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;;;; "ratize.scm" Find simplest number ratios
(define (find-ratio-between x y)
(define (sr x y)
(let ((fx (inexact->exact (floor x))) (fy (inexact->exact (floor y))))
(cond ((>= fx x) (list fx 1))
((= fx fy) (let ((rat (sr (/ (- y fy)) (/ (- x fx)))))
(list (+ (cadr rat) (* fx (car rat))) (car rat))))
(else (list (+ 1 fx) 1)))))
(cond ((< y x) (find-ratio-between y x))
((>= x y) (list x 1))
((positive? x) (sr x y))
((negative? y) (let ((rat (sr (- y) (- x))))
(list (- (car rat)) (cadr rat))))
(else '(0 1))))
(define (find-ratio x e) (find-ratio-between (- x e) (+ x e)))
(define (rationalize x e) (apply / (find-ratio x e)))
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