fast arc tangent routine availa

[Dik T. Winter]

(I did not find the parent article on our system, so I really do not know
what I am talking about.)

In article <207600047 at s.cs.uiuc.edu> mccaugh at 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
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