SICP 1.6-1.8

1.6
由于scheme应用序求值的性质,该函数会陷入循环(一直计算 improve guess x)

1.7

值过小,0.001这个精度远远不够...

值过大,由于浮点数精度有限,(比如使用IEEE754浮点数标准, 32位浮点数表示123456789这样的数会有严重的精度丢失), 所以无法得出正确求两个较大的数的差.

(define (abs x)
  (if (>= x 0)
      x
      (- x)))

(define (average a b)
  (/ (+ a b) 2))

(define (improve guess x)
  (average guess
           (/ x guess)))

(define (good-enough? guess x)
  (< (/ (abs (- (improve guess x)
                guess))
        guess)
     0.01))

(define (sqrt-iter guess x)
  (cond ((good-enough? guess x) guess)
        (else (sqrt-iter (improve guess x) x))
        ))


(define (sqrt x)
  (sqrt-iter 1.0 x))

---> 原则上可以的,但是其实精度损失是肯定的...

1.8

(define (improve2 guess x)
  (/ (+ (/ x
           (* guess guess))
        (* 2 guess))
     3))

(define (good-enough2? guess x)
  (< (/ (abs (- (improve2 guess x)
                guess))
        guess)
     0.01))

(define (cbrt-iter guess x)
  (cond ((good-enough2? guess x) guess)
        (else (cbrt-iter (improve2 guess x)
                         x))))

(define (cbrt x)
  (cbrt-iter 1.0 x))