Just.PreciseMath/1-tests/Just.PreciseMath.Tests/DoubleDoubleRepresentationTests.cs

using Shouldly;
using Xunit;

namespace Just.PreciseMath.Tests;

public class DoubleDoubleRepresentationTests
{
    [Fact]
    public void ArbitraryComponentsUseThePublicFactoryNotAPublicPairConstructor()
    {
        typeof(DoubleDouble).GetConstructor([typeof(double), typeof(double)]).ShouldBeNull();
        DoubleDouble value = DoubleDouble.FromComponents(1.0, 1.0);
        value.High.ShouldBe(2.0);
        value.Low.ShouldBe(0.0);
    }

    [Fact]
    public void TrustedConstructorPreservesAlreadyNormalizedComponents()
    {
        DoubleDouble value = new(1.0, Math.ScaleB(1.0, -54));
        value.High.ShouldBe(1.0);
        value.Low.ShouldBe(Math.ScaleB(1.0, -54));
        DoubleDouble negativeZero = new(-0.0, 0.0);
        BitConverter.DoubleToInt64Bits(negativeZero.High).ShouldBe(long.MinValue);
        BitConverter.DoubleToInt64Bits(negativeZero.Low).ShouldBe(0L);
    }

    [Fact]
    public void NegationPreservesNormalizationAndCanonicalComponents()
    {
        DoubleDouble[] values = [DoubleDouble.NaN, new(double.PositiveInfinity), new(double.NegativeInfinity),
            new(0.0), new(-0.0), new(double.Epsilon), new(-double.Epsilon),
            DoubleDouble.FromComponents(1.0, Math.ScaleB(1.0, -54))];
        foreach (DoubleDouble value in values)
        {
            DoubleDouble negated = -value;
            double expectedHigh = DoubleDouble.IsNaN(value) ? double.NaN : -value.High;
            double expectedLow = value.Low == 0.0 ? 0.0 : -value.Low;
            BitConverter.DoubleToInt64Bits(negated.High).ShouldBe(BitConverter.DoubleToInt64Bits(expectedHigh));
            BitConverter.DoubleToInt64Bits(negated.Low).ShouldBe(BitConverter.DoubleToInt64Bits(expectedLow));
            (-negated).Equals(value).ShouldBeTrue();
        }
    }

    [Fact]
    public void FactoryCanonicalizesNaNPayloadsAndZeroResidualSigns()
    {
        double nan = BitConverter.Int64BitsToDouble(0x7ff8000000000001L);
        foreach (DoubleDouble value in new[] { new DoubleDouble(nan), DoubleDouble.FromComponents(nan, 0.0),
            DoubleDouble.FromComponents(1.0, nan), DoubleDouble.FromComponents(double.PositiveInfinity, double.NegativeInfinity) })
        {
            BitConverter.DoubleToInt64Bits(value.High).ShouldBe(BitConverter.DoubleToInt64Bits(double.NaN));
            BitConverter.DoubleToInt64Bits(value.Low).ShouldBe(0L);
        }
        DoubleDouble negativeZero = DoubleDouble.FromComponents(-0.0, -0.0);
        BitConverter.DoubleToInt64Bits(negativeZero.High).ShouldBe(long.MinValue);
        BitConverter.DoubleToInt64Bits(negativeZero.Low).ShouldBe(0L);
        DoubleDouble cancelled = DoubleDouble.FromComponents(1.0, -1.0);
        BitConverter.DoubleToInt64Bits(cancelled.High).ShouldBe(0L);
        BitConverter.DoubleToInt64Bits(cancelled.Low).ShouldBe(0L);
    }

    [Theory]
    [InlineData(0.0, 1.0, 1.0, 0.0)]
    [InlineData(1.0, 1.0, 2.0, 0.0)]
    [InlineData(1.0, -1.0, 0.0, 0.0)]
    [InlineData(1e300, -1e300, 0.0, 0.0)]
    [InlineData(double.Epsilon, double.Epsilon, 2 * double.Epsilon, 0.0)]
    [InlineData(double.MaxValue, double.MaxValue, double.PositiveInfinity, 0.0)]
    [InlineData(1.0, double.PositiveInfinity, double.PositiveInfinity, 0.0)]
    [InlineData(double.NegativeInfinity, 1.0, double.NegativeInfinity, 0.0)]
    public void FactoryNormalizesComponents(double high, double low, double expectedHigh, double expectedLow)
    {
        DoubleDouble value = DoubleDouble.FromComponents(high, low);
        value.High.ShouldBe(expectedHigh);
        value.Low.ShouldBe(expectedLow);
    }

    [Fact]
    public void NaNHasCanonicalComponentsAndCollectionEquality()
    {
        DoubleDouble value = DoubleDouble.FromComponents(double.PositiveInfinity, double.NegativeInfinity);
        double.IsNaN(value.High).ShouldBeTrue();
        value.Low.ShouldBe(0.0);
        value.Equals(DoubleDouble.NaN).ShouldBeTrue();
        value.GetHashCode().ShouldBe(DoubleDouble.NaN.GetHashCode());
        new HashSet<DoubleDouble> { value }.Contains(DoubleDouble.NaN).ShouldBeTrue();
        (value == DoubleDouble.NaN).ShouldBeFalse();
        (value != DoubleDouble.NaN).ShouldBeTrue();
    }

    [Fact]
    public void FiniteNormalizationPreservesOrderingResidualsAndZeroSigns()
    {
        // Exact dyadic sums, independent of the public factory. Include both
        // magnitude orders, cancellation, subnormals, and signed zero lows.
        double unit = Math.ScaleB(1.0, 970);
        (double High, double Low, double ExpectedHigh, double ExpectedLow)[] cases =
        [
            (-0.0, 0.0, -0.0, 0.0), (-0.0, -0.0, -0.0, 0.0),
            (0.0, -0.0, 0.0, 0.0), (1.0, -1.0, 0.0, 0.0),
            (-1.0, 1.0, 0.0, 0.0), (double.Epsilon, -double.Epsilon, 0.0, 0.0),
            (double.Epsilon, double.Epsilon, 2 * double.Epsilon, 0.0),
            (0.0, double.Epsilon, double.Epsilon, 0.0),
            (double.Epsilon, -1.0, -1.0, double.Epsilon),
            (1.0, double.Epsilon, 1.0, double.Epsilon),
            (double.Epsilon, 1.0, 1.0, double.Epsilon),
            (-1.0, -double.Epsilon, -1.0, -double.Epsilon),
            (-double.Epsilon, -1.0, -1.0, -double.Epsilon),
            (double.MaxValue, 0.0, double.MaxValue, 0.0),
            // MaxValue - 3*2^970 = (MaxValue - 2^971) - 2^970.
            // An unordered TwoSum would overflow an intermediate in the reversed case.
            (double.MaxValue, -3.0 * unit, Math.BitDecrement(double.MaxValue), -unit),
            (-3.0 * unit, double.MaxValue, Math.BitDecrement(double.MaxValue), -unit)
        ];
        foreach ((double high, double low, double expectedHigh, double expectedLow) in cases)
        {
            DoubleDouble actual = PreciseMathHelper.NormalizeFinite(high, low);
            BitConverter.DoubleToInt64Bits(actual.High).ShouldBe(BitConverter.DoubleToInt64Bits(expectedHigh));
            BitConverter.DoubleToInt64Bits(actual.Low).ShouldBe(BitConverter.DoubleToInt64Bits(expectedLow));
        }
    }

    [Fact]
    public void ZeroSignsArePreservedButEqual()
    {
        DoubleDouble negative = new(-0.0);
        BitConverter.DoubleToInt64Bits(negative.High).ShouldBe(long.MinValue);
        negative.Equals(DoubleDouble.Zero).ShouldBeTrue();
        negative.GetHashCode().ShouldBe(DoubleDouble.Zero.GetHashCode());
    }
}