LogicalStringComparer.cs

public sealed class LogicalStringComparer : StringComparer
{
    public static LogicalStringComparer LogicalOrdinal { get; } = new LogicalStringComparer(Ordinal);

    public static LogicalStringComparer LogicalOrdinalIgnoreCase { get; } = new LogicalStringComparer(OrdinalIgnoreCase);

    private readonly StringComparer _comparer;

    public LogicalStringComparer(StringComparer comparer)
    {
        _comparer = comparer ?? throw new ArgumentNullException(nameof(comparer));
    }

    public override int Compare(string x, string y)
    {
        if (x == null)
        {
            return y == null ? 0 : -1;
        }
        else if (y == null)
        {
            return 1;
        }

        bool isDigitSequence = false;
        var i = -1;
        var j = -1;
        var startI = 0;
        var startJ = 0;
        while (true)
        {
            bool? xIsDigit;
            do
            {
                ++i;
                xIsDigit = i < x.Length ? char.IsDigit(x[i]) : (bool?)null;
            } while (xIsDigit == isDigitSequence);
            bool? yIsDigit;
            do
            {
                ++j;
                yIsDigit = j < y.Length ? char.IsDigit(y[j]) : (bool?)null;
            } while (yIsDigit == isDigitSequence);
            var xSub = x.Substring(startI, i - startI);
            var ySub = y.Substring(startJ, j - startJ);
            if (isDigitSequence && ulong.TryParse(xSub, out var xNum) && ulong.TryParse(ySub, out var yNum))
            {
                if (xNum < yNum)
                {
                    return -1;
                }
                else if (yNum < xNum)
                {
                    return 1;
                }
            }
            var result = _comparer.Compare(xSub, ySub);
            if (result != 0)
            {
                return result;
            }
            if (xIsDigit == null)
            {
                return yIsDigit == null ? 0 : -1;
            }
            else if (yIsDigit == null)
            {
                return 1;
            }
            isDigitSequence = xIsDigit.GetValueOrDefault();
            startI = i;
            startJ = j;
        }
    }

    public override bool Equals(string x, string y) => _comparer.Equals(x, y);

    public override int GetHashCode(string obj) => obj != null ? _comparer.GetHashCode(obj) : 0;
}