//
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
//
using System;
using MbUnit.Framework;
namespace MathNet.Numerics.UnitTests
{
[TestFixture]
public sealed class PrecisionTest
{
private const double _acceptableError = 1e-12;
private readonly double _doublePrecision = System.Math.Pow(2, -53);
[Test]
public void Magnitude()
{
Assert.AreEqual(0, Precision.Magnitude(0));
Assert.AreEqual(0, Precision.Magnitude(1));
Assert.AreEqual(1, Precision.Magnitude(10));
Assert.AreEqual(2, Precision.Magnitude(100));
Assert.AreEqual(3, Precision.Magnitude(1000));
Assert.AreEqual(4, Precision.Magnitude(10000));
Assert.AreEqual(5, Precision.Magnitude(100000));
Assert.AreEqual(6, Precision.Magnitude(1000000));
Assert.AreEqual(7, Precision.Magnitude(1e7));
Assert.AreEqual(8, Precision.Magnitude(1e8));
Assert.AreEqual(9, Precision.Magnitude(1e9));
Assert.AreEqual(10, Precision.Magnitude(1e10));
Assert.AreEqual(11, Precision.Magnitude(1e11));
Assert.AreEqual(12, Precision.Magnitude(1e12));
Assert.AreEqual(5, Precision.Magnitude(1.1e5));
Assert.AreEqual(-5, Precision.Magnitude(2.2e-5));
Assert.AreEqual(9, Precision.Magnitude(3.3e9));
Assert.AreEqual(-11, Precision.Magnitude(4.4e-11));
}
// Bug fix test: Magnitude of negative numbers returns zero
[Test]
public void MagnitudeWithNegativeValues()
{
Assert.AreEqual(0, Precision.Magnitude(-1));
Assert.AreEqual(1, Precision.Magnitude(-10));
Assert.AreEqual(2, Precision.Magnitude(-100));
Assert.AreEqual(3, Precision.Magnitude(-1000));
Assert.AreEqual(4, Precision.Magnitude(-10000));
Assert.AreEqual(5, Precision.Magnitude(-100000));
Assert.AreEqual(6, Precision.Magnitude(-1000000));
Assert.AreEqual(7, Precision.Magnitude(-1e7));
Assert.AreEqual(8, Precision.Magnitude(-1e8));
Assert.AreEqual(9, Precision.Magnitude(-1e9));
Assert.AreEqual(10, Precision.Magnitude(-1e10));
Assert.AreEqual(11, Precision.Magnitude(-1e11));
Assert.AreEqual(12, Precision.Magnitude(-1e12));
Assert.AreEqual(5, Precision.Magnitude(-1.1e5));
Assert.AreEqual(-5, Precision.Magnitude(-2.2e-5));
Assert.AreEqual(9, Precision.Magnitude(-3.3e9));
Assert.AreEqual(-11, Precision.Magnitude(-4.4e-11));
}
[Test]
public void Value()
{
Assert.AreApproximatelyEqual(0, Precision.GetMagnitudeScaledValue(0), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(1), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(10), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(100), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(1000), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(10000), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(100000), _acceptableError);
Assert.AreApproximatelyEqual(1, Precision.GetMagnitudeScaledValue(1000000), _acceptableError);
Assert.AreApproximatelyEqual(1.1, Precision.GetMagnitudeScaledValue(1.1e5), _acceptableError);
Assert.AreApproximatelyEqual(2.2, Precision.GetMagnitudeScaledValue(2.2e-5), _acceptableError);
Assert.AreApproximatelyEqual(3.3, Precision.GetMagnitudeScaledValue(3.3e9), _acceptableError);
Assert.AreApproximatelyEqual(4.4, Precision.GetMagnitudeScaledValue(4.4e-11), _acceptableError);
}
// Bug fix test: Magnitude of negative numbers returns zero
[Test]
public void ValueWithNegativeValues()
{
Assert.AreApproximatelyEqual(0, Precision.GetMagnitudeScaledValue(0), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-1), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-10), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-100), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-1000), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-10000), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-100000), _acceptableError);
Assert.AreApproximatelyEqual(-1, Precision.GetMagnitudeScaledValue(-1000000), _acceptableError);
Assert.AreApproximatelyEqual(-1.1, Precision.GetMagnitudeScaledValue(-1.1e5), _acceptableError);
Assert.AreApproximatelyEqual(-2.2, Precision.GetMagnitudeScaledValue(-2.2e-5), _acceptableError);
Assert.AreApproximatelyEqual(-3.3, Precision.GetMagnitudeScaledValue(-3.3e9), _acceptableError);
Assert.AreApproximatelyEqual(-4.4, Precision.GetMagnitudeScaledValue(-4.4e-11), _acceptableError);
}
[Test]
public void IncrementAtZero()
{
double x = -2 * double.Epsilon;
Assert.AreEqual(-2 * double.Epsilon, x);
x = Precision.Increment(x);
x = Precision.Increment(x);
Assert.AreEqual(0.0, x);
x = Precision.Increment(x);
x = Precision.Increment(x);
Assert.AreEqual(2 * double.Epsilon, x);
}
[Test]
public void DecrementAtZero()
{
double x = 2 * double.Epsilon;
Assert.AreEqual(2 * double.Epsilon, x);
x = Precision.Decrement(x);
x = Precision.Decrement(x);
Assert.AreEqual(0.0, x);
x = Precision.Decrement(x);
x = Precision.Decrement(x);
Assert.AreEqual(-2 * double.Epsilon, x);
}
[Test]
public void IncrementAtMinMax()
{
double x = double.MaxValue;
x = Precision.Increment(x);
Assert.AreEqual(double.PositiveInfinity,x);
x = double.MinValue;
Assert.AreEqual(double.MinValue, x);
x = Precision.Increment(x);
Assert.GreaterThan(x, double.MinValue);
}
[Test]
public void DecrementAtMinMax()
{
double x = double.MaxValue;
Assert.AreEqual(double.MaxValue, x);
x = Precision.Decrement(x);
Assert.GreaterThan(double.MaxValue, x);
x = double.MinValue;
Assert.AreEqual(double.MinValue, x);
x = Precision.Decrement(x);
Assert.AreEqual(double.NegativeInfinity, x);
}
[Test]
public void CoerceZero()
{
Assert.AreEqual(0.0, Precision.CoerceZero(0d));
Assert.AreEqual(0.0, Precision.CoerceZero(Precision.Increment(0.0)));
Assert.AreEqual(0.0, Precision.CoerceZero(Precision.Decrement(0.0)));
Assert.AreEqual(1.0, Precision.CoerceZero(1d));
Assert.AreEqual(-1.0, Precision.CoerceZero(-1d));
Assert.AreEqual(0.5, Precision.CoerceZero(0.5d));
Assert.AreEqual(-0.5, Precision.CoerceZero(-0.5d));
Assert.AreEqual(double.PositiveInfinity, Precision.CoerceZero(double.PositiveInfinity));
Assert.AreEqual(double.NegativeInfinity, Precision.CoerceZero(double.NegativeInfinity));
Assert.AreEqual(double.MaxValue, Precision.CoerceZero(double.MaxValue));
Assert.AreEqual(double.MinValue, Precision.CoerceZero(double.MinValue));
Assert.AreEqual(double.NaN, Precision.CoerceZero(double.NaN));
}
[Test]
public void CoerceZeroBasedOnMaxNumbersBetween()
{
Assert.AreEqual(0.0, Precision.CoerceZero(5 * double.Epsilon, 5));
Assert.AreEqual(0.0, Precision.CoerceZero(-5 * double.Epsilon, 5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(5 * double.Epsilon, 4));
Assert.AreNotEqual(0.0, Precision.CoerceZero(-5 * double.Epsilon, 4));
}
[Test]
public void CoerceZeroBasedOnRelativeTolerance()
{
Assert.AreEqual(0.0, Precision.CoerceZero(1e-6, 1e-5));
Assert.AreEqual(0.0, Precision.CoerceZero(-1e-6, 1e-5));
Assert.AreEqual(0.0, Precision.CoerceZero(1e+4, 1e+5));
Assert.AreEqual(0.0, Precision.CoerceZero(-1e+4, 1e+5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(1e-4, 1e-5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(1e-5, 1e-5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(-1e-4, 1e-5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(-1e-5, 1e-5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(1e+6, 1e+5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(1e+5, 1e+5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(-1e+6, 1e+5));
Assert.AreNotEqual(0.0, Precision.CoerceZero(-1e+5, 1e+5));
}
[Test]
public void RangeOfMatchingFloatingPointNumbersWithNegativeUlps()
{
double max;
double min;
Assert.Throws(() => Precision.RangeOfMatchingFloatingPointNumbers(10, -1, out min, out max));
}
[Test]
public void RangeOfMatchingFloatingPointNumbersWithValueAtInfinity()
{
double max;
double min;
Precision.RangeOfMatchingFloatingPointNumbers(double.PositiveInfinity, 1, out min, out max);
Assert.AreEqual(double.PositiveInfinity, min);
Assert.AreEqual(double.PositiveInfinity, max);
Precision.RangeOfMatchingFloatingPointNumbers(double.NegativeInfinity, 1, out min, out max);
Assert.AreEqual(double.NegativeInfinity, min);
Assert.AreEqual(double.NegativeInfinity, max);
}
[Test]
public void RangeOfMatchingFloatingPointNumbersWithValueAtNaN()
{
double max;
double min;
Precision.RangeOfMatchingFloatingPointNumbers(double.NaN, 1, out min, out max);
Assert.IsTrue(double.IsNaN(min));
Assert.IsTrue(double.IsNaN(max));
}
// Numbers are calculated with the UlpsCalculator program which can be found in UlpsCalculator.cs
[Test]
[Row(0, -10 * double.Epsilon, 10 * double.Epsilon)]
[Row(1.0, 0.99999999999999889, 1.0000000000000022)]
[Row(2.0, 1.9999999999999978, 2.0000000000000044)]
[Row(3.0, 2.9999999999999956, 3.0000000000000044)]
[Row(4.0, 3.9999999999999956, 4.0000000000000089)]
[Row(5.0, 4.9999999999999911, 5.0000000000000089)]
[Row(6.0, 5.9999999999999911, 6.0000000000000089)]
[Row(7.0, 6.9999999999999911, 7.0000000000000089)]
[Row(8.0, 7.9999999999999911, 8.0000000000000178)]
public void RangeOfMatchingFloatingPointNumbersWithPositiveValue(double input, double expectedMin, double expectedMax)
{
double max;
double min;
Precision.RangeOfMatchingFloatingPointNumbers(input, 10, out min, out max);
Assert.AreEqual(expectedMin, min);
Assert.AreEqual(expectedMax, max);
}
// Numbers are calculated with the UlpsCalculator program which can be found in UlpsCalculator.cs
[Test]
[Row(0, -10 * double.Epsilon, 10 * double.Epsilon)]
[Row(-1.0, -1.0000000000000022, -0.99999999999999889)]
[Row(-2.0, -2.0000000000000044, -1.9999999999999978)]
[Row(-3.0, -3.0000000000000044, -2.9999999999999956)]
[Row(-4.0, -4.0000000000000089, -3.9999999999999956)]
[Row(-5.0, -5.0000000000000089, -4.9999999999999911)]
[Row(-6.0, -6.0000000000000089, -5.9999999999999911)]
[Row(-7.0, -7.0000000000000089, -6.9999999999999911)]
[Row(-8.0, -8.0000000000000178, -7.9999999999999911)]
public void RangeOfMatchingFloatingPointNumbersWithNegativeValue(double input, double expectedMin, double expectedMax)
{
double max;
double min;
Precision.RangeOfMatchingFloatingPointNumbers(input, 10, out min, out max);
Assert.AreEqual(expectedMin, min);
Assert.AreEqual(expectedMax, max);
}
[Test]
[Row(0, 10 * double.Epsilon)]
[Row(1.0, 1.0000000000000022)]
[Row(2.0, 2.0000000000000044)]
[Row(3.0, 3.0000000000000044)]
[Row(4.0, 4.0000000000000089)]
[Row(5.0, 5.0000000000000089)]
[Row(6.0, 6.0000000000000089)]
[Row(7.0, 7.0000000000000089)]
[Row(8.0, 8.0000000000000178)]
public void MaximumMatchingFloatingPointNumberWithPositiveValue(double input, double expectedMax)
{
double max = Precision.MaximumMatchingFloatingPointNumber(input, 10);
Assert.AreEqual(expectedMax, max);
}
[Test]
[Row(0, 10 * double.Epsilon)]
[Row(-1.0, -0.99999999999999889)]
[Row(-2.0, -1.9999999999999978)]
[Row(-3.0, -2.9999999999999956)]
[Row(-4.0, -3.9999999999999956)]
[Row(-5.0, -4.9999999999999911)]
[Row(-6.0, -5.9999999999999911)]
[Row(-7.0, -6.9999999999999911)]
[Row(-8.0, -7.9999999999999911)]
public void MaximumMatchingFloatingPointNumberWithNegativeValue(double input, double expectedMax)
{
double max = Precision.MaximumMatchingFloatingPointNumber(input, 10);
Assert.AreEqual(expectedMax, max);
}
[Test]
[Row(0, -10 * double.Epsilon)]
[Row(1.0, 0.99999999999999889)]
[Row(2.0, 1.9999999999999978)]
[Row(3.0, 2.9999999999999956)]
[Row(4.0, 3.9999999999999956)]
[Row(5.0, 4.9999999999999911)]
[Row(6.0, 5.9999999999999911)]
[Row(7.0, 6.9999999999999911)]
[Row(8.0, 7.9999999999999911)]
public void MinimumMatchingFloatingPointNumberWithPositiveValue(double input, double expectedMin)
{
double min = Precision.MinimumMatchingFloatingPointNumber(input, 10);
Assert.AreEqual(expectedMin, min);
}
[Test]
[Row(0, -10 * double.Epsilon)]
[Row(-1.0, -1.0000000000000022)]
[Row(-2.0, -2.0000000000000044)]
[Row(-3.0, -3.0000000000000044)]
[Row(-4.0, -4.0000000000000089)]
[Row(-5.0, -5.0000000000000089)]
[Row(-6.0, -6.0000000000000089)]
[Row(-7.0, -7.0000000000000089)]
[Row(-8.0, -8.0000000000000178)]
public void MinimumMatchingFloatingPointNumberWithNegativeValue(double input, double expectedMin)
{
double min = Precision.MinimumMatchingFloatingPointNumber(input, 10);
Assert.AreEqual(expectedMin, min);
}
[Test]
public void RangeOfMatchingUlpsWithNegativeRelativeDifference()
{
long min;
long max;
Assert.Throws(() => Precision.RangeOfMatchingNumbers(1, -1, out min, out max));
}
[Test]
public void RangeOfMatchingUlpsWithValueAtInfinity()
{
long min;
long max;
Assert.Throws(() => Precision.RangeOfMatchingNumbers(double.PositiveInfinity, -1, out min, out max));
}
[Test]
public void RangeOfMatchingUlpsWithValueAtNaN()
{
long min;
long max;
Assert.Throws(() => Precision.RangeOfMatchingNumbers(double.NaN, -1, out min, out max));
}
[Test]
[Row(0, 10 * double.Epsilon, 10, 10)]
[Row(1.0, (1.0000000000000022 - 1.0) / 1.0, 20, 10)]
[Row(2.0, (2.0000000000000044 - 2.0) / 2.0, 20, 10)]
[Row(3.0, (3.0000000000000044 - 3.0) / 3.0, 10, 10)]
[Row(4.0, (4.0000000000000089 - 4.0) / 4.0, 20, 10)]
[Row(5.0, (5.0000000000000089 - 5.0) / 5.0, 10, 10)]
[Row(6.0, (6.0000000000000089 - 6.0) / 6.0, 10, 10)]
[Row(7.0, (7.0000000000000089 - 7.0) / 7.0, 10, 10)]
[Row(8.0, (8.0000000000000178 - 8.0) / 8.0, 20, 10)]
public void RangeOfMatchingUlpsWithPositiveValue(double input, double relativeDifference, long expectedMin, long expectedMax)
{
long min;
long max;
Precision.RangeOfMatchingNumbers(input, relativeDifference, out min, out max);
Assert.AreEqual(expectedMin, min);
Assert.AreEqual(expectedMax, max);
}
[Test]
[Row(0, 10 * double.Epsilon, 10, 10)]
[Row(-1.0, (1.0000000000000022 - 1.0) / 1.0, 10, 20)]
[Row(-2.0, (2.0000000000000044 - 2.0) / 2.0, 10, 20)]
[Row(-3.0, (3.0000000000000044 - 3.0) / 3.0, 10, 10)]
[Row(-4.0, (4.0000000000000089 - 4.0) / 4.0, 10, 20)]
[Row(-5.0, (5.0000000000000089 - 5.0) / 5.0, 10, 10)]
[Row(-6.0, (6.0000000000000089 - 6.0) / 6.0, 10, 10)]
[Row(-7.0, (7.0000000000000089 - 7.0) / 7.0, 10, 10)]
[Row(-8.0, (8.0000000000000178 - 8.0) / 8.0, 10, 20)]
public void RangeOfMatchingUlpsWithNegativeValue(double input, double relativeDifference, long expectedMin, long expectedMax)
{
long min;
long max;
Precision.RangeOfMatchingNumbers(input, relativeDifference, out min, out max);
Assert.AreEqual(expectedMin, min);
Assert.AreEqual(expectedMax, max);
}
[Test]
public void TestNumbersBetween()
{
Assert.AreEqual(0, Precision.NumbersBetween(1.0, 1.0));
Assert.AreEqual(0, Precision.NumbersBetween(0, 0));
Assert.AreEqual(0, Precision.NumbersBetween(-1.0, -1.0));
Assert.AreEqual(1, Precision.NumbersBetween(0, double.Epsilon));
Assert.AreEqual(1, Precision.NumbersBetween(0, -double.Epsilon));
Assert.AreEqual(1, Precision.NumbersBetween(double.Epsilon, 0));
Assert.AreEqual(1, Precision.NumbersBetween(-double.Epsilon, 0));
Assert.AreEqual(2, Precision.NumbersBetween(0, 2 * double.Epsilon));
Assert.AreEqual(2, Precision.NumbersBetween(0, -2 * double.Epsilon));
Assert.AreEqual(3, Precision.NumbersBetween(-double.Epsilon, 2 * double.Epsilon));
Assert.AreEqual(3, Precision.NumbersBetween(double.Epsilon, -2 * double.Epsilon));
}
// AlmostZero
[Test]
public void AlmostZeroWithMaxNumbersBetween()
{
Assert.IsTrue(Precision.AlmostZero(0, 1));
Assert.IsTrue(Precision.AlmostZero(1 * double.Epsilon, 1));
Assert.IsTrue(Precision.AlmostZero(10 * double.Epsilon, 10));
Assert.IsFalse(Precision.AlmostZero(double.NegativeInfinity, 1));
Assert.IsFalse(Precision.AlmostZero(double.PositiveInfinity, 1));
Assert.IsFalse(Precision.AlmostZero(double.NaN, 1));
}
[Test]
public void AlmostZeroWithTolerance()
{
Assert.IsTrue(Precision.AlmostZero(0));
Assert.IsTrue(Precision.AlmostZero(1 * double.Epsilon, 2 * double.Epsilon));
Assert.IsTrue(Precision.AlmostZero(10 * double.Epsilon, 20 * double.Epsilon));
Assert.IsFalse(Precision.AlmostZero(double.NegativeInfinity, 1.0));
Assert.IsFalse(Precision.AlmostZero(double.PositiveInfinity, 1.0));
Assert.IsFalse(Precision.AlmostZero(double.NaN, 1.0));
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void AlmostEqualWithMaxNumbersBetweenWithLessThanOneNumber()
{
Precision.AlmostEqual(1, 2, 0);
}
[Test]
public void AlmostEqual()
{
AssertEx.That(() => 1.0.AlmostEqual(1.0), "1.0 equals 1.0.");
AssertEx.That(() => 1.0.AlmostEqual(1.0 + _doublePrecision), "1.0 equals 1.0 + 2^(-53).");
AssertEx.That(() => 1.0.AlmostEqual(1.0 + _doublePrecision * 10), "1.0 equals 1.0 + 2^(-52).");
AssertEx.That(() => !1.0.AlmostEqual(1.0 + _doublePrecision * 100), "1.0 does not equal 1.0 + 2^(-51).");
AssertEx.That(() => !1.0.AlmostEqual(2.0), "1.0 does not equal 2.0");
}
[Test]
public void AlmostEqualWithRelativeError()
{
// compare zero and negative zero
Assert.IsTrue(Precision.AlmostEqualWithError(0.0, -0.0, 1e-5));
Assert.IsTrue(Precision.AlmostEqualWithError(0.0, -0.0, 1e-15));
// compare two nearby numbers
Assert.IsTrue(Precision.AlmostEqualWithError(1.0, 1.0 + 3 * _doublePrecision, 1e-15));
Assert.IsTrue(Precision.AlmostEqualWithError(1.0, 1.0 + _doublePrecision, 1e-15));
Assert.IsTrue(Precision.AlmostEqualWithError(1.0, 1.0 + 1e-16, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, 1.0 + 1e-15, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, 1.0 + 1e-14, 1e-15));
// compare with the two numbers reversed in compare order
Assert.IsTrue(Precision.AlmostEqualWithError(1.0 + 3 * _doublePrecision, 1.0, 1e-15));
Assert.IsTrue(Precision.AlmostEqualWithError(1.0 + _doublePrecision, 1.0, 1e-15));
Assert.IsTrue(Precision.AlmostEqualWithError(1.0 + 1e-16, 1.0, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0 + 1e-15, 1.0, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0 + 1e-14, 1.0, 1e-15));
// compare different numbers
Assert.IsFalse(Precision.AlmostEqualWithError(2.0, 1.0, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, 2.0, 1e-15));
// compare different numbers with large tolerance
Assert.IsFalse(Precision.AlmostEqualWithError(2.0, 1.0, 1e-5));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, 2.0, 1e-5));
Assert.IsTrue(Precision.AlmostEqualWithError(2.0, 1.0, 1e+1));
Assert.IsTrue(Precision.AlmostEqualWithError(1.0, 2.0, 1e+1));
// compare inf & inf
Assert.IsTrue(Precision.AlmostEqualWithError(double.PositiveInfinity, double.PositiveInfinity, 1e-15));
Assert.IsTrue(Precision.AlmostEqualWithError(double.NegativeInfinity, double.NegativeInfinity, 1e-15));
// compare -inf and inf
Assert.IsFalse(Precision.AlmostEqualWithError(double.PositiveInfinity, double.NegativeInfinity, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(double.NegativeInfinity, double.PositiveInfinity, 1e-15));
// compare inf and non-inf
Assert.IsFalse(Precision.AlmostEqualWithError(double.PositiveInfinity, 1.0, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, double.PositiveInfinity, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(double.NegativeInfinity, 1.0, 1e-15));
Assert.IsFalse(Precision.AlmostEqualWithError(1.0, double.NegativeInfinity, 1e-15));
// compare tiny numbers with opposite signs
Assert.IsFalse(Precision.AlmostEqualWithError(1e-12, -1e-12, 1e-14));
Assert.IsFalse(Precision.AlmostEqualWithError(-1e-12, 1e-12, 1e-14));
Assert.IsFalse(Precision.AlmostEqualWithError(-2.0, 2.0, 1e-14));
Assert.IsFalse(Precision.AlmostEqualWithError(2.0, -2.0, 1e-14));
}
[Test]
public void AlmostEqualWithMaxNumbersBetween()
{
// compare zero and negative zero
Assert.IsTrue(Precision.AlmostEqual(0, -0, 1));
// compare two nearby numbers
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 + 3 * _doublePrecision, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0, 1.0 + _doublePrecision, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0, 1.0 - _doublePrecision, 1));
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 - 3 * _doublePrecision, 1));
// compare with the two numbers reversed in compare order
Assert.IsFalse(Precision.AlmostEqual(1.0 + 3 * _doublePrecision, 1.0, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0 + _doublePrecision, 1.0, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0 - _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.AlmostEqual(1.0 - 3 * _doublePrecision, 1.0, 1));
// compare two slightly more different numbers
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 + 10 * _doublePrecision, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0, 1.0 + 10 * _doublePrecision, 10));
Assert.IsTrue(Precision.AlmostEqual(1.0, 1.0 - 10 * _doublePrecision, 10));
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 - 10 * _doublePrecision, 1));
// compare different numbers
Assert.IsFalse(Precision.AlmostEqual(2.0, 1.0, 1));
Assert.IsFalse(Precision.AlmostEqual(1.0, 2.0, 1));
// compare different numbers with large tolerance
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 + 1e5 * _doublePrecision, 1));
Assert.IsTrue(Precision.AlmostEqual(1.0, 1.0 - 1e5 * _doublePrecision, 200000));
Assert.IsFalse(Precision.AlmostEqual(1.0, 1.0 - 1e5 * _doublePrecision, 1));
// compare inf & inf
Assert.IsTrue(Precision.AlmostEqual(double.PositiveInfinity, double.PositiveInfinity, 1));
Assert.IsTrue(Precision.AlmostEqual(double.NegativeInfinity, double.NegativeInfinity, 1));
// compare -inf and inf
Assert.IsFalse(Precision.AlmostEqual(double.PositiveInfinity, double.NegativeInfinity, 1));
Assert.IsFalse(Precision.AlmostEqual(double.NegativeInfinity, double.PositiveInfinity, 1));
// compare inf and non-inf
Assert.IsFalse(Precision.AlmostEqual(double.PositiveInfinity, 1.0, 1));
Assert.IsFalse(Precision.AlmostEqual(1.0, double.PositiveInfinity, 1));
Assert.IsFalse(Precision.AlmostEqual(double.NegativeInfinity, 1.0, 1));
Assert.IsFalse(Precision.AlmostEqual(1.0, double.NegativeInfinity, 1));
// compare tiny numbers with opposite signs
Assert.IsFalse(Precision.AlmostEqual(double.Epsilon, -double.Epsilon, 1));
Assert.IsFalse(Precision.AlmostEqual(-double.Epsilon, double.Epsilon, 1));
Assert.IsFalse(Precision.AlmostEqual(-2.0, 2.0, 1));
Assert.IsFalse(Precision.AlmostEqual(2.0, -2.0, 1));
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void AlmostEqualWithinDecimalPlacesWithDecimalPlacesLessThanOne()
{
Precision.AlmostEqualInDecimalPlaces(1, 2, 0);
}
[Test]
public void AlmostEqualWithinDecimalPlaces()
{
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(1, double.NaN, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.NaN, 2, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.NaN, double.NaN, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.NegativeInfinity, 2, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(1, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.PositiveInfinity, 2, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(1, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.NegativeInfinity, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(double.PositiveInfinity, double.NegativeInfinity, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(double.PositiveInfinity, double.PositiveInfinity, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(double.NegativeInfinity, double.NegativeInfinity, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(1.0, 1.04, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(1.0, 0.96, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(1.0, 1.06, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(1.0, 0.94, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(100.0, 104.00, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(100.0, 96.000, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(100.0, 106.00, 2));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(100.0, 94.000, 2));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(0.0, 4 * _doublePrecision, 12));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(0.0, -4 * _doublePrecision, 12));
}
[Test]
public void AlmostEqualWithSmallNumbersAndSmallNumberOfDecimalPlaces()
{
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(0.0, 1e-12, 1));
Assert.IsTrue(Precision.AlmostEqualInDecimalPlaces(0.0, -1e-12, 1));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(0.0, 1e-12, 13));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(0.0, -1e-12, 13));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(0.0, 1, 1));
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(0.0, -1, 1));
}
[Test]
public void AlmostEqualWithDecimalPlacesWithSignRevert()
{
Assert.IsFalse(Precision.AlmostEqualInDecimalPlaces(0.5, 0.3, 1));
}
[Test]
public void IsLargerWithMaxNumbersBetween()
{
// compare zero and negative zero
Assert.IsFalse(Precision.IsLarger(0, -0, 1));
// compare two nearby numbers
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 + 3 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 + _doublePrecision, 1));
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 - _doublePrecision, 1));
Assert.IsTrue(Precision.IsLarger(1.0, 1.0 - 3 * _doublePrecision, 1));
// compare with the two numbers reversed in compare order
Assert.IsTrue(Precision.IsLarger(1.0 + 3 * _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.IsLarger(1.0 + _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.IsLarger(1.0 - _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.IsLarger(1.0 - 3 * _doublePrecision, 1.0, 1));
// compare two slightly more different numbers
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 + 10 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 + 10 * _doublePrecision, 10));
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 - 10 * _doublePrecision, 10));
Assert.IsTrue(Precision.IsLarger(1.0, 1.0 - 10 * _doublePrecision, 1));
// compare different numbers
Assert.IsTrue(Precision.IsLarger(2.0, 1.0, 1));
Assert.IsFalse(Precision.IsLarger(1.0, 2.0, 1));
// compare different numbers with large tolerance
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 + 1e5 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsLarger(1.0, 1.0 - 1e5 * _doublePrecision, 200000));
Assert.IsTrue(Precision.IsLarger(1.0, 1.0 - 1e5 * _doublePrecision, 1));
// compare inf & inf
Assert.IsFalse(Precision.IsLarger(double.PositiveInfinity, double.PositiveInfinity, 1));
Assert.IsFalse(Precision.IsLarger(double.NegativeInfinity, double.NegativeInfinity, 1));
// compare -inf and inf
Assert.IsTrue(Precision.IsLarger(double.PositiveInfinity, double.NegativeInfinity, 1));
Assert.IsFalse(Precision.IsLarger(double.NegativeInfinity, double.PositiveInfinity, 1));
// compare inf and non-inf
Assert.IsTrue(Precision.IsLarger(double.PositiveInfinity, 1.0, 1));
Assert.IsFalse(Precision.IsLarger(1.0, double.PositiveInfinity, 1));
Assert.IsFalse(Precision.IsLarger(double.NegativeInfinity, 1.0, 1));
Assert.IsTrue(Precision.IsLarger(1.0, double.NegativeInfinity, 1));
// compare tiny numbers with opposite signs
Assert.IsTrue(Precision.IsLarger(double.Epsilon, -double.Epsilon, 1));
Assert.IsFalse(Precision.IsLarger(-double.Epsilon, double.Epsilon, 1));
}
[Test]
public void IsLargerWithDecimalPlaces()
{
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(1, double.NaN, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.NaN, 2, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.NaN, double.NaN, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.NegativeInfinity, 2, 2));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(1, double.NegativeInfinity, 2));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(double.PositiveInfinity, 2, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(1, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.NegativeInfinity, double.PositiveInfinity, 2));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(double.PositiveInfinity, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.PositiveInfinity, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(double.NegativeInfinity, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(1.0, 1.04, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(1.0, 0.96, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(1.0, 1.06, 2));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(1.0, 0.94, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(100.0, 104.00, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(100.0, 96.000, 2));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(100.0, 106.00, 2));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(100.0, 94.000, 2));
double max = 4 * System.Math.Pow(10, Precision.Magnitude(_doublePrecision));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(0.0, max, -Precision.Magnitude(_doublePrecision)));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(0.0, -max, -Precision.Magnitude(_doublePrecision)));
max = 6 * System.Math.Pow(10, Precision.Magnitude(_doublePrecision));
Assert.IsFalse(Precision.IsLargerWithDecimalPlaces(0.0, max, -Precision.Magnitude(_doublePrecision)));
Assert.IsTrue(Precision.IsLargerWithDecimalPlaces(0.0, -max, -Precision.Magnitude(_doublePrecision)));
}
[Test]
public void IsSmallerWithMaxNumbersBetween()
{
// compare zero and negative zero
Assert.IsFalse(Precision.IsSmaller(0, -0, 1));
// compare two nearby numbers
Assert.IsTrue(Precision.IsSmaller(1.0, 1.0 + 3 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 + _doublePrecision, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - _doublePrecision, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - 3 * _doublePrecision, 1));
// compare with the two numbers reversed in compare order
Assert.IsFalse(Precision.IsSmaller(1.0 + 3 * _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.IsSmaller(1.0 + _doublePrecision, 1.0, 1));
Assert.IsFalse(Precision.IsSmaller(1.0 - _doublePrecision, 1.0, 1));
Assert.IsTrue(Precision.IsSmaller(1.0 - 3 * _doublePrecision, 1.0, 1));
// compare two slightly more different numbers
Assert.IsTrue(Precision.IsSmaller(1.0, 1.0 + 10 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 + 10 * _doublePrecision, 10));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - 10 * _doublePrecision, 10));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - 10 * _doublePrecision, 1));
// compare different numbers
Assert.IsFalse(Precision.IsSmaller(2.0, 1.0, 1));
Assert.IsTrue(Precision.IsSmaller(1.0, 2.0, 1));
// compare different numbers with large tolerance
Assert.IsTrue(Precision.IsSmaller(1.0, 1.0 + 1e5 * _doublePrecision, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - 1e5 * _doublePrecision, 200000));
Assert.IsFalse(Precision.IsSmaller(1.0, 1.0 - 1e5 * _doublePrecision, 1));
// compare inf & inf
Assert.IsFalse(Precision.IsSmaller(double.PositiveInfinity, double.PositiveInfinity, 1));
Assert.IsFalse(Precision.IsSmaller(double.NegativeInfinity, double.NegativeInfinity, 1));
// compare -inf and inf
Assert.IsFalse(Precision.IsSmaller(double.PositiveInfinity, double.NegativeInfinity, 1));
Assert.IsTrue(Precision.IsSmaller(double.NegativeInfinity, double.PositiveInfinity, 1));
// compare inf and non-inf
Assert.IsFalse(Precision.IsSmaller(double.PositiveInfinity, 1.0, 1));
Assert.IsTrue(Precision.IsSmaller(1.0, double.PositiveInfinity, 1));
Assert.IsTrue(Precision.IsSmaller(double.NegativeInfinity, 1.0, 1));
Assert.IsFalse(Precision.IsSmaller(1.0, double.NegativeInfinity, 1));
// compare tiny numbers with opposite signs
Assert.IsFalse(Precision.IsSmaller(double.Epsilon, -double.Epsilon, 1));
Assert.IsTrue(Precision.IsSmaller(-double.Epsilon, double.Epsilon, 1));
}
[Test]
public void IsSmallerWithDecimalPlaces()
{
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(1, double.NaN, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.NaN, 2, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.NaN, double.NaN, 2));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(double.NegativeInfinity, 2, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(1, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.PositiveInfinity, 2, 2));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(1, double.PositiveInfinity, 2));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(double.NegativeInfinity, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.PositiveInfinity, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.PositiveInfinity, double.PositiveInfinity, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(double.NegativeInfinity, double.NegativeInfinity, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(1.0, 1.04, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(1.0, 0.96, 2));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(1.0, 1.06, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(1.0, 0.94, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(100.0, 104.00, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(100.0, 96.000, 2));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(100.0, 106.00, 2));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(100.0, 94.000, 2));
double max = 4 * System.Math.Pow(10, Precision.Magnitude(_doublePrecision));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(0.0, max, -Precision.Magnitude(_doublePrecision)));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(0.0, -max, -Precision.Magnitude(_doublePrecision)));
max = 6 * System.Math.Pow(10, Precision.Magnitude(_doublePrecision));
Assert.IsTrue(Precision.IsSmallerWithDecimalPlaces(0.0, max, -Precision.Magnitude(_doublePrecision)));
Assert.IsFalse(Precision.IsSmallerWithDecimalPlaces(0.0, -max, -Precision.Magnitude(_doublePrecision)));
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void CompareToWithMaxNumbersBetweenWithNegativeNumber()
{
double value = 10.0;
Precision.CompareTo(value, value, -1);
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void CompareToWithMaxNumbersBetweenWithZeroNumber()
{
double value = 10.0;
Precision.CompareTo(value, value, 0);
}
[Test]
public void CompareToWithMaxNumbersBetweenWithInfinityValue()
{
Assert.AreEqual(0, Precision.CompareTo(double.PositiveInfinity, double.PositiveInfinity, 1));
Assert.AreEqual(0, Precision.CompareTo(double.NegativeInfinity, double.NegativeInfinity, 1));
Assert.AreEqual(1, Precision.CompareTo(double.PositiveInfinity, double.NegativeInfinity, 1));
Assert.AreEqual(-1, Precision.CompareTo(double.NegativeInfinity, double.PositiveInfinity, 1));
Assert.AreEqual(-1, Precision.CompareTo(1, double.PositiveInfinity, 1));
Assert.AreEqual(1, Precision.CompareTo(double.PositiveInfinity, 1, 1));
Assert.AreEqual(1, Precision.CompareTo(1, double.NegativeInfinity, 1));
Assert.AreEqual(-1, Precision.CompareTo(double.NegativeInfinity, 1, 1));
}
[Test]
public void CompareToWithMaxNumbersBetweenWithNaNValue()
{
// compare nan & not-nan
Assert.AreEqual(1, Precision.CompareTo(1, double.NaN, 1));
Assert.AreEqual(0, Precision.CompareTo(double.NaN, double.NaN, 1));
Assert.AreEqual(-1, Precision.CompareTo(double.NaN, 1, 1));
}
// Bug fix test: In the old system comparing -2 and 2 creates a long value that is equal
// to long.MinValue and you can't get the absolute value of that because long.MinValue is
// 1 bigger than long.MaxValue
[Test]
public void CompareToWithMaxNumbersBetweenForValuesThatOverFlowALong()
{
Assert.AreEqual(1, Precision.CompareTo(2.0, -2.0, 1));
Assert.AreEqual(-1, Precision.CompareTo(-2.0, 2.0, 1));
}
[Test]
public void CompareToWithMaxNumbersBetween()
{
// compare zero and negative zero
Assert.AreEqual(0, Precision.CompareTo(0, -0, 1));
// compare two nearby numbers
Assert.AreEqual(-1, Precision.CompareTo(1.0, 1.0 + 3 * _doublePrecision, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0, 1.0 + _doublePrecision, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0, 1.0 - _doublePrecision, 1));
Assert.AreEqual(1, Precision.CompareTo(1.0, 1.0 - 3 * _doublePrecision, 1));
// compare with the two numbers reversed in compare order
Assert.AreEqual(1, Precision.CompareTo(1.0 + 3 * _doublePrecision, 1.0, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0 + _doublePrecision, 1.0, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0 - _doublePrecision, 1.0, 1));
Assert.AreEqual(-1, Precision.CompareTo(1.0 - 3 * _doublePrecision, 1.0, 1));
// compare two slightly more different numbers
Assert.AreEqual(-1, Precision.CompareTo(1.0, 1.0 + 10 * _doublePrecision, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0, 1.0 + 10 * _doublePrecision, 10));
Assert.AreEqual(0, Precision.CompareTo(1.0, 1.0 - 10 * _doublePrecision, 10));
Assert.AreEqual(1, Precision.CompareTo(1.0, 1.0 - 10 * _doublePrecision, 1));
// compare different numbers
Assert.AreEqual(1, Precision.CompareTo(2.0, 1.0, 1));
Assert.AreEqual(-1, Precision.CompareTo(1.0, 2.0, 1));
// compare different numbers with large tolerance
Assert.AreEqual(-1, Precision.CompareTo(1.0, 1.0 + 1e5 * _doublePrecision, 1));
Assert.AreEqual(0, Precision.CompareTo(1.0, 1.0 - 1e5 * _doublePrecision, 200000));
Assert.AreEqual(1, Precision.CompareTo(1.0, 1.0 - 1e5 * _doublePrecision, 1));
// compare inf & inf
Assert.AreEqual(0, Precision.CompareTo(double.PositiveInfinity, double.PositiveInfinity, 1));
Assert.AreEqual(0, Precision.CompareTo(double.NegativeInfinity, double.NegativeInfinity, 1));
// compare -inf and inf
Assert.AreEqual(1, Precision.CompareTo(double.PositiveInfinity, double.NegativeInfinity, 1));
Assert.AreEqual(-1, Precision.CompareTo(double.NegativeInfinity, double.PositiveInfinity, 1));
// compare inf and non-inf
Assert.AreEqual(1, Precision.CompareTo(double.PositiveInfinity, 1.0, 1));
Assert.AreEqual(-1, Precision.CompareTo(1.0, double.PositiveInfinity, 1));
Assert.AreEqual(-1, Precision.CompareTo(double.NegativeInfinity, 1.0, 1));
Assert.AreEqual(1, Precision.CompareTo(1.0, double.NegativeInfinity, 1));
// compare tiny numbers with opposite signs
Assert.AreEqual(1, Precision.CompareTo(double.Epsilon, -double.Epsilon, 1));
Assert.AreEqual(-1, Precision.CompareTo(-double.Epsilon, double.Epsilon, 1));
}
[Test]
public void CompareToWithDecimalPlaces()
{
// compare zero and negative zero
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(0, -0, 1));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(0, -0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(0, -0, Precision.NumberOfDecimalPlacesForFloats));
// compare two nearby numbers
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0, 1.0 + 10 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0, 1.0 + _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0, 1.0 - _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(1.0, 1.0 - 10 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
// compare with the two numbers reversed in compare order
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(1.0 + 10 * _doublePrecision, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0 + _doublePrecision, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0 - _doublePrecision, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0 - 10 * _doublePrecision, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
// compare two slightly more different numbers
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0, 1.0 + 50 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0, 1.0 + 50 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles - 2));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0, 1.0 - 50 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles - 2));
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(1.0, 1.0 - 50 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
// compare different numbers
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(2.0, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0, 2.0, Precision.NumberOfDecimalPlacesForDoubles));
// compare different numbers with large tolerance
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0, 1.0 + 1e5 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(1.0, 1.0 - 1e5 * _doublePrecision, 10));
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(1.0, 1.0 - 1e5 * _doublePrecision, Precision.NumberOfDecimalPlacesForDoubles));
// compare inf & inf
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(double.PositiveInfinity, double.PositiveInfinity, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(0, Precision.CompareToInDecimalPlaces(double.NegativeInfinity, double.NegativeInfinity, Precision.NumberOfDecimalPlacesForDoubles));
// compare -inf and inf
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(double.PositiveInfinity, double.NegativeInfinity, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(double.NegativeInfinity, double.PositiveInfinity, Precision.NumberOfDecimalPlacesForDoubles));
// compare inf and non-inf
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(double.PositiveInfinity, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(1.0, double.PositiveInfinity, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(-1, Precision.CompareToInDecimalPlaces(double.NegativeInfinity, 1.0, Precision.NumberOfDecimalPlacesForDoubles));
Assert.AreEqual(1, Precision.CompareToInDecimalPlaces(1.0, double.NegativeInfinity, Precision.NumberOfDecimalPlacesForDoubles));
}
}
}