## Introduction

I work quite a bit with matrices. I work with them enough that at some point, I decided to create my own generic classes for a matrix and a half matrix. Among other things, I wanted my classes to provide a method to calculate the sum of items in a row or column. I immediately had a problem. *How does one calculate the sum of two generic objects?*

To simplify things, let's say that we're working with a descendant of `List<T>`

and we want to add a method called `Sum()`

.

We start by deriving a class from `List<T>`

:

class SummableList : List{}

Let's go ahead and add the `Sum()`

method:

class SummableList<t> : List<t> {
public T Sum() {
T result = default(T);
foreach (T item in this)
result += item;
return result;
}
}

Unfortunately, this will not compile. It won't compile because the compiler doesn't know how to add two `object`

s together. In .NET, a type parameter (the `T`

in `List<T>`

) that is not constrained is assumed to be of type `System.Object`

, and there's not much you can do with a plain old object.

There are ways to get around this, but they have their problems. My goal is to be able to write my generic classes with the syntax as close to the example above with as little trouble as possible.

## Would a constraint help?

So far, we know that our code will not compile because the type parameter is assumed to be an `object`

. What if we were to constrain the type parameter to some type that the compiler does know how to add? Then, it is only a matter of picking an appropriate class. Well, rather than trying to find an appropriate class, let's go ahead and make one ourselves:

public abstract class MathClass {
public abstract MathClass Add(MathClass other);
public abstract MathClass Subtract(MathClass other);
public abstract MathClass Divide(MathClass other);
public abstract MathClass Divide(int other);
public static MathClass operator +(MathClass a, MathClass b) {
return a.Add(b);
}
public static MathClass operator -(MathClass a, MathClass b) {
return a.Subtract(b);
}
public static MathClass operator /(MathClass a, MathClass b) {
return a.Divide(b);
}
public static MathClass operator /(MathClass a, int b) {
return a.Divide(b);
}
}

Now, all we need to do is derive any class on which we might want to do arithmetic from this new `MathClass`

. Then, we can write our `SummableList<T>`

with a constraint on it, as follows:

public class SummableListC<T> : List<T> where T : MathClass, new() {
public T Sum() {
T result = new T();
foreach (T thing in this) {
result = (T)(result + thing);
}
return result;
}
public T Average() {
return (T)(Sum() / Count);
}
}

But, the problem is that we can only work with classes derived from `MathClass`

. We can't use `int`

or `double`

. Not only that, but the derived classes we have to write aren't that straightforward:

public class IntMathClass : MathClass {
private int fValue = 0;
public IntMathClass(int value) {
fValue = value;
}
public IntMathClass() {
fValue = 0;
}
public static implicit operator IntMathClass(int a) {
return new IntMathClass(a);
}
public static implicit operator int(IntMathClass a) {
return a.fValue;
}
public override MathClass Add(MathClass other) {
if (other is IntMathClass) {
return new IntMathClass(this.fValue + (IntMathClass)other);
}
return this;
}
public override MathClass Subtract(MathClass other) {
if (other is IntMathClass) {
return new IntMathClass(this.fValue - (IntMathClass)other);
}
return this;
}
public override MathClass Divide(MathClass other) {
if (other is IntMathClass) {
return new IntMathClass(this.fValue / (IntMathClass)other);
}
return this;
}
public override MathClass Divide(int other) {
return new IntMathClass(this.fValue / other);
}
}

That's a lot of work just to be able to use integers in our list. However, it does allow us to do the following:

SummableList<IntMathClass> list = new SummableList<IntMathClass>();
list.Add(4);
list.Add(5);
list.Add(6);
list.Add(7);

If you're an applications programmer and all you need to do is work with this `SummableList<T>`

, then this works pretty well. However, what if you are the one that has to write all the sub-classes of `MathClass`

? There are better ways.

## What about an *interface* constraint?

If we use an interface constraint, then we can simply apply the interface to whatever class we need to use. Also, the interface definition is much simpler than the abstract class:

public interface IArithmetic<T> {
T Add(T a);
T Subtract(T a);
T Divide(T a);
T Divide(int a);
}

That is much simpler, but we still have to implement this interface in any class we want to work with. We also have to write replacements for the built-in types like `int`

and `double`

because we can't simply add the interface to those. Here's the interface that lets us use integers in our `SummableList<T>`

.

public class IntMathI : IArithmetic<IntMathI> {
private int fValue = 0;
public IntMathI() {
}
public IntMathI(int value) {
fValue = value;
}
public static implicit operator IntMathI(int a) {
return new IntMathI(a);
}
public static implicit operator int(IntMathI a) {
return a.fValue;
}
#region IArithmetic<intmathi> Members
public IntMathI Add(IntMathI a) {
return new IntMathI(this.fValue + a.fValue);
}
public IntMathI Subtract(IntMathI a) {
return new IntMathI(this.fValue - a.fValue);
}
public IntMathI Divide(IntMathI a) {
return new IntMathI(this.fValue / a.fValue);
}
public IntMathI Divide(int a) {
return new IntMathI(this.fValue / a);
}
#endregion
}

Now, we can write our `SummableList<T>`

by placing an interface constraint on the type parameter:

public class SummableList<T> : List<T> where T : IArithmetic<T>, new() {
public T Sum() {
T result = new T();
foreach (T thing in this) {
result = result.Add(thing);
}
return result;
}
public T Average() {
return Sum().Divide(Count) ;
}
}

Notice, however, that in our generic class, we now have to do arithmetic with methods like `.Add()`

and `.Divide()`

instead of using operators like `+`

and `/`

. This is because static methods cannot be defined in an interface, and operator overloads are defined as static methods. Without those static methods, we cannot use operators in our generic class, and we have to use the methods instead.

This does work though, and now we can write the following:

SummableList<IntMathI> list = new SummableList<IntMathI>();
list.Add(4);
list.Add(5);
list.Add(6);
list.Add(7);

So, this works, and it is much simpler than working with the abstract base classes, but it is still limiting. Again, if you are the applications programmer and you only have to work with the `SummableList<T>`

, then this works very well. However, if you are writing your own generic classes, the inability to use operators is a deal breaker. Again, there is a better way.

## Introducing the Calculator utility

After much though about this, I came up with a calculator utility that isn't limited to base classes or interfaces and still allows the class programmer to work with familiar syntax and operators.

The utility has three parts:

- The interface
`ICalculator<T>`

defines all of the operations that can be done.
- Struct implementations of
`ICalculator<T>`

define how the operations are done for any particular type.
- The class
`Number<T>`

stands for any number in a generic class. It uses Reflection to automatically create the correct `ICalculator<T>`

based on the type of `T`

. It has operation method implementations as defined in the interface `ICalculator<T>`

to be performed. It defines operators to make arithmetic easy for the classes programmer.

### ICalculator<T>

The `ICalculator<T>`

interface defines all of the operations that can ever be done in a generic class that uses this utility.

public interface ICalculator<T> {
T Sum(T a, T b);
T Difference(T a, T b);
int Compare(T a, T b);
T Multiply(T a, T b);
T Divide(T a, T b);
T Divide(T a, int b);
}

While this is indeed an interface, the utility does not require that any classes implement it. The interface is used internal to the utility.

### Struct implementations of ICalculator<T>

For each type on which we might do arithmetic, there must be an implementation of `ICalculator<T>`

. The attached code includes implementations for `int32`

, `int64`

, `single`

, `double`

, and `string`

.

Here is what the implementation of `int32`

looks like:

struct Int32Calculator : ICalculator<Int32> {
public Int32 Sum(Int32 a, Int32 b) {
return a + b;
}
public Int32 Difference(Int32 a, Int32 b) {
return a - b;
}
public int Compare(Int32 a, Int32 b) {
return Difference(a, b);
}
public int Multiply(Int32 a, Int32 b) {
return a * b;
}
public int Divide(Int32 a, Int32 b) {
return a / b;
}
}

This is pretty straightforward code that simply defines how to do the operations for any given type. Any programmer that wants to use types that are not already included in the utility could easily add a struct for any other type. In fact, the utility includes a struct implementation for `string`

. I included it to show that *any* type could be added to without having to modify the type itself.

### Class Number<T>

The class `Number<T>`

is where all of the work is done. The programmer using this utility uses `Number<T>`

to stand in for the numbers in his generic class. When `Number<T>`

is used, it uses Reflection to create an instance of the correct `ICalculator<T>`

. It is this instance of the `ICalculator<T>`

that does the actual calculations.

There is an `if`

chain to decide which `ICalculator<T>`

to create, but `Number<T>`

uses a static variable and the Singleton pattern to ensure that the `if`

chain is only entered once per type.

Here is the code for `Number<T>`

:

public class Number<T> {
private T value;
public Number(T value) {
this.value = value;
}
public static Type GetCalculatorType() {
Type tType = typeof(T);
Type calculatorType = null;
if (tType == typeof(Int32)) {
calculatorType = typeof(Int32Calculator);
}
else if (tType == typeof(Int64)) {
calculatorType = typeof(Int64Calculator);
}
else if (tType == typeof(Double)) {
calculatorType = typeof(DoubleCalculator);
}
else if (tType == typeof(string)) {
calculatorType = typeof(StringCalculator);
}
else {
throw new InvalidCastException(String.Format("Unsupported Type- Type {0}" +
" does not have a partner implementation of interface " +
"ICalculator<T> and cannot be used in generic " +
"arithmetic using type Number<T>", tType.Name));
}
return calculatorType;
}
private static ICalculator<T> fCalculator = null;
public static ICalculator<T> Calculator {
get {
if (fCalculator == null) {
MakeCalculator();
}
return fCalculator;
}
}
public static void MakeCalculator() {
Type calculatorType = GetCalculatorType();
fCalculator = Activator.CreateInstance(calculatorType) as ICalculator<T>;
}
#region operation methods
public static T Sum(T a, T b) {
return Calculator.Sum(a, b);
}
public static T Difference(T a, T b) {
return Calculator.Difference(a, b);
}
public static int Compare(T a, T b) {
return Calculator.Compare(a, b);
}
public static T Multiply(T a, T b) {
return Calculator.Multiply(a, b);
}
public static T Divide(T a, T b) {
return Calculator.Divide(a, b);
}
public static T Divide(T a, int b) {
return Calculator.Divide(a, b);
}
#endregion
#region Operators
public static implicit operator Number<T>(T a) {
return new Number<T>(a);
}
public static implicit operator T(Number<T> a) {
return a.value;
}
public static Number<T>
operator +(Number<T> a, Number<T> b) {
return Calculator.Sum(a.value, b.value);
}
public static Number<T>
operator -(Number<T> a, Number<T> b) {
return Calculator.Difference(a, b);
}
public static bool operator >(Number<T> a, Number<T> b) {
return Calculator.Compare(a, b) > 0;
}
public static bool operator <(Number<T> a, Number<T> b) {
return Calculator.Compare(a, b) < 0;
}
public static Number<T>
operator *(Number<T> a, Number<T> b) {
return Calculator.Multiply(a, b);
}
public static Number<T>
operator /(Number<T> a, Number<T> b) {
return Calculator.Divide(a, b);
}
public static Number<T>
operator /(Number<T> a, int b) {
return Calculator.Divide(a, b);
}
#endregion
}

### Final SummableList<T>

With all three pieces in place, `SummableList<T>`

can now be written without using any constraints, abstract classes, or interfaces.

class SummableList<T> : List<T> {
public T Sum() {
Number<T> result = default(T);
foreach (T item in this)
result += item;
return result;
}
public T Average() {
Number<T> sum = Sum();
return sum / Count;
}
}

This looks very much like the first example that we said wouldn't compile. The difference is that the result variable in the `Sum()`

method is of type `Number<T>`

instead of just type `T`

. Also, I've thrown in an `Average()`

method for good measure.

You may notice that the `Sum()`

method is supposed to return a `T`

while the last line of code returns the variable result, which is a `Number<T>`

. This is possible because the class `Number<T>`

defined two implicit operators that tell the compiler how to implicitly convert a `T`

into a `Number<T>`

.

public static implicit operator Number<T>(T a) {
return new Number<T>(a);
}
public static implicit operator T(Number<T> a) {
return a.value;
}

It is this that allows the classes programmer to seamlessly use the `Number<T>`

in place of a `T`

. Also, because `Number<T>`

has arithmetic methods and operators defined for it, it allows the programmer to do arithmetic where he normally wouldn't be able to.

## Adding types or operations

Since there are no base classes or interfaces that need to be used in order to use this utility, it is fairly self contained. However, there may come a time when you want to use this utility with a type that is not included, or you want to perform some arithmetic operation that isn't already defined. Here's how you can do it:

#### Adding types

- Add a type to
`Number<T>.GetCalculatorType(Type tType)`

- Create an implementation of
`ICalculator<T>`

#### Adding operations

- Add an operation to the
`ICalculator<T>`

interface.
- Add an operation to each implementation of
`ICalculator<T>`

.
- Add an operation and an operator overload to the class
`Number<T>`

.

## Performance

The attached solution includes a SpeedTest that will add any number of random numbers together using each of the three methods described in this article and shows the elapsed time. At ten million iterations, the utility comes out about .2 or .3 seconds faster.

## MiscUtil

There is another way to go about this that is completely different. This way requires .NET 3.5, and uses LINQ classes to generate expressions and compile them on the fly. It uses the operator overloads on any class to generate the required expressions. This means that it can work with any class that implements suitable operators.

Compiling code on the fly can be very slow, but Jon Skeet and Marc Gravell have put together a project called MiscUtil, that among other things includes a framework that caches the compiled expressions to make it very fast. In my crude speed test, at 1 million iterations, it is not as fast as my utility, but having it work on any class that implements operators is very attractive. Also, using LINQ this way is **very, very cool**.

## References

The following articles really helped me when I was trying to figure out what I was going to do about my matrices:

- Gunnerson, Eric. “Generics Algorithms” Eric Gunnerson's C# Compendium. November 13, 2003. http://blogs.msdn.com/ericgu/archive/2003/11/14/52852.aspx
- Klaehn, Rüdiger. “Using Generics for calculations” The Code Project. October 11, 2004. http://www.codeproject.com/KB/cs/genericnumerics.aspx
- Skeet, Jon and Gravell, Mark. “Generic operators” Jon Skeet's C# and .NET articles and links. Last accessed July 13, 2008. http://www.yoda.arachsys.com/csharp/genericoperators.html