>>>>> "Richard" == Richard Fateman <fateman@cs.berkeley.edu> writes:
Richard> As a general goal we could try to have bigfloat evaluation
Richard> of every function. This can be done by mapping to a bigfloat
Richard> evaluation of 2F3 hypergeometric functions, which I suspect
Richard> is how Mathematica does it. The programs may not achieve
Richard> adequate relative error at critical points (e.g. zeros of
Richard> Bessel functions).
This looks promising. From functions.wolfram.com, there's a continued
fraction for 2F3 that would make a nice algorithm. Unfortunately, it
doesn't say where the fraction converges. The confluent
hypergeometric function could also be promising for evaluating Bessel
functions and other functions.
Ray