yao2030

public class Binary
{
    public static void main(String[] args)
    {
	int N = Integer.parseInt(args[0]);
	int v = 1;
	while (v <= N/2)
	    v = v*2;
	int n = N;
	while (v > 0)

yao2030

(define (smallest-divisor n)
  (find-divisor n 2))
(define (find-divisor n test-divisor)
  (cond ((> (square test-divisor) n) n)
	((divides? test-divisor n) test-divisor)
	(else (find-divisor n (next test-divisor)))))

(define (divides? a b)
  (= 0 (remainder b a)))

yao2030

(define (expmod base exp m)
  (cond ((= exp 0) 1)
	((even? exp)
	 (remainder (square (expmod base (/ exp 2) m)) m))
	(else (remainder (* base (expmod base (- exp 1) m)) m))))

(define (fermat-every n)
  (fermat-helper (- n 1) n))

(define (fermat-helper a n)

yao2030

(define (integral f a b n)
	(define h (/ (- b a) n))
	(define (i-next x) (+ x 1))
	(define (i-term x)
	(cond ((or (= x 0) (= x n)) (f (+ a (* x h))))
	      ((even? x) (* 2 (f (+ a (* x h)))))
	      (else (* 4 (f (+ a (* x h)))))))
	(* (/ h 3) (sum i-term 0 i-next n)))

yao2030

(define (pi n)
	(define (p-term x)
	  (if (even? x)
	      (/ x (- x 1))
	      (/ (- x 1) x)))
	(define (p-next x)
	      (+ x 1))
	(* 4.0 (product p-term 3 p-next n)))

yao2030

(define (filtered-accumulate combiner null-value term a next b predicate)
  (if (> a b)
      null-value
      (combiner (if (predicate (term a))
		    (term a)
		    null-value)
		(filtered-accumulate combiner null-value term (next a) next b predicate))))
		    

yao2030

(define (cont-frac n d k)
  (define (cont-help i result)
    (if (= i k)
	(/ 1.0 result)
	(cont-help (+ i 1) (/ (n i) (+ (d i) result)))))
  (cont-help 1 0.0))

(cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 100)
;; A so-called k-term finite continued fraction
;; gives the value of the gold ratio

yao2030

(define (cont-frac n d k)
  (define (cont-help i result)
    (if (= i 0)
	 result
	(cont-help (- i 1) (/ (n i) (+ (d i) result)))))
  (cont-help k 0.0))

(cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 100)
;; A so-called k-term finite continued fraction
;; gives the value of the gold ratio

yao2030

(define (d x)
	(if (= (remainder x 3) 2)
	    (* 2 (+ (quotient x 3) 1))
	    1))
;; exercise 1.38, sicp

yao2030

;; Exercise 1.39
;; sicp
(define (tan-cf x k)
  (define (n i)
    (if (= i 1)
	x
	(square x)))
  (define (d i)
    (- (* 2 i) 1))
  (define (cont-frac n d k)