#lang racket
(require "3-5-streams.rkt")

;;;;;;;;;;
;; 3.81 ;;
;;;;;;;;;;

(define (make-prng seed)
  (define (rand-update x)
    (remainder (+ 11 (* 23 x)) 493))
  (define (random-stream request-stream x0)
    (define m0 (stream-car request-stream))
    (define x1
      (cond [(eq? m0 'generate) (rand-update x0)]
            [(eq? m0 'reset) seed]
            [else (error "Unknown request -- PRNG:" m0)]))
    (cons-stream x0
                 (random-stream (stream-cdr request-stream)
                                x1)))
  (lambda (ms) (random-stream ms seed)))

;; TEST

(define example-request-stream
  ; Reset every fourth request.
  (my-stream-map (lambda (x)
                   (if (zero? (remainder x 4))
                     'reset
                     'generate))
                 integers))

(define rand-stream ((make-prng 10) example-request-stream))

(display-this-many 10 rand-stream)
;; 10 241 131 66 10 241 131 66 10 241 
;; 'done

;;;;;;;;;;
;; 3.82 ;;
;;;;;;;;;;

(define (monte-carlo experiment-stream passed failed)
  (define (next passed failed)
    (cons-stream
      (exact->inexact (/ passed (+ passed failed)))
      (monte-carlo
        (stream-cdr experiment-stream) passed failed)))
  (if (stream-car experiment-stream)
    (next (add1 passed) failed)
    (next passed (add1 failed))))

(define (inexact-random low high)
  (+ low (* (random) (- high low))))

(define (estimate-integral predicate x1 x2 y1 y2)
  (define (rand-update . args)
    ; Produce a random pair in the right ranges when applied to any argument.
    (list (inexact-random x1 x2)
          (inexact-random y1 y2)))
  (define area (* (- x2 x1) (- y2 y1)))
  (define random-pairs
    (cons-stream (rand-update)
                 (my-stream-map rand-update
                                random-pairs)))
  (define experiment-stream
    (my-stream-map (lambda (pr) (apply predicate pr))
                   random-pairs))
  (scale-stream (monte-carlo experiment-stream 0 0) area))

(define (in-unit-circle? x y)
  (< (+ (sqr x)
        (sqr y))
     1))

(define pi-stream (estimate-integral in-unit-circle? -1 1 -1 1))

(my-stream-ref pi-stream 100)
;; 3.00990099009901
(my-stream-ref pi-stream 1000)
;; 3.1888111888111887
(my-stream-ref pi-stream 10000)
;; 3.1632836716328367
(my-stream-ref pi-stream 100000)
;; 3.153968460315397
(my-stream-ref pi-stream 1000000)
;; 3.1423408576591423