SICP 学习2 -- 个人学习过程中的代码。有对有错。不做解释。

1.1.7 牛顿法求平方根

 

 

 (define (average x y)

    (/ (+ x y) 2))

(define (improve guess x)

    (average guess (/ x guess)))

(define (good-enough? guess x)

    (< (abs (- (* guess guess) x) )0.0000000000001) )

(define (sqrt-iter guess x)

    (if (good-enough? guess x)

    guess

    (sqrt-iter (improve guess x) 

               x)

    ))

(define (sqrt-g x)

  (sqrt-iter 1.0 x))

 

 

 

Welcome to DrRacket, version 5.1.1 [3m].

Language: R5RS; memory limit: 128 MB.

> (sqrt-g 2)

1.414213562373095

> (sqrt 2)

1.4142135623730951

> (sqrt-g 3)

1.7320508075688772

> (sqrt 3)

1.7320508075688772

>  

 

 

;练习 1.6 .newif

 (define (newif predicate  thenClause elseClause)

    (cond (predicate thenClause)

          (else elseClause)))

 (define (newSqrt-iter guess x)

    (newif (good-enough? guess x)

           guess

           (newsqrt-iter (improve guess x)

                         x)))

 (define (newSqrt-g x)

    (newSqrt-iter 1.0 x)) 

 

Welcome to DrRacket, version 5.1.1 [3m].

Language: R5RS; memory limit: 128 MB.

> (newSqrt-g 2)

Interactions disabled //因为超出内存使用量而终止，死循环，原因：函数使用 应用序 ，先求参数值后应用规则。

 

 

 ;练习1.7

 (define (good-enough? guess x)

    (< (abs (- (improve guess x) guess) )0.00000000000000001) )

 

 > (sqrt 2000000000000000000000000000000000000000000000000)

1.414213562373095e+024

> (sqrt 0.0000000000000000000000000000000000000000000000002)

 4.472135954999579e-025

>

 

 

;练习1.8

  (define (CubeImprove y x)

    (/ (+ ( / x (* y y)) (* 2 y)) 3))

  (define (CubeGood? guess x)

    (< (abs (- (CubeImprove guess x) guess)) 0.0000000001))

 (define (Cube-iter guess x)

    (if (CubeGood? guess x)

        guess

        (Cube-iter (CubeImprove guess x) x)))

 (define (CubeGood? guess x)

    (< (abs (- (CubeImprove guess x) guess)) 0.0000000001))

 (define (Cube x)

    (Cube-iter 1.0 x)) 

 

 

 Welcome to DrRacket, version 5.1.1 [3m].

Language: R5RS; memory limit: 128 MB.

> (Cube 8)

2.000000000012062

> (Cube 27)

3.0000000000000977

> (Cube -64)

-4.000000000004644

> (Cube -125)

-5.000000000076353

>