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)..


 
compassangle(1, 'North',n, 0.00).
compassangle(2, 'North by east', nbe, 11.25).
compassangle(3, 'North-northeast', nne,22.50).
compassangle(4, 'Northeast by north', nebn,33.75).
compassangle(5, 'Northeast', ne,45.00).
compassangle(6, 'Norteast by east', nebe,56.25).
compassangle(7, 'East-northeast', ene,67.50).
compassangle(8, 'East by North', ebn,78.75).
compassangle(9, 'East', e,90.00).
compassangle(10, 'East by south', ebs, 101.25).
compassangle(11, 'East-southeast', ese,112.50).
compassangle(12, 'Southeast by east', sebe, 123.75).
compassangle(13, 'Southeast', se, 135.00).
compassangle(14, 'Southeast by south', sebs, 146.25).
compassangle(15, 'South-southeast',sse, 157.50).
compassangle(16, 'South by east', sbe, 168.75).
compassangle(17, 'South', s, 180.00).
compassangle(18, 'South by west', sbw, 191.25).
compassangle(19, 'South-southwest', ssw, 202.50).
compassangle(20, 'Southwest by south', swbs, 213.75).
compassangle(21, 'Southwest', sw, 225.00).
compassangle(22, 'Southwest by west', swbw, 236.25).
compassangle(23, 'West-southwest', wsw, 247.50).
compassangle(24, 'West by south', wbs, 258.75).
compassangle(25, 'West', w, 270.00).
compassangle(26, 'West by north', wbn, 281.25).
compassangle(27, 'West-northwest', wnw, 292.50).
compassangle(28, 'Northwest by west', nwbw, 303.75).
compassangle(29, 'Northwest', nw, 315.00).
compassangle(30, 'Northwest by north', nwbn, 326.25).
compassangle(31, 'North-northwest', nnw, 337.50).
compassangle(32, 'North by west', nbw, 348.75).
compassangle(1, 'North', n, 360.00).
compassangle(Index , Name, Heading, Angle) :- nonvar(Angle), resolveindex(Angle, Index), 
                                               compassangle(Index,Name, Heading, _).
 
resolveindex(Angle, Index) :- N is Angle / 11.25 + 0.5, I is floor(N),Index is (I mod 32) + 1.
 