The Math Converter

Quite often I have wanted to adjust a bound value in my XAML by a mathematical formula.

For example, I might want to size a control to 50% of it’s parent’s size. Or I’ll want to position it 30% down and 20% left of a parent panel. Or I might even want to make a control’s width something like 50% of (WindowHeight – 200). Of course, I could always write converters for this, but I got tired of doing that repeatedly so sat down one day to write one big MathConverter.

Using the Math Converter

Using the MathConverter is simple. All you have to do is pass the Converter a math equation as the ConverterParameter, substituting @VALUE for your bound value. The equation can consist of numbers, basic operators (+, -, *, /, %), parentheses, and @VALUE.

For example, if you wanted a control whose height was 50% of the current Window Size, you would create a binding that looked like this:

Height="{Binding ElementName=RootWindow, Path=ActualHeight,
                 Converter={StaticResource MathConverter},
                 ConverterParameter=@VALUE/2}"

Or if you wanted to make the control’s width equal to 30% of (WindowWidth – 200) your binding might look like this:

Width="{Binding ElementName=RootWindow, Path=ActualWidth,
                Converter={StaticResource MathConverter},
                ConverterParameter=((@VALUE-200)*.3)}"

The Math Converter

Here’s the actual converter code.

It takes the ConverterParameter, substitutes the bound value for @VALUE, then starts reading the equation from left-to-right. If it encounters an operator, it performs the specified operation on the previous number and the next number in the list. If it encounters a parentheses, it handles the equation inside the group first, then replaces the grouped equation in the string with the result of the grouped equation. Any character it finds that is not a number, operator, or parentheses throws an exception.

// Does a math equation on the bound value.
// Use @VALUE in your mathEquation as a substitute for bound value
// Operator order is parenthesis first, then Left-To-Right (no operator precedence)
public class MathConverter : IValueConverter
{
    private static readonly char[] _allOperators = new[] { '+', '-', '*', '/', '%', '(', ')' };

    private static readonly List<string> _grouping = new List<string> { "(", ")" };
    private static readonly List<string> _operators = new List<string> { "+", "-", "*", "/", "%" };

    #region IValueConverter Members

    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        // Parse value into equation and remove spaces
        var mathEquation = parameter as string;
        mathEquation = mathEquation.Replace(" ", "");
        mathEquation = mathEquation.Replace("@VALUE", value.ToString());

        // Validate values and get list of numbers in equation
        var numbers = new List<double>();
        double tmp;

        foreach (string s in mathEquation.Split(_allOperators))
        {
            if (s != string.Empty)
            {
                if (double.TryParse(s, out tmp))
                {
                    numbers.Add(tmp);
                }
                else
                {
                    // Handle Error - Some non-numeric, operator, or grouping character found in string
                    throw new InvalidCastException();
                }
            }
        }

        // Begin parsing method
        EvaluateMathString(ref mathEquation, ref numbers, 0);

        // After parsing the numbers list should only have one value - the total
        return numbers[0];
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        throw new NotImplementedException();
    }

    #endregion

    // Evaluates a mathematical string and keeps track of the results in a List<double> of numbers
    private void EvaluateMathString(ref string mathEquation, ref List<double> numbers, int index)
    {
        // Loop through each mathemtaical token in the equation
        string token = GetNextToken(mathEquation);

        while (token != string.Empty)
        {
            // Remove token from mathEquation
            mathEquation = mathEquation.Remove(0, token.Length);

            // If token is a grouping character, it affects program flow
            if (_grouping.Contains(token))
            {
                switch (token)
                {
                    case "(":
                        EvaluateMathString(ref mathEquation, ref numbers, index);
                        break;

                    case ")":
                        return;
                }
            }

            // If token is an operator, do requested operation
            if (_operators.Contains(token))
            {
                // If next token after operator is a parenthesis, call method recursively
                string nextToken = GetNextToken(mathEquation);
                if (nextToken == "(")
                {
                    EvaluateMathString(ref mathEquation, ref numbers, index + 1);
                }

                // Verify that enough numbers exist in the List<double> to complete the operation
                // and that the next token is either the number expected, or it was a ( meaning
                // that this was called recursively and that the number changed
                if (numbers.Count > (index + 1) &&
                    (double.Parse(nextToken) == numbers[index + 1] || nextToken == "("))
                {
                    switch (token)
                    {
                        case "+":
                            numbers[index] = numbers[index] + numbers[index + 1];
                            break;
                        case "-":
                            numbers[index] = numbers[index] - numbers[index + 1];
                            break;
                        case "*":
                            numbers[index] = numbers[index] * numbers[index + 1];
                            break;
                        case "/":
                            numbers[index] = numbers[index] / numbers[index + 1];
                            break;
                        case "%":
                            numbers[index] = numbers[index] % numbers[index + 1];
                            break;
                    }
                    numbers.RemoveAt(index + 1);
                }
                else
                {
                    // Handle Error - Next token is not the expected number
                    throw new FormatException("Next token is not the expected number");
                }
            }

            token = GetNextToken(mathEquation);
        }
    }

    // Gets the next mathematical token in the equation
    private string GetNextToken(string mathEquation)
    {
        // If we're at the end of the equation, return string.empty
        if (mathEquation == string.Empty)
        {
            return string.Empty;
        }

        // Get next operator or numeric value in equation and return it
        string tmp = "";
        foreach (char c in mathEquation)
        {
            if (_allOperators.Contains(c))
            {
                return (tmp == "" ? c.ToString() : tmp);
            }
            else
            {
                tmp += c;
            }
        }

        return tmp;
    }
}

One day I plan on expanding this further to use an IMultiValueConverter that accepts multiple bindings, but I haven’t had a need for that yet so it hasn’t gotten done.