11-03-2004 06:58

Pat Fairbank

Re: White Paper Discuss: 296's CORDIC Math Library

Hello all,

We at 296 decided to share our student-developed math library with the CD community. We needed trig functions for our robot positioning system, so we wrote our own using the CORDIC algorithm. The library includes integer sine, cosine, and arctangent, all accurate to +- 1/16777216, as well as a few other useful functions.

I hope this comes in useful for those of you who need accurate trig functions.

12-03-2004 13:55

Astronouth7303

Re: White Paper Discuss: 296's CORDIC Math Library

A "Short Long"? Isn't this contradictive? or just an oxymoron? I thought there were short ints and long ints.

12-03-2004 17:55

Pat Fairbank

Re: White Paper Discuss: 296's CORDIC Math Library

Well, short ints are 16 bit, long ints are 32, and I guess that they needed a name for a 24 bit int, so they called it a short long.

27-04-2004 21:51

mtrawls

Re: White Paper Discuss: 296's CORDIC Math Library

We didn't use trig in our final implementation ... but in testing we did consider it, and also decided on the CORDIC algorithm. There is an added advantage of CORDIC that your library currently doesn't utilize -- it can compute both the sin and cosine at the same time (which you do, but then you throw one of them away). For our trig needs, anyway, we needed the sin and cos of the same angles.

Implementing this in a math library (admittedly more general than our custom implementation), would be interesting conceptually. Maybe create a structure called angle.

struct angle {
  short long angle;
  short long sin, cos;
  ...
};
...
short long Sin (angle ang) {
  ...
  ang.cos = blah;
  ang.sin = more blah;
  return ang.sin;
}

28-04-2004 20:01

Greg Ross

Re: White Paper Discuss: 296's CORDIC Math Library

typedef enum {wantsSin, wantsCos} WhichFunc;

short long cordic(short long theAngle, WhichFunc theRequestedFunction)
{
	static char firstTime = 1;
	static short long prevAngle;
	static short long prevSin;
	static short long prevCos;

	unsigned char i;
	short long X = K, Y = 0, t = theAngle;
	short long dx, dy;

	// If this is the first time the function has been called, or if the
	// requested angle is different than the last time, then go ahead and
	// calculate the sine and cosine, otherwise we can skip the calculations,
	// and just return the value calculated last time.
		
	if (firstTime || (theAngle != prevAngle)) {
		if ((long) abs((long)theAngle) > 4194304)
			t = (short long) sgn((long) theAngle) * (8388608 - (short long) abs(theAngle));

		for (i = 0; i < 23; i++) {
			dx = sgn((long) X) * ((unsigned short long) abs((long) X) >> i);
			dy = sgn((long) Y) * ((unsigned short long) abs((long) Y) >> i);
			X -= (t > 0) ? dy : -dy;
			Y += (t > 0) ? dx : -dx;
			t -= (t > 0) ? e[i] : -e[i];
		} // for

		if (abs((long) theAngle) > 4194304) X = -X;

		firstTime = 0;
		prevAngle = theAngle;
		prevSin = Y;
		prevCos = X;
	} // if (firstTime ...

	if (theRequestedFunction == wantsSin)
		return prevSin;
	else
		return prevCos;
}

short long sin(short long theAngle)
{
	return cordic(theAngle, wantsSin);
}

short long cos(short long theAngle)
{
	return cordic(theAngle, wantsCos);
}

• I unrolled the nested ::gasp:: ternary operators in the return statement to make it more readable.
• I changed the name of the "ang" parameter to theAngle, so that someone unfamiliar with the code won't have to stop and think "Ang? What's that? Anger? Angst? Angstrom? Automatic Number Generator?" (Yeah, I know it's FAIRLY obvious from the context, but I prfr rdg fl wrds nstd f abbrvs. cn u dg it?)
• I changed the name of the second parameter of the cordic() routine (again so it's more obvious what the parameter is used for) and I made it an enum so that you never have to wonder whether 0 or 1 means sine or cosine.
• I added a couple of end brace comments so it's easier to match up opening and closing braces.
• I moved the cordic() function in front of sin() and cos(), so I wouldn't need a prototype for cordic().