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