CultMath: Burn cases with a divisor of exactly 0, and tests for what the film hides (guards returning 0) and for rgb_to_hsv's primaries

Stryker's survivors in math.Cycles.cs that were not equivalent: Burn's divisor <= 0 boundary, Logarithm's
a <= 0 guard, and rgb_to_hsv's h < 0 wrap. mix.json is regenerated in a later commit, so
FamilyMatchesBlender is unchanged here and the new Burn rows are absent. Builds.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

packages/cultmath/tests/CultMath.Tests/CyclesOracleTests.cs

@@ -216,6 +216,39 @@ public sealed class CyclesOracleTests
         Assert.True(worst <= Math.ScaleB(1.0, -22), $"a lookup is {worst} from (index + weight) / (size - 1), more than 2^-22");
     }
 
+    [Theory]
+    [MemberData(nameof(Targets))]
+    public void ResultsTheFilmCannotShowFollowTheCyclesSource(string target)
+    {
+        // Cycles' film writes 0 for an infinite or NaN result, so the fixtures cannot tell the guards that return 0
+        // from the division that would return an infinity. These are the guards in svm_math (util/math_base.h):
+        // safe_logf, safe_divide and inversesqrtf return 0 where the plain operation is not finite.
+        float One(string function, params float[] arguments) => (float)Call(target, function, arguments.Cast<object>().ToArray());
+        Assert.Equal(0.0f, One("cycles_logarithm", 0.0f, 2.0f));
+        Assert.Equal(0.0f, One("cycles_logarithm", -1.0f, 2.0f));
+        Assert.Equal(0.0f, One("cycles_logarithm", 2.0f, 0.0f));
+        Assert.Equal(0.0f, One("cycles_logarithm", 2.0f, -1.0f));
+        Assert.Equal(0.0f, One("cycles_divide", 1.0f, 0.0f));
+        Assert.Equal(0.0f, One("cycles_inverse_sqrt", 0.0f));
+        Assert.Equal(0.0f, One("cycles_modulo", 1.0f, 0.0f));
+        Assert.Equal(0.0f, One("cycles_floored_modulo", 1.0f, 0.0f));
+    }
+
+    [Theory]
+    [MemberData(nameof(Targets))]
+    public void HueSaturationAndValueOfThePrimariesFollowCycles(string target)
+    {
+        // util/color.h rgb_to_hsv: hue 0 for red, 1/3 for green, 2/3 for blue, saturation 1, value 1; a grey has
+        // hue 0 and saturation 0. Red's hue is exactly 0 and not 1, which hsv_to_rgb would read the same.
+        float[] Hsv(float r, float g, float b) => Flatten(Call(target, "cycles_rgb_to_hsv", new float3(r, g, b)));
+        Assert.Equal(new[] { 0.0f, 1.0f, 1.0f }, Hsv(1.0f, 0.0f, 0.0f));
+        Assert.Equal(new[] { 0.0f, 0.0f, 0.5f }, Hsv(0.5f, 0.5f, 0.5f));
+        Assert.Equal(1.0f / 3.0f, Hsv(0.0f, 1.0f, 0.0f)[0], 6);
+        Assert.Equal(2.0f / 3.0f, Hsv(0.0f, 0.0f, 1.0f)[0], 6);
+        var back = Flatten(Call(target, "cycles_hsv_to_rgb", new float3(0.0f, 1.0f, 1.0f)));
+        Assert.Equal(new[] { 1.0f, 0.0f, 0.0f }, back);
+    }
+
     [Fact]
     public void RgbToBwCoefficientsAreTheOnesBlenderReads()
     {

packages/cultmath/tools/cycles-oracle/oracle.py

@@ -241,6 +241,9 @@ EXTRA_ROWS = {
                      # A base of -1 keeps a finite result for any exponent, so the film shows the exponent past the int range.
                      (-1.0, 3.0e9), (-1.0, -3.0e9), (-1.0, 2147483648.0), (-1.0, 16777216.0), (-1.0, 16777215.0)],
     "cycles_compare": [(0.0, 1.0e-7, 0.0), (1.0, 1.0000001, 0.0), (1.0, 1.0000002, 0.0), (0.0, 1.0e-7, 1.0e-8), (5.0, 5.0, 0.0), (0.0, 2.0e-7, 1.0e-7)],
+    # Burn with a divisor of exactly 0 (tm + t col2 = 0) and a colour above 1: the result is 1 for the channel Cycles reads
+    # as 0, and an infinity the film would hide for the others.
+    "cycles_mix_burn": [(2.0, 1.5, 0.5, 1.0, 0.5, 0.5, 0.5), (0.5, 1.5, 2.0, 1.0, -1.0, -1.0, -1.0)],
     "cycles_modulo": [(0.3, 0.1), (-0.3, 0.1), (5.5, -2.0), (-5.5, -2.0), (1.0, 0.0), (1.0e7, 3.0), (7.0, 7.0), (-7.0, 7.0)],
 }
 
@@ -405,7 +408,7 @@ def family_mix():
     functions.append({"function": "cycles_mix_vector", "node": "ShaderNodeMix VECTOR UNIFORM", "cases": encode_cases(columns, vector_bake("mix_vector", images, build_vector))})
 
     for function, blend in MIX_MODES:
-        columns = mix_columns(function, blend)
+        columns = with_extra(function, mix_columns(function, blend), 7)
         images = pack_operands(columns)
 
         def build(tree, imgs, blend=blend):