Clojure code to generate the nth Fibonacci number in logarithmic time.

fibonacci_logarithmic.clj

(defn fibonacci
  "Returns the nth Fibonacci number using a logarithmic squaring algorithm."
  [n]
  (let [square (fn [x] (* x x))]
    (loop [current 0N next 1N p 0N q 1N count n]
      (cond (= count 0) current
            (even? count) (recur current
                                 next
                                 (+ (square p) (square q))
                                 (+ (square q) (* 2 p q))
                                 (/ count 2))
            :else (recur (+ (* p current) (* q next))
                         (+ (* q current) (* (+ p q) next))
                         p
                         q
                         (dec count))))))