Re: Re[4]: Numeric inconsistency

[Raymond T. <to...@rt...>]

>>>>> "Arseny" == Arseny Slobodjuck <am...@ic...> writes:

    Arseny> Hello, Raymond,
    Arseny> Friday, July 19, 2002, 3:11:35 AM, you wrote:

    Raymond> Yes.  If you could, can you tell me why the computation of tan
    Raymond> requires the computation of sqrt?  Don't bother if it's lengthy.  Just
    Raymond> curious.
    Arseny> I have an supposition: it allows to compute only one of sin or cos, not both
    Arseny> (supposing sqrt being calculated more quickly than trigonometric function).
    Arseny> For example tg(a) = (+-)sqrt((1-cos(2a))/(1+cos(2a))).

    >> Sounds reasonable.  Seems that this has lots of extra round-off
    >> problems than just computing cos(a), though.

    Arseny> This formula doesn't have sqrt(0) problem for tg(pi/2) (it haves
    Arseny> sqrt(inf) one).

Yep.

    Arseny> If you mean sqrt(x - > 0) error, it can be fixed (if the code doesn't
    Arseny> contain a workaround already). For example sqrt(x) = sqrt(n^2 * x) /
    Arseny> n (There are possibly exist smarter workarounds, I don't know).

Somehow these workarounds just seem to complicate things.  Aren't they
good algorithms that can comput sin and cos at the same time with only
slightly more cost than just sin?  I know the CORDIC algorithms do
this.

Ray