(defun similarity (a b)
  (/ (float (dot-product a b)) (float (* (magnitude a) (magnitude b)))))

(defun dot-product (a b)
  (if (null a)
      0
      (+ (* (first a) (first b)) (dot-product (rest a) (rest b)))))

(defun magnitude (a)
  (sqrt (sum-of-squares a)))

(defun sum-of-squares (a)
  (if (null a)
      0
      (+ (square (first a)) (sum-of-squares (rest a)))))

(defun diff-angle (a b)
  (let ((k (similarity a b)))
    (if (> k 1)
	(setf k 1.0))
    (radians-to-degrees (acos k))))

(defun radians-to-degrees (theta)
  (* theta (/ 180.0 pi)))