Add implementation of exercise 3-58

Author: ramsayleung

README.org

@@ -25,7 +25,7 @@
   习题完成情况:
   - 章节一: 43/46
   - 章节二: 88/97
-  - 章节三: 57/82
+  - 章节三: 58/82
   - 章节四: TODO
   - 章节五: TODO
 * 运行

chapter3/exercise3-58.rkt

@@ -0,0 +1,20 @@
+#lang racket
+(require "stream.rkt")
+
+;;; 实际上实现了一个流式长除法算法, 用于将分数num/den转换为以radix为基数的无限小数表示
+(define (expand num den radix)
+  (cons-stream
+   (quotient (* num radix) den)
+   (expand (remainder (* num radix) den) den radix)))
+
+(module+ test
+  (require rackunit)
+
+  (test-case "Test for expand"
+             (define x (expand 3 8 10))
+             ;; 3/8 = 0.375 (有限小数)
+             (check-equal? (stream-to-list x 10) '(3 7 5 0 0 0 0 0 0 0))
+
+             (define s (expand 1 7 10))
+             ;; (expand 1 7 10) 对应 1/7 = 0.142857142857... (循环小数)
+             (check-equal? (stream-to-list s 10) '(1 4 2 8 5 7 1 4 2 8))))