[Haskell-cafe] Floating phi, round and even Fibonnaci numbers

[Robert Daniel Emerson]

Brian,

I am also a Haskell newbie, and unfortunately can not answer your type 
question, but wish to make a 'side comment'. The use of a floating point phi 
to calculate Fibonacci numbers makes me a bit nervous. In 'Structure and 
Interpretation of Computer Programs' 2n Edition Exercise 1.19 there is an 
algorithm for calculating the n'th  Fibonacci number in order of log n steps. 
Take a look at:

http://mitpress.mit.edu/sicp/full-text/sicp/book/node18.html

I would use the type Integer, with this algorithm, for arbitrary precision 
Fibonacci numbers. My concern is that your lazy list will start to deviate at 
some point from Fibonacci numbers because of the floating point calculations. 
Comments welcome, and I look forward to seeing the experts answer your type 
question.

Best Regards,
Robert

On Wednesday 11 July 2007 05:11, Brian L. Troutwine wrote:
> I'm rather new to Haskell and need, in typical newbie style,
> a bit of help understanding the type system.
>
> The Nth even Fibonacci number, EF(n) can be defined by the recursive
> relation EF(0) = 2, EF(n) = [EF(n-1) * (phi**3)], where phi is the
> golden ratio and [] is the nearest integer function. An infinite lazy
> list of this sequence would be nice to have for my Project Euler, er,
> project. Defining phi thusly,
>
> > phi :: (Floating t) => t
> > phi = (1+sqrt(5))/2
>
> With phi in place, if I understood types properly (and if I understand
> iterate correctly as I think), the lazy list should be a relatively
> quick matter.
>
> > even_fibs :: (Num t) => [t]
> > even_fibs = iterate (\x -> round(x * (phi**3))) 2
>
> Dynamically typed even_fibs :: (Floating t, Integral t, RealFrac t) =>
> [t], assuming I pass -fno-monomorphism-restriction to ghci. That's not
> at all the type I assumed even_fibs would take, as can be seen from
> above. So, I went on a bit of sojourn. Having seen the sights of the
> Haskell Report section 6.4, the marvels of the references cited in the
> wiki's article on the monomorphism restriction and the Gentle
> Introduction's chapter 10 I must say I'm rather more terribly confused
> than when I started out, possibly.
>
> Can someone explain where my type statements have gone wrong?
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