scheme - 代码在 stk-simply 中有效，但在 mit-scheme 中无效

Question

我一直在阅读类(class)CS61A (Spring 2011)来自 Berkeley Opencourseware和 MIT 6.001来自 OCW .一个使用STk (称为 stk-simply)，另一个使用 mit-scheme 作为讲座的编程语言。

我刚刚使用 Heron's method 编写了一个简单的平方根程序.文件保存为 sqrt.scm

;; setting an accuracy or tolerance to deviation between the actual and the expected values
(define tolerance 0.001)

;; gives average of two numbers
(define (average x y)
  (/ (+ x y) 2))

;; gives the absolute values of any number
(define (abs x)
  (if (< x 0) (- x) x))

;; gives the square of a number
(define (square x) (* x x))

;; tests whether the guess is good enough by checking if the difference between square of the guess
;; and the number is tolerable
(define (good-enuf? guess x)
  (< (abs (- (square guess) x)) tolerance))

;; improves the guess by averaging guess the number divided by the guess
(define (improve guess x)
  (average (/ x guess) guess))

;;  when a tried guess does not pass the good-enuf test then the tries the improved guess
(define (try guess x)
  (if (good-enuf? guess x)
      guess
      (try (improve guess x) x)))

;; gives back square root of number by starting guess with 1 and then improving the guess until good-enuf
(define (sqr-root x)
  (try 1 x))

这在 STk 中运行良好。

sam@Panzer:~/code/src/scheme$ sudo stk-simply
[sudo] password for sam: 
Welcome to the STk interpreter version 4.0.1-ucb1.3.6 [Linux-2.6.16-1.2108_FC4-i686]
Copyright (c) 1993-1999 Erick Gallesio - I3S - CNRS / ESSI <eg@unice.fr>
Modifications by UCB EECS Instructional Support Group
Questions, comments, or bug reports to <inst@EECS.Berkeley.EDU>.
STk> (load "sqrt.scm")
okay
STk> (sqr-root 25)
5.00002317825395
STk>

但不在方案中。

sam@Panzer:~/code/src/scheme$ sudo scheme
[sudo] password for sam: 
MIT/GNU Scheme running under GNU/Linux
Type `^C' (control-C) followed by `H' to obtain information about interrupts.

Copyright (C) 2011 Massachusetts Institute of Technology
This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Image saved on Thursday October 27, 2011 at 7:44:21 PM
  Release 9.1 || Microcode 15.3 || Runtime 15.7 || SF 4.41 || LIAR/i386 4.118 || Edwin 3.116

1 ]=> (load "sqrt.scm")

;Loading "sqrt.scm"... done
;Value: sqr-root

1 ]=> (sqr-root 25)

;Value: 1853024483819137/370603178776909

1 ]=> 

我查了手册，但找不到原因。谁能告诉我这是为什么？或者我忽略的代码中是否存在错误？我是 scheme 和 STk 的初学者。

Answer 1

试试这个，现在代码应该在两个解释器中返回相同的结果(忽略微小的舍入差异):

(define (sqr-root x)
  (exact->inexact (try 1 x)))

答案一直都是一样的，只是 MIT Scheme 默认生成一个精确的结果，而 STk 返回一个不精确的值。有了上面的代码，我们在执行计算后将结果转换为不精确的数字。或者，我们可以从头开始执行转换(在此过程中可能会损失一些精度):

(define (sqr-root x)
  (try 1 (exact->inexact x)))

这quote解释观察到的行为:

Scheme numbers are either exact or inexact. A number is exact if it was written as an exact constant or was derived from exact numbers using only exact operations. A number is inexact if it was written as an inexact constant, if it was derived using inexact ingredients, or if it was derived using inexact operations. Thus inexactness is a contagious property of a number.