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cultmath tests: snoise second-difference check tolerates kernel-edge points by a stated fraction

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Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-14 06:51:42 +02:00
commit 00a477e387
1 changed files with 12 additions and 3 deletions
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15
packages/cultmath/tests/CultMath.Tests/SpanPrimitiveTests.cs
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@ -144,6 +144,7 @@ public sealed class SpanPrimitiveTests
var random = new System.Random(0x5A12);
double worst = 0.0, largest = 0.0;
var compared = 0;
var outside = 0;
for (var k = 0; k < 4000; k++)
{
var p = LatticePoint(random);
@ -154,7 +155,11 @@ public sealed class SpanPrimitiveTests
// Richardson on the O(h^2) second difference: (4 S(h/2) - S(h)) / 3 is O(h^4). Two such
// extrapolations, from (h, h/2) and from (h/2, h/4), differ by about fifteen times the
// error of the finer one, so the comparison is against the finer and its tolerance is
// four times that gap, plus the roundoff of snoise (a few ulp) over (h/4)^2.
// four times that gap, plus the roundoff of snoise (a few ulp) over (h/4)^2. Near a
// kernel's edge (m = 0) snoise's fourth derivative jumps and the extrapolation loses its
// order: such an entry may exceed the tight tolerance, but never by more than the gap
// between the last two second differences (an error that shrinks at least linearly in h
// is at most that gap), and the tight tolerance must hold for all but a fraction.
const float h = 1.0f / 16.0f;
var s0 = SecondDifference(p, i, j, h);
var s1 = SecondDifference(p, i, j, h / 2.0f);
@ -162,16 +167,20 @@ public sealed class SpanPrimitiveTests
var coarseExtrapolation = (4.0 * s1 - s0) / 3.0;
var extrapolated = (4.0 * s2 - s1) / 3.0;
var tolerance = 4.0 * Math.Abs(extrapolated - coarseExtrapolation) + 64.0 * Unit / ((h / 4.0) * (h / 4.0));
var loose = tolerance + 2.0 * Math.Abs(s1 - s2);
var error = Math.Abs(hessian[i][j] - extrapolated);
worst = Math.Max(worst, error / tolerance);
largest = Math.Max(largest, Math.Abs(hessian[i][j]));
compared++;
Assert.True(error <= tolerance, $"snoise_hessian({p})[{i}][{j}] = {hessian[i][j]:R} differs from the extrapolated second difference of snoise {extrapolated:R} by {error:R}, over the measured tolerance {tolerance:R}");
if (error > tolerance)
outside++;
Assert.True(error <= loose, $"snoise_hessian({p})[{i}][{j}] = {hessian[i][j]:R} differs from the extrapolated second difference of snoise {extrapolated:R} by {error:R}, over the measured tolerance {loose:R}");
}
}
output.WriteLine($"snoise_hessian vs Richardson second differences of snoise over 4000 seeded points: {compared} entries, worst error {worst:F3} of its tolerance, largest |H| {largest:R}");
output.WriteLine($"snoise_hessian vs Richardson second differences of snoise over 4000 seeded points: {compared} entries, {outside} over the tight tolerance, worst error {worst:F3} of it, largest |H| {largest:R}");
Assert.True(largest > 10.0, $"the sample never meets curvature above 10 (largest {largest:R})");
Assert.True(outside <= compared / 200, $"{outside} of {compared} entries are over the tight Richardson tolerance, more than 0.5%");
}
[Fact]