Can an Apfloat number be rationalized?

[axkr]

There is a constructor for double:

  Aprational(double value)

is it also possible to have a constructor (or valueOf method) which converts an approximate number Apfloat to a "nearby" rational Aprational?

  Aprational(Apfloat value)

[mtommila]

Somebody once suggested this (by email)

Basically, the algorithm is to calculate the continued fraction for the given Apfloat and then take the n:th convergent to get a rational approximation of the floating-point number (the bigger the n, the better the approximation)

The corresponding function in Mathematica is Convergents

It currently isn't implemented in the apfloat library but I suppose it shouldn't be that hard to implement