Even Fibonacci Numbers

fibonacci_solver.rb

# Uses matrix exponantion algorithm to solve fibonacci sequences
# Complexity O(log n)
# Usage : 
# f = FibonacciSolver.new 
# f.sum_even(max_value)
# Example: below class declaration, Uncomment to test. 

class FibonacciSolver
  # calculates the fibonacci sequence's (n)th element
  def fib(n)
    # Because the first element is 1 we get the n+1 in the matrix multiplication
    calculate_fib(n)[1]
  end

  # Sums the even values until it reaches the maxiumu value
  def sum_even(max)
    validate!(max)
    res = 0
    collection = create_collection(max)

    collection.each do |val|
      res += val if val.even?
    end
    res
  end

  # creates an array of fibonacci sequence until the max value is reached
  def create_collection(max)
    res = []
    val = 0
    i = 0
    while val < max do
      val = fib(i)
      res << val
      i = i.next
    end
    res
  end

  private
  # Recursive method to calculate matrix multiplication formula
  # Fib(2n) = Fib(n) * [2 * Fib(n+1) - Fib(n)]
  # Fib(2n + 1) = Fib(n + 1) ^ 2 + Fib(n) ^ 2
  def calculate_fib(n)
    if n == 0
      [0, 1]
    else
      elements = calculate_fib(n / 2)
      a = elements[0]
      b = elements[1]

      c = a * ( b * 2 - a )
      d = (a ** 2) + (b ** 2)

      if n.even?
        [c, d]
      else
        [d, (d + c)]
      end
    end
  end

  def validate!(val)
    raise ArgumentError, 'Invalid integer' unless val.is_a? Integer
  end
end

# f = FibonacciSolver.new 
# f.sum_even(4000000)