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>
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>
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>
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>
CultMath's hash is the shader-style frac(sin(x) * 43758.5453) and
returns float. Unity.Mathematics' hash returned a well-mixed uint, and
seeding from the float hash collapses: a 100x100 position grid gave 1625
distinct values in Aetheria's zone generator.
- math.pcg(uint), pcg3d(int3/float2/float3), and pcg4d(int4/float4)
follow Jarzynski and Olano, "Hash Functions for GPU Rendering"
(JCGT 9(3), 2020). pcg3d and pcg4d are the paper's code from page 32.
pcg is O'Neill's RXS-M-XS 32/32 output over one LCG step, with the
constants checked against pcg-c's pcg_variants.h.
- CultMath has no uint vectors, so pcg3d and pcg4d carry uint bit
patterns in int3/int4. The float overloads hash IEEE-754 bits via the
HLSL intrinsic asuint(float), which is new. pcg3d(float2) holds z at
0, the paper's route for 2 -> N inputs.
- The HLSL mirror gains the same functions, written over scalar uints
so the text compiles both in dxc 1.9.0.5402 (lib_6_3, HV 2021, clean)
and in C#. HlslSourceCompatibilityTests now compares int and uint
arguments and results by value; a wrong shift in the mirror's pcg4d
gives 208 mismatches.
- Known-answer vectors come from an independent Python transcription.
pcg3d separates a 100x100 half-unit grid (the full int3). One
component alone has one birthday collision there, as a 32-bit value
can. The same grid on the integer lattice has none.
- design.md states that the hashes are integer-exact in HLSL and on the
CPU: dxc wraps uint multiply and add modulo 2^32, as C# unchecked does.
- Bump to 0.2.3 and rebuild the tracked Unity DLL and pdb.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
dxc 1.9.0.5402 lowers float2/3/4 normalize(x) to x * Rsqrt(Dot(x, x)),
and DXIL.rst defines Rsqrt as 1 / sqrt(src). A zero vector normalizes
to NaN and a NaN component poisons every component. CultMath divided
by max(length, 1e-20), which returned 0 for a zero vector and a huge
finite component beside a NaN one.
- math.normalize(float2/3/4) is now value * (1 / sqrt(dot(value, value))).
- The HLSL mirror drops cultmath_normalize and its epsilon constant: it
now equals the normalize intrinsic, and nothing consumed it.
- HlslSemanticsTests pins zero and NaN normalize, the rsqrt bit pattern,
and zero length/distance. design.md states the rule and notes that
DXIL.rst's Rsqrt special-value table is a copy of Round's.
- GameCult.Geometry's iso-surface gave degenerate triangles (an inside
vertex on the isovalue) a zero normal through the old epsilon. It now
guards them explicitly, with a test.
- quaternion normalize keeps its identity fallback: quaternion is not
an HLSL type.
- Bump to 0.2.2 and rebuild the tracked Unity DLL and pdb.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
The mirror compiles under using static CultMath.math, so it proves composition,
not intrinsic rules; HlslSemanticsTests alone pins those. design.md also states
where FMin/FMax/Saturate turn NaN or infinity into numbers and tells callers to
check isnan first.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
SequenceEqual on floats treats -0 as 0. The mirror test now compares
SingleToInt32Bits, with any NaN equal to any NaN. Its summary and
design.md now say the test proves CultMath.hlsl's text computes the same
float32 results as C# math on the CPU, not that a GPU agrees: driver sin
precision alone makes cultmath_hash and value noise differ on hardware.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Only cultmath_snoise was compared, at four inputs, so a flipped cultmath_step,
a changed hash constant, and a snoise2 tie change all passed. The mirror is
now discovered by reflection: every cultmath_* overload with a math
counterpart (26 functions) runs over 104 deterministic cases - each special
value in every argument (0, -0, +-1, ties, 1e-7, +-1e4, 1e7, NaN), special
pairs, seeded randoms, and vectors with x == y (snoise's x0.x == x0.y) - and
must match exactly. Both sides are float32 C# over the same intrinsics, so no
tolerance. A cultmath_* function with no counterpart must be named in
MirrorOnly. The four-input snoise theory is gone.
Mutations: flipped step args fail (349 mismatches); hash constants changed
by more than one float32 ulp fail (43758.55: 467, 127.2: 289, 74.8: 97).
43758.5453 -> .5454 is the same float32 and cannot fail. snoise2 x0.x > x0.y
-> >= is invisible: over 1,829,415 exact ties the result is bit-identical,
because the off-simplex corner's kernel is <= 0 on the shared edge.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
HlslSourceCompatibilityTests now reads shaders/CultMath.hlsl, applies only
the documented transformations (drop include guards, drop Texture2D/
SamplerState functions, file-scope static const -> const, f literal
suffixes, wrap in a class), and compiles it with Roslyn against CultMath.
Any compile error fails the test (probed with an undeclared call). The
compiled cultmath_snoise(float3/float2) also matches math.snoise.
dxc -T lib_6_3 -HV 2021 rejected the mirror: cultmath_snoise(float2) called
the undeclared cultmath_simplex_mod289/permute. Renamed to the declared
cultmath_snoise_* helpers. Vector const locals became plain locals (C# const
is primitives only), and cultmath_step uses value >= edge like HLSL step and
the C# mirror. dxc 1.9.0.5402 now compiles the file cleanly. The Unity
package's Shaders copy is synced.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
HLSL is now CultMath's semantic authority where it defines one.
- float2/3/4, int2, double2/3, bool2 and quaternion are plain structs with
public mutable fields instead of record structs. Indexers and swizzles
(float2.yx; float3 xy xz yx yz zy xyz xzy yzx zyx; float4 xy xyz xyw yzx)
have setters.
- ==, !=, <, >, <=, >= are component-wise and return bool2/3/4. Equals and
GetHashCode stay value-based so vectors remain dictionary keys.
quaternion is not an HLSL type and keeps a bool ==.
- Scalar/vector arithmetic and comparisons get explicit overloads on both
sides instead of leaning on implicit splat.
- New types: bool3, bool4, int3, int4, float2x2, float3x3 (row-major like
HLSL, _mRC fields, Rotate / RotateX/Y/Z / Euler with math.RotationOrder).
- New intrinsics: mul (matrix-vector both sides, matrix-matrix), any, all,
select (HLSL argument order), log, vector pow/sqrt/sin/cos/acos/atan2,
double min/max, int3/int4/bool3/bool4/float2x2/float3x3 constructor
functions.
- simplex_noise is renamed snoise and gains the Ashima 3D variant; the HLSL
mirror follows as cultmath_snoise(float2/float3).
- Random gains NextFloat3() and NextFloat3(float3 max) on the same draw order.
Tests pin snoise(float3), float3x3.Euler and float2x2.Rotate to
Unity.Mathematics reference values, and an HLSL-shaped source block compiles
under using static CultMath.math.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
