Cordic trig assembly code for PIC18f

[ScaleRobotics]

I have been trying to use cordic code that was originally written for a PIC18F device. I have made some changes to it to try to make it compatible with PicBasic Pro, but I am getting some unexpected results. I am compiling it to a PIC18F4620 device using 2.50b. It compiles without any errors, and prints the values to an LCD, but the results vary, and are unexpected. Any ideas would be greatly appreciated.

Here is the original code:
http://www.chiefdelphi.com/media/papers/2016


Here is my stab at making it compatible:

;*******************************************************************************
; --- CORDIC TRIG LIBRARY ---
;http://www.chiefdelphi.com/media/papers/2016
; FILE NAME:        trig.asm
; AUTHOR:           Patrick Fairbank
; LAST MODIFIED:    Jan. 16, 2008
;
; DESCRIPTION:      This file contains functions implementing the COORDIC
;                   algorithm.
;
; USAGE:            Add this file to your project.
;
; LICENSE:          Users are free to use, modify, and distribute this code
;                   as they see fit.
;
;    sin_cos: input ang, output x = sin and y = cos     
;
;         
;     atan2_sqrt: input x and y coordinates
;     Output the calculated angle and hypotenuse values
;     as output:    ang = angle x = hypotenuse
;
;******************************************************************************/





i       var byte    
j       Var byte
quad    var byte
x       var word
y       var word
ang     var word  
dy      var word
dx      var word

goto main

asm
    ;IDATA

; Table of arctan values
atans   DW D'16384', D'9672', D'5110', D'2594', D'1302', D'652', D'326', D'163'
        DW D'81', D'41', D'20', D'10', D'5', D'3', D'1'


    ;CODE

; Calculates the sine and cosine of the given angle
sin_cos:

  ; Set up the stack
  movff FSR2L, POSTINC1
  movff FSR1L, FSR2L

  ; Initialize _x to 18218
  movlw 0x2a
  movwf _x
  movlw 0x47
  movwf _x+1

  ; Initialize _y to 0
  clrf _y
  clrf _y+1

  ; Initialize _ang to passed parameter
  movlw 0xfd
  movff PLUSW2, _ang
  movlw 0xfe
  movff PLUSW2, _ang+1

  ; Initialize _quad to 0
  clrf _quad

  ; Check if the angle is greater than 16383 (90°)
sc_check_greaterthan:
  btfss _ang+1, 7
  btfss _ang+1, 6
  bra sc_check_lessthan
  bra sc_adjust_quad2
  
  ; Check if the angle is less than -16384 (-90°)
sc_check_lessthan:
  btfsc _ang+1, 7
  btfsc _ang+1, 6
  bra sc_setup_end

  ; If the angle is in quadrant 3, adjust it to quadrant 4
sc_adjust_quad3:
  negf _ang
  bc sc_negate_quad3
  comf _ang+1
  bra sc_adjust_end

  ; If the low byte negation causes a carry, negate the upper byte
sc_negate_quad3:
  negf _ang+1
  bra sc_adjust_end

  ; If the angle is in quadrant 2, adjust it to quadrant 1
sc_adjust_quad2:
  comf _ang
  comf _ang+1

  ; Toggle the sign bit and set the '_quad' flag
sc_adjust_end:
  btg _ang+1, 7
  setf _quad

  ; Multiply the angle by 2 to get better resolution
sc_setup_end:
  bcf STATUS, 0
  rlcf _ang
  rlcf _ang+1

  ; Set up the main loop
sc_loop_start:
  clrf _i
  banksel atans
  lfsr FSR0, atans

    ; The main loop label
sc_loop:
    movff _x, _dy
    movff _x+1, _dy+1
    movff _i, _j
    movf _j
    bz sc_bs_x_done

      ; Loop to shift _dy right
sc_bs_x_loop:
      bcf STATUS, 0
      rrcf _dy+1
      rrcf _dy
      btfsc _x+1, 7
      bsf _dy+1, 7
      decfsz _j
      bra sc_bs_x_loop

    ; Calculate what needs to be added to _x
sc_bs_x_done:
    movff _y, _dx
    movff _y+1, _dx+1
    movff _i, _j
    movf _j
    bz sc_do_rotation

      ; Loop to shift _dx right
sc_bs_y_loop:
      bcf STATUS, 0
      rrcf _dx+1
      rrcf _dx
      btfsc _y+1, 7
      bsf _dx+1, 7
      decfsz _j
      bra sc_bs_y_loop

    ; Perform adding operations on _x, _y and _ang
sc_do_rotation:
    btfss _ang+1, 7
    bra sc_sub_angle

    ; If _ang is negative
    movf POSTINC0, W
    addwf _ang
    movf POSTINC0, W
    addwfc _ang+1
    movf _dx, W
    addwf _x
    movf _dx+1, W
    addwfc _x+1
    movf _dy, W
    subwf _y
    movf _dy+1, W
    subwfb _y+1
    bra sc_loop_bottom

    ; If _ang is positive
sc_sub_angle:
    movf POSTINC0, W
    subwf _ang
    movf POSTINC0, W
    subwfb _ang+1
    movf _dx, W
    subwf _x
    movf _dx+1, W
    subwfb _x+1
    movf _dy, W
    addwf _y
    movf _dy+1, W
    addwfc _y+1

    ; Increment the counter and exit the loop if done
sc_loop_bottom:
    incf _i
    movlw 0x0f
    cpfseq _i
    bra sc_loop

  ; Negate _x if it was initially in quadrant 2 or 3
sc_finished:
  btfss _quad, 7
  bra sc_output
  negf _x
  bc sc_negate_x
  comf _x+1
  bra sc_output

  ; If the low byte negation causes a carry, negate the upper byte
sc_negate_x:
  negf _x+1

  ; Output the calculated _x and _y values
sc_output:
  ;movff _y, AARGB3
  ;movff _y+1, AARGB3+1
  ;movff _x, AARGB3+2
  ;movff _x+1, AARGB3+3

  ; Restore the stack to its previous state
  movf POSTDEC1
  movff INDF1, FSR2L

  return


; Calculates the magnitude and direction of the given ordered pair
atan2_sqrt:

  ; Set up the stack
  movff FSR2L, POSTINC1
  movff FSR1L, FSR2L

  ; Initialize _x to passed parameter
  movlw 0xfb
  movff PLUSW2, _x
  movlw 0xfc
  movff PLUSW2, _x+1
;  movff POSTINC2, _x
;  movff POSTDEC2, _x+1

  ; Initialize _y to passed parameter
  movlw 0xfd
  movff PLUSW2, _y
  movlw 0xfe
  movff PLUSW2, _y+1
;  movlw 0x03
;  movff PLUSW2, _y+1
;  movlw 0x02
;  movff PLUSW2, _y

  ; Initialize _ang to 0
  clrf _ang
  clrf _ang+1

  ; Initialize _quad to 0
  clrf _quad

  ; If the point is in quadrant 2 or 3, make _x positive and set flag
as_check_negative:
  btfss _x+1, 7
  bra as_shift_x
  setf _quad
  negf _x
  bc as_negate_x
  comf _x+1
  bra as_shift_x

  ; If the low byte negation causes a carry, negate the upper byte
as_negate_x:
  negf _x+1

  ; Divide the _x coordinate by 2 to prevent overflowing
as_shift_x:
  bcf STATUS, 0
  rrcf _x+1
  rrcf _x

  ; Divide the _y coordinate by 2 to prevent overflowing
as_shift_y:
  bcf STATUS, 0
  rrcf _y+1
  rrcf _y
  btfsc _y+1, 6
  bsf _y+1, 7

  ; Set up the main loop
as_loop_start:
  clrf _i
  banksel atans
  lfsr FSR0, atans

    ; The main loop label
as_loop:
    movff _x, _dy
    movff _x+1, _dy+1
    movff _i, _j
    movf _j
    bz as_bs_x_done

      ; Loop to shift _dy right
as_bs_x_loop:
      bcf STATUS, 0
      rrcf _dy+1
      rrcf _dy
      btfsc _x+1, 7
      bsf _dy+1, 7
      decfsz _j
      bra as_bs_x_loop

    ; Calculate what needs to be added to _x
as_bs_x_done:
    movff _y, _dx
    movff _y+1, _dx+1
    movff _i, _j
    movf _j
    bz as_do_rotation

      ; Loop to shift _dx right
as_bs_y_loop:
      bcf STATUS, 0
      rrcf _dx+1
      rrcf _dx
      btfsc _y+1, 7
      bsf _dx+1, 7
      decfsz _j
      bra as_bs_y_loop

    ; Perform adding operations on _x, _y and _ang, shifting the atans right one
as_do_rotation:
    movff POSTINC0, PRODL
    movff POSTINC0, PRODH
    bcf STATUS, 0
    rrcf PRODH
    rrcf PRODL
    btfsc  _y+1, 7
    bra as_sub_angle

    ; If _y is positive
    movf PRODL, W
    addwf _ang
    movf PRODH, W
    addwfc _ang+1
    movf _dx, W
    addwf _x
    movf _dx+1, W
    addwfc _x+1
    movf _dy, W
    subwf _y
    movf _dy+1, W
    subwfb _y+1
    bra as_loop_bottom

    ; If _y is negative
as_sub_angle:
    movf PRODL, W
    subwf _ang
    movf PRODH, W
    subwfb _ang+1
    movf _dx, W
    subwf _x
    movf _dx+1, W
    subwfb _x+1
    movf _dy, W
    addwf _y
    movf _dy+1, W
    addwfc _y+1

    ; Increment the counter and exit the loop if done
as_loop_bottom:
    incf _i
    movlw 0x0e
    cpfseq _i
    bra as_loop

  ; Multiply the _x value by 19898 and divide by 2^14 to scale it
as_scale_x:
  movff _x, _dx
  movff _x+1, _dx+1
  movlw 0xba
  mulwf _dx
  movff PRODH, _x
  movlw 0x4d
  mulwf _dx+1
  movff PRODH, _dy
  movff PRODL, _x+1
  movlw 0xba
  mulwf _dx+1
  movf PRODL, W
  addwf _x, F
  movf PRODH, W
  addwfc _x+1, F
  clrf WREG
  addwfc _dy, F
  movlw 0x4d
  mulwf _dx
  movf PRODL, W
  addwf _x, F
  movf PRODH, W
  addwfc _x+1, F
  clrf WREG
  addwfc _dy, F
  movlw 0x06
  movwf _j
as_scale_bs_loop:
    bcf STATUS, 0
    rrcf _dy
    rrcf _x+1
    rrcf _x
    decfsz _j
    bra as_scale_bs_loop

  ; Check if the quadrant was originally changed
as_check_quad:
  btfss _quad, 7
  bra as_output
  btfss _ang+1,7
  bra as_adjust_quad1

  ; If the angle is in quadrant 4, adjust it to quadrant 3
as_adjust_quad4:
  negf _ang
  bc as_negate_quad4
  comf _ang+1
  bra as_adjust_end

  ; If the low byte negation causes a carry, negate the upper byte
as_negate_quad4:
  negf _ang+1
  bra as_adjust_end

  ; If the angle is in quadrant 1, adjust it to quadrant 2
as_adjust_quad1:
  comf _ang
  comf _ang+1

  ; Toggle the sign bit
as_adjust_end:
  btg _ang+1, 7

  ; Output the calculated angle and hypotenuse values
as_output:
  ;movff _ang, AARGB3
  ;movff _ang+1, AARGB3+1
  ;movff _x, AARGB3+2
  ;movff _x+1, AARGB3+3

  ; Restore the stack to its previous state
  movf POSTDEC1
  movff INDF1, FSR2L

  return

endasm
    ; Export the functions to the linker
    'GLOBAL sin_cos
    'GLOBAL atan2_sqrt

    'END

I am using this as an includes file, but I am getting values so far from expected, that I can't figure out what is going on.

Any help would be greatly appreciated.

[ScaleRobotics]

Here are the changes I have made to the assembly code to try to get it to work with PicBasic:


commented out EXTERN AARGB3, UDATA_ACS, IDATA, CODE, edited variable descriptions so that variables are declared in PicBasic.

Original Code:

  ; Import the address the compiler uses to store 32-bit return values
    EXTERN AARGB3


    UDATA_ACS

; Variable declarations
i       RES 1
j       RES 1
quad    RES 1
x       RES 2
y       RES 2
ang     RES 2
dy      RES 2
dx      RES 2


    IDATA

; Table of arctan values
atans   DW D'16384', D'9672', D'5110', D'2594', D'1302', D'652', D'326', D'163'
        DW D'81', D'41', D'20', D'10', D'5', D'3', D'1'


    CODE

I edited out where the result is moved to AARGB3, and just use the word variables _x, _y, and _ang to store the results. Commented out Globals and End. And of course added ASM and ENDASM.

My code:

i       var byte    
j       Var byte
quad    var byte
x       var word
y       var word
ang     var word  
dy      var word
dx      var word

goto main

asm
    ;IDATA

; Table of arctan values
atans   DW D'16384', D'9672', D'5110', D'2594', D'1302', D'652', D'326', D'163'
        DW D'81', D'41', D'20', D'10', D'5', D'3', D'1'


    ;CODE


-snip

  ; Output the calculated _x and _y values
sc_output:
  ;movff _y, AARGB3
  ;movff _y+1, AARGB3+1
  ;movff _x, AARGB3+2
  ;movff _x+1, AARGB3+3

-snip

  ; Output the calculated angle and hypotenuse values
as_output:
  ;movff _ang, AARGB3
  ;movff _ang+1, AARGB3+1
  ;movff _x, AARGB3+2
  ;movff _x+1, AARGB3+3

  ; Restore the stack to its previous state
  movf POSTDEC1
  movff INDF1, FSR2L

  return

endasm
    ; Export the functions to the linker
    'GLOBAL sin_cos
    'GLOBAL atan2_sqrt

    'END

Please let me know if you have any suggestions. It does compile without errors, but I do not get useful data out. When I input 5461 as the angle, I get the sin=29998, and cos=405. The result should be 15000, and 25980. But then if I run it again, a different value pops up for cos, that still does not get close to expected values.

Thanks,

Walter

[Darrel Taylor]

Hi Walter,
I thought we had this working already.

Here's one thing I see...

  ; Set up the main loop
sc_loop_start:
  clrf i
  banksel atans
  lfsr FSR0, atans

banksel will put it in the proper bank for a variable in RAM.
But he's trying to use it with with a Label in FLASH.

I'm sure it was just a mistake on his part because the lfsr is correct.
And with his ASM code at the very beginning, it probably would have come up with bank 0 without him even knowing it.

However, now that it's in an include file for PBP, that atans table will be at a much higher address in Flash and you'll end up in a different bank than where the variables are.

Just comment it out.

I was only 1/3 of the way thru when I found that.
If it doesn't help, let me know, I'll keep looking for more.

P.S. You should specify BANK0 for all the variables used with this routine.
<br>

[ScaleRobotics]

I thought we had this working already.

Thanks Darrel! Yes, we had the cordic working for pic16 chips (can be found here http://www.picbasic.co.uk/forum/show...6307#post46307 ), but this one is more better. I feel the need for speed, and this one performs a hypotenuse length routine while it does the atan function. Also a bit more precise than the other one.

I tried commenting out the banksel, and putting all the variables for the function in bank0, but I am still getting unexpected results.

Thanks a lot for the help.

Walter

[Darrel Taylor]

OK, next problem ...

There's an issue with the indirect addressing.
I don't use C, but I think it uses a "stack" structure to pass variables back and forth to functions.

All the POSTINC's and PLUSW's etc, are moving things around to unknown locations because PBP doesn't use a stack.

It's a little hard to follow (since I don't know how C works), so I thought I'd let you work on it too. Maybe you'll see something I don't (yet).

If I figure out what it's doing with the FSR's I'll let you know.
<br>

[Darrel Taylor]

Oh! It wasn't as hard as I thought it would be.

And yup, it's trying to pull the parameters off the stack, and would be overwriting the variables with random values from RAM.
I assume you've set those variables before calling the routine.

Commenting these should help...

  ; Set up the stack
;  movff FSR2L, POSTINC1
;  movff FSR1L, FSR2L


  ; Initialize _ang to passed parameter
;  movlw 0xfd
;  movff PLUSW2, _ang
;  movlw 0xfe
;  movff PLUSW2, _ang+1<hr>; Calculates the magnitude and direction of the given ordered pair
atan2_sqrt:

  ; Set up the stack
;  movff FSR2L, POSTINC1
;  movff FSR1L, FSR2L

  ; Initialize _x to passed parameter
;  movlw 0xfb
;  movff PLUSW2, _x
;  movlw 0xfc
;  movff PLUSW2, _x+1
;  movff POSTINC2, _x
;  movff POSTDEC2, _x+1

  ; Initialize _y to passed parameter
;  movlw 0xfd
;  movff PLUSW2, _y
;  movlw 0xfe
;  movff PLUSW2, _y+1
;  movlw 0x03
;  movff PLUSW2, _y+1
;  movlw 0x02
;  movff PLUSW2, _y

ADDED: OOPs, missed a couple ...

  ; Restore the stack to its previous state
;  movf POSTDEC1
;  movff INDF1, FSR2L

and there's another banksel atans in the as_loop_start: part.

[ScaleRobotics]

Hi Chris,

Well, I might have to admit that the cordic may not be the best solution for a single axis tilt sensor. It is a natural for a dual or triple axis sensor. If you just have a single axis sensor, I might suggest a lookup table. Now I'm not really good at converting mathematical equations back and forth, so I can't say for sure if you are on the right track with the one you have. It doesn't resemble the ones I have used enough for me to tell. But I can show you some that I think would work. And, perhaps yours would work too. I just can't tell from here.

Here is the app note I worked with before. As you can see, the arctan equation "theta = arctan(Ax/Az)" on page 4 is a pretty cool thing. Of course, this one requires a two axis sensor, but it keeps resolution up to about 1.3 degrees. It also fits in pretty well with are atan2 cordic.
Attachment 4533

Now for a single axis sensor, your resolution at near 90 degree angles goes down to about 9 degree accuracy. This seems to lend itself better to just a lookup table. But, if you really wanted to use the cordic, you could.

For a single axis sensor, one equation for determining angle is arcsin (x) where x is acceleration in g's . Our cordic, can't do arcsin, but it can do arctan. We can use the following equation from Wikipedia:




and solve for theta.

atan(y) = atan2(y,1)

But, in our case, we are feeding y with a value which at its peak, = 1g. So, whatever value your sensor gives for 1g, you should fill in for the "1" value. y will equal 2 arctan x/((1+sqr(1-x^2)) , then run it through the cordic. I just feel if its going to be off by up to 9 degrees (because we are using a single sensor) why not just use a lookup table.