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Created Sep 25, 2012
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(define (rationalize3 x e)
(define (refine xn yn an) ; returns reverse continued fraction
(cond [(or (null? xn) (null? yn)) an]
[(= (car xn) (car yn))
(refine (cdr xn) (cdr yn) (cons (car xn) an))]
[else (cons (+ 1 (min (car xn) (car yn))) an)]))
(define (realize rcf) ; reverse continued fraction -> rational
(fold (^[a r] (+ a (/ r))) (car rcf) (cdr rcf)))
(if (< x 0)
(- (rationalize3 (- x) e))
(realize (refine (continued-fraction (exact (- x e)))
(continued-fraction (exact (+ x e)))
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