NoSyu의 주저리주저리 :: SICP Exercise 연습문제 3.65

이 문제는 ln2의 power series를 구현하는 방법 중

책에 소개된 세 가지 방법 모두를 해보고 그 시간 차이를 알아보는 것입니다.

전에 측정하였던 방법으로 해보았으나 잘 되지 않아 조금 무식하게 해보았습니다.^^

그 차이를 보면 가속기를 쓰지 않으면 대략 70초 가량이 걸립니다.

그리고 오일러 가속기를 쓰게 되면 10ms정도,

태블로(tableau)를 이용하면 그보다 더 빠르게 수행 결과를 내놓는 것을 알 수 있습니다.

하지만 그 결과값은 각각 다릅니다.

왜 그러한지는 잘 모르겠습니다.OTL....

참조

해럴드 애빌슨, 김재우 역, <컴퓨터 프로그램의 구조와 해석>, 인사이트, 2007, pp. 441

; stream
(define true (= 0 0))
(define false (= 1 0))

(define (cons-stream a b)
(cons a (delay b)))
(define the-empty-stream '())
(define stream-null? null?)
(define (stream-car stream) (car stream))
(define (stream-cdr stream) (force (cdr stream)))

; section 3.5
(define (stream-ref s n)
(if (= n 0)
(stream-car s)
(stream-ref (stream-cdr s) (- n 1))))

(define (stream-for-each proc s)
(if (stream-null? s)
      'done
      (begin (proc (stream-car s))
             (stream-for-each proc (stream-cdr s)))))

(define (display-stream s)
(stream-for-each display-line s))

(define (display-line x)
(newline)
(display x))

(define (stream-enumerate-interval low high)
(if (> low high)
      the-empty-stream
      (cons-stream
       low
       (stream-enumerate-interval (+ low 1) high))))

(define (stream-filter pred stream)
(cond ((stream-null? stream) the-empty-stream)
        ((pred (stream-car stream))
         (cons-stream (stream-car stream)
                      (stream-filter pred
                                     (stream-cdr stream))))
        (else (stream-filter pred (stream-cdr stream)))))

(define (memo-proc proc)
(let ((already-run? false) (result false))
    (lambda ()
      (if (not already-run?)
          (begin (set! result (proc))
                 (set! already-run? true)
                 result)
          result))))

(define (scale-stream stream factor)
(stream-map (lambda (x) (* x factor)) stream))

; exercise 3.50
(define (stream-map proc . argstreams)
(if (stream-null? (car argstreams))
      the-empty-stream
      (cons-stream
       (apply proc (map stream-car argstreams))
       (apply stream-map
              (cons proc (map stream-cdr argstreams))))))

;;;SECTION 3.5.2
(define (add-streams s1 s2)
(stream-map + s1 s2))

(define ones (cons-stream 1 ones))
(define integers (cons-stream 1 (add-streams ones integers)))

; exercise 3.54
(define (mul-streams s1 s2)
(stream-map * s1 s2))

; exercise 3.55
(define (partial-sums S)
(cons-stream (stream-car S) (add-streams (stream-cdr S)
(partial-sums S))))

; exercise 3.56
(define (merge s1 s2)
(cond ((stream-null? s1) s2)
        ((stream-null? s2) s1)
        (else
         (let ((s1car (stream-car s1))
               (s2car (stream-car s2)))
           (cond ((< s1car s2car)
                  (cons-stream s1car (merge (stream-cdr s1) s2)))
                 ((> s1car s2car)
                  (cons-stream s2car (merge s1 (stream-cdr s2))))
                 (else
                  (cons-stream s1car
                               (merge (stream-cdr s1)
                                      (stream-cdr s2)))))))))

; print-stream-n
(define (print-stream-n S n)
(define (iter i)
    (if (= i n)
        'done
        (begin (display (stream-ref S i))
               (newline)
               (iter (+ i 1)))))
(iter 0))

; exercise 3.59
(define (div-streams s1 s2)
(stream-map / s1 s2))

(define (integrate-series coff_stm)
(let ((integrate_s (cons-stream 1 ; 상수 c
(div-streams coff_stm integers))))
(stream-cdr integrate_s)))

(define exp-series
(cons-stream 1 (integrate-series exp-series)))
(define cosine-series
(cons-stream 1
(integrate-series (scale-stream sine-series -1))))
(define sine-series
(cons-stream 0
(integrate-series cosine-series)))

; exercise 3.60
(define (mul-series s1 s2)
(cons-stream (* (stream-car s1) (stream-car s2))
               (add-streams (mul-series (stream-cdr s1) s2)
                            (scale-stream (stream-cdr s2) (stream-car s1)))))
; exercise 3.61
(define (invert-unit-series S)
(define X
    (cons-stream 1
                 (scale-stream (mul-series (stream-cdr S) X) -1)))
X)

; exercise 3.62
; s1 / s2
(define (div-series s1 s2)
(if (= 0 (stream-car s2))
(error "Divide by zero" s2)
(mul-series s1 (invert-unit-series s2))))

; exercise 3.63
(define (sqrt-improve guess x)
(average guess (/ x guess)))

(define (average x y)
(/ (+ x y) 2))

(define (sqrt-stream x)
(define guesses
    (cons-stream 1.0
                 (stream-map (lambda (guess)
                               (sqrt-improve guess x))
                             guesses)))
guesses)

; exercise 3.64
(define (stream-limit stm tolerance)
(let ((element1 (stream-car stm)) ; 앞의 원소
        (element2 (stream-car (stream-cdr stm)))) ; 뒤의 원소
    (if (< (abs (- element1 element2)) tolerance)
        element2
        (stream-limit (stream-cdr stm) tolerance))))
(define (sqrt x tolerance)
(stream-limit (sqrt-stream x) tolerance))

; exercise 3.65
(define ln2-stream
(partial-sums (ln2-summands 1)))
(define (ln2-summands n)
(cons-stream (/ 1.0 n)
(stream-map - (ln2-summands (+ n 1)))))

(define (euler-transform s)
(let ((s0 (stream-ref s 0))           ; Sn-1
        (s1 (stream-ref s 1))           ; Sn
        (s2 (stream-ref s 2)))          ; Sn+1
    (cons-stream (- s2 (/ (square (- s2 s1))
                          (+ s0 (* -2 s1) s2)))
                 (euler-transform (stream-cdr s)))))

(define (make-tableau transform s)
(cons-stream s
(make-tableau transform
(transform s))))

(define (accelerated-sequence transform s)
(stream-map stream-car
(make-tableau transform s)))

(define (square x) (* x x))

;; check time
;(define (timed-test proc)
; (start-test proc (current-milliseconds)))
;
;(define (start-test proc start-time)
; (let ((result (proc)))
;    (if result
;        (report-timed (- (current-milliseconds) start-time) result)
;        (= 0 1))))
;
;(define (report-timed elapsed-time result)
; (display "time : ")
; (display elapsed-time)
; (display ", result : ")
; (display result)
; (newline))

; execute
(define (f)
(let ((start-time 0))
    (begin
      (display "value : ")
      (set! start-time (current-milliseconds))
      (display (stream-limit (accelerated-sequence euler-transform ln2-stream) 0.001))
      (display " time : ")
      (display (- (current-milliseconds) start-time))
      (newline)
      (display "value : ")
      (set! start-time (current-milliseconds))
      (display (stream-limit (euler-transform ln2-stream) 0.001))
      (display " time : ")
      (display (- (current-milliseconds) start-time))
      (newline)
      (display "value : ")
      (set! start-time (current-milliseconds))
      (display (stream-limit ln2-stream 0.001))
      (display " time : ")
      (display (- (current-milliseconds) start-time))
      (newline))))
(f)