C# Memoization of functions with arbitrary number of arguments

Question

I'm trying to create a memoization interface for functions with arbitrary number of arguments, but I'm failing miserably I feel like my solution is not very flexible. I tried to define an interface for a function which gets memoized automatically upon execution and each function will have to implement this interface. Here is an example with a two parameter Exponential Moving Average function:

class EMAFunction:IFunction
{
    Dictionary<List<object>, List<object>> map;

    class EMAComparer : IEqualityComparer<List<object>>
    {
        private int _multiplier = 97;

        public bool Equals(List<object> a, List<object> b)
        {
            List<object> aVals = (List<object>)a[0];
            int aPeriod = (int)a[1];

            List<object> bVals = (List<object>)b[0];
            int bPeriod = (int)b[1];

            return (aVals.Count == bVals.Count) && (aPeriod == bPeriod);
        }

        public int GetHashCode(List<object> obj)
        {
            // Don't compute hash code on null object.
            if (obj == null)
            {
                return 0;
            }

            List<object> vals = (List<object>) obj[0];
            int period = (int) obj[1];

            return (_multiplier * period.GetHashCode()) + vals.Count;

        }
    }

    public EMAFunction()
    {
        NumParams = 2;
        Name = "EMA";
        map = new Dictionary<List<object>, List<object>>(new EMAComparer());
    }
    #region IFunction Members

    public int NumParams
    {
        get;
        set;
    }

    public string Name
    {
        get;
        set;
    }

    public object Execute(List<object> parameters)
    {
        if (parameters.Count != NumParams)
            throw new ArgumentException("The num params doesn't match!");

        if (!map.ContainsKey(parameters))
        {
            //map.Add(parameters,
            List<double> values = new List<double>();
            List<object> asObj = (List<object>)parameters[0];
            foreach (object val in asObj)
            {
                values.Add((double)val);
            }
            int period = (int)parameters[1];

            asObj.Clear();
            List<double> ema = TechFunctions.ExponentialMovingAverage(values, period);
            foreach (double val in ema)
            {
                asObj.Add(val);
            }
            map.Add(parameters, asObj);
        }
        return map[parameters];
    }

    public void ClearMap()
    {
        map.Clear();
    }

    #endregion
}

Here are my tests of the function:

private void MemoizeTest()
{
    DataSet dataSet = DataLoader.LoadData(DataLoader.DataSource.FROM_WEB, 1024);
    List<String> labels = dataSet.DataLabels;

    Stopwatch sw = new Stopwatch();
    IFunction emaFunc = new EMAFunction();
    List<object> parameters = new List<object>();
    int numRuns = 1000;
    long sumTicks = 0;
    parameters.Add(dataSet.GetValues("open"));
    parameters.Add(12);

    // First call

    for(int i = 0; i < numRuns; ++i)
    {
        emaFunc.ClearMap();// remove any memoization mappings
        sw.Start();
        emaFunc.Execute(parameters);
        sw.Stop();
        sumTicks += sw.ElapsedTicks;
        sw.Reset();
    }
    Console.WriteLine("Average ticks not-memoized " + (sumTicks/numRuns));


    sumTicks = 0;
    // Repeat call
    for (int i = 0; i < numRuns; ++i)
    {
        sw.Start();
        emaFunc.Execute(parameters);
        sw.Stop();
        sumTicks += sw.ElapsedTicks;
        sw.Reset();
    }
    Console.WriteLine("Average ticks memoized " + (sumTicks/numRuns));
}

Update:
Thanks for pointing out my n00bish error... I always forget to call Reset on the stopwatch!

I've seen another approach to memoization as well... it doesn't offer n-argument memoization, but my approach with the Interface is not much more advantageous since I have to write a class for each function. Is there a reasonable way that I can merge these ideas into something more robust? I want to make it easier to memoize a function without making the user write a class for each function that they intend to use.

Answer 1

How about this? First write a one-argument memoizer:

static Func<A, R> Memoize<A, R>(this Func<A, R> f)
{
    var d = new Dictionary<A, R>();
    return a=> 
    {
        R r;
        if (!d.TryGetValue(a, out r))
        {
            r = f(a);
            d.Add(a, r);
        }
        return r;
    };
}  

Straightforward. Now write a function tuplifier:

static Func<Tuple<A, B>, R> Tuplify<A, B, R>(this Func<A, B, R> f)
{
    return t => f(t.Item1, t.Item2);
}

And a detuplifier:

static Func<A, B, R> Detuplify<A, B, R>(this Func<Tuple<A, B>, R> f)
{
    return (a, b) => f(Tuple.Create(a, b));
}

and now a two-argument memoizer is easy:

static Func<A, B, R> Memoize<A, B, R>(this Func<A, B, R> f)
{
    return f.Tuplify().Memoize().Detuplify();
}

To write a three-argument memoizer just keep following this pattern: make a 3-tuplifier, a 3-untuplifier, and a 3-memoizer.

Of course, if you don't need them, there's no need to make the tuplifiers nominal methods:

static Func<A, B, R> Memoize<A, B, R>(this Func<A, B, R> f)
{
    Func<Tuple<A, B>, R> tuplified = t => f(t.Item1, t.Item2);
    Func<Tuple<A, B>, R> memoized = tuplified.Memoize();
    return (a, b) => memoized(Tuple.Create(a, b));
}

UPDATE: You ask what to do if there is no tuple type. You could write your own; it's not hard. Or you could use anonymous types:

static Func<T, R> CastByExample<T, R>(Func<T, R> f, T t) { return f; }

static Func<A, B, R> Memoize<A, B, R>(this Func<A, B, R> f)
{
    var example = new { A=default(A), B=default(B) };
    var tuplified = CastByExample(t => f(t.A, t.B), example);
    var memoized = tuplified.Memoize();
    return (a, b) => memoized(new {A=a, B=b});
}

Slick, eh?

---

UPDATE: C# 7 now has value tuples built in to the language; use them rather than rolling your own or using anonymous types.