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Project: programmingpraxis
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programmingpraxis - Scheme, pasted on Sep 3:
; 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))


Output:
1
Programming Praxis


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