Hi Mike,

[Rescaling]

 MB> Of course this is true, but my point was that the rescaling is necessary
 MB> regardless of the underlying computational method.

No need to argue about that, we agree.

 MB> I understood him to be making the (incorrect) inference that, since
 MB> rescaling was occurring, this was an indication that a Taylor expansion
 MB> was being used.

In the context of a Taylor polynomial expansion of sine or cosine. Even
when using techniques like a look-up table, local Taylor expansion, i.e.
(x=t+eps)

sin(x) = sin(t+eps) = sin(t) + eps * cos(t) - eps^2 * sin(t) /(2!) ....

is a usefull method to increase the accuracy.

I never realized how many values should be stored in the FPU look-up
tables, nor the fact that look-up techniques were applied. So i estimated
that when using a double (8 bytes IEEE floating point representation), the
FPU will need terms in the local expansion of the order eps^4 and a table
with a spacing between tabulated values of the order of 0.0001 radians. The
implication is a table of the order of 10000 doubles to store in the FPU.
Amazing!

Nevertheless i'm still puzzled how a trig. function, what ever method, will
calculate a value outside (-1,1).


73 es cuagn,
 Henk

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