On Wed, Oct 10, 2007 at 08:49:56AM -0700, Dan Piponi wrote:
Jules Bean said:
If it is true of many Floating instances that (atan 1 * 4) is an accurate way to calculate pi (and it appears to be 'accurate enough' for Float and Double, on my computer) then adding it as a default doesn't appear to do any harm.
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. 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. Now you could counter that by saying that power series are an esoteric case. But apart from code in the libraries, most code I've seen that provides an instance of Num is doing something mildly esoteric.
It sounds like what you're actually saying is atan is buggy in these cases, since it leads to an infinite summation. Programmers who define a buggy atan would certainly be punished by this default for pi, but those who recognize that there is no reason to define a buggy atan at all and leave it undefined would have the same result as when there is no default for pi. -- David Roundy Department of Physics Oregon State University