A-M baby

Task/Fibonacci-sequence/Scheme/fibonacci-sequence-4.ss

@@ -0,0 +1,19 @@
+;;; Fibonacci numbers using Edsger Dijkstra's algorithm
+;;; http://www.cs.utexas.edu/users/EWD/ewd06xx/EWD654.PDF
+
+(define (fib n)
+  (define (fib-aux a b p q count)
+    (cond ((= count 0) b)
+          ((even? count)
+           (fib-aux a
+                    b
+                    (+ (* p p) (* q q))
+                    (+ (* q q) (* 2 p q))
+                    (/ count 2)))
+          (else
+           (fib-aux (+ (* b q) (* a q) (* a p))
+                    (+ (* b p) (* a q))
+                    p
+                    q
+                    (- count 1)))))
+  (fib-aux 1 0 0 1 n))