module Sass::Value::Number::Unit

def canonical_multiplier(units)
  units.reduce(1) do |multiplier, unit|
    multiplier * canonical_multiplier_for_unit(unit)
  end
end

def canonical_multiplier_for_unit(unit)
  inner_map = CONVERSIONS[unit]
  inner_map.nil? ? 1 : 1 / inner_map.values.first
end

def canonicalize_units(units)
  return units if units.empty?
  if units.length == 1
    type = TYPES_BY_UNIT[units.first]
    return type.nil? ? units : [UNITS_BY_TYPE[type].first]
  end
  units.map do |unit|
    type = TYPES_BY_UNIT[unit]
    type.nil? ? units : [UNITS_BY_TYPE[type].first]
  end.sort
end

def conversion_factor(unit1, unit2)
  return 1 if unit1 == unit2
  CONVERSIONS.dig(unit1, unit2)
end