; chutes and ladders
(define rand #f)
(define randint #f)
(let ((two31 #x80000000) (a (make-vector 56 -1)) (fptr #f))
(define (mod-diff x y) (modulo (- x y) two31)) ; generic version
; (define (mod-diff x y) (logand (- x y) #x7FFFFFFF)) ; fast version
(define (flip-cycle)
(do ((ii 1 (+ ii 1)) (jj 32 (+ jj 1))) ((< 55 jj))
(vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj))))
(do ((ii 25 (+ ii 1)) (jj 1 (+ jj 1))) ((< 55 ii))
(vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj))))
(set! fptr 54) (vector-ref a 55))
(define (init-rand seed)
(let* ((seed (mod-diff seed 0)) (prev seed) (next 1))
(vector-set! a 55 prev)
(do ((i 21 (modulo (+ i 21) 55))) ((zero? i))
(vector-set! a i next) (set! next (mod-diff prev next))
(set! seed (+ (quotient seed 2) (if (odd? seed) #x40000000 0)))
(set! next (mod-diff next seed)) (set! prev (vector-ref a i)))
(flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle)))
(define (next-rand)
(if (negative? (vector-ref a fptr)) (flip-cycle)
(let ((next (vector-ref a fptr))) (set! fptr (- fptr 1)) next)))
(define (unif-rand m)
(let ((t (- two31 (modulo two31 m))))
(let loop ((r (next-rand)))
(if (<= t r) (loop (next-rand)) (modulo r m)))))
(init-rand 19380110) ; happy birthday donald e knuth
(set! rand (lambda seed
(cond ((null? seed) (/ (next-rand) two31))
((eq? (car seed) 'get) (cons fptr (vector->list a)))
((eq? (car seed) 'set) (set! fptr (caadr seed))
(set! a (list->vector (cdadr seed))))
(else (/ (init-rand (modulo (numerator
(inexact->exact (car seed))) two31)) two31)))))
(set! randint (lambda args
(cond ((null? (cdr args))
(if (< (car args) two31) (unif-rand (car args))
(floor (* (next-rand) (car args)))))
((< (car args) (cadr args))
(let ((span (- (cadr args) (car args))))
(+ (car args)
(if (< span two31) (unif-rand span)
(floor (* (next-rand) span))))))
(else (let ((span (- (car args) (cadr args))))
(- (car args)
(if (< span two31) (unif-rand span)
(floor (* (next-rand) span))))))))))
(define chutes '((16 . 6) (47 . 26) (49 . 11)
(56 . 53) (62 . 19) (64 . 60) (87 . 24)
(93 . 73) (95 . 75) (98 . 78)))
(define ladders '((1 . 38) (4 . 14) (9 . 31)
(21 . 42) (28 . 84) (36 . 44) (51 . 67)
(71 . 91) (80 . 100)))
(define (game)
(let loop ((ps '(0)))
(let* ((die (randint 6 0)) (p (+ (car ps) die)))
(cond ((= 100 (car ps)) (cdr (reverse ps)))
((< 100 p) (loop (cons (car ps) ps)))
((or (assoc p chutes) (assoc p ladders))
=> (lambda (x) (loop (cons (cdr x) ps))))
(else (loop (cons p ps)))))))
(define (games n)
(let loop ((n n) (gs '()))
(if (zero? n) gs
(loop (- n 1) (cons (length (game)) gs)))))
(define (compete k n)
(let loop ((n n) (gs '()))
(if (zero? n) gs
(loop (- n 1) (cons (apply min (games k)) gs)))))
(define (stats k n)
(let ((gs (compete k n)))
(values (apply min gs) (apply max gs)
(exact->inexact (/ (apply + gs) n)))))
(call-with-values
(lambda () (stats 1 5000))
(lambda (mn mx av)
(display mn) (display " ")
(display mx) (display " ")
(display av) (newline)))
(call-with-values
(lambda () (stats 2 2000))
(lambda (mn mx av)
(display mn) (display " ")
(display mx) (display " ")
(display av) (newline)))
(call-with-values
(lambda () (stats 3 2000))
(lambda (mn mx av)
(display mn) (display " ")
(display mx) (display " ")
(display av) (newline)))
(call-with-values
(lambda () (stats 4 2000))
(lambda (mn mx av)
(display mn) (display " ")
(display mx) (display " ")
(display av) (newline)))
(call-with-values
(lambda () (stats 5 1000))
(lambda (mn mx av)
(display mn) (display " ")
(display mx) (display " ")
(display av) (newline)))