Data update

Task/Fibonacci-sequence/Scheme/fibonacci-sequence-6.scm

@@ -0,0 +1,29 @@
+(define (fast-fib-pair n)
+  ;; By Arnold Schönhage, personal communication, 2004
+  ;; returns f_n f_{n+1}
+  (case n
+    ((1) (values 1 1))
+    ((2) (values 1 2))
+    (else
+     (let ((m (quotient n 2)))
+       (call-with-values
+           (lambda () (fast-fib-pair m))
+         (lambda (f_m f_m+1)
+           (let ((f_m^2   (square f_m))
+                 (f_m+1^2 (square f_m+1)))
+             (if (even? n)
+                 (values (- (* 2 f_m+1^2)
+                            (* 3 f_m^2)
+                            (if (odd? m) -2 2))
+                         (+ f_m^2 f_m+1^2))
+                 (values (+ f_m^2 f_m+1^2)
+                         (- (* 3 f_m+1^2)
+                            (* 2 f_m^2)
+                            (if (odd? m) -2 2)))))))))))
+
+(call-with-values
+    (lambda ()
+      (fast-fib-pair 100000000))
+  (lambda (f_n f_n+1)
+    (display (list (modulo f_n 100000) (modulo f_n+1 100000)))
+    (newline)))