Continued fraction/Arithmetic/Construct from rational number: Difference between revisions

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The task is vague about how the "lazy evaluation" works, and it seems to me a function with side effects suffices. Nevertheless, what I did was write such a function that has side effects, and then wrap that function in a thunk (a closure taking no arguments). One might wish to go farther and produce a lazy stream, but I did not do that.
The task is vague about how the "lazy evaluation" works, and it seems to me a function with side effects suffices. Nevertheless, what I did was write such a function that has side effects, and then wrap that function in a thunk (a closure taking no arguments). One might wish to go farther and produce a lazy stream, but I did not do that.


I hope the point is not that one must use lazy evaluation to do this algorithm! Rather, it should be that, at each step, you are performing the same process, merely with a different starting point. If the function returned the next N1 and N2, along with the next digit, you would have a purely functional version.
I hope the point is not that one must use lazy evaluation to do this algorithm! That would beg the question of what "lazy evaluation" means. Rather, the point seems to write ''some'' method of producing the digits of the continued fraction. ''This process itself'' will be regarded as the value of the number.

(I have, by the way, long viewed "a real number" as such a process. It does not matter whether or not the process involves continued fractions, as long as it produces an arbitrarily precise rational number.)


I demonstrate concretely that the method of integer division matters. I use 'Euclidean division' (see ACM Transactions on Programming Languages and Systems, Volume 14, Issue 2, pp 127–144. https://doi.org/10.1145/128861.128862) and show that you get a different continued fraction if you start with (-151)/77 than if you start with 151/(-77). I verified that both continued fractions do equal -(151/77).
I demonstrate concretely that the method of integer division matters. I use 'Euclidean division' (see ACM Transactions on Programming Languages and Systems, Volume 14, Issue 2, pp 127–144. https://doi.org/10.1145/128861.128862) and show that you get a different continued fraction if you start with (-151)/77 than if you start with 151/(-77). I verified that both continued fractions do equal -(151/77).
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