mccaugh@s.cs.uiuc.edu (10/04/89)
I really don't mean to sound pedantic (after all, if I did mean to, I would go over to the numerical-analysis group to do so) but I fail to see the virtue of speed for only a few decimal places: it doesn't seem terribly profound to cough up the first few terms of a Taylor Series, factoring the powers to exploit Horner's Rule and exclaim: "well, here is such a fast ArcTan series it doesn't require a loop!" I.e., yes it's fast--but at the expense of what? ACCURACY. (But for all that, it may be the fastest 3-place ArcTan routine available: for that, I commend the author!) Scott McCaughrin (mccaugh@s.cs.uiuc.edu)
dik@cwi.nl (Dik T. Winter) (10/05/89)
(I did not find the parent article on our system, so I really do not know what I am talking about.) In article <207600047@s.cs.uiuc.edu> mccaugh@s.cs.uiuc.edu writes: > > I really don't mean to sound pedantic Nor do I. > (after all, if I did mean to, I would > go over to the numerical-analysis group to do so) I do so on occasion. > but I fail to see the > virtue of speed for only a few decimal places: Simply depends on what you want. > it doesn't seem terribly > profound to cough up the first few terms of a Taylor Series, factoring the > powers to exploit Horner's Rule and exclaim: "well, here is such a fast > ArcTan series it doesn't require a loop!" Any arctan routine worth its money does not require a loop. > I.e., yes it's fast--but at the > expense of what? ACCURACY. (But for all that, it may be the fastest 3-place > ArcTan routine available: for that, I commend the author!) Given the method you arrived at it, it may be, but it is certainly not the fastest 3-place ArcTan routine possible. In most cases, given a Taylor series truncated to an order n polynomial there is a polynomial of lower order that gives better accuracy. (Keywords: telescoping Taylor series; Chebyshov polynomials.) -- dik t. winter, cwi, amsterdam, nederland INTERNET : dik@cwi.nl BITNET/EARN: dik@mcvax