Rational sequence

[Jerzy Karczmarczuk]

Alastair Reid:

> Ferenc Wagner <wferi@bolyai1.elte.hu> writes:

> Hmmmm, the CVS copy of Hugs seems to suffer from a different problem:
> 
> Prelude> [0.5,1.5..5.5]::[Rational]
> [0 % 1,1 % 1,2 % 1,3 % 1,4 % 1,5 % 1]
> 
> I'm expecting to see:
> 
> [1 % 2,3 % 2,5 % 2,7 % 2,9 % 2,11 % 2]

Rationals in Hugs were always a bit obscure. What do you think, what
is the Rational form of 2.3 ? (GHCi says 23/10).

The answer is:

2589569785738035 % 1125899906842624

(Old Hugs, Feb. 2001)
If you look at the Prelude, you will see that the algorithms used for
rationals are not always a rocket science. I replaced (for myself)
that stuff by the continued fraction expansions which are fast and give
decent results. The rational arithmetics can also be optimised by using
algorithms in the 2nd volume of Knuth (the favourite book of Ralf Hinze...)

I found similar bugs in sequences as above already (if I am not mistaken) 
about 7 - 8 years ago, when we discussed a bit the usage of Haskell to 
some numerics. But nobody really cared about it, and it seems that some 
small but nasty insects are still alive.

Jerzy Karczmarczuk