fibo-algebraic.clj

(defn fibonacci [n]
  (letfn [(power-accumulate-positive [r a n op]
            (let [r (if (odd? n) (op r a) r)]
              ( if (= 1 n) r (recur r (op a a) (bigint (/ n 2)) op))))
          (power [a n op]
            (if (odd? n)
              (let [n (bigint (/ n 2))]
                (if (zero? n) a (power-accumulate-positive a (op a a) n op)))
              (recur (op a a) (bigint (/ n 2)) op)))
          (fibonacci-matrix-multiply [[x0 x1] [y0 y1]]
            [ (+ (* x0 (+ y1 y0)) (* x1 y0))
              (+ (* x0 y0) (* x1 y1))])]
    (if (zero? n) 0N)
    (first (power [1N 0N] n fibonacci-matrix-multiply))))