Re: A92: RE: Trig
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Re: A92: RE: Trig
I would like to correct myself. The interval of [0, pi/2] is entirely
sufficient.
At an increment of .01, it requires a table of less than 160 entries. At
two bytes per entry (which should more than suffice for accuracy required in
most applications), that's 320 bytes. Not too shabby...
Anton Ivanov wrote:
> You should be aware that the power series converges for |x|<1, as you
> can easily verify. Consequently, I would not recommend that you use
> |x|<2*pi for your interval. The power series for tan(x) is derived in a
> straightforward fashion by means of long division of the series of
> sin(x) and cos(x). Series for inverse trig functions are easily
> derivable from Integration/Differentiation Theorem for Power Series.
> Check with a book on the Calculus for more info.
> However, I surmise that emulated floating point routines on a 10MHZ
> processor would be too slow to be practical in this application
> (especially if you have a rendering loop requiring a multitude of such
> computations). It is therefore more practical to sacrifice a little
> memory and build a table of values to required precision (which should
> not be too excessive). Furthermore, keep in mind that, with a little
> manipulation, the interval [0, pi] of either sin or cos is entirely
> sufficient, something which you could not exploit if you merely computed
> the value every time.
>
> -AI
> ivanova@ucs.orst.edu
> ant_i@hotmail.com
> >Well, if you impliment all that stuff division and multiplication and
> >stuff...you should know that trig is pretty easy with a power series.
> For
> >instance, for sin(x), you need x in radians, and it would probably be
> best to
> >reduce it to + or - 2pi or so. Then you can approximate sin(x) with: x
>
> >- -x^3/3! + x^5/5! - x^7/7! ... it gives a very close approximation
> after adding
> >only a few terms (seven terms or so would probably be good) try it out
> on a
> >calculator, see how close it gets you. If you like it, and you write
> those
> >routines, there's also a power series for cos(x). I don't think it
> would work
> >well for tan(x) though. Anyhow, sin(x) and cos(x) would be good for
> start on
> >trig, once you have the basic addition, subtraction, multiplication and
>
> >division implimented.
> >
References: