; credit card validation
(define (digits n . args)
(let ((b (if (null? args) 10 (car args))))
(let loop ((n n) (d '()))
(if (zero? n) d
(loop (quotient n b)
(cons (modulo n b) d))))))
(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-syntax assert
(syntax-rules ()
((assert expr result)
(if (not (equal? expr result))
(for-each display `(
#\newline "failed assertion:" #\newline
expr #\newline "expected: " ,result
#\newline "returned: " ,expr #\newline))))))
(define (luhn n)
(define (x2 n) (vector-ref #(0 2 4 6 8 1 3 5 7 9) n))
(let loop ((ds (reverse (digits n))) (s 0) (two? #t))
(cond ((null? ds)
(let* ((sum (modulo s 10))
(check (if (zero? sum) 0 (- 10 sum))))
(+ (* n 10) check)))
(two? (loop (cdr ds) (+ s (x2 (car ds))) #f))
(else (loop (cdr ds) (+ s (car ds)) #t)))))
(define (luhn? n)
(define (x2 n) (vector-ref #(0 2 4 6 8 1 3 5 7 9) n))
(let loop ((ds (reverse (digits n))) (s 0) (two? #f))
(cond ((null? ds) (zero? (modulo s 10)))
(two? (loop (cdr ds) (+ s (x2 (car ds))) #f))
(else (loop (cdr ds) (+ s (car ds)) #t)))))
(define (luhn-test)
(assert (luhn 4992739871) 49927398716)
(assert (luhn? 49927398716) #t)
(assert (luhn? 49927398715) #f)
(do ((i 0 (+ i 1))) ((= i 10000))
(assert (luhn? (luhn (randint #e1e8))) #t))
(do ((i 0 (+ i 1))) ((= i 100))
(assert (luhn? (luhn (randint (expt 10 i)))) #t)))
(luhn-test)
(define luhn #f)
(define luhn? #f)
(letrec ((x2 (lambda (n)
(vector-ref #(0 2 4 6 8 1 3 5 7 9) n)))
(luhn-sum (lambda (n two?)
(let loop ((ds (reverse (digits n))) (s 0) (two? two?))
(cond ((null? ds) s)
(two? (loop (cdr ds) (+ s (x2 (car ds))) #f))
(else (loop (cdr ds) (+ s (car ds)) #t)))))))
(set! luhn (lambda (n)
(let* ((sum (modulo (luhn-sum n #t) 10))
(check (if (zero? sum) 0 (- 10 sum))))
(+ (* n 10) check))))
(set! luhn? (lambda (n)
(zero? (modulo (luhn-sum n #f) 10)))))
(luhn-test)
(display (luhn 4992739871)) (newline)
(display (luhn? 49927398716)) (newline)