# Maths Library by Guy Walker
# www.logoarts.co.uk

To Dec2Bin :Num
  # convert decimal number Num to an 8 item binary list
  If :Num >255 [Print [Rule is too large!] Stop]
  LocalMake "Bin []
  For [C 7 0 -1] [
    LocalMake "Bin LPut (Quotient :Num Power 2 :C) :Bin
    LocalMake "Num :Num -((Power 2 :C) *Last :Bin)]
  Output :Bin
End

to distancebetween :point1 :point2
  # return distance between two points
  Make "Hor (First :Point1) - (First :Point2)
  Make "Ver (Last :Point1) - (Last :Point2)
  Output SqRt ((Power :Hor 2) + (Power :Ver 2))
end

To Even? :Num
  # return 'true' if Num even, else return 'false'
  If (Mod :Num 2)=0 [Output "True] [Output "False]
End

to least :i :j
  # return lowest value 
  If Before :I :J [Output :I] [Output :J] 
end

to most :i :j
  # return greatest value 
  If Before :I :J [Output :J] [Output :I] 
end

to odd :num
  # return True if Num odd, else return False 
  If Not (Mod :Num 2) = 0 [Output "True] [Output "False]
end

To PtoR :RadDist :Theta
  # convert polar to rectangular co-ordinates
  LocalMake "X :RadDist *Sin :Theta
  LocalMake "Y :RadDist *Cos :Theta
  Output List :X :Y
End

To RtoP :X :Y
  # convert rectangular to polar co-ordinates
  LocalMake "Dist Sqrt ((Power :X 2) +(Power :Y 2))
  If :X<0 [Output List :Dist 180 +ATan :Y/:X] [
    # else :X >0
    If :Y<0 [Output List :Dist 360 +ATan :Y/:X]
    [Output List :Dist ATan :Y/:X]]
  # else :X =0
  If :Y<=0 [Output List :Dist 270] [Output List :Dist 90]
End

To RtoP :X :Y
  # use a second turtle to convert rectangular to polar co-ordinates
  SetTurtle 1 PenUp SetXY :X :Y
  LocalMake "RadDist Sqrt ((Power :X 2)+(Power :Y 2))
  SetHeading Towards [0 0]
  LocalMake "myHeading Mod Int (Heading+180) 360 SetTurtle 0
  Output List :RadDist :myHeading
End

To Root2
  # return sqrt of 2 (approx 1.414)
  Output Power 2 0.5
End

To Root3
  # return sqrt of 3 (approx 1.732)
  Output Power 3 0.5
End

to sign :num 
  # return sign (-1 or 1) of number 
  If :Num < 0 [Output Minus 1] [Output 1] 
end