diff options
Diffstat (limited to 'ratize.scm')
| -rw-r--r-- | ratize.scm | 26 |
1 files changed, 15 insertions, 11 deletions
@@ -1,13 +1,17 @@ -;;;; "ratize.scm" Convert number to rational number +;;;; "ratize.scm" Find simplest number ratios -(define (rational:simplest x y) - (define (sr x y) (let ((fx (floor x)) (fy (floor y))) - (cond ((not (< fx x)) fx) - ((= fx fy) (+ fx (/ (sr (/ (- y fy)) (/ (- x fx)))))) - (else (+ 1 fx))))) - (cond ((< y x) (rational:simplest y x)) - ((not (< x y)) (if (rational? x) x (slib:error))) +(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) (- (sr (- y) (- x)))) - (else (if (and (exact? x) (exact? y)) 0 0.0)))) -(define (rationalize x e) (rational:simplest (- x e) (+ x e))) + ((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))) |