I think you can either use an approximated lookup table OR use the trig functions, but you won't be able to avoid both.  Best I could come up with is to have an approximated lookup table of tangent values for 22.5, 45, and 67.5 degrees (.4142, 1, and 2.4142, respectively), and compare abs(y/x) to each (warning, awful pseudocode):

//You've already figured out the quad with negative/positive x and y

tans = array(0 = .4142, 1 = 1, 2 = 2.4142)

sector = 3

for tc = 0 to 2 do

  if (abs(y/x) < tans[tc]) then sector = tc

done

return sector

Obviously some glaring flaws in it (doesn't account for (x == 0), for starters) but it might be a starting point.

Hope it helps!

-Moik

hey i found an approach for 8 directions which works great. this is coded in a script language that uses a state machine, but the logic is all here:

if "($xdistance > 0) and ($ydistance > 0) and ($absx > 0.414*$absy) and ($absx < 2.414*$absy)" "down_right"
        if "($xdistance < 0) and ($ydistance > 0) and ($absx > 0.414*$absy) and ($absx < 2.414*$absy)" "down_left"
       
        if "($xdistance > 0) and ($ydistance < 0) and ($absx > 0.414*$absy) and ($absx < 2.414*$absy)" "up_right"
        if "($xdistance < 0) and ($ydistance < 0) and ($absx > 0.414*$absy) and ($absx < 2.414*$absy)" "up_left"
       
        if "($xdistance > 0) and ($absx > $absy)" "right"
        if "($xdistance < 0) and ($absx > $absy)" "left"
       
        if "($ydistance > $absx) and ($absx < 0.5*$absy)" "down"
        if "($ydistance < $absx) and ($absx < 0.5*$absy)" "up"

$absx and $absy are variables for the absolute values of x and y distance, respectively.

X is negative to the left, positive to the right, Y is negative up, positive down.

when the IF condition is met, the script jumps to the state specified in the last word, in this case, the directions.

thank you all (and a couple other team mates who wanted this badly :P )