Suppose we restrict ourselves to dyadic streams. In order to obtain
*n* digits of *f*(*x*), we compute (1-*x*) which has a lookahead of
(*n*+1) (because the subtraction operation uses a shift), multiply this
by *x* which gives (*n*+2), and shift the result left to achieve
multiplication by 4. This means the function will require (*n*+4)
lookahead. If this is now iterated, at the second iteration we will
require (*n*+4) digits of *f*(*x*) which is ((*n*+4)+4) digits of *x*. Hence
at the iteration the lookahead will be (*n*+4*i*).

If we use the (mantissa, exponent) representation in which a
multiplication by four can be accomplished by simple modification of
the exponent, the lookahead required will be (*n*+*i*) as the only
increase comes from the multiplication. Note that if the exponent
increases, however, we need more digits of output to obtain the same
precision.