; fountain codes
(define (take n xs)
(let loop ((n n) (xs xs) (ys '()))
(if (or (zero? n) (null? xs))
(reverse ys)
(loop (- n 1) (cdr xs)
(cons (car xs) ys)))))
(define (range . args)
(case (length args)
((1) (range 0 (car args) (if (negative? (car args)) -1 1)))
((2) (range (car args) (cadr args) (if (< (car args) (cadr args)) 1 -1)))
((3) (let ((le? (if (negative? (caddr args)) >= <=)))
(let loop ((x(car args)) (xs '()))
(if (le? (cadr args) x)
(reverse xs)
(loop (+ x (caddr args)) (cons x xs))))))
(else (error 'range "unrecognized arguments"))))
(define (logxor a b)
(cond ((zero? a) b)
((zero? b) a)
(else
(+ (* (logxor (floor (/ a 2)) (floor (/ b 2))) 2)
(if (even? a)
(if (even? b) 0 1)
(if (even? b) 1 0))))))
(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 (shuffle x)
(do ((v (list->vector x)) (n (length x) (- n 1)))
((zero? n) (vector->list v))
(let* ((r (randint n)) (t (vector-ref v r)))
(vector-set! v r (vector-ref v (- n 1)))
(vector-set! v (- n 1) t))))
(define (degree-distribution n)
(let* ((len (* n (+ n 1) 1/2))
(k (randint len)))
(let loop ((i 0) (s 0) (t 1))
(if (< k s) (- n i -1)
(loop (+ i 1) (+ s t) (+ t 1))))))
(define (make-fountain str)
(let* ((cv (list->vector (map char->integer (string->list str))))
(len (vector-length cv)))
(lambda ()
(let* ((d (degree-distribution len))
(blocks (take d (shuffle (range len)))))
(let loop ((bs blocks) (x 0))
(if (null? bs) (cons x blocks)
(loop (cdr bs) (logxor x (vector-ref cv (car bs))))))))))
(define fountain (make-fountain "Programming Praxis"))
(define (decode fountain len)
(let* ((cv (make-vector len #f)) (n len))
(define (store packet)
(cond ((vector-ref cv (cadr packet)) #f)
(else (vector-set! cv (cadr packet) (car packet))
(set! n (- n 1)) #t)))
(define (reduce packet)
(let loop ((x (car packet)) (bs (cdr packet)) (zs (list)))
(cond ((null? bs) (cons x zs))
((vector-ref cv (car bs))
(loop (logxor x (vector-ref cv (car bs)))
(cdr bs) zs))
(else (loop x (cdr bs) (cons (car bs) zs))))))
(define (ripple hold)
(let ((done? #t))
(let loop ((hold hold) (out-hold (list)))
(if (null? hold)
(if done? out-hold (ripple out-hold))
(let ((p (reduce (car hold))))
(cond ((equal? p (list 0))
(loop (cdr hold) out-hold))
((null? (cddr p))
(if (store p) (set! done? #f))
(loop (cdr hold) out-hold))
((equal? (cdar hold) (reverse (cdr p)))
(loop (cdr hold) (cons p out-hold)))
(else (set! done? #f)
(loop (cdr hold) (cons p out-hold)))))))))
(let loop ((hold (list)))
(if (zero? n)
(list->string (map integer->char (vector->list cv)))
(let ((p (fountain)))
(if (null? (cddr p))
(if (store p)
(loop (ripple hold))
(loop hold))
(loop (cons p hold))))))))
(display (decode fountain 18))