
// 0.999f is really 0.9990000128746033 as a double), not the decimal literal, because
|
|
// erfinv's derivative diverges near +-1: at y = 0.999f that rounding alone moves the
|
|
// true answer by ~2.6e-6, larger than the test's own error bar, if ignored.
|
|
[InlineData(0.0f, 0.0)]
|
|
[InlineData(0.1f, 0.08885599182530649)]
|
|
[InlineData(-0.1f, -0.08885599182530649)]
|
|
[InlineData(0.3f, 0.2724627261055238)]
|
|
[InlineData(-0.3f, -0.2724627261055238)]
|
|
[InlineData(0.5f, 0.4769362762044699)]
|
|
[InlineData(-0.5f, -0.4769362762044699)]
|
|
[InlineData(0.7f, 0.7328690598827587)]
|
|
[InlineData(-0.7f, -0.732869059882759)]
|
|
[InlineData(0.9f, 1.1630870719457724)]
|
|
[InlineData(-0.9f, -1.1630870719457729)]
|
|
[InlineData(0.95f, 1.3859037522360764)]
|
|
[InlineData(-0.95f, -1.3859037522360773)]
|
|
[InlineData(0.99f, 1.8213866009002766)]
|
|
[InlineData(-0.99f, -1.8213866009002793)]
|
|
[InlineData(0.999f, 2.3267563267961435)]
|
|
[InlineData(-0.999f, -2.3267563267961657)]
|
|
[InlineData(0.9999f, 2.751035437903192)]
|
|
[InlineData(-0.9999f, -2.751035437903383)]
|
|
public void ErfinvMatchesReferenceValues(float y, double expected)
|
|
{
|
|
Assert.True(
|
|
Math.Abs(math.erfinv(y) - expected) <= 2e-6,
|
|
$"erfinv({y}) = {math.erfinv(y)}, expected {expected}");
|
|
}
|
|
|
|
[Fact]
|
|
public void ErfinvAtDomainEdgesAndBeyond()
|
|
{
|
|
// Domain is [-1, 1]. The edges are the correctly-signed infinite limits; anything
|
|
// outside, including +-infinity itself, has no real inverse and is NaN.
|
|
Assert.Equal(float.PositiveInfinity, math.erfinv(1.0f));
|
|
Assert.Equal(float.NegativeInfinity, math.erfinv(-1.0f));
|
|
Assert.True(float.IsNaN(math.erfinv(1.0001f)));
|
|
Assert.True(float.IsNaN(math.erfinv(-1.0001f)));
|
|
Assert.True(float.IsNaN(math.erfinv(2.0f)));
|
|
Assert.True(float.IsNaN(math.erfinv(-2.0f)));
|
|
Assert.True(float.IsNaN(math.erfinv(float.PositiveInfinity)));
|
|
Assert.True(float.IsNaN(math.erfinv(float.NegativeInfinity)));
|
|
Assert.True(float.IsNaN(math.erfinv(float.NaN)));
|
|
}
|
|
|
|
// The deleted ErfinvIsMonotonicallyIncreasing asserted a property erfinv does not have:
|
|
// Soul measured 9662 backward steps scanning every representable float32 in [0, 0.999999],
|
|
// first at y = 0.00022214651, worst drop 5.960464e-8 (one ULP at that scale) -- invisible
|
|
// only because that fixture stepped by 0.001. erf has the same shape: 100 backward steps
|
|
// over [0, 4.5], worst drop 1.192093e-7. Pin what is actually true: monotone to within a
|
|
// tolerance comfortably above that measured noise floor.
|
|
[Fact]
|
|
public void ErfinvIsMonotonicWithinFloatingPointTolerance()
|
|
{
|
|
const float tolerance = 1e-6f;
|
|
var previous = float.NegativeInfinity;
|
|
for (var i = -999; i <= 999; i++)
|
|
{
|
|
var y = i / 1000.0f;
|
|
var x = math.erfinv(y);
|
|
Assert.True(
|
|
x >= previous - tolerance,
|
|
$"erfinv({y}) = {x} dropped more than {tolerance} below previous value {previous}");
|
|
previous = x;
|
|
}
|
|
}
|
|
|
|
// One property the consumer needs, not the whole of correctness: fire control turns
|
|
// adjacent erf values into a cell's probability mass, so a backward step in erf would
|
|
// show up as a negative mass. An erf that returned a constant would pass this and is
|
|
// caught by ErfMatchesReferenceValues instead.
|
|
// Soul checked these geometries clean: 16/64/256/1024/4096 cells over
|
|
// +-4 sigma, plus a tight 1 sigma spread and a very tight 0.25 sigma spread.
|
|
[Theory]
|
|
[InlineData(16, 4f)]
|
|
[InlineData(64, 4f)]
|
|
[InlineData(256, 4f)]
|
|
[InlineData(1024, 4f)]
|
|
[InlineData(4096, 4f)]
|
|
[InlineData(256, 1f)]
|
|
[InlineData(64, 0.25f)]
|
|
public void ErfCellMassesStayNonNegativeAcrossRealisticGeometries(int cells, float sigmaRange)
|
|
{
|
|
var lo = -sigmaRange;
|
|
var hi = sigmaRange;
|
|
var step = (hi - lo) / cells;
|
|
var previous = math.erf(lo / MathF.Sqrt(2f));
|
|
for (var i = 1; i <= cells; i++)
|
|
{
|
|
var edge = lo + step * i;
|
|
var current = math.erf(edge / MathF.Sqrt(2f));
|
|
var mass = current - previous;
|
|
Assert.True(mass >= 0f, $"cell {i} of {cells} over +-{sigmaRange} sigma has negative mass {mass}");
|
|
previous = current;
|
|
}
|
|
}
|
|
}
|