paper: CORDIC Trigonometric Math Library

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CORDIC Trigonometric Math Library
by: Pat Fairbank

Provides functions to calculate the sine and cosine of angles, and the magnitude and direction (arctangent) of Cartesian coordinates, using integer math and minimal memory space.

This is an updated version of Team 296’s CORDIC trigonometric math library.

The CORDIC algorithm simultaneously calculates the sine and cosine of a given angle, or the
arctangent and magnitude of a given pair of co-ordinates, using only a small table of arctangent values and the bit-shift and addition/subtraction operators. This implementation uses 16-bit integer math throughout, and is generally accurate to within 0.01%.

Improvements from the last version include:

  • Returning the sine & cosine (or arctangent & magnitude) in a structure so that both can be used
  • 16-bit math instead of 24-bit math (because 24 bits is overkill)
  • Re-writing of the functions from C to PIC assembly for a 2.5x speed increase

Instructions for use are found in trig.h. (3.54 KB)

I felt like doing some programming, so I updated the CORDIC math library I posted a few years ago.

I made a few changes such as returning both the sine and cosine values instead of throwing one away (since CORDIC calculates both at once), and downgrading from 24-bit math to 16-bit math in the interest of speed. However, the biggest change is that the library is now written in PIC assembly instead of C, since I was curious to see if there was any speed advantage to be had.

I did some speed testing by calling the function as many times as possible in one Process_Data_From_Master_uP() loop before the RC crashed. The assembly implementation of the sin_cos() function took 4500 calls to crash while the C implementation took 1800 calls; the atan2_sqrt() function took 4700 and 1900, respectively. So it seems that the assembly implementation is about 2.5 times faster than the C implementation.

Any questions or comments are welcome.

I just uploaded a second revision to the trig library. There was a bug in the way the previous versions were handling the C function calls in assembly - the software stack wasn’t being manipulated properly, with the result that the trig functions would work as expected when called from a function that didn’t have local variables, but would return strange values when called from a function that did.

So if you’re using the library and are seeing strange return values, you probably have an older version and need to update to Revision 2.

EDIT: Ignore this post, I can not delete it

What is the advantage to using this vs a lookup table to the desired degree of accuracy?

How much more accurate and slow is the built in <math.h>?

Well, the math.h implementation can be called ~100 times per second (speed test that was posted on CD at some point this month), and this function takes a half second for 4500 calls (a half second being the max time a loop can execute before the OI says it ‘crashed’)

so id say its about… 90x faster?

someone call me on this if my math is wrong.

Ok i just found out what is needed to get this code to compile with the new 3.02 or higher compiler,
you need to replace all instances of AARGB3 with the new definition of __AARGB3
you can see the reference to this naming change here:
ref (27624)