MathAssertions 0.4.1

Prefix Reserved
.NET 10.0 This package targets .NET 10.0. The package is compatible with this framework or higher.
There is a newer version of this package available.
See the version list below for details. 
dotnet add package MathAssertions --version 0.4.1
                    


                    

                
NuGet\Install-Package MathAssertions -Version 0.4.1
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package. 
<PackageReference Include="MathAssertions" Version="0.4.1" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
<PackageVersion Include="MathAssertions" Version="0.4.1" />
                    


                            Directory.Packages.props
                        

                    

                
<PackageReference Include="MathAssertions" />
                    


                            Project file
For projects that support Central Package Management (CPM), copy this XML node into the solution Directory.Packages.props file to version the package. 
paket add MathAssertions --version 0.4.1
                    


                    

                
#r "nuget: MathAssertions, 0.4.1"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package. 
#:package MathAssertions@0.4.1
#:package directive can be used in C# file-based apps starting in .NET 10 preview 4. Copy this into a .cs file before any lines of code to reference the package. 
#addin nuget:?package=MathAssertions&version=0.4.1
                    


                            Install as a Cake Addin
                        

                    

                
#tool nuget:?package=MathAssertions&version=0.4.1
                    


                            Install as a Cake Tool

MathAssertions

NuGet License: MIT .NET

Scope: Test projects only. Not intended for production code.

Framework-agnostic core of the MathAssertions package family. Math assertion helpers for .NET tests, spanning tolerance comparisons, sequences, statistics, linear algebra, number theory, and 3D geometry. Test-framework-specific entry points ship in adapter packages (currently MathAssertions.TUnit for TUnit).

Most users want MathAssertions.TUnit, not this package directly. This package ships the framework-agnostic helper classes (MathTolerance, Sequences, Statistics, LinearAlgebra, NumberTheory, plus the Geometry3D namespace); the adapter package adds the fluent Assert.That(value).Method(...) entry points your test framework expects.

What's in this package

Pure, NaN-aware, infinity-aware mathematical-assertion helpers. Six static classes plus the Geometry3D namespace cover ~85 methods:

  • MathTolerance: scalar IsApproximatelyEqual for double/float plus the System.Numerics compounds (Vector2/Vector3/Vector4, Quaternion with IsRotationallyEquivalent and (v0.2.0+) HasAxisAngleApproximately, Matrix4x4, Plane with IsGeometricallyEquivalent, Complex), span / tensor overloads (ReadOnlySpan<double>/<float>, generic ReadOnlyTensorSpan<T>), ULP-distance equality (IsCloseInUlps), combined relative+absolute tolerance, finiteness/probability/percentage predicates, HasRoundtripIdentity for invertible-transformation checks, and (v0.4.0+) the pose primitives RotationAngleDegrees, PositionDistance, and IsPoseApproximatelyEqual.
  • (v0.2.0+) Adapter packages such as MathAssertions.TUnit use an internal per-component / per-cell / first-failing-element failure-message renderer so every compound IsApproximatelyEqualTo failure shows the diverging axis and its delta. The renderer is reachable across the assembly boundary via [InternalsVisibleTo]; consumers do not interact with it directly.
  • Sequences: monotonicity (strict + non-strict), boundedness, arithmetic and geometric progressions, ConvergesTo, single-step IsCauchyConvergent, generic length predicates over ReadOnlySpan<T>.
  • Statistics: Welford's MeanAndVariance, HasMean/Variance/StdDev/Sum/Median/PercentileApproximately, IsWithinSigmasOfMean, AreAllWithinSigmasOfMean. Median and percentile use overflow-safe forms.
  • LinearAlgebra: Matrix4x4 invariants (IsSymmetric, IsOrthogonal, IsIdentity, HasDeterminantApproximately, HasTraceApproximately, IsInvertible) plus Vector3 pair properties (AreOrthogonal, AreParallel, AreLinearlyIndependent).
  • NumberTheory: exact integer predicates over long: IsDivisibleBy, IsPrime, AreCoprime, GreatestCommonDivisor, LeastCommonMultiple, IsPowerOf, IsPerfectSquare, IsCongruent. Overflow-safe and long.MinValue-aware.
  • Geometry3D: eight primitive record struct types (Sphere, AxisAlignedBox, OrientedBox, Ray3D, LineSegment3D, Triangle3D, Capsule, Cylinder) and five static classes: Properties (degeneracy, collinearity, coplanarity), Containment (point/box/sphere/OBB/convex hull), Distance (point-to-plane/segment/triangle), Intersection (sphere-sphere, AABB-AABB, ray-plane/sphere/triangle/AABB with citations to Real-Time Rendering §§22.6, 22.7, 22.8), Pointcloud (boundedness, centroid, on-plane / on-sphere). Algorithm citations preserved per Real-Time Collision Detection and Real-Time Rendering.

All tolerance- and sigma-taking methods validate the bound up front; invalid input throws ArgumentOutOfRangeException even on early-return paths.

Test-framework adapters

Package Test framework Status
MathAssertions.TUnit TUnit Available now
MathAssertions.NUnit NUnit Possible if there is demand
MathAssertions.xUnit xUnit Possible if there is demand
MathAssertions.MSTest MSTest Possible if there is demand

If you'd find a non-TUnit adapter useful, open a feature request. Adapters are not built proactively.

When to install this package directly

Only when authoring a non-TUnit adapter for the assertion family, or when calling MathTolerance from a [GenerateAssertion] extension on a private type. For any TUnit testing use case, install MathAssertions.TUnit.

Installation

dotnet add package MathAssertions.TUnit

MathAssertions comes transitively. You don't need to install it directly unless you're building your own adapter package.

Stability

The public surface above is semver-bound. Breaking changes require a major version bump. The exact text of any future failure-message rendering produced inside MathTolerance is not stable and may gain extra detail or change formatting in any release.

Repository

github.com/JohnVerheij/MathAssertions.TUnit for the full README, design notes, and roadmap.

License

MIT. Copyright (c) 2026 John Verheij.

Product Compatible and additional computed target framework versions.
.NET net10.0 is compatible.  net10.0-android was computed.  net10.0-browser was computed.  net10.0-ios was computed.  net10.0-maccatalyst was computed.  net10.0-macos was computed.  net10.0-tvos was computed.  net10.0-windows was computed. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.

NuGet packages (1)

Showing the top 1 NuGet packages that depend on MathAssertions:

Package Downloads
MathAssertions.TUnit

TUnit-native math assertions for .NET tests. Fluent .Method(...) entry points (generated via TUnit's [GenerateAssertion]) covering tolerance comparisons (scalar, vector, quaternion, matrix, plane, complex, double[]/float[]), sequences, statistics, Vector3 linear algebra, long-integer number theory, and the Geometry3D primitive surface (containment, distance, intersection, pointcloud aggregates). Extensible: consumers add tolerance assertions for their own domain types via [GenerateAssertion] extensions calling MathTolerance helpers. AOT-compatible, trimmable, no reflection.

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last Updated
0.5.0 549 6/14/2026
0.4.3 1,458 6/12/2026
0.4.2 167 6/5/2026
0.4.1 254 6/3/2026
0.4.0 157 6/2/2026
0.3.0 278 5/14/2026
0.2.0 290 5/12/2026
0.1.0 196 5/9/2026
0.0.1 160 5/8/2026

View the rendered release notes: https://github.com/JohnVerheij/MathAssertions.TUnit/releases/tag/v0.4.1

Bug-fix release. No public API signature change.

### Fixed

- **`IsPoseApproximatelyEqualTo`** (and the `Matrix4x4` overload `IsRigidTransformApproximatelyEqualTo`, and the underlying `MathTolerance.RotationAngleDegrees`) reported a non-zero rotation angle for a pose compared with itself, failing on identical inputs. The geodesic angle was computed as `2 * acos(|dot|)`, and `acos` has infinite slope at `dot = 1`, so the residual float error of normalizing a non-unit quaternion (any quaternion whose magnitude is not exactly 1) was amplified into a spurious angle large enough to exceed a tight rotation tolerance. The metric is now the numerically-stable `theta = 2 * atan2(||imag(q1 * conj(q2))||, |real(q1 * conj(q2))|)`, which is well-conditioned across the whole 0-180 degree range, and both quaternions are normalized in double precision before measuring (a quaternion and any positive scalar multiple are the same rotation), so a quaternion compared with itself now measures exactly zero.
- **`IsPoseApproximatelyEqual`** now handles a degenerate, non-normalizable orientation (squared magnitude underflows to zero, e.g. `default(Quaternion)` = `(0, 0, 0, 0)`), which has no defined geodesic angle. The orientation half falls back to a componentwise comparison against a tight fixed tolerance, independent of the caller's rotation tolerance: the rotation tolerance is a degrees value, and reusing it would be far too permissive (a tolerance of 1 or more would accept a zero quaternion as equal to a real rotation, whose nearest component delta is at most 1). So a default-pose round-trip (`(0,0,0,0)` vs `(0,0,0,0)`) passes, while `(0,0,0,0)` compared with a real rotation fails regardless of the angular tolerance, with the combined diagnostic naming the rotation half.