Re: Best processors for trig?

On Fri, 30 Mar 2007 20:06:57 GMT, Tauno Voipio
<tauno.voipio@xxxxxxxxxxxxx> wrote:

larwe wrote:
On Mar 30, 1:46 pm, Tim Wescott <t...@xxxxxxxxxxxxxxxx> wrote:

A floating point DSP, as noted.

What's the canonical method of doing this? Taylor series
approximations?

Of course, the arguments have to be reduced first to
the range of the period (2 * pi for sin and cos, pi
for tan). The reduced range is often split into some
sub-ranges with different coefficients.

For float (6 digits) the 3 .. 4 order is usually enough, for double,
you may have to calculate to the 6th - 8th degree.

The least-maximum error polynomial for approximation
is obtained by developing the function to a series
of Chebysev polynomials. This method gives less error
than a corresponding Taylor or MacLaurin series.

Taylor series are far too computationally intensive for any practical
purpose, so in practice some kind of polynomial is used.

The trig functions and exponential are quite polynomial-
friendly.

3-4(float) or 6-8 order polynomials are usually sufficient.

The most difficult of the elementary functions
is the logarithm, its Taylor series uses half of an
infinity to converge.

After all, the only real problem with logs is that you must be able to
calculate it in the 1.0 .. 2.0 range, the rest is trivial.

Do you really need anything more than a 6th degree polynomial ?

Paul

.

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