Box the compass

func point (index) {
    var ix = (index % 32)
    if    (ix & 1) { "#{point((ix + 1) & 28)} by #{point(((2 - (ix & 2)) * 4) + ix & 24)}" }
    elsif (ix & 2) { "#{point((ix + 2) & 24)}-#{point((ix | 4) & 28)}" }
    elsif (ix & 4) { "#{point((ix + 8) & 16)}#{point((ix | 8) & 24)}" }
    else           { <north east south west>[ix / 8] }
}
 
func test_angle (ix) { ix * 11.25 + [0, 5.62, -5.62][ ix % 3 ] }
func angle_to_point(𝜽) { (𝜽 / 360 * 32) + 0.5 -> floor }
 
for ix in range(0, 32) {
    var 𝜽 = test_angle(ix)
    printf("  %2d %6.2f° %s\n", ix % 32 + 1, 𝜽, point(angle_to_point(𝜽)).tc)
}

Output:

   1   0.00° North
   2  16.87° North by east
   3  16.88° North-northeast
   4  33.75° Northeast by north
   5  50.62° Northeast
   6  50.63° Northeast by east
   7  67.50° East-northeast
   8  84.37° East by north
   9  84.38° East
  10 101.25° East by south
  11 118.12° East-southeast
  12 118.13° Southeast by east
  13 135.00° Southeast
  14 151.87° Southeast by south
  15 151.88° South-southeast
  16 168.75° South by east
  17 185.62° South
  18 185.63° South by west
  19 202.50° South-southwest
  20 219.37° Southwest by south
  21 219.38° Southwest
  22 236.25° Southwest by west
  23 253.12° West-southwest
  24 253.13° West by south
  25 270.00° West
  26 286.87° West by north
  27 286.88° West-northwest
  28 303.75° Northwest by west
  29 320.62° Northwest
  30 320.63° Northwest by north
  31 337.50° North-northwest
  32 354.37° North by west
   1 354.38° North