Compute pi with common lisp using leibnix formula

leibniz_pi.lisp

;; Way to compute pi in common lisp using Leibniz formula

(defun ^ (x n) 
  (if (> n 0)
    (* x (^ x (- n 1)))
    (if (< n 0)
      (* (/ 1 x) (^ x (+ n 1)))
      1)))

(defun oddnum (n) (+ (* 2 n) 1))

(defun sum (numbers)
  (reduce 
    (lambda (x y) (+ x y))
    numbers))


(defun N (start end &optional acc)
  (if (< end start)
    acc 
    (N start 
      (- end 1)
      (cons end acc))))

(defun pirange (start end)
    (* 4 (sum 
            (mapcar 
              (lambda (x) (/ (^ -1 x)
                             (oddnum x)))
              (N start end))))
  )

(let ((mypi 0))
  (setq mypi (+ mypi (pirange 0 10000)))
  (princ "Approximation of pi: ")
  (print (coerce mypi 'long-float)))