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cultmath: near-origin fold test checks the exact departure to 1e-13

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The additive 1e-9 absorbed the whole exact departure at scales 1e-4 and 1e-2 (1e-11 to 1e-9),
so dropping the value allowance's absolute term 2^-14 survived the test. The tolerance is 1e-13.
Test only; builds.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
Meta Vens 2026-10-16 03:11:04 +02:00
commit 338a952be0
1 changed files with 5 additions and 1 deletions
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6
packages/cultmath/tests/CultMath.Tests/SpanStageTests.cs
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@ -688,6 +688,10 @@ public sealed class SpanStageTests
/// opposite to the float one in about a fifth of the draws, so fold must still cover the exact
/// departure there: a fold forced to 0 at halfLength 0, or an S_o whose reach term drives e_n below
/// zero under the loose bound, leaves it 0 and fails. span_fbm's fold is 0 throughout.
/// Near the origin S_o is tiny (scales 1e-4 and 1e-2 of the coordinate), and only the value allowance's
/// absolute term 2^-14 carries the kernel's own rounding: the exact departure there is the coordinate's
/// rounding times the gradient (1e-11 to 1e-9), so the exact check's additive tolerance is 1e-13, under it.
/// A larger tolerance absorbs a dropped absolute term whole.
/// </summary>
[Theory]
[InlineData(false)]
@ -706,7 +710,7 @@ public sealed class SpanStageTests
var fold = stage.Ridged(span.Path).fold;
var (departureFloat, departureExact, rounding) = BranchDeparture(stage, span, 2);
Assert.Equal(0.0f, stage.Fbm(span.Path).fold);
Assert.True(departureExact <= fold * (1.0 + 1.0e-3) + 1.0e-9, $"midpoint {q}, speed {speed:R}: the exact branch departure is {departureExact:R}, above fold {fold:R}");
Assert.True(departureExact <= fold * (1.0 + 1.0e-3) + 1.0e-13, $"midpoint {q}, speed {speed:R}: the exact branch departure is {departureExact:R}, above fold {fold:R}");
Assert.True(departureFloat <= fold * (1.0 + 1.0e-3) + 1.0e-9 + rounding, $"midpoint {q}, speed {speed:R}: the float branch departure is {departureFloat:R}, above fold {fold:R}");
if (departureExact > 0.0)
crossing++;