1.37, 1.38, 1.39 SICP

cont-frac.scm

(define (cont-frac n d k)
  (define (loop i k)
    (if (= k i)
	(/ (n i) (d i))
	(/ (n i) (+ (d i) (loop (+ i 1) k)))))
  (loop 1 k))

; 1.37

(define golden-ratio 1.61803398875)

(define (check-for-k f k uncertainty)
  (let ((result (f (lambda (i) 1.0) (lambda (i) 1.0) k)))
    (if (< (abs (- golden-ratio (/ 1.0 result))) uncertainty)
	k
	(check-for-k f (+ k 1) uncertainty))))

(check-for-k cont-frac 1 0.0001) ; so k=11 gives 0.0001 precision

(define (cont-frac-iterative n d k)
  (define (iter i result)
    (if (= i 0)
	result
	(iter (- i 1)
	      (/ (n i) (+ (d i) result)))))
  (iter k (/ (n k) (d k))))

(/ 1.0 (cont-frac-iterative (lambda (i) 1.0) (lambda (i) 1.0) 1000))
(check-for-k cont-frac-iterative 1 0.000000001)


; 1.38

(define e (+ 2 (cont-frac (lambda (i) 1.0) (lambda (i)
					 (if (= 0 (remainder (+ i 1) 3))
					     (* (/ (+ i 1) 3) 2)
					     1))
			  100))) ; => 2.7182...

; 1.39

(define (tan-cf x k)
  (let ((x2 (* x x -1)))
    (cont-frac (lambda (i)
		 (if (= i 1) x x2))
	       (lambda (i) (let ((result (+ 1 (* (- i 1) 2))))
			     result))
	       k)))