Nuclex.Support/Tests/FloatHelperTest.cs

#region Apache License 2.0
/*
Nuclex .NET Framework
Copyright (C) 2002-2024 Markus Ewald / Nuclex Development Labs

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
#endregion // Apache License 2.0

using System;
using System.Collections.Generic;

using NUnit.Framework;

namespace Nuclex.Support {

  /// <summary>Unit Test for the FloatHelper class</summary>
  [TestFixture]
  internal class FloatHelperTest {

    /// <summary>Tests the floating point value comparison helper</summary>
    [Test]
    public void UlpDistancesOnFloatsCompareAsEqual() {
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(0.00000001f, 0.0000000100000008f, 1),
        "Minimal difference between very small floating point numbers is considered equal"
      );
      Assert.IsFalse(
        FloatHelper.AreAlmostEqual(0.00000001f, 0.0000000100000017f, 1),
        "Larger difference between very small floating point numbers is not considered equal"
      );

      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(1000000.00f, 1000000.06f, 1),
        "Minimal difference between very large floating point numbers is considered equal"
      );
      Assert.IsFalse(
        FloatHelper.AreAlmostEqual(1000000.00f, 1000000.13f, 1),
        "Larger difference between very large floating point numbers is not considered equal"
      );
    }

    /// <summary>Tests the double precision floating point value comparison helper</summary>
    [Test]
    public void UlpDistancesOnDoublesCompareAsEqual() {
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(0.00000001, 0.000000010000000000000002, 1),
        "Minimal difference between very small double precision floating point " +
        "numbers is considered equal"
      );
      Assert.IsFalse(
        FloatHelper.AreAlmostEqual(0.00000001, 0.000000010000000000000004, 1),
        "Larger difference between very small double precision floating point " +
        "numbers is not considered equal"
      );

      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(1000000.00, 1000000.0000000001, 1),
        "Minimal difference between very large double precision floating point " +
        "numbers is considered equal"
      );
      Assert.IsFalse(
        FloatHelper.AreAlmostEqual(1000000.00, 1000000.0000000002, 1),
        "Larger difference between very large double precision floating point " +
        "numbers is not considered equal"
      );
    }

    /// <summary>Tests the integer reinterpretation functions</summary>
    [Test]
    public void IntegersCanBeReinterpretedAsFloats() {
      Assert.AreEqual(
        12345.0f,
        FloatHelper.ReinterpretAsFloat(FloatHelper.ReinterpretAsInt(12345.0f)),
        "Number hasn't changed after mirrored reinterpretation"
      );
    }

    /// <summary>Tests the long reinterpretation functions</summary>
    [Test]
    public void LongsCanBeReinterpretedAsDoubles() {
      Assert.AreEqual(
        12345.67890,
        FloatHelper.ReinterpretAsDouble(FloatHelper.ReinterpretAsLong(12345.67890)),
        "Number hasn't changed after mirrored reinterpretation"
      );
    }

    /// <summary>Tests the floating point reinterpretation functions</summary>
    [Test]
    public void FloatsCanBeReinterpretedAsIntegers() {
      Assert.AreEqual(
        12345,
        FloatHelper.ReinterpretAsInt(FloatHelper.ReinterpretAsFloat(12345)),
        "Number hasn't changed after mirrored reinterpretation"
      );
    }

    /// <summary>
    ///   Verifies that the IsZero() method can distinguish zero from very small values
    /// </summary>
    [Test]
    public void CanDetermineIfFloatIsZero() {
      Assert.IsTrue(FloatHelper.IsZero(FloatHelper.PositiveZeroFloat));
      Assert.IsTrue(FloatHelper.IsZero(FloatHelper.NegativeZeroFloat));
      Assert.IsFalse(FloatHelper.IsZero(1.401298E-45f));
      Assert.IsFalse(FloatHelper.IsZero(-1.401298E-45f));
    }

    /// <summary>
    ///   Verifies that the IsZero() method can distinguish zero from very small values
    /// </summary>
    [Test]
    public void CanDetermineIfDoubleIsZero() {
      Assert.IsTrue(FloatHelper.IsZero(FloatHelper.PositiveZeroDouble));
      Assert.IsTrue(FloatHelper.IsZero(FloatHelper.NegativeZeroDouble));
      Assert.IsFalse(FloatHelper.IsZero(4.94065645841247E-324));
      Assert.IsFalse(FloatHelper.IsZero(-4.94065645841247E-324));
    }

    /// <summary>
    ///   Tests the double prevision floating point reinterpretation functions
    /// </summary>
    [Test]
    public void DoublesCanBeReinterpretedAsLongs() {
      Assert.AreEqual(
        1234567890,
        FloatHelper.ReinterpretAsLong(FloatHelper.ReinterpretAsDouble(1234567890)),
        "Number hasn't changed after mirrored reinterpretation"
      );
    }

    /// <summary>
    ///   Verifies that two denormalized floats can be compared in ulps
    /// </summary>
    [Test]
    public void DenormalizedFloatsCanBeCompared() {
      float zero = 0.0f;
      float zeroPlusOneUlp = FloatHelper.ReinterpretAsFloat(
        FloatHelper.ReinterpretAsInt(zero) + 1
      );
      float zeroMinusOneUlp = -zeroPlusOneUlp;

      // Across zero
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zeroMinusOneUlp, zeroPlusOneUlp, 1));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zeroPlusOneUlp, zeroMinusOneUlp, 2));

      // Against zero
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zero, zeroPlusOneUlp, 0));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zero, zeroPlusOneUlp, 1));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zero, zeroMinusOneUlp, 0));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zero, zeroMinusOneUlp, 1));
    }

    /// <summary>
    ///   Verifies that the negative floating point zero is within one ulp of the positive
    ///   floating point zero and vice versa
    /// </summary>
    [Test]
    public void NegativeZeroFloatEqualsPositiveZero() {
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(
          FloatHelper.NegativeZeroFloat, FloatHelper.PositiveZeroFloat, 0
        )
      );
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(
          FloatHelper.PositiveZeroFloat, FloatHelper.NegativeZeroFloat, 0
        )
      );
    }

    /// <summary>Verifies that floats can be compared across the zero boundary</summary>
    [Test]
    public void FloatsCanBeComparedAcrossZeroInUlps() {
      float tenUlps = float.Epsilon * 10.0f;

      Assert.IsTrue(FloatHelper.AreAlmostEqual(-tenUlps, tenUlps, 20));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(tenUlps, -tenUlps, 20));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(-tenUlps, tenUlps, 19));

      Assert.IsTrue(FloatHelper.AreAlmostEqual(-tenUlps, 0, 10));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(0, -tenUlps, 10));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(-tenUlps, 0, 9));

      Assert.IsTrue(FloatHelper.AreAlmostEqual(0, tenUlps, 10));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(tenUlps, 0, 10));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(0, tenUlps, 9));
    }

    /// <summary>
    ///   Verifies that two denormalized doubles can be compared in ulps
    /// </summary>
    [Test]
    public void DenormalizedDoublesCanBeCompared() {
      double zero = 0.0;
      double zeroPlusOneUlp = FloatHelper.ReinterpretAsDouble(
        FloatHelper.ReinterpretAsLong(zero) + 1
      );
      double zeroMinusOneUlp = -zeroPlusOneUlp;

      // Across zero
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zeroMinusOneUlp, zeroPlusOneUlp, 1));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zeroPlusOneUlp, zeroMinusOneUlp, 2));

      // Against zero
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zero, zeroPlusOneUlp, 0));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zero, zeroPlusOneUlp, 1));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(zero, zeroMinusOneUlp, 0));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(zero, zeroMinusOneUlp, 1));
    }

    /// <summary>
    ///   Verifies that the negative double precision floating point zero is within one ulp
    ///   of the positive double precision floating point zero and vice versa
    /// </summary>
    [Test]
    public void NegativeZeroDoubleEqualsPositiveZero() {
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(
          FloatHelper.NegativeZeroDouble, FloatHelper.NegativeZeroDouble, 0
        )
      );
      Assert.IsTrue(
        FloatHelper.AreAlmostEqual(
          FloatHelper.NegativeZeroDouble, FloatHelper.NegativeZeroDouble, 0
        )
      );
    }

    /// <summary>Verifies that doubles can be compared across the zero boundary</summary>
    [Test]
    public void DoublesCanBeComparedAcrossZeroInUlps() {
      double tenUlps = double.Epsilon * 10.0;

      Assert.IsTrue(FloatHelper.AreAlmostEqual(-tenUlps, tenUlps, 20));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(tenUlps, -tenUlps, 20));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(-tenUlps, tenUlps, 19));

      Assert.IsTrue(FloatHelper.AreAlmostEqual(-tenUlps, 0, 10));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(0, -tenUlps, 10));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(-tenUlps, 0, 9));

      Assert.IsTrue(FloatHelper.AreAlmostEqual(0, tenUlps, 10));
      Assert.IsTrue(FloatHelper.AreAlmostEqual(tenUlps, 0, 10));
      Assert.IsFalse(FloatHelper.AreAlmostEqual(0, tenUlps, 9));
    }

  }

} // namespace Nuclex.Support