On 11 Oct 2007, at 4:49 am, Dan Piponi wrote:
Maybe this is the wrong point of view, but I think of defaults as impementations that are meant to be correct, but not necessarily the best way of doing things, leaving you the option to provide something better.
The example of tanh in the report (page 106) shows that this view cannot be sustained. As an algorithm for computing tanh, it cannot be defended, producing NaN in a vast range of cases where 1.0 is the easily obtained correct answer.
For the case of power series as an instance of Num, using 4*atan 1 gives me the wrong thing as it triggers an infinite summation, whereas I'd want pi to simply equal the constant power series.
So if you have a default for pi in Float, you still have to provide your own definition for power series. Without a default for pi, you have to provide your own definition for power series. It doesn't sound as though providing a default makes anything worse. One alternative would of course be to simply provide a definition with say 64 digits, to be rounded as appropriate by the compiler. That would be as accurate as 4*atan 1 for Float, Double, and Complex based on them, even for 128-bit floats.