A real $r$ is computable if given any $i\in \mathbb{N}$, the $i$th bit can be outputed by a Turing Machine or an algorithm. So, what is computational complexity or complexity measure of computing the real? Since there is just a Turing Machine or a program without input,



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> what is the computational complexity or complexity measure of computing reals?
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Any definition and result? Intuitively, the computational complexity or complexity measure may be defined in terms of the size of output, like length of the binary sequence of the outputed real. 



The definition of computational complexity or complexity measure of computing reals
This is interesting. I think a number could be of low complexity in terms of approximating it to within smaller and smaller $\epsilon $, while of high complexity in terms of finding its binary representation. Just imagine that its binary representation has extremely long stretches of 0s (and/or 1s) so the number is unusually close to dyadic rationals in a sense.


You may find something about this in Chapter 7 of Weihrauch's book *Computable Analysis*.


