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cultmath tests: second differences of snoise compared against a two-level Richardson extrapolation

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Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-14 06:45:41 +02:00
commit 276484e15b
1 changed files with 10 additions and 7 deletions
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17
packages/cultmath/tests/CultMath.Tests/SpanPrimitiveTests.cs
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@ -151,14 +151,17 @@ public sealed class SpanPrimitiveTests
for (var i = 0; i < 3; i++)
for (var j = i; j < 3; j++)
{
// Richardson on the O(h^2) second difference: the extrapolation (4 S(h/2) - S(h)) / 3 is
// O(h^4); its own error is bounded by the gap between the two quotients, and the roundoff
// of snoise (a few ulp) over h^2 is added.
// 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.
const float h = 1.0f / 16.0f;
var coarse = SecondDifference(p, i, j, h);
var fine = SecondDifference(p, i, j, h / 2.0f);
var extrapolated = (4.0 * fine - coarse) / 3.0;
var tolerance = 2.0 * Math.Abs(coarse - fine) + 64.0 * Unit / ((h / 2.0) * (h / 2.0));
var s0 = SecondDifference(p, i, j, h);
var s1 = SecondDifference(p, i, j, h / 2.0f);
var s2 = SecondDifference(p, i, j, h / 4.0f);
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 error = Math.Abs(hessian[i][j] - extrapolated);
worst = Math.Max(worst, error / tolerance);
largest = Math.Max(largest, Math.Abs(hessian[i][j]));