unitType.rb

def encode(time)
  #example does not provide am pm.
  #am pm implicit possible due to no overlap of pm am work day hours
  hours, minutes = time.split(":")
  halfHours, minutes = 2 * hours.to_f, minutes.to_f
  halfHours += (minutes / 30).to_i
  minutes -= (minutes / 30).to_i * 30
  #convert to military time
  if hours.to_i < 8 #if pm as inferred by context
    halfHours += 2 * 12
  end
  #reduce dimensions of unit
  #possible because time forms a line with minutes and smaller frames of time expressed in decimal range
  halfHours += 100**-1 * minutes
  return halfHours
end

def decode(time)
  #timeInTermsOfAppointments -> stringTime
  minutes = (((time % 2).to_i * 30 + 100 * (time % time.to_i)).to_i).to_s
  hours = ((time / 2).to_i - 12 * (time / 24).to_i).to_s
  if hours == "0"
    hours = "12"
  end

  while minutes.length < 2
    minutes = "0" + minutes
  end
  return hours + ":" + minutes
end

class Unit
  # continuous scaler with hybrid numeral system
  # decimal is base 30, none decimal is base 24
  # unit is timeInTermsOfAppointments
  # origin is 12 am
  attr_accessor :halfHours

  def initialize(time)
    if time.instance_of? String
      @halfHours = encode(time)
    elsif time.instance_of? Rational or time.instance_of? Float
      @halfHours = time
    else
      raise
    end
  end

  def -(other)
    #example 15.20 - 13.25 = 1.25 one halfHour, 25 min difference
    halfHours, minutes = @halfHours.divmod(1)
    otherHalf, otherMin = other.halfHours.divmod(1)
    #handle ruby's unecessary incompatiability with arithmetic by casting to int
    minutes, otherMin = (minutes * 10 ** 2).to_i * 10 ** -2, (otherMin * 10 ** 2).to_i * 10 ** -2
    resultHalf = halfHours - otherHalf
    resultMin = minutes - otherMin
    if resultMin < 0
      resultHalf -= 1
      resultMin += 0.30
    end
    return resultHalf + resultMin
  end
end