# Difference between revisions of "Generic number type"

## Problem

Question: Can I have a generic numeric data type in Haskell which covers `Integer`, `Rational`, `Double` and so on, like it is done in scripting languages like Perl and MatLab?

Answer: In principle you can define a type like

```data GenericNumber =
Integer Integer
| Rational Rational
| Double Double
```

and define appropriate instances for `Num` class et. al. However you will find that it is difficult to implement these methods in a way that is appropriate for each use case. There is simply no type that can emulate the others. Floating point numbers are imprecise - a/b*b=a does not hold in general. Rationals are precise but pi and sqrt 2 are not rational. That is, when using `GenericNumber<hask>s you will encounter exactly the problems that all scripting language users have encountered so far (or ignored :-). == Solutions == It is strongly advised to carefully check whether a GenericNumber is indeed useful for your application. So let's revisit some examples and their idiomatic solutions in plain Haskell 98. === average === You may find it cumbersome to write <haskell> average :: Fractional a => [a] -> a average xs = sum xs / fromIntegral (length xs) </haskell> and you may prefer <haskell> average :: [GenericNumber] -> GenericNumber average xs = sum xs / genericNumberLength xs </haskell> with an appropriate implementation of <hask>genericNumberLength`. However, there is already `Data.List.genericLength` and you can write

```average :: Fractional a => [a] -> a
average xs = sum xs / genericlength xs
```

### ratios

You find it easy to write

```1 / 3 :: Rational
```

but uncomfortable that

```1 / floor pi :: Rational
```

does not work. The first example works, because the numeric literals `1` and `3` are interpreted as rationals itself. The second example fails, because `floor` always returns an `Integral` number type, where `Rational` is not an instance. You should use `%` instead. This constructs a fraction out of two integers:

```1 % 3 :: Rational
1 % floor pi :: Rational
```