On Mon, 31 Jan 2000, Phu T. Van wrote:

> Hi. I've got a problem I don't quite know how to tackle.
> I need to program the following function for a 16F84 :
>
> P(n) = x - (x^3/6) + (x^5/120) - (x^7/5040)
>
> I don't know what this approximation is called or if it really works the
> way it's supposed to. I got it from a local math whiz; supposedly it
> will approximate sine of x where x is the angle in radians.
>
> Anyhow, I need a reliable, fast and efficient way to calculate sine in
> realtime to do navigation. I've heard about lookup tables but apparently
> that is said to consume a huge amount of memory and processing power.
> I'd like to stick with the PIC if possible.

The fastest way to compute the sine function on a pic is with a lookup
table. Period.

I'll buy anyone a beer who can write a program (on a pic) that can
evaluate the sine faster than:

http://www.brouhaha.com/~eric/pic/sine.html

You can't beat 13 cycles (or 6 if you know the quadrant of the angle prior
to the call).

But as I've said perhaps before, Eric's implementation does no linear
interpolation between the samples. Consequently you'll get some 'stair
stepping' or quantization errors. I have no idea what your ultimate
application is, but if you need a more precise sine calculation then see:

http://www.dattalo.com/technical/software/pic/picsine.html

I've recently improved the execution time so that it only takes 48 cycles
to compute the sine(). If you're using the 18cxxx family, then you may
wish to consider this

http://www.dattalo.com/technical/software/pic/sine18.asm

This one only takes 30 cycles.

If you wish to roll your own sine wave algorithm, then visit

http://www.dattalo.com/technical/theory/sinewave.html

Where you'll find a comparison of different techniques/algorithms for
computing the sine().

As far as arbitrary math stuff, I'll add to the advice given by others by
suggesting you visit:

http://www.dattalo.com/technical/software/software.html

There you'll find pic code for arcsine, arctan, sqrt, and logarithms.

Scott