How to parse a decimal fraction into Rational in Haskell?

Question

I've been participating in a programming contest and one of the problems' input data included a fractional number in a decimal format: 0.75 is one example.

Parsing that into Double is trivial (I can use read for that), but the loss of precision is painful. One needs to be very careful with Double comparisons (I wasn't), which seems redundant since one has Rational data type in Haskell.

When trying to use that, I've discovered that to read a Rational one has to provide a string in the following format: numerator % denominator, which I, obviously, do not have.

So, the question is:

What is the easiest way to parse a decimal representation of a fraction into Rational?

The number of external dependencies should be taken into consideration too, since I can't install additional libraries into the online judge.

score 20 · Accepted Answer · answered Aug 14 '11 at 12:54

20

The function you want is Numeric.readFloat:

Numeric Data.Ratio> fst . head $ readFloat "0.75" :: Rational
3 % 4

answered Aug 14 '11 at 12:54

Yitz

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you might want to add `readSigned` if you want to be able to read negative numbers: `fst . head $ readSigned readFloat "-3.14" :: Rational` – newacct Sep 05 '11 at 06:16

score 3 · Answer 2 · answered Aug 14 '11 at 13:01

3

How about the following (GHCi session):

> :m + Data.Ratio
> approxRational (read "0.1" :: Double) 0.01
1 % 10

Of course you have to pick your epsilon appropriately.

answered Aug 14 '11 at 13:01

bzn

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This is a good idea! I think this should be used instead of `toRational` in most circumstances! – Rotsor Aug 14 '11 at 13:05
Unfortunately, the choice of epsilon is not obvious here. For example, `approxRational 0.999 0.0001` is `909 % 910`, which is not what I want. The proper epsilon to use in this case is `0.000001` (precision squared?) – Rotsor Aug 14 '11 at 13:21

score 2 · Answer 3 · answered Sep 17 '12 at 15:09

2

Perhaps you'd get extra points in the contest for implementing it yourself:

import Data.Ratio ( (%) )

readRational :: String -> Rational
readRational input = read intPart % 1 + read fracPart % (10 ^ length fracPart)
  where (intPart, fromDot) = span (/='.') input
        fracPart           = if null fromDot then "0" else tail fromDot

answered Sep 17 '12 at 15:09

jazmit

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I don't think so. In such contests only the submission time and correctness matters. Nice solution still, short enough to code in an emergency. – Rotsor Sep 19 '12 at 13:58

How to parse a decimal fraction into Rational in Haskell?

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