On Tue, 13 Apr 1999, Jason Wolfson wrote:

> OK, now I'm starting to spin my wheels,
>
> What would be the best way to calculate
> an arcTangent with a PIC?
>
> I have 2 values, x and y, values are 0-100,
> I need to find an angle by taking the
> arcTan of (y/x).

I don't have the arctan(y/x) function, but I've got the arcsin which is
pretty close (epecially for small angles). It's attached below. It's a
look up table with first-order (linear) interpolation solution. You see
other examples here:

http://www.interstice.com/~sdattalo/technical/software/pic/picsine.html

and

http://www.interstice.com/~sdattalo/technical/software/pic/piclog.html

for sin(x) and log(x) solutions.



;----------------------------------------------------------
;
;arcsine
;
;  The purpose of this routine is to take the arcsine of an
;8-bit number that ranges from 0 < x < 255/256. In other
;words, the input, x, is an unsigned fraction whose implicit
;divisor is 256.
;  The output is in a conveniently awkward format of binary
;radians (brads?). The output corresponds to the range of zero
;to pi/2 for the normal arcsine function. Specifically, this
;algorithm computes:
;
; arcsine(x) = real_arcsine(x/256) * 256 / (pi/2)
;
;  where, real_arcsine returns the real arcsine of its argument
;in radians.
;
;  The algorithm is a table look-up algorithm plus first order
;linear interpolation. The psuedo code is:
;
;unsigned char arcsine(unigned char x)
;{
;  unsigned char i;
;
;  i = x >> 4;
;  return(arcsin[i] + ((arcsin[i+1] - arcsin[i]) * (x & 0xf))/16);
;}
;
;
;  The accuracy is reasonable for x<150 or so. After that, the
;relatively steep arcsine severly deviates from a straight line
;approximation. The maximum error is around 5.


arcsine

        SWAPF   x,W
        ANDLW   0xf
        ADDLW   1
        MOVWF   temp                    ;Temporarily store the index
        CALL    arc_sine_table          ;Get a2=asin( (x>>4) + 1)
        MOVWF   result                  ;Store temporarily in result

        DECF    temp,W                  ;Get the saved index
        CALL    arc_sine_table          ;Get a1=asin( (x>>4) )

        SUBWF   result,W                ;W=a2-a1, This is always positive.
        SUBWF   result,F                ;a1 = a1 - (a1-W) = W

        CLRF    temp                    ;Clear the product
        CLRC

        BTFSC   x,0
         ADDWF  temp,F
        RRF     temp,F
        CLRC

        BTFSC   x,1
         ADDWF  temp,F
        RRF     temp,F
        CLRC

        BTFSC   x,2
         ADDWF  temp,F
        RRF     temp,F
        CLRC

        BTFSC   x,3
         ADDWF  temp,F
        RRF     temp,W

        ADDWF   result,F

        RETURN

arc_sine_table
        ADDWF   PCL,F
        RETLW   0
        RETLW   10     ;asin(1/16) = 3.583deg * 256/90
        RETLW   20
        RETLW   31
        RETLW   41
        RETLW   52
        RETLW   63
        RETLW   74
        RETLW   85
        RETLW   97
        RETLW   110
        RETLW   124
        RETLW   138
        RETLW   154
        RETLW   173
        RETLW   198
        RETLW   240