Finish exercises for chapter 3

ex-3_73-82.scm

@@ -180,6 +180,43 @@
 (assert (take 10 rs)
         (take 10 rs))
 
-(display "\nex-3.82\n")
+(display "\nex-3.82 - estimate-integral-stream\n")
 
+(define (rand) (random 65536))
+
+(define (monte-carlo experiment-stream passed failed)
+  (define (next passed failed)
+    (cons-stream
+     (/ passed (+ passed failed))
+     (monte-carlo
+      (stream-cdr experiment-stream) passed failed)))
+  (if (stream-car experiment-stream)
+      (next (+ passed 1) failed)
+      (next passed (+ failed 1))))
+
+(define radius-circle 5000.)
+
+(define (estimate-integral-stream P x1 x2 y1 y2)
+  ; Probably this stream should be based on a random stream,
+  ; but it does not really matter for the exercise.
+  (define (area-test-stream)
+    (cons-stream
+      (P (random-in-range x1 (inc x2))
+         (random-in-range y1 (inc y2)))
+      (area-test-stream)))
+  (let ((area-rectangle (* (abs (- x2 x1)) (abs (- y2 y1)))))
+    (stream-map (lambda (x) (* x area-rectangle))
+                (monte-carlo (area-test-stream) 0 0))))
+
+(define (p x y) (<= (+ (square (- x radius-circle))
+                       (square (- y radius-circle)))
+                    (square radius-circle)))
+
+(let ((area-circle-stream
+        (estimate-integral-stream p 0 (* 2 radius-circle)
+                                    0 (* 2 radius-circle))))
+  (let ((pi (/ (stream-ref area-circle-stream 10000)
+               (square radius-circle))))
+    (assert (< pi 3.4) #t)
+    (assert (> pi 3.0) #t)))
 

ex-4_01-xx.scm

@@ -0,0 +1,4 @@
+(load "util.scm")
+
+(display "\nex-4.1\n")
+