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(defun fact (n)
(if (<= n 1) 1 (* (fact (1- n)) n)))
(defun fib (n)
(if (< n 2)
n
(+ (fib (1- n)) (fib (- n 2)))))
(defun ifib (n)
(declare (fixnum n))
(if (< n 2)
n
(+ (the integer (ifib (1- n))) (the integer (ifib (- n 2))))))
(defun ffib (n)
(declare (fixnum n))
(if (< n 2)
n
(+ (the fixnum (ffib (1- n))) (the fixnum (ffib (- n 2))))))
(defun xfib (n0 n1 end)
(let ((a (make-array (1+ end) :initial-element 0)))
(setf (aref a 0) n0)
(setf (aref a 1) n1)
(do ((i 2 (1+ i)))
((> i end))
(setf (aref a i) (+ (aref a (1- i)) (aref a (- i 2)))))
a))
(defvar fibm (make-array 1000))
(defun mfib (n)
(if (aref fibm n)
(aref fibm n)
(if (< n 2)
(setf (aref fibm n) 1)
(setf (aref fibm n) (+ (mfib (1- n)) (mfib (- n 2)))))))
(defvar fiblist nil)
(defun afib (n)
(if (assoc n fiblist)
(second (assoc n fiblist))
(if (< n 2)
1
(progn
(push (list n (+ (afib (1- n)) (afib (- n 2)))) fiblist)
(cadar fiblist)) ) ) )
(defun etafib (n)
(if (< n 2)
n
(+ (etafib (sub1 n)) (etafib (- n 2)))))
(defun gcd (a b)
(if (= b 0)
a
(gcd b (mod a b))))
(defun factor (x &optional (y 2))
(if (<= x y)
(list x)
(if (= (mod x y) 0)
(cons y (factor (/ x y) y) )
(factor x (1+ y) ) ) ) )
(defun power (a n)
(if (= n 0)
1
(let ((b (power a (/ n 2))))
(setq b (* b b))
(if (= (mod n 2) 1) (setq b (* b a)))
b)))
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