Subject:
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Re: evaluate inverse cosine, sine in IC
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Newsgroups:
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lugnet.robotics.handyboard
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Date:
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Mon, 29 Nov 1999 21:46:30 GMT
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Viewed:
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1074 times
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Another technique for finding trig functions and their inverses used by both
HP and TI in their calculators is the CORDIC algrorithm. A description of the
technique with lots of references can be found at:
http://www.ti.com/calc/docs/faq/83faq086.htm
Barry
In lugnet.robotics.handyboard, "Jeroen van der Vegt"
<A.J.vanderVegt@ITS.TUDelft.nl> writes:
> Taylor series should converge quite rapidly. After 2 or 3 terms, the error
> is usually neglectable (depending or your demands, of course: this should be
> fine for up to a few decimals)
>
> For those not familiar with the Taylor expansion, I've added a small picture
> containing the formula.
>
>
> ----- Original Message -----
> From: Gary Livick <glivick@pacbell.net>
> To: Will <nepenthe@montana.com>
> Cc: Handyboard Mailing List <handyboard@media.mit.edu>
> Sent: Monday, November 29, 1999 7:44 PM
> Subject: Re: evaluate inverse cosine, sine in IC
>
>
> > I've been trying to do this as well. The problem I have found is that the
> Taylor series expansion needs to be developed near the solution to get
> accurate results.
> >
> > Some may wonder why finding the arcsine of a number might be of interest.
> If one has a robot that is sitting at some angle to a wall, and by using a
> ranging device of some kind (SONAR, IR ranging) mounted on a servo is able
> to get two ranges to the wall, the first at one angle from the robot and the
> second at a different angle from
> > the robot, then the angle of the robot axis to the wall can be determined.
> In dead reckoning navigation, it is often necessary to update robot position
> from known landmarks.
> >
> > To do this calculation, the "law of cosines" is first used, and the
> interim results are then used in the "law of sines" to get the angle.
> Arcsine is needed in the last calculation.
> >
> > One could generate a lookup table to go into in memory to find the angle,
> but what a waste of space. It would be nice if Motorola had a freeware math
> function of arcsine, but they appear not to. After days of head scratching,
> I have yet to turn up a simple algorithm to calculate arcsine from a random
> argument. Any math majors out
> > there with nothing to do?
> >
> > Thanks for any help,
> >
> > Gary Livick
> >
> >
> >
> > Will wrote:
> >
> > > bedirhan wrote:
> > > >
> > > > Hi, is there a way to evaluate inverse cosine and sine using IC? Thx
> > >
> > > The most efficient way to do it is to use Taylor Series approximations
> of the functions. Decide how much precision you need, and then write
> functions that evaluate the first few terms in the appropriate series.
> > >
> > > Usually, a series will converge quite rapidly, and only half a dozen or
> so terms are needed. For example, if the sixth term in the series is on the
> order of 1.0E-6, then you're getting close to the limit of single-precision
> arithmetic anyway (and certainly close enough for horse shoes, hand
> grenades, and tactical nuclear weapons).
> > >
> > > -- Will
>
>
>
> --
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Message is in Reply To:
 | | Re: evaluate inverse cosine, sine in IC
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| Taylor series should converge quite rapidly. After 2 or 3 terms, the error is usually neglectable (depending or your demands, of course: this should be fine for up to a few decimals) For those not familiar with the Taylor expansion, I've added a (...) (25 years ago, 29-Nov-99, to lugnet.robotics.handyboard)
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