Merge pull request #6 from Nihlus/fix-equal-approxequal
Add new approximation algorithm and replace current usages in tests
This commit is contained in:
varon
GitHub
commit
c3210d4bd3
7 changed files with 804 additions and 311 deletions
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@ -10,6 +10,7 @@
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using System;
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using System.Collections.Generic;
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using System.Diagnostics.CodeAnalysis;
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using System.Text;
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namespace OpenTK
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@ -354,6 +355,119 @@ namespace OpenTK
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return intDiff <= (1 << maxDeltaBits);
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}
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/// <summary>
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/// Approximates double-precision floating point equality by an epsilon (maximum error) value.
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/// This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.
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/// </summary>
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/// <param name="a">The first float.</param>
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/// <param name="b">The second float.</param>
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/// <param name="epsilon">The maximum error between the two.</param>
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/// <returns><value>true</value> if the values are approximately equal within the error margin; otherwise, <value>false</value>.</returns>
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[SuppressMessage("ReSharper", "CompareOfFloatsByEqualityOperator")]
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public static bool ApproximatelyEqualEpsilon(double a, double b, double epsilon)
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{
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const double doubleNormal = (1L << 52) * double.Epsilon;
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double absA = Math.Abs(a);
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double absB = Math.Abs(b);
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double diff = Math.Abs(a - b);
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if (a == b)
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{
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// Shortcut, handles infinities
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return true;
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}
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if (a == 0.0f || b == 0.0f || diff < doubleNormal)
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{
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// a or b is zero, or both are extremely close to it.
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// relative error is less meaningful here
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return diff < (epsilon * doubleNormal);
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}
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// use relative error
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return diff / Math.Min((absA + absB), double.MaxValue) < epsilon;
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}
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/// <summary>
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/// Approximates single-precision floating point equality by an epsilon (maximum error) value.
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/// This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.
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/// </summary>
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/// <param name="a">The first float.</param>
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/// <param name="b">The second float.</param>
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/// <param name="epsilon">The maximum error between the two.</param>
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/// <returns><value>true</value> if the values are approximately equal within the error margin; otherwise, <value>false</value>.</returns>
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[SuppressMessage("ReSharper", "CompareOfFloatsByEqualityOperator")]
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public static bool ApproximatelyEqualEpsilon(float a, float b, float epsilon)
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{
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const float floatNormal = (1 << 23) * float.Epsilon;
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float absA = Math.Abs(a);
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float absB = Math.Abs(b);
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float diff = Math.Abs(a - b);
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if (a == b)
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{
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// Shortcut, handles infinities
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return true;
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}
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if (a == 0.0f || b == 0.0f || diff < floatNormal)
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{
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// a or b is zero, or both are extremely close to it.
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// relative error is less meaningful here
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return diff < (epsilon * floatNormal);
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}
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// use relative error
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float relativeError = diff / Math.Min((absA + absB), float.MaxValue);
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return relativeError < epsilon;
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}
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/// <summary>
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/// Approximates equivalence between two single-precision floating-point numbers on a direct human scale.
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/// It is important to note that this does not approximate equality - instead, it merely checks whether or not
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/// two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is
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/// inclusive.
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/// </summary>
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/// <param name="a">The first value to compare.</param>
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/// <param name="b">The second value to compare·</param>
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/// <param name="tolerance">The tolerance within which the two values would be considered equivalent.</param>
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/// <returns>Whether or not the values can be considered equivalent within the tolerance.</returns>
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[SuppressMessage("ReSharper", "CompareOfFloatsByEqualityOperator")]
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public static bool ApproximatelyEquivalent(float a, float b, float tolerance)
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{
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if (a == b)
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{
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// Early bailout, handles infinities
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return true;
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}
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float diff = Math.Abs(a - b);
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return diff <= tolerance;
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}
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/// <summary>
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/// Approximates equivalence between two double-precision floating-point numbers on a direct human scale.
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/// It is important to note that this does not approximate equality - instead, it merely checks whether or not
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/// two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is
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/// inclusive.
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/// </summary>
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/// <param name="a">The first value to compare.</param>
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/// <param name="b">The second value to compare·</param>
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/// <param name="tolerance">The tolerance within which the two values would be considered equivalent.</param>
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/// <returns>Whether or not the values can be considered equivalent within the tolerance.</returns>
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[SuppressMessage("ReSharper", "CompareOfFloatsByEqualityOperator")]
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public static bool ApproximatelyEquivalent(double a, double b, double tolerance)
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{
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if (a == b)
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{
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// Early bailout, handles infinities
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return true;
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}
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double diff = Math.Abs(a - b);
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return diff <= tolerance;
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}
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#endregion
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#endregion
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@ -9,26 +9,68 @@ open OpenTK
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[<AutoOpen>]
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module private AssertHelpers =
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[<Literal>]
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let private BitAccuracy = 13
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let private BitAccuracy = 16
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let approxEq a b = MathHelper.ApproximatelyEqual(a,b,BitAccuracy)
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[<Literal>]
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let private EquivalenceTolerance = 0.00005f
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let approxEq a b = MathHelper.ApproximatelyEquivalent(a, b, EquivalenceTolerance)
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let approxEqDelta a b = MathHelper.ApproximatelyEqual(a,b,BitAccuracy)
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let approxEqSingleEpsilon a b = MathHelper.ApproximatelyEqualEpsilon(a, b, 0.00001f)
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let approxEqDoubleEpsilon a b = MathHelper.ApproximatelyEqualEpsilon(a, b, 0.00001)
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let approxEqSingleEpsilonWithError (a, b, c : float32) = MathHelper.ApproximatelyEqualEpsilon(a, b, c)
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let approxEqDoubleEpsilonWithError (a, b, c : float) = MathHelper.ApproximatelyEqualEpsilon(a, b, c)
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let anyZero2 (a : Vector2) = (approxEq a.X 0.0f || approxEq a.Y 0.0f)
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let anyZero3 (a : Vector3) = (approxEq a.X 0.0f || approxEq a.Y 0.0f || approxEq a.Z 0.0f)
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let anyZero4 (a : Vector4) = (approxEq a.X 0.0f || approxEq a.Y 0.0f || approxEq a.Z 0.0f || approxEq a.W 0.0f)
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/// We use a full type here instead of a module, as the overloading semantics are more suitable for our desired goal.
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[<Sealed>]
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type internal Assert =
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static member ApproximatelyEqual(a : Vector2,b : Vector2) =
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static member ApproximatelyEquivalent(a : Vector2,b : Vector2) =
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if not <| approxEq a.X b.X && approxEq a.Y b.Y then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqual(a : Vector3,b : Vector3) =
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static member ApproximatelyEquivalent(a : Vector3,b : Vector3) =
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if not <| approxEq a.X b.X && approxEq a.Y b.Y && approxEq a.Z b.Z then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqual(a : Vector4,b : Vector4) =
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static member ApproximatelyEquivalent(a : Vector4,b : Vector4) =
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if not <| approxEq a.X b.X && approxEq a.Y b.Y && approxEq a.Z b.Z && approxEq a.W b.W then
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raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqual(a : float32,b : float32) =
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static member ApproximatelyEquivalent(a : float32,b : float32) =
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if not <| approxEq a b then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqualEpsilon(a : float32, b : float32) =
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if not <| approxEqSingleEpsilon a b then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqualEpsilon(a : float32, b : float32, c : float32) =
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if not <| approxEqSingleEpsilonWithError(a, b, c) then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqualEpsilon(a : float, b : float) =
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if not <| approxEqDoubleEpsilon a b then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ApproximatelyEqualEpsilon(a : float, b : float, c : float) =
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if not <| approxEqDoubleEpsilonWithError(a, b, c) then raise <| new Xunit.Sdk.EqualException(a,b)
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static member NotApproximatelyEqualEpsilon(a : float32, b : float32) =
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if approxEqSingleEpsilon a b then raise <| new Xunit.Sdk.EqualException(a,b)
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static member NotApproximatelyEqualEpsilon(a : float32, b : float32, c : float32) =
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if approxEqSingleEpsilonWithError(a, b, c) then raise <| new Xunit.Sdk.EqualException(a,b)
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static member NotApproximatelyEqualEpsilon(a : float, b : float) =
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if approxEqDoubleEpsilon a b then raise <| new Xunit.Sdk.EqualException(a,b)
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static member NotApproximatelyEqualEpsilon(a : float, b : float, c : float) =
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if approxEqDoubleEpsilonWithError(a, b, c) then raise <| new Xunit.Sdk.EqualException(a,b)
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static member ThrowsIndexExn(f:unit -> unit) = Assert.Throws<IndexOutOfRangeException>(f) |> ignore
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@ -6,8 +6,9 @@ open FsCheck.Xunit
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open System
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open OpenTK
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[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
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module MathHelper =
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[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
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module ``ApproximatelyEqual (delta)`` =
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/// This test ensures that approximately equal can never get it 'wrong' about the values.
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[<Property>]
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let ``ApproximatelyEqual is never incorrect`` (a : float32,b : float32,bits : int32) =
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@ -53,3 +54,299 @@ module MathHelper =
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let b = 0.0f
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Assert.Equal(a,b)
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Assert.True(MathHelper.ApproximatelyEqual(a,b,0))
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[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
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module ``ApproximatelyEqual (single-precision epsilon)`` =
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//
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for large positive values``() =
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Assert.ApproximatelyEqualEpsilon(1000000.0f, 1000001.0f);
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Assert.ApproximatelyEqualEpsilon(1000001.0f, 1000000.0f);
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Assert.NotApproximatelyEqualEpsilon(10000.0f, 10001.0f);
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Assert.NotApproximatelyEqualEpsilon(10001.0f, 10000.0f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for large negative values``() =
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Assert.ApproximatelyEqualEpsilon(-1000000.0f, -1000001.0f);
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Assert.ApproximatelyEqualEpsilon(-1000001.0f, -1000000.0f);
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Assert.NotApproximatelyEqualEpsilon(-10000.0f, -10001.0f);
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Assert.NotApproximatelyEqualEpsilon(-10001.0f, -10000.0f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for positive values around 1``() =
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Assert.ApproximatelyEqualEpsilon(1.0000001f, 1.0000002f);
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Assert.ApproximatelyEqualEpsilon(1.0000002f, 1.0000001f);
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Assert.NotApproximatelyEqualEpsilon(1.0002f, 1.0001f);
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Assert.NotApproximatelyEqualEpsilon(1.0001f, 1.0002f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for negative values around -1``() =
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Assert.ApproximatelyEqualEpsilon(-1.000001f, -1.000002f);
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Assert.ApproximatelyEqualEpsilon(-1.000002f, -1.000001f);
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Assert.NotApproximatelyEqualEpsilon(-1.0001f, -1.0002f);
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Assert.NotApproximatelyEqualEpsilon(-1.0002f, -1.0001f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values between 1 and 0``() =
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Assert.ApproximatelyEqualEpsilon(0.000000001000001f, 0.000000001000002f);
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Assert.ApproximatelyEqualEpsilon(0.000000001000002f, 0.000000001000001f);
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Assert.NotApproximatelyEqualEpsilon(0.000000000001002f, 0.000000000001001f);
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Assert.NotApproximatelyEqualEpsilon(0.000000000001001f, 0.000000000001002f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values between -1 and 0``() =
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Assert.ApproximatelyEqualEpsilon(-0.000000001000001f, -0.000000001000002f);
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Assert.ApproximatelyEqualEpsilon(-0.000000001000002f, -0.000000001000001f);
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Assert.NotApproximatelyEqualEpsilon(-0.000000000001002f, -0.000000000001001f);
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Assert.NotApproximatelyEqualEpsilon(-0.000000000001001f, -0.000000000001002f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for comparisons involving 0``() =
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Assert.ApproximatelyEqualEpsilon(0.0f, 0.0f);
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Assert.ApproximatelyEqualEpsilon(0.0f, -0.0f);
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Assert.ApproximatelyEqualEpsilon(-0.0f, -0.0f);
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Assert.NotApproximatelyEqualEpsilon(0.00000001f, 0.0f);
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Assert.NotApproximatelyEqualEpsilon(0.0f, 0.00000001f);
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Assert.NotApproximatelyEqualEpsilon(-0.00000001f, 0.0f);
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Assert.NotApproximatelyEqualEpsilon(0.0f, -0.00000001f);
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Assert.ApproximatelyEqualEpsilon(0.0f, 1e-40f, 0.01f);
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Assert.ApproximatelyEqualEpsilon(1e-40f, 0.0f, 0.01f);
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Assert.NotApproximatelyEqualEpsilon(1e-40f, 0.0f, 0.000001f);
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Assert.NotApproximatelyEqualEpsilon(0.0f, 1e-40f, 0.000001f);
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Assert.ApproximatelyEqualEpsilon(0.0f, -1e-40f, 0.1f);
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Assert.ApproximatelyEqualEpsilon(-1e-40f, 0.0f, 0.1f);
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Assert.NotApproximatelyEqualEpsilon(-1e-40f, 0.0f, 0.00000001f);
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Assert.NotApproximatelyEqualEpsilon(0.0f, -1e-40f, 0.00000001f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for extreme values with overflow potential``() =
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Assert.ApproximatelyEqualEpsilon(System.Single.MaxValue, System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(System.Single.MaxValue, -System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(-System.Single.MaxValue, System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(System.Single.MaxValue, System.Single.MaxValue / 2.0f);
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Assert.NotApproximatelyEqualEpsilon(System.Single.MaxValue, -System.Single.MaxValue / 2.0f);
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Assert.NotApproximatelyEqualEpsilon(-System.Single.MaxValue, System.Single.MaxValue / 2.0f);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values involving infinities``() =
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Assert.ApproximatelyEqualEpsilon(System.Single.PositiveInfinity, System.Single.PositiveInfinity);
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Assert.ApproximatelyEqualEpsilon(System.Single.NegativeInfinity, System.Single.NegativeInfinity);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NegativeInfinity, System.Single.PositiveInfinity);
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Assert.NotApproximatelyEqualEpsilon(System.Single.PositiveInfinity, System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NegativeInfinity, -System.Single.MaxValue);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values involving NaN``() =
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, 0.0f);
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Assert.NotApproximatelyEqualEpsilon(-0.0f, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, -0.0f);
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Assert.NotApproximatelyEqualEpsilon(0.0f, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, System.Single.PositiveInfinity);
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Assert.NotApproximatelyEqualEpsilon(System.Single.PositiveInfinity, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, System.Single.NegativeInfinity);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NegativeInfinity, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(System.Single.MaxValue, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, -System.Single.MaxValue);
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Assert.NotApproximatelyEqualEpsilon(-System.Single.MaxValue, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(System.Single.Epsilon, System.Single.NaN);
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Assert.NotApproximatelyEqualEpsilon(System.Single.NaN, -System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(-System.Single.Epsilon, System.Single.NaN);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values on opposite sides of 0``() =
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Assert.NotApproximatelyEqualEpsilon(1.000000001f, -1.0f);
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Assert.NotApproximatelyEqualEpsilon(-1.0f, 1.000000001f);
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Assert.NotApproximatelyEqualEpsilon(-1.000000001f, 1.0f);
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Assert.NotApproximatelyEqualEpsilon(1.0f, -1.000000001f);
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Assert.ApproximatelyEqualEpsilon(10.0f * System.Single.Epsilon, 10.0f * -System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(10000.0f * System.Single.Epsilon, 10000.0f * -System.Single.Epsilon);
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[<Fact>]
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let ``ApproximatelyEqual (single precision) is correct for values very close to 0``() =
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Assert.ApproximatelyEqualEpsilon(System.Single.Epsilon, System.Single.Epsilon);
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Assert.ApproximatelyEqualEpsilon(System.Single.Epsilon, -System.Single.Epsilon);
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Assert.ApproximatelyEqualEpsilon(-System.Single.Epsilon, System.Single.Epsilon);
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Assert.ApproximatelyEqualEpsilon(System.Single.Epsilon, 0.0f);
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Assert.ApproximatelyEqualEpsilon(0.0f, System.Single.Epsilon);
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Assert.ApproximatelyEqualEpsilon(-System.Single.Epsilon, 0.0f);
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Assert.ApproximatelyEqualEpsilon(0.0f, -System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(0.000000001f, -System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(0.000000001f, System.Single.Epsilon);
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Assert.NotApproximatelyEqualEpsilon(System.Single.Epsilon, 0.000000001f);
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Assert.NotApproximatelyEqualEpsilon(-System.Single.Epsilon, 0.000000001f);
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[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
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module ``ApproximatelyEqual (double-precision epsilon)`` =
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//
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[<Fact>]
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let ``ApproximatelyEqual (double precision) is correct for large positive values``() =
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Assert.ApproximatelyEqualEpsilon(1000000.0, 1000001.0);
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Assert.ApproximatelyEqualEpsilon(1000001.0, 1000000.0);
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Assert.NotApproximatelyEqualEpsilon(10000.0, 10001.0);
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Assert.NotApproximatelyEqualEpsilon(10001.0, 10000.0);
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[<Fact>]
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let ``ApproximatelyEqual (double precision) is correct for large negative values``() =
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Assert.ApproximatelyEqualEpsilon(-1000000.0, -1000001.0);
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Assert.ApproximatelyEqualEpsilon(-1000001.0, -1000000.0);
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Assert.NotApproximatelyEqualEpsilon(-10000.0, -10001.0);
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Assert.NotApproximatelyEqualEpsilon(-10001.0, -10000.0);
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[<Fact>]
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||||
let ``ApproximatelyEqual (double precision) is correct for positive values around 1``() =
|
||||
Assert.ApproximatelyEqualEpsilon(1.0000001, 1.0000002);
|
||||
Assert.ApproximatelyEqualEpsilon(1.0000002, 1.0000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(1.0002, 1.0001);
|
||||
Assert.NotApproximatelyEqualEpsilon(1.0001, 1.0002);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for negative values around -1``() =
|
||||
Assert.ApproximatelyEqualEpsilon(-1.000001, -1.000002);
|
||||
Assert.ApproximatelyEqualEpsilon(-1.000002, -1.000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-1.0001, -1.0002);
|
||||
Assert.NotApproximatelyEqualEpsilon(-1.0002, -1.0001);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values between 1 and 0``() =
|
||||
Assert.ApproximatelyEqualEpsilon(0.000000001000001, 0.000000001000002);
|
||||
Assert.ApproximatelyEqualEpsilon(0.000000001000002, 0.000000001000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.000000000001002, 0.000000000001001);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.000000000001001, 0.000000000001002);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values between -1 and 0``() =
|
||||
Assert.ApproximatelyEqualEpsilon(-0.000000001000001, -0.000000001000002);
|
||||
Assert.ApproximatelyEqualEpsilon(-0.000000001000002, -0.000000001000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-0.000000000001002, -0.000000000001001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-0.000000000001001, -0.000000000001002);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for comparisons involving 0``() =
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, 0.0);
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, -0.0);
|
||||
Assert.ApproximatelyEqualEpsilon(-0.0, -0.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.00000001, 0.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.0, 0.00000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-0.00000001, 0.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.0, -0.00000001);
|
||||
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, 1e-310, 0.01);
|
||||
Assert.ApproximatelyEqualEpsilon(1e-310, 0.0, 0.01);
|
||||
Assert.NotApproximatelyEqualEpsilon(1e-310, 0.0, 0.000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.0, 1e-310, 0.000001);
|
||||
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, -1e-310, 0.1);
|
||||
Assert.ApproximatelyEqualEpsilon(-1e-310, 0.0, 0.1);
|
||||
Assert.NotApproximatelyEqualEpsilon(-1e-310, 0.0, 0.00000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.0, -1e-310, 0.00000001);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for extreme values with overflow potential``() =
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.MaxValue, System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.MaxValue, -System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(-System.Double.MaxValue, System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.MaxValue, System.Double.MaxValue / 2.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.MaxValue, -System.Double.MaxValue / 2.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(-System.Double.MaxValue, System.Double.MaxValue / 2.0);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values involving infinities``() =
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.PositiveInfinity, System.Double.PositiveInfinity);
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.NegativeInfinity, System.Double.NegativeInfinity);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NegativeInfinity, System.Double.PositiveInfinity);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.PositiveInfinity, System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NegativeInfinity, -System.Double.MaxValue);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values involving NaN``() =
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, 0.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(-0.0, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, -0.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.0, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, System.Double.PositiveInfinity);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.PositiveInfinity, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, System.Double.NegativeInfinity);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NegativeInfinity, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.MaxValue, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, -System.Double.MaxValue);
|
||||
Assert.NotApproximatelyEqualEpsilon(-System.Double.MaxValue, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, System.Double.Epsilon);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.Epsilon, System.Double.NaN);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.NaN, -System.Double.Epsilon);
|
||||
Assert.NotApproximatelyEqualEpsilon(-System.Double.Epsilon, System.Double.NaN);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values on opposite sides of 0``() =
|
||||
Assert.NotApproximatelyEqualEpsilon(1.000000001, -1.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(-1.0, 1.000000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-1.000000001, 1.0);
|
||||
Assert.NotApproximatelyEqualEpsilon(1.0, -1.000000001);
|
||||
Assert.ApproximatelyEqualEpsilon(10.0 * System.Double.Epsilon, 10.0 * -System.Double.Epsilon);
|
||||
Assert.NotApproximatelyEqualEpsilon(100000000000.0 * System.Double.Epsilon, 100000000000.0 * -System.Double.Epsilon);
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEqual (double precision) is correct for values very close to 0``() =
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.Epsilon, System.Double.Epsilon);
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.Epsilon, -System.Double.Epsilon);
|
||||
Assert.ApproximatelyEqualEpsilon(-System.Double.Epsilon, System.Double.Epsilon);
|
||||
Assert.ApproximatelyEqualEpsilon(System.Double.Epsilon, 0.0);
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, System.Double.Epsilon);
|
||||
Assert.ApproximatelyEqualEpsilon(-System.Double.Epsilon, 0.0);
|
||||
Assert.ApproximatelyEqualEpsilon(0.0, -System.Double.Epsilon);
|
||||
|
||||
Assert.NotApproximatelyEqualEpsilon(0.000000001, -System.Double.Epsilon);
|
||||
Assert.NotApproximatelyEqualEpsilon(0.000000001, System.Double.Epsilon);
|
||||
Assert.NotApproximatelyEqualEpsilon(System.Double.Epsilon, 0.000000001);
|
||||
Assert.NotApproximatelyEqualEpsilon(-System.Double.Epsilon, 0.000000001);
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module ``ApproximatelyEquivalent (tolerance diff)`` =
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent correctly approximates equivalence where the difference falls below the tolerance``() =
|
||||
let a = 0.0001f
|
||||
let b = 0.00019f
|
||||
Assert.NotEqual(a,b)
|
||||
Assert.True(MathHelper.ApproximatelyEquivalent(a, b, 0.0001f))
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent correctly approximates equivalence where the difference is the tolerance``() =
|
||||
let a = 0.0001f
|
||||
let b = 0.0002f
|
||||
Assert.NotEqual(a,b)
|
||||
Assert.True(MathHelper.ApproximatelyEquivalent(a, b, 0.0001f))
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent correctly approximates inequivalence where the difference exceeds the tolerance``() =
|
||||
let a = 0.0001f
|
||||
let b = 0.00021f
|
||||
Assert.NotEqual(a,b)
|
||||
Assert.False(MathHelper.ApproximatelyEquivalent(a, b, 0.0001f))
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent reports very different values as non-equal even with a high tolerance``() =
|
||||
let a = 3.0f
|
||||
let b = 1.0f
|
||||
Assert.NotEqual(a,b)
|
||||
Assert.False(MathHelper.ApproximatelyEquivalent(a, b, 1.0f))
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent works with single zero value``() =
|
||||
let a = 1.0f
|
||||
let b = 0.0f
|
||||
Assert.NotEqual(a,b)
|
||||
Assert.False(MathHelper.ApproximatelyEquivalent(a, b, 0.0001f))
|
||||
|
||||
[<Fact>]
|
||||
let ``ApproximatelyEquivalent works with both zero values``() =
|
||||
let a = 0.0f
|
||||
let b = 0.0f
|
||||
Assert.Equal(a,b)
|
||||
Assert.True(MathHelper.ApproximatelyEquivalent(a, b, 0.0001f))
|
||||
|
|
@ -145,20 +145,20 @@ module Vector2 =
|
|||
[<Property>]
|
||||
let ``Vector addition is the same as component addition`` (a : Vector2,b : Vector2) =
|
||||
let c = a + b
|
||||
Assert.ApproximatelyEqual(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEqual(a.Y + b.Y,c.Y)
|
||||
Assert.ApproximatelyEquivalent(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y + b.Y,c.Y)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector addition is commutative`` (a : Vector2,b : Vector2) =
|
||||
let c = a + b
|
||||
let c2 = b + a
|
||||
Assert.ApproximatelyEqual(c,c2)
|
||||
Assert.ApproximatelyEquivalent(c,c2)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector addition is associative`` (a : Vector2,b : Vector2,c : Vector2) =
|
||||
let r1 = (a + b) + c
|
||||
let r2 = a + (b + c)
|
||||
Assert.ApproximatelyEqual(r1,r2)
|
||||
Assert.ApproximatelyEquivalent(r1,r2)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2 addition method is the same as component addition`` (a : Vector2, b : Vector2) =
|
||||
|
|
@ -166,7 +166,7 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X + b.X, a.Y + b.Y)
|
||||
let sum = Vector2.Add(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2 addition method by reference is the same as component addition`` (a : Vector2, b : Vector2) =
|
||||
|
|
@ -174,7 +174,7 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X + b.X, a.Y + b.Y)
|
||||
let sum = Vector2.Add(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Multiplication =
|
||||
|
|
@ -210,7 +210,7 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X * b.X, a.Y * b.Y)
|
||||
let sum = Vector2.Multiply(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2 multiplication method by reference is the same as component multiplication`` (a : Vector2, b : Vector2) =
|
||||
|
|
@ -218,7 +218,7 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X * b.X, a.Y * b.Y)
|
||||
let sum = Vector2.Multiply(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static method Vector2-scalar multiplication is the same as component-scalar multiplication`` (a : Vector2, f : float32) =
|
||||
|
|
@ -242,7 +242,7 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X - b.X, a.Y - b.Y)
|
||||
let sum = Vector2.Subtract(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2 subtraction method by reference is the same as component addition`` (a : Vector2, b : Vector2) =
|
||||
|
|
@ -250,49 +250,50 @@ module Vector2 =
|
|||
let v1 = Vector2(a.X - b.X, a.Y - b.Y)
|
||||
let sum = Vector2.Subtract(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Division =
|
||||
//
|
||||
[<Property>]
|
||||
let ``Vector2-float division is the same as component-float division`` (a : Vector2, f : float32) =
|
||||
if not (approxEq f 0.0f) then
|
||||
let r = a / f
|
||||
|
||||
Assert.ApproximatelyEqual(a.X / f,r.X)
|
||||
Assert.ApproximatelyEqual(a.Y / f,r.Y)
|
||||
Assert.ApproximatelyEquivalent(a.X / f,r.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y / f,r.Y)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2-Vector2 division method is the same as component division`` (a : Vector2, b : Vector2) =
|
||||
|
||||
if not (anyZero2 a || anyZero2 b) then
|
||||
let v1 = Vector2(a.X / b.X, a.Y / b.Y)
|
||||
let sum = Vector2.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2-Vector2 divison method by reference `` (a : Vector2, b : Vector2) =
|
||||
|
||||
if not (anyZero2 a || anyZero2 b) then
|
||||
let v1 = Vector2(a.X / b.X, a.Y / b.Y)
|
||||
let sum = Vector2.Divide(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2-scalar division method is the same as component division`` (a : Vector2, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then
|
||||
let v1 = Vector2(a.X / b, a.Y / b)
|
||||
let sum = Vector2.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector2-scalar divison method by reference is the same as component division`` (a : Vector2, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then
|
||||
let v1 = Vector2(a.X / b, a.Y / b)
|
||||
let sum = Vector2.Divide(ref a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Negation =
|
||||
|
|
@ -406,8 +407,8 @@ module Vector2 =
|
|||
if not (approxEq l 0.0f) then
|
||||
let norm = v.Normalized()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization of instance transforms the instance into a unit length vector with the correct components`` (a, b) =
|
||||
|
|
@ -418,8 +419,8 @@ module Vector2 =
|
|||
let norm = Vector2(a, b)
|
||||
norm.Normalize()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization of instance transforms the instance into a unit length vector with the correct components`` (a, b) =
|
||||
|
|
@ -429,21 +430,25 @@ module Vector2 =
|
|||
|
||||
let scale = MathHelper.InverseSqrtFast(a * a + b * b)
|
||||
|
||||
Assert.ApproximatelyEqual(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y * scale, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y * scale, norm.Y)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization by reference is the same as division by magnitude`` (a : Vector2) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
let vRes = Vector2.Normalize(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization is the same as division by magnitude`` (a : Vector2) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector2.Normalize(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector2.Normalize(a));
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization by reference is the same as multiplication by the fast inverse square`` (a : Vector2) =
|
||||
|
|
@ -452,7 +457,7 @@ module Vector2 =
|
|||
let norm = a * scale
|
||||
let vRes = Vector2.NormalizeFast(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization is the same as multiplication by the fast inverse square`` (a : Vector2) =
|
||||
|
|
@ -460,13 +465,15 @@ module Vector2 =
|
|||
|
||||
let norm = a * scale
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector2.NormalizeFast(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector2.NormalizeFast(a));
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module ``Magnitude min and max`` =
|
||||
//
|
||||
[<Property>]
|
||||
let ``MagnitudeMin selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector2, v2: Vector2) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -481,6 +488,8 @@ module Vector2 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax selects the vector with equal or greater magnitude given two vectors`` (v1 : Vector2, v2: Vector2) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -495,6 +504,8 @@ module Vector2 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMin by reference selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector2, v2: Vector2) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -509,6 +520,8 @@ module Vector2 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax by reference selects the vector with equal greater magnitude given two vectors`` (v1 : Vector2, v2: Vector2) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -567,7 +580,7 @@ module Vector2 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = Vector2(transformedQuat.X, transformedQuat.Y)
|
||||
|
||||
Assert.Equal(transformedVector, Vector2.Transform(v, q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector2.Transform(v, q))
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by quaternion by reference is the same as multiplication by quaternion and its conjugate`` (v : Vector2, q : Quaternion) =
|
||||
|
|
@ -577,7 +590,7 @@ module Vector2 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = Vector2(transformedQuat.X, transformedQuat.Y)
|
||||
|
||||
Assert.Equal(transformedVector, Vector2.Transform(ref v, ref q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector2.Transform(ref v, ref q))
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Serialization =
|
||||
|
|
|
|||
|
|
@ -136,9 +136,9 @@ module Vector3 =
|
|||
if not (approxEq l 0.0f) then
|
||||
let norm = v.Normalized()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z / l, norm.Z)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization of instance transforms the instance into a unit length vector with the correct components`` (a, b, c) =
|
||||
|
|
@ -149,9 +149,9 @@ module Vector3 =
|
|||
let norm = Vector3(a, b, c)
|
||||
norm.Normalize()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z / l, norm.Z)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization of instance transforms the instance into a unit length vector with the correct components`` (a, b, c) =
|
||||
|
|
@ -161,22 +161,26 @@ module Vector3 =
|
|||
|
||||
let scale = MathHelper.InverseSqrtFast(a * a + b * b + c * c)
|
||||
|
||||
Assert.ApproximatelyEqual(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y * scale, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z * scale, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y * scale, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z * scale, norm.Z)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization by reference is the same as division by magnitude`` (a : Vector3) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
let vRes = Vector3.Normalize(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization is the same as division by magnitude`` (a : Vector3) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector3.Normalize(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector3.Normalize(a));
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization by reference is the same as multiplication by the fast inverse square`` (a : Vector3) =
|
||||
|
|
@ -185,7 +189,7 @@ module Vector3 =
|
|||
let norm = a * scale
|
||||
let vRes = Vector3.NormalizeFast(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization is the same as multiplication by fast inverse square`` (a : Vector3) =
|
||||
|
|
@ -193,7 +197,7 @@ module Vector3 =
|
|||
|
||||
let norm = a * scale
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector3.NormalizeFast(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector3.NormalizeFast(a));
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Addition =
|
||||
|
|
@ -202,23 +206,23 @@ module Vector3 =
|
|||
let ``Vector3 addition is the same as component addition`` (a : Vector3, b : Vector3) =
|
||||
let c = a + b
|
||||
|
||||
Assert.ApproximatelyEqual(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEqual(a.Y + b.Y,c.Y)
|
||||
Assert.ApproximatelyEqual(a.Z + b.Z,c.Z)
|
||||
Assert.ApproximatelyEquivalent(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y + b.Y,c.Y)
|
||||
Assert.ApproximatelyEquivalent(a.Z + b.Z,c.Z)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector3 addition is commutative`` (a : Vector3, b : Vector3) =
|
||||
let c = a + b
|
||||
let c2 = b + a
|
||||
|
||||
Assert.ApproximatelyEqual(c, c2)
|
||||
Assert.ApproximatelyEquivalent(c, c2)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector3 addition is associative`` (a : Vector3, b : Vector3, c : Vector3) =
|
||||
let r1 = (a + b) + c
|
||||
let r2 = a + (b + c)
|
||||
|
||||
Assert.ApproximatelyEqual(r1, r2)
|
||||
Assert.ApproximatelyEquivalent(r1, r2)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3 addition method is the same as component addition`` (a : Vector3, b : Vector3) =
|
||||
|
|
@ -226,7 +230,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X + b.X, a.Y + b.Y, a.Z + b.Z)
|
||||
let sum = Vector3.Add(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3 addition method by reference is the same as component addition`` (a : Vector3, b : Vector3) =
|
||||
|
|
@ -234,7 +238,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X + b.X, a.Y + b.Y, a.Z + b.Z)
|
||||
let sum = Vector3.Add(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Subtraction =
|
||||
|
|
@ -253,7 +257,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X - b.X, a.Y - b.Y, a.Z - b.Z)
|
||||
let sum = Vector3.Subtract(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3 subtraction method by reference is the same as component addition`` (a : Vector3, b : Vector3) =
|
||||
|
|
@ -261,7 +265,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X - b.X, a.Y - b.Y, a.Z - b.Z)
|
||||
let sum = Vector3.Subtract(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Multiplication =
|
||||
|
|
@ -334,7 +338,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X * b.X, a.Y * b.Y, a.Z * b.Z)
|
||||
let sum = Vector3.Multiply(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3 multiplication method by reference is the same as component multiplication`` (a : Vector3, b : Vector3) =
|
||||
|
|
@ -342,7 +346,7 @@ module Vector3 =
|
|||
let v1 = Vector3(a.X * b.X, a.Y * b.Y, a.Z * b.Z)
|
||||
let sum = Vector3.Multiply(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Division =
|
||||
|
|
@ -352,41 +356,41 @@ module Vector3 =
|
|||
if not (approxEq f 0.0f) then // we don't support diving by zero.
|
||||
let r = a / f
|
||||
|
||||
Assert.ApproximatelyEqual(a.X / f,r.X)
|
||||
Assert.ApproximatelyEqual(a.Y / f,r.Y)
|
||||
Assert.ApproximatelyEqual(a.Z / f,r.Z)
|
||||
Assert.ApproximatelyEquivalent(a.X / f,r.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y / f,r.Y)
|
||||
Assert.ApproximatelyEquivalent(a.Z / f,r.Z)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3-Vector3 division method is the same as component division`` (a : Vector3, b : Vector3) =
|
||||
|
||||
if not (anyZero3 a || anyZero3 b) then
|
||||
let v1 = Vector3(a.X / b.X, a.Y / b.Y, a.Z / b.Z)
|
||||
let sum = Vector3.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3-Vector3 divison method by reference is the same as component division`` (a : Vector3, b : Vector3) =
|
||||
|
||||
if not (anyZero3 a || anyZero3 b) then
|
||||
let v1 = Vector3(a.X / b.X, a.Y / b.Y, a.Z / b.Z)
|
||||
let sum = Vector3.Divide(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3-scalar division method is the same as component division`` (a : Vector3, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then // we don't support diving by zero.
|
||||
let v1 = Vector3(a.X / b, a.Y / b, a.Z / b)
|
||||
let sum = Vector3.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector3-scalar divison method by reference is the same as component division`` (a : Vector3, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then // we don't support diving by zero.
|
||||
let v1 = Vector3(a.X / b, a.Y / b, a.Z / b)
|
||||
let sum = Vector3.Divide(ref a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Negation =
|
||||
|
|
@ -532,6 +536,8 @@ module Vector3 =
|
|||
//
|
||||
[<Property>]
|
||||
let ``MagnitudeMin selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector3, v2: Vector3) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -546,6 +552,8 @@ module Vector3 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax selects the vector with equal or greater magnitude given two vectors`` (v1 : Vector3, v2: Vector3) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -560,6 +568,8 @@ module Vector3 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMin by reference selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector3, v2: Vector3) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -574,6 +584,8 @@ module Vector3 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax by reference selects the vector with equal or greater magnitude given two vectors`` (v1 : Vector3, v2: Vector3) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -706,7 +718,7 @@ module Vector3 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = transformedQuat.Xyz
|
||||
|
||||
Assert.ApproximatelyEqual(transformedVector, Vector3.Transform(v, q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector3.Transform(v, q))
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by quaternion by reference is the same as multiplication by quaternion and its conjugate`` (v : Vector3, q : Quaternion) =
|
||||
|
|
@ -716,7 +728,7 @@ module Vector3 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = transformedQuat.Xyz
|
||||
|
||||
Assert.ApproximatelyEqual(transformedVector, Vector3.Transform(ref v, ref q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector3.Transform(ref v, ref q))
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by quaternion by multiplication using right-handed notation is the same as multiplication by quaternion and its conjugate`` (v : Vector3, q : Quaternion) =
|
||||
|
|
@ -726,7 +738,7 @@ module Vector3 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = transformedQuat.Xyz
|
||||
|
||||
Assert.ApproximatelyEqual(transformedVector, q * v)
|
||||
Assert.ApproximatelyEquivalent(transformedVector, q * v)
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by identity quaternion does not alter vector`` (v : Vector3) =
|
||||
|
|
@ -737,6 +749,6 @@ module Vector3 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = transformedQuat.Xyz
|
||||
|
||||
Assert.ApproximatelyEqual(v, transformedVector)
|
||||
Assert.ApproximatelyEqual(v, Vector3.Transform(v, q))
|
||||
Assert.ApproximatelyEqual(transformedVector, Vector3.Transform(v, q))
|
||||
Assert.ApproximatelyEquivalent(v, transformedVector)
|
||||
Assert.ApproximatelyEquivalent(v, Vector3.Transform(v, q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector3.Transform(v, q))
|
||||
|
|
@ -153,25 +153,29 @@ module Vector4 =
|
|||
let v = Vector4(x, y, z, w)
|
||||
let l = v.Length
|
||||
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq l 0.0f) then
|
||||
let norm = v.Normalized()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEqual(v.W / l, norm.W)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.W / l, norm.W)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization of instance transforms the instance into a unit length vector with the correct components`` (x, y, z, w) =
|
||||
let v = Vector4(x, y, z, w)
|
||||
let l = v.Length
|
||||
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq l 0.0f) then
|
||||
let norm = Vector4(x, y, z, w)
|
||||
norm.Normalize()
|
||||
|
||||
Assert.ApproximatelyEqual(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEqual(v.W / l, norm.W)
|
||||
Assert.ApproximatelyEquivalent(v.X / l, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y / l, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z / l, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.W / l, norm.W)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization of instance transforms the instance into a unit length vector with the correct components`` (x, y, z, w) =
|
||||
|
|
@ -181,23 +185,27 @@ module Vector4 =
|
|||
|
||||
let scale = MathHelper.InverseSqrtFast(x * x + y * y + z * z + w * w)
|
||||
|
||||
Assert.ApproximatelyEqual(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEqual(v.Y * scale, norm.Y)
|
||||
Assert.ApproximatelyEqual(v.Z * scale, norm.Z)
|
||||
Assert.ApproximatelyEqual(v.W * scale, norm.W)
|
||||
Assert.ApproximatelyEquivalent(v.X * scale, norm.X)
|
||||
Assert.ApproximatelyEquivalent(v.Y * scale, norm.Y)
|
||||
Assert.ApproximatelyEquivalent(v.Z * scale, norm.Z)
|
||||
Assert.ApproximatelyEquivalent(v.W * scale, norm.W)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization by reference is the same as division by magnitude`` (a : Vector4) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
let vRes = Vector4.Normalize(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Normalization is the same as division by magnitude`` (a : Vector4) =
|
||||
// Zero-length vectors can't be normalized
|
||||
if not (approxEq a.Length 0.0f) then
|
||||
let norm = a / a.Length
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector4.Normalize(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector4.Normalize(a));
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization by reference is the same as multiplication by the fast inverse square`` (a : Vector4) =
|
||||
|
|
@ -206,15 +214,14 @@ module Vector4 =
|
|||
let norm = a * scale
|
||||
let vRes = Vector4.NormalizeFast(ref a)
|
||||
|
||||
Assert.ApproximatelyEqual(norm, vRes)
|
||||
Assert.ApproximatelyEquivalent(norm, vRes)
|
||||
|
||||
[<Property>]
|
||||
let ``Fast approximate normalization is the same as multiplication by the fast inverse square`` (a : Vector4) =
|
||||
let scale = MathHelper.InverseSqrtFast(a.X * a.X + a.Y * a.Y + a.Z * a.Z + a.W * a.W)
|
||||
|
||||
let norm = a * scale
|
||||
|
||||
Assert.ApproximatelyEqual(norm, Vector4.NormalizeFast(a));
|
||||
Assert.ApproximatelyEquivalent(norm, Vector4.NormalizeFast(a));
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Addition =
|
||||
|
|
@ -223,24 +230,24 @@ module Vector4 =
|
|||
let ``Vector4 addition is the same as component addition`` (a : Vector4, b : Vector4) =
|
||||
let c = a + b
|
||||
|
||||
Assert.ApproximatelyEqual(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEqual(a.Y + b.Y,c.Y)
|
||||
Assert.ApproximatelyEqual(a.Z + b.Z,c.Z)
|
||||
Assert.ApproximatelyEqual(a.W + b.W,c.W)
|
||||
Assert.ApproximatelyEquivalent(a.X + b.X,c.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y + b.Y,c.Y)
|
||||
Assert.ApproximatelyEquivalent(a.Z + b.Z,c.Z)
|
||||
Assert.ApproximatelyEquivalent(a.W + b.W,c.W)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector4 addition is commutative`` (a : Vector4, b : Vector4) =
|
||||
let c = a + b
|
||||
let c2 = b + a
|
||||
|
||||
Assert.ApproximatelyEqual(c, c2)
|
||||
Assert.ApproximatelyEquivalent(c, c2)
|
||||
|
||||
[<Property>]
|
||||
let ``Vector4 addition is associative`` (a : Vector4, b : Vector4, c : Vector4) =
|
||||
let r1 = (a + b) + c
|
||||
let r2 = a + (b + c)
|
||||
|
||||
Assert.ApproximatelyEqual(r1, r2)
|
||||
Assert.ApproximatelyEquivalent(r1, r2)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4 addition method is the same as component addition`` (a : Vector4, b : Vector4) =
|
||||
|
|
@ -248,7 +255,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X + b.X, a.Y + b.Y, a.Z + b.Z, a.W + b.W)
|
||||
let sum = Vector4.Add(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4 addition method by reference is the same as component addition`` (a : Vector4, b : Vector4) =
|
||||
|
|
@ -256,7 +263,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X + b.X, a.Y + b.Y, a.Z + b.Z, a.W + b.W)
|
||||
let sum = Vector4.Add(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Subtraction =
|
||||
|
|
@ -276,7 +283,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X - b.X, a.Y - b.Y, a.Z - b.Z, a.W - b.W)
|
||||
let sum = Vector4.Subtract(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4 subtraction method by reference is the same as component addition`` (a : Vector4, b : Vector4) =
|
||||
|
|
@ -284,7 +291,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X - b.X, a.Y - b.Y, a.Z - b.Z, a.W - b.W)
|
||||
let sum = Vector4.Subtract(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Multiplication =
|
||||
|
|
@ -364,7 +371,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X * b.X, a.Y * b.Y, a.Z * b.Z, a.W * b.W)
|
||||
let sum = Vector4.Multiply(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4 multiplication method by reference is the same as component multiplication`` (a : Vector4, b : Vector4) =
|
||||
|
|
@ -372,7 +379,7 @@ module Vector4 =
|
|||
let v1 = Vector4(a.X * b.X, a.Y * b.Y, a.Z * b.Z, a.W * b.W)
|
||||
let sum = Vector4.Multiply(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Division =
|
||||
|
|
@ -382,42 +389,42 @@ module Vector4 =
|
|||
if not (approxEq f 0.0f) then // we don't support diving by zero.
|
||||
let r = a / f
|
||||
|
||||
Assert.ApproximatelyEqual(a.X / f, r.X)
|
||||
Assert.ApproximatelyEqual(a.Y / f, r.Y)
|
||||
Assert.ApproximatelyEqual(a.Z / f, r.Z)
|
||||
Assert.ApproximatelyEqual(a.W / f, r.W)
|
||||
Assert.ApproximatelyEquivalent(a.X / f, r.X)
|
||||
Assert.ApproximatelyEquivalent(a.Y / f, r.Y)
|
||||
Assert.ApproximatelyEquivalent(a.Z / f, r.Z)
|
||||
Assert.ApproximatelyEquivalent(a.W / f, r.W)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4-Vector4 division method is the same as component division`` (a : Vector4, b : Vector4) =
|
||||
|
||||
if not (anyZero4 a || anyZero4 b) then
|
||||
let v1 = Vector4(a.X / b.X, a.Y / b.Y, a.Z / b.Z, a.W / b.W)
|
||||
let sum = Vector4.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4-Vector4 divison method by reference is the same as component division`` (a : Vector4, b : Vector4) =
|
||||
|
||||
if not (anyZero4 a || anyZero4 b) then
|
||||
let v1 = Vector4(a.X / b.X, a.Y / b.Y, a.Z / b.Z, a.W / b.W)
|
||||
let sum = Vector4.Divide(ref a, ref b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4-scalar division method is the same as component division`` (a : Vector4, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then // we don't support diving by zero.
|
||||
let v1 = Vector4(a.X / b, a.Y / b, a.Z / b, a.W / b)
|
||||
let sum = Vector4.Divide(a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Property>]
|
||||
let ``Static Vector4-scalar divison method by reference is the same as component division`` (a : Vector4, b : float32) =
|
||||
|
||||
if not (approxEq b 0.0f) then // we don't support diving by zero.
|
||||
let v1 = Vector4(a.X / b, a.Y / b, a.Z / b, a.W / b)
|
||||
let sum = Vector4.Divide(ref a, b)
|
||||
|
||||
Assert.ApproximatelyEqual(v1, sum)
|
||||
Assert.ApproximatelyEquivalent(v1, sum)
|
||||
|
||||
[<Properties(Arbitrary = [| typeof<OpenTKGen> |])>]
|
||||
module Negation =
|
||||
|
|
@ -696,6 +703,8 @@ module Vector4 =
|
|||
//
|
||||
[<Property>]
|
||||
let ``MagnitudeMin selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector4, v2: Vector4) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -710,6 +719,8 @@ module Vector4 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax selects the vector with equal or greater magnitude given two vectors`` (v1 : Vector4, v2: Vector4) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -724,6 +735,8 @@ module Vector4 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMin by reference selects the vector with equal or lesser magnitude given two vectors`` (v1 : Vector4, v2: Vector4) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -738,6 +751,8 @@ module Vector4 =
|
|||
|
||||
[<Property>]
|
||||
let ``MagnitudeMax by reference selects the vector with equal or greater magnitude given two vectors`` (v1 : Vector4, v2: Vector4) =
|
||||
// Results do not matter for equal vectors
|
||||
if not (v1 = v2) then
|
||||
let l1 = v1.LengthSquared
|
||||
let l2 = v2.LengthSquared
|
||||
|
||||
|
|
@ -885,7 +900,7 @@ module Vector4 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = Vector4(transformedQuat.X, transformedQuat.Y, transformedQuat.Z, transformedQuat.W)
|
||||
|
||||
Assert.Equal(transformedVector, Vector4.Transform(v, q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector4.Transform(v, q))
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by quaternion with static method by reference is the same as multiplication by quaternion and its conjugate`` (v : Vector4, q : Quaternion) =
|
||||
|
|
@ -895,7 +910,7 @@ module Vector4 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = Vector4(transformedQuat.X, transformedQuat.Y,transformedQuat.Z, transformedQuat.W)
|
||||
|
||||
Assert.Equal(transformedVector, Vector4.Transform(ref v, ref q))
|
||||
Assert.ApproximatelyEquivalent(transformedVector, Vector4.Transform(ref v, ref q))
|
||||
|
||||
[<Property>]
|
||||
let ``Transformation by quaternion by multiplication using right-handed notation is the same as multiplication by quaternion and its conjugate`` (v : Vector4, q : Quaternion) =
|
||||
|
|
@ -905,4 +920,4 @@ module Vector4 =
|
|||
let transformedQuat = q * vectorQuat * inverse
|
||||
let transformedVector = Vector4(transformedQuat.X, transformedQuat.Y, transformedQuat.Z, transformedQuat.W)
|
||||
|
||||
Assert.Equal(transformedVector, q * v)
|
||||
Assert.ApproximatelyEquivalent(transformedVector, q * v)
|
||||
Loading…
Reference in a new issue