using System.Globalization;
using Just.PreciseMath.Tests.ReferenceData;

namespace Just.PreciseMath.Tests;

public class PreciseMathLogTests
{
    public static IEnumerable<TheoryDataRow<string, double, double, string>> ReferenceCases => LogReferenceData.Cases();

    public static IEnumerable<TheoryDataRow<string, double, double, double, double, string, bool, bool>> FamilyReferenceCases =>
        LogarithmicFunctionsReferenceData.Cases();

    [Theory]
    [MemberData(nameof(FamilyReferenceCases))]
    public void LogarithmicFamilyMeetsIndependentReferenceBound(string operation, double high, double low,
        double baseHigh, double baseLow, string reference, bool overflow, bool underflow)
    {
        // Decimal.ln at 450/650 digits; sums, including 1+x, are exact at 2200
        // digits and checked with Fraction before taking logs. No DD-derived oracle.
        DoubleDouble input = DoubleDouble.FromComponents(high, low);
        DoubleDouble newBase = DoubleDouble.FromComponents(baseHigh, baseLow);
        (Units(input.High) + Units(input.Low)).ShouldBe(Units(high) + Units(low));
        (Units(newBase.High) + Units(newBase.Low)).ShouldBe(Units(baseHigh) + Units(baseLow));
        DoubleDouble actual = operation == "LogBase" ? DoubleDouble.Log(input, newBase) : Evaluate(operation, input);
        DoubleDouble generic = operation == "LogBase" ? LogGeneric(input, newBase) : EvaluateGeneric(operation, input);
        AssertBits(generic, actual.High, actual.Low);
        string context = $"{operation}({high:R}, {low:R}), base=({baseHigh:R}, {baseLow:R})";
        if (overflow)
        {
            AssertBits(actual, reference[0] == '-' ? double.NegativeInfinity : double.PositiveInfinity, 0.0);
        }
        else if (underflow)
        {
            AssertBits(actual, reference[0] == '-' ? -0.0 : 0.0, 0.0);
        }
        else
        {
            AssertReferenceBound(actual, reference, 1, context);
            if (input != DoubleDouble.One && !DoubleDouble.IsZero(input))
            {
                DoubleDouble.IsZero(actual).ShouldBeFalse(context);
            }
        }
    }

    [Theory]
    [InlineData("Log")]
    [InlineData("Log2")]
    [InlineData("Log10")]
    [InlineData("LogP1")]
    [InlineData("Log2P1")]
    [InlineData("Log10P1")]
    public void FamilyDomainAndSpecialValuesHaveGenericDispatch(string operation)
    {
        bool plusOne = operation.EndsWith("P1", StringComparison.Ordinal);
        DoubleDouble[] inputs = [DoubleDouble.Zero, DoubleDouble.NegativeZero,
            DoubleDouble.NaN, DoubleDouble.PositiveInfinity, DoubleDouble.NegativeInfinity,
            new(-2.0), new(-1.0), new(1.0),
            DoubleDouble.FromComponents(-1.0, -double.Epsilon)];
        foreach (DoubleDouble input in inputs)
        {
            DoubleDouble actual = Evaluate(operation, input);
            AssertBits(EvaluateGeneric(operation, input), actual.High, actual.Low);
            if (DoubleDouble.IsNaN(input) || input < (plusOne ? DoubleDouble.NegativeOne : DoubleDouble.Zero))
            {
                AssertBits(actual, double.NaN, 0.0);
            }
            else if (DoubleDouble.IsPositiveInfinity(input))
            {
                AssertBits(actual, double.PositiveInfinity, 0.0);
            }
            else if (plusOne && input == DoubleDouble.NegativeOne || !plusOne && DoubleDouble.IsZero(input))
            {
                AssertBits(actual, double.NegativeInfinity, 0.0);
            }
            else if (DoubleDouble.IsZero(input))
            {
                AssertBits(actual, input.High, 0.0);
            }
            else if (!plusOne)
            {
                AssertBits(actual, 0.0, 0.0);
            }
        }
    }

    [Fact]
    public void BinaryLogarithmOfEveryRepresentablePowerOfTwoIsExact()
    {
        for (int exponent = -1074; exponent <= 1023; ++exponent)
        {
            DoubleDouble input = new(Math.ScaleB(1.0, exponent));
            AssertBits(Log2Generic(input), exponent, 0.0);
        }
    }

    [Fact]
    public void DecimalLogarithmAndArbitraryBaseHaveElementaryValues()
    {
        AssertReferenceBound(Log10Generic(new DoubleDouble(10.0)), "1e+0", 1, "log10(10)");
        AssertReferenceBound(LogGeneric(new DoubleDouble(8.0), new DoubleDouble(2.0)), "3e+0", 1, "log2(8)");
        AssertReferenceBound(LogGeneric(new DoubleDouble(8.0), new DoubleDouble(0.5)), "-3e+0", 1, "log0.5(8)");
    }

    [Fact]
    public void ArbitraryBaseSpecialValuesMatchRuntimeWithCanonicalNaNs()
    {
        double[] values = [-1.0, -0.0, 0.0, 0.5, 1.0, 2.0,
            double.PositiveInfinity, double.NegativeInfinity, double.NaN];
        foreach (double value in values)
        {
            foreach (double newBase in values)
            {
                DoubleDouble expected = new(Math.Log(value, newBase));
                AssertBits(LogGeneric(new DoubleDouble(value), new DoubleDouble(newBase)), expected.High, 0.0);
            }
        }
    }

    [Theory]
    [InlineData("LogP1")]
    [InlineData("Log2P1")]
    [InlineData("Log10P1")]
    public void PlusOneFunctionsPreserveSignedZero(string operation)
    {
        AssertBits(EvaluateGeneric(operation, DoubleDouble.NegativeZero), -0.0, 0.0);
        AssertBits(EvaluateGeneric(operation, DoubleDouble.Zero), 0.0, 0.0);
    }

    [Fact]
    public void NaturalPlusOneLogarithmRetainsTinyQuadraticCorrection()
    {
        foreach (double sign in new[] { -1.0, 1.0 })
        {
            double tiny = sign * Math.ScaleB(1.0, -100);
            // ln(1+x) = x-x²/2+O(x³). The cubic is far below half an ulp
            // of this low. Adding one first loses the sparse input's second component.
            AssertBits(EvaluateGeneric("LogP1", new DoubleDouble(tiny)), tiny, -Math.ScaleB(1.0, -201));
            DoubleDouble sparse = DoubleDouble.FromComponents(tiny, Math.ScaleB(1.0, -180));
            AssertBits(EvaluateGeneric("LogP1", sparse), tiny, Math.ScaleB(1.0, -180) - Math.ScaleB(1.0, -201));
            AssertBits(EvaluateGeneric("LogP1", new DoubleDouble(sign * double.Epsilon)), sign * double.Epsilon, 0.0);
        }
    }

    [Fact]
    public void SpecialValuesHaveExplicitCanonicalResults()
    {
        // Legacy Log(0) reached Exp(-Infinity) and threw. Domain handling must
        // precede finite range reduction, with either zero mapping to -Infinity.
        double[] values = [0.0, -0.0, 1.0, -1.0, -double.Epsilon, double.MinValue,
            double.PositiveInfinity, double.NegativeInfinity, double.NaN];
        foreach (double value in values)
        {
            DoubleDouble expected = new(Math.Log(value));
            AssertBits(DoubleDouble.Log(new DoubleDouble(value)), expected.High, 0.0);
        }
        DoubleDouble negative = DoubleDouble.FromComponents(-1.0, Math.ScaleB(1.0, -54));
        AssertBits(DoubleDouble.Log(negative), double.NaN, 0.0);
    }

    [Theory]
    [MemberData(nameof(ReferenceCases))]
    public void FiniteInputsMeetIndependentReferenceBound(string label, double high, double low, string reference)
    {
        // Decimal.ln at 450/650 digits, from exact component sums formed at
        // 2200 digits and checked with Fraction. No binary64 log supplies the oracle.
        DoubleDouble input = DoubleDouble.FromComponents(high, low);
        (Units(input.High) + Units(input.Low)).ShouldBe(Units(high) + Units(low));
        DoubleDouble actual = DoubleDouble.Log(input);
        AssertReferenceBound(actual, reference, 1, $"{label}: ({high:R}, {low:R})");
        if (input == DoubleDouble.One)
        {
            AssertBits(actual, 0.0, 0.0);
        }
        else
        {
            Math.Sign(actual.High).ShouldBe(input > DoubleDouble.One ? 1 : -1);
        }
    }

    [Fact]
    public void PowersOfTwoCoverEveryFiniteBinaryInputExponent()
    {
        // ln(2^k) = k*ln(2). Multiply the independent decimal reference by k
        // with exact integers, never using the library constant or DD arithmetic.
        for (int exponent = -1074; exponent <= 1023; ++exponent)
        {
            DoubleDouble input = new(Math.ScaleB(1.0, exponent));
            AssertReferenceBound(DoubleDouble.Log(input), LogReferenceData.Ln2, exponent, $"2^{exponent}");
        }
    }

    [Theory]
    [InlineData(1e308)]
    [InlineData(double.MaxValue)]
    [InlineData(1e-308)]
    public void ExtremeFiniteInputsRetainExtendedPrecisionWithoutDenominatorOverflow(double input)
    {
        // The legacy Log(1e308) formed u+value and overflowed. The finite
        // kernel must reduce the mantissa before constructing its denominator.
        DoubleDouble actual = DoubleDouble.Log(new DoubleDouble(input));
        DoubleDouble.IsFinite(actual).ShouldBeTrue();
        actual.Low.ShouldNotBe(0.0);
        DoubleDouble.IsCanonical(actual).ShouldBeTrue();
        // ReferenceCases independently pins the complete result for these inputs.
    }

    [Fact]
    public void NearOneRetainsSparseCorrectionsOfEitherSign()
    {
        foreach (double sign in new[] { -1.0, 1.0 })
        {
            AssertBits(DoubleDouble.Log(DoubleDouble.FromComponents(1.0, sign * double.Epsilon)),
                sign * double.Epsilon, 0.0);
            double delta = sign * Math.ScaleB(1.0, -500);
            // ln(1+d) = d-d^2/2+O(d^3). Here the cubic tail is below half
            // the minimum subnormal, so these two binary components are exact.
            AssertBits(DoubleDouble.Log(DoubleDouble.FromComponents(1.0, delta)),
                delta, -Math.ScaleB(1.0, -1001));
        }
    }

    [Fact]
    public void ArbitraryPairsAreNormalizedByThePublicFactoryBeforeLog()
    {
        DoubleDouble positive = DoubleDouble.FromComponents(0.0, 2.0);
        AssertReferenceBound(DoubleDouble.Log(positive), LogReferenceData.Ln2, 1, "zero-high public construction");
        AssertBits(DoubleDouble.Log(DoubleDouble.FromComponents(0.0, -2.0)), double.NaN, 0.0);
    }

    private static DoubleDouble Evaluate(string operation, DoubleDouble value)
    {
        return operation switch
        {
            "Log" => DoubleDouble.Log(value),
            "Log2" => DoubleDouble.Log2(value),
            "Log10" => DoubleDouble.Log10(value),
            "LogP1" => DoubleDouble.LogP1(value),
            "Log2P1" => DoubleDouble.Log2P1(value),
            "Log10P1" => DoubleDouble.Log10P1(value),
            _ => throw new ArgumentOutOfRangeException(nameof(operation))
        };
    }

    private static T EvaluateGeneric<T>(string operation, T value) where T : ILogarithmicFunctions<T>
    {
        return operation switch
        {
            "Log" => T.Log(value),
            "Log2" => T.Log2(value),
            "Log10" => T.Log10(value),
            "LogP1" => T.LogP1(value),
            "Log2P1" => T.Log2P1(value),
            "Log10P1" => T.Log10P1(value),
            _ => throw new ArgumentOutOfRangeException(nameof(operation))
        };
    }

    private static T LogGeneric<T>(T value, T newBase) where T : ILogarithmicFunctions<T> => T.Log(value, newBase);

    private static T Log2Generic<T>(T value) where T : ILogarithmicFunctions<T> => T.Log2(value);

    private static T Log10Generic<T>(T value) where T : ILogarithmicFunctions<T> => T.Log10(value);

    private static void AssertReferenceBound(DoubleDouble actual, string reference, int factor, string context)
    {
        DoubleDouble.IsFinite(actual).ShouldBeTrue(context);
        DoubleDouble.IsCanonical(actual).ShouldBeTrue(context);
        string[] parts = reference.Split('e');
        int point = parts[0].IndexOf('.', StringComparison.Ordinal);
        int decimals = point < 0 ? 0 : parts[0].Length - point - 1;
        BigInteger numerator = factor * BigInteger.Parse(parts[0].Replace(".", "", StringComparison.Ordinal), CultureInfo.InvariantCulture);
        int exponent = int.Parse(parts[1], CultureInfo.InvariantCulture) - decimals;
        BigInteger denominator = BigInteger.One;
        if (exponent >= 0)
        {
            numerator *= BigInteger.Pow(10, exponent);
        }
        else
        {
            denominator = BigInteger.Pow(10, -exponent);
        }
        BigInteger actualUnits = Units(actual.High) + Units(actual.Low);
        BigInteger error = BigInteger.Abs((actualUnits * denominator) - (numerator << 1074));
        BigInteger magnitude = BigInteger.Abs(numerator);
        // 2^-100 relative + one minimum subnormal, with independent reference
        // uncertainty <2^-350 relative explicitly included. No component collapse.
        BigInteger bound = (magnitude << 1324) + (denominator << 350) + (magnitude << 1074);
        ((error << 350) <= bound).ShouldBeTrue(
            $"Log bound failed for {context}: ({actual.High:R}, {actual.Low:R})");
    }

    private static BigInteger Units(double value)
    {
        long bits = BitConverter.DoubleToInt64Bits(value);
        int exponent = (int)((bits >> 52) & 0x7ff);
        BigInteger significand = bits & 0xfffffffffffffL;
        if (exponent != 0)
        {
            significand += BigInteger.One << 52;
            significand <<= exponent - 1;
        }
        return bits < 0 ? -significand : significand;
    }

    private static void AssertBits(DoubleDouble actual, double high, double low)
    {
        BitConverter.DoubleToInt64Bits(actual.High).ShouldBe(BitConverter.DoubleToInt64Bits(high));
        BitConverter.DoubleToInt64Bits(actual.Low).ShouldBe(BitConverter.DoubleToInt64Bits(low));
        DoubleDouble.IsCanonical(actual).ShouldBeTrue();
    }
}