Farey sequence

# title: Farey sequence
# source: https://rosettacode.org/wiki/Farey_sequence
# category: Rosetta Code
# difficulty: Medium
# summary: Generate Farey sequences of small orders with the classic iterative recurrence.
# tags: popular, math, fractions, sequences
# vibe: 0.2

def fraction_text(numerator, denominator)
  ("" + numerator) + "/" + ("" + denominator)
end

def farey_sequence(order)
  left_numerator = 0
  left_denominator = 1
  right_numerator = 1
  right_denominator = order
  values = [fraction_text(left_numerator, left_denominator)]

  while right_numerator <= order
    values = values.push(fraction_text(right_numerator, right_denominator))

    multiplier = (order + left_denominator) / right_denominator
    next_left_numerator = right_numerator
    next_left_denominator = right_denominator
    next_right_numerator = (multiplier * right_numerator) - left_numerator
    next_right_denominator = (multiplier * right_denominator) - left_denominator

    left_numerator = next_left_numerator
    left_denominator = next_left_denominator
    right_numerator = next_right_numerator
    right_denominator = next_right_denominator
  end

  values
end

def run
  {
    order_five: farey_sequence(5),
    order_seven_count: farey_sequence(7).length
  }
end