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 test_cases = [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];;
 
let directions = ["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";];;
 
let get_direction_index input =
  let shifted = (input +. 5.6201) in
  let shifted = if shifted > 360. then shifted -. 360. else shifted in
  int_of_float (shifted /. 11.25);;
 
let print_direction input =
  let index = get_direction_index input in
  let direction = List.nth directions index in
  let test = Printf.printf "%3d %-20s %.2f\n" (index + 1) direction in
  test input;; 
 
List.iter (print_direction) test_cases;;
 
 