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#utilities.lisp#
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#utilities.lisp#
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(defun sq (x) (* x x))
(defun mag (vec)
(sqrt (apply #'+ (mapcar #'sq vec))))
(defun list-copies (thing n)
(if (= n 0)
nil
(cons thing (list-copies thing (- n 1)))))
(defun vdif (v1 v2)
(mapcar #'- v1 v2))
(defun vdot (v1 v2)
(apply #'+ (mapcar #'* v1 v2)))
(defmacro v+ (&rest list-of-args)
`(mapcar #'+ ,@list-of-args))
(defun vs* (s v)
(mapcar #'* v (list-copies s (length v))))
(defun unitize (v)
(vs* (/ 1 (mag v)) v))
(defun vcross (x y)
(list
(- (* (nth 2 x) (nth 1 y)) (* (nth 1 x) (nth 2 y)))
(- (* (nth 0 x) (nth 2 y)) (* (nth 2 x) (nth 0 y)))
(- (* (nth 0 x) (nth 1 y)) (* (nth 1 x) (nth 0 y)))))
(defun random-elt (choices)
"Choose an element from a list at random."
(elt choices (random (length choices))))
(defun average (&rest lst)
(/ (apply #'+ lst) (length lst)))
(defun vdistance (v1 v2)
(mag (vdif v1 v2)))
(defun minroot (a b c)
(if (zerop a)
(/ (- c) b)
(let ((disc (- (sq b) (* 4 a c))))
(unless (minusp disc)
(let ((discrt (sqrt disc)))
(min (/ (+ (- b) discrt) (* 2 a))
(/ (- (- b) discrt) (* 2 a))))))))
(defun mand (lst)
(not (member nil lst)))
(defmacro in (obj &rest choices)
"Tests if obj is in choices. From Graham"
(let ((insym (gensym)))
`(let ((,insym ,obj))
(or ,@(mapcar #'(lambda (c) `(eql ,insym ,c))
choices)))))