Difference between revisions of "Generic number type"

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(extracted from the Haskell-Cafe discussion)
 
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Floating point numbers are imprecise - a/b*b=a does not hold in general.
 
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.
 
Rationals are precise but pi and sqrt 2 are not rational.
That is, when using GenericNumbers you will encounter exactly the problems
+
That is, when using <hask>GenericNumber<hask>s you will encounter exactly the problems
 
that all scripting language users have encountered so far (or ignored :-).
 
that all scripting language users have encountered so far (or ignored :-).
   

Revision as of 12:16, 20 June 2007

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


See also