There be many a land lubber that knows naught of the pirate ways and gives direction by degree!
They know not how to box the compass!



Task description

 Create a function that takes a heading in degrees and returns the correct 32-point compass heading.
 Use the function to print and display a table of Index, Compass point, and Degree; rather like the corresponding columns from, the first table of the wikipedia article, but use only the following 33 headings as input:
[0.0, 16.87, 16.88, 33.75, 50.62, 50.63, 67.5, 84.37, 84.38, 101.25, 118.12, 118.13, 135.0, 151.87, 151.88, 168.75, 185.62, 185.63, 202.5, 219.37, 219.38, 236.25, 253.12, 253.13, 270.0, 286.87, 286.88, 303.75, 320.62, 320.63, 337.5, 354.37, 354.38]. (They should give the same order of points but are spread throughout the ranges of acceptance).


Notes;
 The headings and indices can be calculated from this pseudocode:
for i in 0..32 inclusive:
    heading = i * 11.25
    case i %3:
      if 1: heading += 5.62; break
      if 2: heading -= 5.62; break
    end
    index = ( i mod 32) + 1
 The column of indices can be thought of as an enumeration of the thirty two cardinal points (see talk page)..


let box = [|
    "North"; "North by east"; "North-northeast"; "Northeast by north";
    "Northeast"; "Northeast by east"; "East-northeast"; "East by north";
    "East"; "East by south"; "East-southeast"; "Southeast by east";
    "Southeast"; "Southeast by south"; "South-southeast"; "South by east";
    "South"; "South by west"; "South-southwest"; "Southwest by south";
    "Southwest"; "Southwest by west"; "West-southwest"; "West by south";
    "West"; "West by north"; "West-northwest"; "Northwest by west";
    "Northwest"; "Northwest by north"; "North-northwest"; "North by west" |]
 
[ 0.0; 16.87; 16.88; 33.75; 50.62; 50.63; 67.5; 84.37; 84.38;
101.25; 118.12; 118.13; 135.0; 151.87; 151.88; 168.75; 185.62;
185.63; 202.5; 219.37; 219.38; 236.25; 253.12; 253.13; 270.0;
286.87; 286.88; 303.75; 320.62; 320.63; 337.5; 354.37; 354.38 ]
|> List.iter (fun phi ->
    let i =  (int (phi * 32. / 360. + 0.5)) % 32
    printf "%3d %18s %6.2f°\n" (i + 1) box.[i] phi)