#lang sicp

;;For Section 3.1.2 -- written as suggested in footnote,
;; though the values of a, b, m may not be very "appropriately chosen"
(define (rand-update x)
  (let ((a 27) (b 26) (m 127))
    (modulo (+ (* a x) b) m)))

(define random-init 7)			;**not in book**

(define rand
  (let ((x random-init))
    (lambda (arg)
      (cond ((eq? arg 'reset)
             (lambda (seed)
               (set! random-init seed)))
            ((eq? arg 'generate)
             (set! x (rand-update x))
             x)
            (else
             (error "rand - unknown argument" arg))))))

(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))

(define (in-circle-test radius x1 x2 y1 y2)
  (lambda ()
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (in-circle? radius x y))))

(define (in-circle? radius x y)
  (<= (+ (* x x) (* y y))
      (* radius radius)))
  
(define (monte-carlo trials experiment)
  (define (iter trials-remaining trials-passed)
    (cond ((= trials-remaining 0)
           (/ trials-passed trials))
          ((experiment)
           (iter (- trials-remaining 1) (+ trials-passed 1)))
          (else
           (iter (- trials-remaining 1) trials-passed))))
  (iter trials 0))

(define (estimate-integral pred x1 x2 y1 y2 trials)
  (monte-carlo trials (in-circle-test 1.0 x1 x2 y1 y2)))

;; Area of circle is pi/r^2.  Area of square is 2*2 = 4
;; So calculated probability is pi/4.
(define (estimate-pi trials)
  (* 4.0 (estimate-integral in-circle-test -1.0 1.0 -1.0 1.0 trials)))