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

namespace Just.PreciseMath.Tests;

public class DoubleDoubleExponentialFunctionsTests
{
    public static IEnumerable<TheoryDataRow<string, double, double, string, bool, bool>> ReferenceCases =>
        ExponentialFunctionsReferenceData.Cases();

    [Theory]
    [MemberData(nameof(ReferenceCases))]
    public void FiniteInputsMeetIndependentReferenceBound(string operation, double high, double low,
        string reference, bool overflow, bool underflow)
    {
        // Exact binary64 sums and Decimal ln/exp/expm1 at 450/650 digits;
        // integer base-two/base-ten powers are independently rational-checked.
        DoubleDouble input = DoubleDouble.FromComponents(high, low);
        (Units(input.High) + Units(input.Low)).ShouldBe(Units(high) + Units(low));
        DoubleDouble actual = Evaluate(operation, input);
        DoubleDouble.IsCanonical(actual).ShouldBeTrue();
        AssertBits(actual, EvaluateGeneric(operation, input));
        AssertBits(actual, EvaluateFacade(operation, input));
        if (overflow)
        {
            AssertBits(DoubleDouble.PositiveInfinity, actual);
            return;
        }
        if (underflow)
        {
            AssertBits(new DoubleDouble(reference[0] == '-' ? -0.0 : 0.0), actual);
            return;
        }
        DoubleDouble.IsFinite(actual).ShouldBeTrue();
        DoubleDouble.IsZero(actual).ShouldBeFalse();
        string[] parts = reference.Split('e');
        int point = parts[0].IndexOf('.', StringComparison.Ordinal);
        int decimals = point < 0 ? 0 : parts[0].Length - point - 1;
        BigInteger numerator = 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 + epsilon absolute + 2^-350 relative reference allowance.
        BigInteger bound = (magnitude << 1324) + (denominator << 350) + (magnitude << 1074);
        ((error << 350) <= bound).ShouldBeTrue(
            $"{operation} bound failed for ({high:R}, {low:R}): ({actual.High:R}, {actual.Low:R})");
    }

    [Fact]
    public void NaturalExponentialIsAvailableOnTheTypeAndMatchesFacadeBits()
    {
        DoubleDouble[] values = [DoubleDouble.Zero, DoubleDouble.NegativeZero,
            DoubleDouble.NaN, DoubleDouble.PositiveInfinity, DoubleDouble.NegativeInfinity,
            new(-1.0), new(double.Epsilon), new(1.0), new(709.5), new(-740.0),
            new(double.MaxValue), DoubleDouble.FromComponents(1.0, Math.ScaleB(1.0, -1000))];
        foreach (DoubleDouble value in values)
        {
            AssertBits(DDMath.Exp(value), DoubleDouble.Exp(value));
        }
    }

    [Fact]
    public void BinaryAndDecimalExponentialsHaveExactElementaryValues()
    {
        for (int exponent = -1074; exponent <= 1023; ++exponent)
        {
            AssertBits(new DoubleDouble(Math.ScaleB(1.0, exponent)), DoubleDouble.Exp2(new DoubleDouble(exponent)));
        }
        AssertBits(DoubleDouble.Zero, DoubleDouble.Exp2(new DoubleDouble(-1075.0)));
        AssertBits(DoubleDouble.Epsilon, DoubleDouble.Exp2(DoubleDouble.FromComponents(-1075.0, double.Epsilon)));
        AssertBits(DoubleDouble.Zero, DoubleDouble.Exp2(DoubleDouble.FromComponents(-1075.0, -double.Epsilon)));
        AssertBits(DoubleDouble.PositiveInfinity, DoubleDouble.Exp2(new DoubleDouble(1024.0)));
        DoubleDouble ten = DoubleDouble.Exp10(DoubleDouble.One);
        ten.High.ShouldBe(10.0);
        Math.Abs(ten.Low).ShouldBeLessThan(1e-30);
        AssertBits(DoubleDouble.One, DoubleDouble.Exp10(DoubleDouble.Zero));
    }

    [Fact]
    public void MinusOneFunctionsRetainTinyResultsAndSignedZeros()
    {
        double tiny = Math.ScaleB(1.0, -100);
        // exp(±x)-1 = ±x + x²/2 + O(x³). At x=2^-100 the tail is
        // below half an ulp of the low, so these particular splits are exact.
        AssertBits(DoubleDouble.FromComponents(tiny, Math.ScaleB(1.0, -201)), DoubleDouble.ExpM1(new DoubleDouble(tiny)));
        AssertBits(DoubleDouble.FromComponents(-tiny, Math.ScaleB(1.0, -201)), DoubleDouble.ExpM1(new DoubleDouble(-tiny)));
        foreach (double sign in new double[] { -1.0, 1.0 })
        {
            DoubleDouble input = new(sign * double.Epsilon);
            AssertBits(input, DoubleDouble.ExpM1(input));
            AssertBits(input, DoubleDouble.Exp2M1(input));
            AssertBits(new DoubleDouble(sign * (2.0 * double.Epsilon)), DoubleDouble.Exp10M1(input));
        }
    }

    [Theory]
    [InlineData(1, double.Epsilon)]
    [InlineData(500, 1.1210060331144859e-173)]
    [InlineData(1000, 3.6694906201918696e-23)]
    public void BinaryExponentialScalesSparseCorrectionsBeforeRounding(int exponent, double expectedLow)
    {
        // For delta=±2^-1074, 2^(n+delta)=2^n+delta*ln(2)*2^n+O(2^(n-2148)).
        // Decimal ln(2)*2^(n-1074) at 450/650 digits gives the literals above.
        // The quadratic term is far below their binary64 rounding intervals.
        foreach (double sign in new double[] { -1.0, 1.0 })
        {
            DoubleDouble input = DoubleDouble.FromComponents(exponent, sign * double.Epsilon);
            DoubleDouble expected = DoubleDouble.FromComponents(Math.ScaleB(1.0, exponent), sign * expectedLow);
            AssertBits(expected, DoubleDouble.Exp2(input));
            AssertBits(expected, DDMath.Exp2(input));
        }
    }

    [Theory]
    [InlineData("Exp")]
    [InlineData("Exp2")]
    [InlineData("Exp10")]
    [InlineData("ExpM1")]
    [InlineData("Exp2M1")]
    [InlineData("Exp10M1")]
    public void CompleteContractHasGenericDispatchAndThinFacade(string operation)
    {
        bool minusOne = operation.EndsWith("M1", StringComparison.Ordinal);
        DoubleDouble[] values = [DoubleDouble.Zero, DoubleDouble.NegativeZero,
            DoubleDouble.NaN, DoubleDouble.PositiveInfinity, DoubleDouble.NegativeInfinity,
            new(double.MaxValue), new(double.MinValue), new(double.Epsilon),
            new(0.125), new(-0.125), new(1.0), new(-1.0),
            DoubleDouble.FromComponents(1.0, Math.ScaleB(1.0, -1000))];
        foreach (DoubleDouble value in values)
        {
            DoubleDouble actual = Evaluate(operation, value);
            DoubleDouble.IsCanonical(actual).ShouldBeTrue();
            AssertBits(actual, EvaluateGeneric(operation, value));
            AssertBits(actual, EvaluateFacade(operation, value));
            if (DoubleDouble.IsZero(value))
            {
                AssertBits(minusOne ? value : DoubleDouble.One, actual);
            }
            else if (DoubleDouble.IsNaN(value))
            {
                AssertBits(DoubleDouble.NaN, actual);
            }
            else if (value.High == double.PositiveInfinity || value.High == double.MaxValue)
            {
                AssertBits(DoubleDouble.PositiveInfinity, actual);
            }
            else if (value.High == double.NegativeInfinity || value.High == double.MinValue)
            {
                AssertBits(minusOne ? DoubleDouble.NegativeOne : DoubleDouble.Zero, actual);
            }
        }
    }

    private static DoubleDouble Evaluate(string operation, DoubleDouble value)
    {
        return operation switch
        {
            "Exp" => DoubleDouble.Exp(value),
            "Exp2" => DoubleDouble.Exp2(value),
            "Exp10" => DoubleDouble.Exp10(value),
            "ExpM1" => DoubleDouble.ExpM1(value),
            "Exp2M1" => DoubleDouble.Exp2M1(value),
            "Exp10M1" => DoubleDouble.Exp10M1(value),
            _ => throw new ArgumentOutOfRangeException(nameof(operation))
        };
    }

    private static T EvaluateGeneric<T>(string operation, T value) where T : IExponentialFunctions<T>
    {
        return operation switch
        {
            "Exp" => T.Exp(value),
            "Exp2" => T.Exp2(value),
            "Exp10" => T.Exp10(value),
            "ExpM1" => T.ExpM1(value),
            "Exp2M1" => T.Exp2M1(value),
            "Exp10M1" => T.Exp10M1(value),
            _ => throw new ArgumentOutOfRangeException(nameof(operation))
        };
    }

    private static DoubleDouble EvaluateFacade(string operation, DoubleDouble value)
    {
        return operation switch
        {
            "Exp" => DDMath.Exp(value),
            "Exp2" => DDMath.Exp2(value),
            "Exp10" => DDMath.Exp10(value),
            "ExpM1" => DDMath.ExpM1(value),
            "Exp2M1" => DDMath.Exp2M1(value),
            "Exp10M1" => DDMath.Exp10M1(value),
            _ => throw new ArgumentOutOfRangeException(nameof(operation))
        };
    }

    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 expected, DoubleDouble actual)
    {
        BitConverter.DoubleToInt64Bits(actual.High).ShouldBe(BitConverter.DoubleToInt64Bits(expected.High));
        BitConverter.DoubleToInt64Bits(actual.Low).ShouldBe(BitConverter.DoubleToInt64Bits(expected.Low));
    }
}