Two families appended after phacelle, cultmath_snoise(vec3) and
cultmath_snoise_grad(vec3) over TiePoint3 (seven of eight cases on lattice
diagonals, one of eight on (t, t, t)); the shared Random leaves every earlier
family's draws unchanged. Both carry the tolerance text "ulp-bounded, on the
simplex tie set" and share a glsl name with the random families, so a consumer
tells them apart by index or tolerance.
Regenerated on Yggdrasil (Linux, the fixture's platform) with
CULTMATH_WRITE_GLSL=1. CultMath.glsl: the two tie lines, the constant, one
comment sentence. Fixture: 41 cases of iv_snoise_ball(vec3) and iv_fbm_ball move
with L, everything else is byte-identical before the appended families. Full
suite on Yggdrasil: 290 of 290.
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
MeasureLipschitz on e89fd687 (Yggdrasil): sampled 7.1933103, refined 7.2400064,
x 1.10 = 7.9640074, witness (229.92526, 73.37927, -66.14595). The old 9.181147
sat on the diagonal tie. C#, both Interval.hlsl copies, the pin test's witness
and design.md's provenance numbers move together; CultMath.glsl follows with the
regenerated fixture.
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
The cyclic non-strict step(x0.yzx, x0.xyz) made the four corners a non-simplex
where x0's components are equal: the origin and every (t, t, t) read a different
function (snoise(0) was -0.4358730, jumps up to 0.77). One strict compare, z
against x, gives simplexnoise1234's order. Off the tie set old and new return
the same bits.
NoiseGradTests.SnoiseIsContinuousOnTheSimplexDiagonal fails against the old
rule (0.054 within 1 ulp of (-53.6, -53.6, -53.6)). The origin golden is 0 and a
(1.25, 1.25, 1.25) diagonal row joins it. SNOISE_LIPSCHITZ and the GLSL follow
in the next commits, so the ratio pin and CommittedGlslEqualsLowering are red here.
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
The GLSL is generated from the HLSL by one lowering, mirrored against C# by a
committed fixture evaluated on its own arguments (portable across OSes), with
the frustum ball checked by two-sided enclosure and Phacelle by a scaled
absolute bound. design.md conflict: keeps the branch's sqrt-precision text and
drops the 6e-4 sentence interval-ops r4 removed.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
GoldenFixtureMatchesCSharp draws arguments only under CULTMATH_WRITE_GLSL=1: the draw calls MathF.Pow,
whose bits differ by OS. Checking decodes each committed case's arguments and evaluates C# on them.
phacelle is compared across platforms within 2^-20 max(|v|, 1) per component; iv_exp keeps one ulp.
The iv_frustum_ball check gains the upper side r + d + 2^-19 (r + |c|_1) that NoiseBoundTests pins.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
iv_frustum_ball's sqrt is not correctly rounded on WebGL2, so its family is ulp-bounded and
its entry carries the enclosure rule the consumer applies in double; GoldenFixtureMatchesCSharp
applies it to C#'s results too. A phacelle family (normalization 0.5, platform exp, sin, cos)
is appended after iv_exp; every earlier family's cases are byte-identical.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
EveryPublicFunctionIsLowered compares (name, parameter types) after the lowering's own
step 3, so a dropped overload such as cultmath_pcg3d(vec2) fails. TwoFileHeaderContract
pins distinct guards, the MIT and MPL-2.0 provenance labels, and the MIT file's pointer
to CultMath.Phacelle.glsl. GlslLowering exposes step 3 as LowerTypeNames; output unchanged.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
The footprint march's optical depth at the body start is measured against a
converged midpoint march (h = 0.5, every cell) and may be at most twice as
wrong as the fixed-step march; the end-of-ray assertion goes. BodyDepth owns
the body's optical depth and its pin compares depths, not transmittances.
(c) asserts probe overhead >= 0.90 and a hard cull floor of 0.5 (ruling
wells-overhead-plus-floor); the oracle ceiling, efficiency and cull fraction
are printed. WeightBoundEnclosesOneSignedNoise pins VoidField's weight bound.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
GlslLowering.SeparateFiles is the one name-keyed rule: CultMath.Phacelle.hlsl
lowers into shaders/CultMath.Phacelle.glsl (MPL-2.0, guard
CULTMATH_PHACELLE_GLSL) and its include line leaves CultMath.glsl, which is
now MIT and says so in its provenance line. ReadShaderSource takes an
include predicate (one resolver); the C# mirror still inlines everything.
GlslMirrorTests pins both files, checks tokens in each, takes the union of
definitions and asserts cultmath_phacelle( and CultPhasor live only in the
Phacelle file. The fixture appends cultmath_iv_frustum_ball (exact) and
cultmath_iv_exp ("ulp-bounded, platform exp", platform named); the
comparison is per family, the platform family within 1 ulp with the
maximum printed. THIRD-PARTY-NOTICES lists CultMath.Phacelle.glsl, not
CultMath.glsl, as MPL-2.0.
Regenerated on Yggdrasil (Ubuntu 24.04.5, .NET 10.0.12); 286/286 green,
iv_exp within 0 ulp.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
README conflict resolved by keeping r3's Intervals bullet, then the GLSL
bullet. design.md and HlslSourceCompatibilityTests.cs merged clean.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
MarchTile reports a body start where the gated bound over the rest of the
grid is a positive point and appends the rest unprobed; MarchLod takes one
closed-form Beer-Lambert step there. AnalyticBodyMatchesFineMarch pins it
against the ungated field and the fixed-step product, and pins that no
(a)-(d) tile reports a body. VoidField takes a focal length; LOD-far
(Rh 4000, S 50, f 467) joins the enclosure test, which now asserts it
sampled weights in (0, 1) and at 0. The void grid ends at Rc + 6/K. The
doc derives the one shipped void (198, 50) and records the [w(z1), 1]
deviation. (c) is held to 0.90 of its probe-free ceiling.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
The radius gains (|c|_1 + radius) 2^-20 in C# and both HLSL copies; the
doc's strictness claim leaves. TileBallEnclosesEveryRaySegment measures in
double over the r2 domain and seven extreme families with outward corner
flows, pins the radius two-sided, and counts misses per family. The noise
ball enclosure tests draw radii to 1e3.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
MarchTile runs the pre-pass once per tile on cell-index ranges. It starts from
the whole grid, skips and doubles on proof, halves on maybe, and runs to the
grid's end. Every ray of the tile integrates exactly the dense cells with the
dense march's Integrate. MarchLod is the void's footprint-aware march inside the
unmasked runs. IntervalSkipHalvesEvaluations prints (a)-(d) at N in {1, 4, 8, 16}
and warp in {0, D}, the void grid (Rh x camera offset x S), and the shipped point
with three marches. It asserts transmittance agreement and skips naming
saving-2x-scenarios when (a), (c) or (e) misses its 2x contract.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Deleted: SavingField's MarchIntervals (per-ray probes, the StepMax growth cap,
probes attempted where the ball could never prove emptiness), its unconditional
three-snoise sample, and the saving test that skipped naming r1's fork.
Added, test-side only: the scenario model. FogField is Aetheria's nebula over its
gravity-well height map (Volumetric.cginc, Zone.cs, Settings.asset cited by
line): (a) height fog, (b) inside the fog, (c) the zone bowl and four wells.
SlabField is r1's slab, kept as the worst case. VoidField is the shipped cavity
with footprint octave weights. Each composes one bound from existing iv_* ops:
the envelope over the tile slice's box, its fade, and the noise ball from
iv_frustum_ball enlarged by the warp. The pointwise density is envelope-gated.
EnvelopeBoundEnclosesDensity checks 2,000 slices x 64 warped points with no
tolerance.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
One new function in C# and both tracked HLSL copies (one blob): the centre on the
tile's central ray at mid-depth, radius ((z1 - z0) / 2) |(m_c, 1)| + z1 N / (sqrt(2) f)
+ warp. TileBallEnclosesEveryRaySegment checks 2,000 seeded tiles x 64 points
(sub-pixel corners at both depth ends with full-length flows) with no tolerance,
and pins the ball to the derivation so a grown ball fails too. The mirror's
compared-function count moves from 52 to 53.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
GlslLowering (test project) is the HLSL -> GLSL ES 3.00 transformation as named steps: includes
inlined by the C# mirror's own resolver, guards and texture functions dropped, type names,
static const, casts by a balanced scanner, intrinsic renames, literals passed through, the
CULTMATH_GLSL guard and a provenance line. GlslMirrorTests pins the committed file to the
lowering (CULTMATH_WRITE_GLSL=1 regenerates it), finds no HLSL-only token, finds every public
function but the texture samplers, and pins fixtures/glsl-parity.json (256 seeded cases per
family as float32 bit patterns) to C#.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
IntervalTests runs every op over 10,000 seeded intervals x 16 points with no tolerance, and
kills each op's one-ulp-shrunk lo and hi; exp's widening is an equivalent mutant on this CPU,
and smoothstep's is killed by a constructed non-monotone step. NoiseBoundTests encloses snoise
and fbm over 2,000 balls x 64 points and the bounded domain warp, pins SNOISE_LIPSCHITZ against
1e5 points and the ascent from MeasureLipschitz's witness, prints tightness, and prints the
march saving. The saving is 0.93x, not 2x: that test skips with the fork named.
MeasureLipschitz and MeasureMonotonicity are explicit, slow tests.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
math.Interval.cs and shaders/CultMath.Interval.hlsl (included from CultMath.hlsl after Phacelle;
both tracked copies) add iv_point, iv_add, iv_sub, iv_neg, iv_mul, iv_scale, iv_abs, iv_min,
iv_max, iv_sqr, iv_sqrt, iv_exp, iv_clamp, iv_saturate, iv_smoothstep, iv_lerp, iv_snoise_ball
and iv_fbm_ball, and SNOISE_LIPSCHITZ = 10.099261 (1.10 x the refined max |snoise_grad| that
NoiseBoundTests.MeasureLipschitz prints). iv_exp and iv_smoothstep widen by one ulp through
asfloat(uint), added beside asuint as the HLSL intrinsic. The mirror test now compares 52
functions; the Unity package and the NuGet content files carry the new include.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
MPL-2.0 is file-level and the Phacelle port sat inside MIT files. phacelle and
CultPhasor now live in math.Phacelle.cs and CultPhasor.cs, and cultmath_phacelle
in CultMath.Phacelle.hlsl (included by CultMath.hlsl, both tracked copies), each
with the MPL header and Johansen / Luke Mitchell attribution. math stays one
partial class, so math.phacelle is called exactly as before. The GameCult.Math
package declares MIT AND MPL-2.0 and packs THIRD-PARTY-NOTICES.md and the new
include; the Unity LICENSE.md points at CultLib; build-unity-package.ps1
requires the new include.
The random sweeps never met a cell whose box bound sits just under the 2.25 cut
while its weight is still nonzero, so cuts of 2.245, 2.24 and 2.2 survived.
Six hard-coded points (found by an offline search) sit next to such cells; the
C# pruned-vs-unpruned test and the HLSL mirror test both use them, with a
witness check that re-derives the property from the hash.
Docs: the prune keeps about 45 of 64 cells (14 is the nonzero-weight count),
the support radius is 1.49998 (d^2 = 2.24995), normalization's range and
saturation, W = 0 only for adversarial hashes, and the support-edge gradient
seam size.
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
The generic mirror comparison passes about a hundred inputs through the shader and
missed a mirror whose prune cut was 2.0 instead of 2.25, because only a rare cell has
a nonzero weight under that cut. Twenty thousand random arguments compare the shader
text and math.phacelle field by field and kill that mutant.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Cut 2a-ii-b. phacelle(float3 p, float3 side, float offset, float normalization)
returns CultPhasor { float4 cos; float4 sin }, each float4(gradient.xyz, value.w).
- 4x4x4 cells, pcg3d-hashed jitter in [-0.5, 0.5), weight max(0, exp(-2 d^2) - 0.01111),
normalization as upstream (lpmitchell/AdvancedTerrainErosion PhacelleNoise). The
caller supplies the stripe wave vector; offset is in cycles.
- The gradient is exact: weight derivatives and the normalization are included, not
upstream's grad(cos) ~ -sin * side.
- Cells whose per-axis lower bound is at least 2.25 have weight exactly 0 and are
skipped. An internal overload switches the prune off so the test can pin bit
equality without a second copy of the loop.
- cultmath_phacelle and CultPhasor mirror it in both tracked CultMath.hlsl copies
(the same blob). The mirror test compares the struct field by field; it now covers
34 functions.
- PhacelleTests: value against an independent double-precision reference, quarter-cycle
phase rotation, gradient against central differences on both sides of the
normalization threshold (excluding the threshold and each cell's weight-support
edge, where the exact gradient is discontinuous), stripes along the flow on the unit
sphere (0.215 against the 0.25 bound), step-difference continuity across cell planes,
and pruned == unpruned bit for bit.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Soul: no defect; independent port of stegu 22434e04d7 matches (3D and 2D), goldens
confirmed independently, value jump 2.2e-6 over 20k crossings, gradient FD 9.7e-6,
every hand mutant killed. 2D follows upstream by ruling. Release follow-ups: rebuild
the Unity CultMath.dll, CHANGELOG entry, pin the two HLSL copies equal.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Batches of small boxed problems whose passes end with the KKT test failing and
the cost unmoved (dependent free columns, releases the factor drops, weak-direction
noise-floor problems). They must report Converged, and land within the documented
gap of an exact active-set enumeration. Pins the stall comparison and the cost
scale in Objective, which no test reached before.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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>
Drops the unreproducible floors and detection-scale claims, and the seam-fluke
consistency filter (the spikes it hid were the snoise seam, now fixed and pinned by the
continuity probe). Tightens the tolerances to at least 5x the harness maximum (ridged
0.5 -> 0.05), corrects the point count in the bit-equality test, and caps the ridged
compounding loop so a mutant fails loudly instead of hanging.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
With b along the smallest left singular vector, |A^T b| is tiny, so the KKT
tolerance (1e-6 of it) sits below the gradient's rounding noise at cond(A) >=
1e6 and can never be met. The solver must stop on the progress rule, in at most
six passes, never at the cap. This is the path the progress rule exists for;
the earlier fixtures reached it only by accident.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Two tolerance behaviours had no observer: the scale taken at the box point
nearest the origin (a 6e-5 release on a 1000-scale problem, in either column
position), and the strict comparisons when the scale and the gradient are both
exactly zero (b = 0 at the origin takes no iteration).
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
The full-step clamp repairs an out-of-box start on a free column, so the
warm-start clamp was invisible to the old test (Stryker: five survivors). The
new table runs one column with b beyond the box and a cap of 0, where the
solver returns the clamped start untouched, across finite, infinite and NaN
starts and finite and infinite bounds.
Workspace junk (including NaN doubles) is now checked on random boxed problems
that release bounds and use the tolerance, with bit-identical x and equal
iteration counts.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Stryker left the refinement step (removed, negated, or subtracted) unobserved,
and it is unobservable for a reason: refinement with a same-precision residual
does not improve forward error, and Cholesky is backward stable, so the
residual the KKT test reads is already at rounding level. Measured on n=24
problems at cond(A) 1e3..1e6, the solver with and without the step gives the
same iteration counts and the same x error against a Gram-Schmidt QR
reference (both limited by cond(A^T A) * eps).
The refinement pass, its dp buffer and the scratch vector are deleted;
WorkspaceLength returns to 4n^2 + 15n. The doc states where the normal
equations stop being optimal (cost gap below 1e-6 |b|^2 through cond(A) 3e5,
about 2e-5 at 1e6, independent of the scale of A) and that a ridge row beyond
that is the caller's policy.
status is now initialised: the unassigned local made Stryker discard every
mutant inside Solve as a compile error, so 255 mutants were never measured.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
- n=24 fully free problems at cond 1e2/1e3/1e4, and A x 1e6 with unscaled
bounds, converge in at most two iterations (a regression to cap-spinning
fails on the count, not on a clock).
- b = 0 from a far start reaches the optimum instead of the start.
- Warm-start clamp table, free duplicate column gets no step, parallel columns
at absolute scales 1e3 and 1e-3, near-singular free sets confirm once and
stop, near-collinear optimum at A x 1e6, and zero allocation on the invalid,
converged and cap paths (first and second call).
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
snoise_grad.w is bit-equal to snoise (stronger than the spec's 1e-6
floor, measured over 20,000 points). fbm_grad/ridged_grad with 1/3
octaves are pinned bit-exact against a closed form built with the same
incremental gain/lacunarity multiply chain the production loop uses,
catching both a swapped-argument mutant and an applied-once mutant.
The shared invariant-8 property harness central-differences all three
functions' own .w, filtering simplex-lattice seam flukes by comparing
the estimate at two step sizes (measured tolerances and detection
floor in the harness comment). A dedicated fixture bisects to a snoise
zero crossing and pins that ridged_grad's two one-sided gradients there
have opposite sign.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Adds explicit function-presence assertions and bumps the reflective
bit-parity oracle's expected mirror count from 30 to 33 now that the
three new cultmath_ mirrors are covered automatically.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
EveryMirrorFunctionMatchesCSharpMath's generic random/special-value cases
never happen to hit a point where a radius-2 cell wins (about 3.5e-5 of
points) or an integer point at or past 2^23, so an HLSL mutant of cellular's
search radius, its lower-bound prune, or the removed F2=0 guard could change
cultmath_cellular's real output and still pass this test.
Adds three targeted point cases, reusing CellularAndSminGradTests' own
fixtures so the mirror test does not carry a second copy of the construction:
- the six points from AxisAlignedRadiusTwoOffsets/FindPointRealizingOffset,
each of which realizes a different axis-aligned radius-2 offset as F1 or
F2 in the independent 7x7x7 oracle;
- four integer points at 2^24 (both signs), where distinct cells' jittered
features can round onto the same float32 value, reaching the F2 = 0 guard;
- one exact F1 = F2 tie point, the midpoint of two adjacent cells' feature
points (bit-exact-equidistant from both by construction, no search
needed).
Verified against four HLSL mutants applied to shaders/CultMath.hlsl on
scratch copies (not committed) and reverted after each check:
- `dz < 2` instead of `dz <= 2`: killed by the axis-slice point at
(-56.671272, -67.01973, -79.001).
- `dx` starting at -1 instead of -2: killed by the axis-slice point at
(62, -77.91331, -79.42451).
- pruning against f1 instead of f2: killed by an axis-slice point and both
of the 2^24 integer points (3 mismatches).
- the F2 = 0 guard removed (`grad2 = (p - c2) / f2`, unconditional): killed
by the (2^24, 2^24, 2^24) integer point (NaN vs the guarded zero).
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
CellularAndSminGradTests.cs changes for cut 2a-i's pass-2 findings:
- FeaturePoint and the two other independent pcg3d/pcg4d call sites now hash
int3(cell)/int4(int3(cellId), 0) to match production's integer-hashing fix
(previous commit); the oracle would otherwise diverge from cellular() and
every comparison test would fail.
- New JitterAndIdPassAChiSquareUniformityTest: jitter.x/y/z and id each pass
a chi-square uniformity test (16 bins, 15 df, critical value 37.7 at
alpha=0.001) over 200,000 cells. This is the behavioural pin for the
hashing fix; reverting to pcg3d(cell)'s float-bit hash fails it.
- Two false comments corrected to the measured facts: the
NearestFeatureWins test's claim that |component|=2 offsets are "provably
never the true nearest" is false (their lower bound is 1, not sqrt(3); Soul
measured 3 F1 wins in 2,000,000 samples), and SearchReachesEveryAxis...'s
claim of "lower bound is exactly 2" and "zero hits in 3,000,000" is also
false (lower bound is 1; Soul measured about 1 hit in 28,000).
- PrunedSearchIsBitIdentical... renamed to
...BelowTwoToTheTwentyFifth and its comment states that domain explicitly
(design.md, previous commit).
- GradientTolerance split into SminGradientTolerance (2.5e-4f) and
CellularGradientTolerance (1.3e-3f): the two functions have different
curvature (smin_grad is exactly quadratic in a band; cellular's F1/F2 are
real distance fields), so a shared 3e-4 tolerance carried almost no
headroom over either's actual measured noise (re-measured here at 5.3e-4
for smin's old eps, 2.0e-4/2.6e-4 for cellular), not the "~6e-5" the old
comment claimed. smin_grad's eps moves from 0.001f to 0.01f (no truncation
cost there; dilutes float noise 8x) with a matching widened seam-exclusion
band so p +/- eps cannot step across the seam the check at p already
avoided. cellular's eps stays at 0.0005f (a small sweep found it already
near the truncation/noise sweet spot for a real distance field). Both new
tolerances keep >5x headroom over their own measured worst case and both
still die under a 1.01x-scale mutant on the returned gradient — smin down
to 1.0005x, cellular (M9/M16-style, either gradient) down to 1.002x.
- GradientMatchesCentralDifferencesAwayFromTheF1EqualsF2Seam also excludes a
band around F2 = F3 now, not just F1 = F2: the second-nearest feature's
identity swaps there too, a genuine kink the old test could silently hit
(an unfiltered large sample found a 0.78 edge error this way, swamping the
~2e-4 the filtered test actually sees).
- AxisAlignedRadiusTwoOffsets and FindPointRealizingOffset are extracted from
SearchReachesEveryAxisAlignedRadiusTwoSlice as internal fixtures so
HlslSourceCompatibilityTests (next commit) can reuse the same construction
instead of a second copy.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Stryker (mtp, --since 29e50ad3) found 261 survivors / 24 timeouts across the
whole repo; triaging the ones in this fix batch's own new code (cellular's
loop, its prune, cellular_unit) surfaced one real gap disguised as
collateral timeout noise from a batched infinite-loop mutant: dz < 2 (and
the dy/dx equivalents), silently dropping the +2 layer on one axis alone,
passed every existing random-sampled test. That is not the sweeps being
weak: the exactness proof's own margin (F1, F2 always < sqrt(3), radius-2
cells' lower bound is exactly 2) makes a genuine win from any single
|offset component| = 2 cell astronomically rare over uniformly random
points (measured zero hits in 3,000,000 samples).
SearchReachesEveryAxisAlignedRadiusTwoSlice constructs a real example for
each of the six axis-aligned radius-2 offsets directly: for a candidate
integer cell, build the query point that is the closest point of that
cell's own unit cube to the target neighbour's actual jittered feature.
That construction finds a hit for every offset within a couple thousand
candidate cells, deterministically. This kills dz < 2 / dy < 2 / dx < 2 (all
manually confirmed).
Also manually confirmed via Stryker's own reported mutants: the dz--/dy--/
dx-- (increment-to-decrement) mutants are genuine infinite loops, correctly
caught as timeouts. The f2 >= 0.0f mutant (disabling the F2 = 0 guard) is
killed by the existing NoNaNAtIntegerPointsNear2To24 test. The remaining
survivors/timeouts in the new code (the lower-bound prune's >>= vs >
comparison, its arithmetic terms, and cellular_unit's >> vs >>> shift on an
already-unsigned operand) are equivalent mutants: since the per-axis lower
bound is always 0 or 1 by construction, and pruning is a proven-safe
optimization that never changes cellular's output, no mutation confined to
"when does the prune trigger" can be observed by any value-based test.
Verified by hand: disabling pruning entirely reproduces the unpruned
reference bit for bit, as it must.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Cut 2a-i fix batch 1, findings F1, F3, F4, F5, F6, F7 (Soul falsification of
the first landing):
- cellular now searches a provably exact 5x5x5 neighbourhood (radius 2), not
3x3x3: 3x3x3 missed the true F2 for 9 of 400,000 sampled points. The
comment in math.cs proves 5x5x5 always contains the true F1 and F2 (both
are always < sqrt(3), every excluded cell is always > 2). A cheap
position-only lower-bound prune skips the pcg3d/jitter/distance work for
cells that provably cannot beat the running F2, without changing any
output bit (F6).
- F2 = 0 now gets the same degenerate-gradient guard F1 = 0 already had,
fixing a NaN that was reachable past |p| of about 2^23 (F3).
- id now comes from pcg4d over the winning cell alone, never from the pcg3d
hash that produced that cell's jitter, so id and jitter are no longer
deterministic functions of each other (F4).
- cellular_unit maps the top 24 bits instead of a plain divide-by-2^32, so
the mapping is always inside [0, 1); the old formula rounded
0xFFFFFF80..0xFFFFFFFF up to exactly 1.0f (F7).
- Central-difference tolerances tightened from 0.02 to 3e-4 (measured float
noise at the committed eps is about 6e-5), and cellular's own gradient
test now differentiates cellular's RETURNED .w values instead of a
duplicate FindF1F2 search, so a mutant that corrupts only the returned
gradient can't hide behind an independently-computed value (F1, F5).
- The struct-mirror comparison in HlslSourceCompatibilityTests now checks
field name and declared type in declaration order, not just position, so
a reordered-and-relabelled mirror struct (H2) or a renamed/retyped one
(H3) both fail the walk instead of surviving on values alone (F2).
- FindF1F2 widened to a true independent 7x7x7 brute-force oracle; new tests
pin production's exact agreement with it, the pruned search's bit-for-bit
equivalence to an unpruned 5x5x5 reference, no NaN at 2^24, and id's
correlation with jitter under 0.05.
- Comment/doc fix: smin_grad is Quilez's quadratic-polynomial smin, not
cubic.
Both shaders/CultMath.hlsl and unity/.../Shaders/CultMath.hlsl stay
byte-identical.
Manually verified mutants M9 (grad1 x 1.01), M16 (grad2 x 1.01), and M18 (id
from hash.y) all die against these tests; H2/H3 struct mutants die via the
new comparator tests. Local dotnet test: 191/191 passing. FXC cs_5_0 compile
of a scratch kernel using both cultmath_smin_grad and cultmath_cellular
succeeds.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
dotnet test found two failures where a fixed-decimal-place Assert.Equal
snapped two numbers that already agreed to within about 2e-5 to different
rounded digits, because their true difference straddled a rounding boundary
(0.824987829 vs 0.825006127 -> 0.82 vs 0.83). Both were central-difference
checks (smin_grad's own invariant-8 property test, and cellular's gradient-
matches-central-differences test), not a correctness bug in the primitives.
AssertWithinTolerance replaces the precision-based assertion for both central-
difference comparisons with an explicit absolute-difference check, which
states the actual claim (agreement within the finite-difference step's own
truncation error) without the rounding-boundary artifact. Also dropped an
unused local function (F2At) the build flagged.
Found by the third ygg-verify.sh test run on 77c3580.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Inside namespace CultMath.Tests, unqualified `Random` resolves to the
enclosing CultMath namespace's own Random struct (design.md: "Random is
CultMath's own xorshift32") before `using System;` is even considered, so
`new Random(seed)` in the new test file was constructing CultMath.Random,
which has no NextSingle(). HlslSourceCompatibilityTests.cs already works
around this the same way (`new System.Random(...)`); CellularAndSminGradTests
now qualifies every use the same way.
Found by the second ygg-verify.sh build/test run on e613ed6.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
CellularAndSminGradTests pins the rules the cut map calls out, each against a
mutant it must kill:
- smin's value never exceeds the ordinary minimum, and matches min with that
input's own gradient once |a.w - b.w| exceeds k on either side.
- smin_grad's gradient matches central differences of its own .w at random
seeded points (the formula is exact, not an approximation, so no exclusion
band is needed away from the |a.w-b.w|=k seam itself).
- A direct case falsifies blending the gradient with a constant 0.5 or with
(1 - h) instead of h.
- cellular's F1 never exceeds F2, matched against an independent brute-force
Worley search that shares only the public pcg3d hash, not cellular's control
flow.
- The true nearest feature wins even when an independent search finds it in
the (1, 1, 1) neighbour offset, the last one cellular's own loop order
visits, ruling out a "first found" or early-exit mutant.
- The gradient at a feature point is finite zero, not NaN.
- Both nearest and edge gradients match central differences away from a band
around the F1 = F2 set, where the nearest and second-nearest identity swap
discontinuously.
- id is constant across small moves that stay in the same feature's region and
differs from a distant cell's id.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
HlslSourceCompatibilityTests previously flattened only bare vector returns to
scalar leaves. Values() now recurses through struct fields of any type, so a
struct return (invariant 8's one shape, e.g. CultCellular) is compared field
by field down to bit-for-bit scalars, exactly like a vector return already
was. Components() stays scoped to scalar-typed fields, since it only ever
builds function arguments and must not recurse.
TransformHlslToCSharp gains transformation 5: struct fields gain `public`,
since HLSL has no field access-modifier concept and a C# struct's fields
default to private, which would hide them from Values()' reflection. The old
wrap-in-a-class transformation is renumbered 6. design.md's transformation
list documents both, matching design.md:92's numbered list.
StructReturnComparisonRejectsAMismatchedField is the extension's own test: two
hand-built structs with the same shape (mirroring a real mirror-vs-C#
comparison) prove the field-by-field, bit-for-bit walk actually rejects a
struct whose leaf field differs, or whose nested vector's own component
differs, not just a length check.
EveryMirrorFunctionMatchesCSharpMath and HlslMirrorTests' required-symbol list
now cover cultmath_smin_grad and cultmath_cellular; the mirrored-function
count moves from 28 to 30.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
