## Credit Card Validation

### April 8, 2011

This is fairly straight forward. The variable `two?` alternates between true and false, telling us when to double the current digit. At the end of the input, the check digit is calculated as 10 − sum mod 10, except that if the sum is divisible by 10 the check digit is 0; the check digit is added to the end of the input number by multiplying the input number by 10 then adding the check digit. The only trick we employ is to pre-compute the digit-sums of the doubled digits and store them in an array:

```(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)))))```

Checking is even simpler:

```(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)))))```

The definition of the pre-computed array of doubled digits and the calculation of the sum are duplicated between the two functions. If you object to that, you can define the two functions like this:

```(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)))))```

In this case the duplicated code is small enough that it probably doesn’t matter, but this technique of hiding the duplicated code inside a `letrec` can be useful if the duplicated code is larger.

A small test assures us that everything is working properly:

```(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)))```

We used digits, randint and assert from the Standard Prelude. You can run the program at http://programmingpraxis.codepad.org/io514WKh.

Pages: 1 2

### 14 Responses to “Credit Card Validation”

```import Data.Char
import Data.List.HT

luhnSum :: Integral a => a -> a
luhnSum n = digitSum a + digitSum (show . (* 2) . digitToInt =<< b)
where [a,b] = sliceHorizontal 2 . reverse \$ show n
digitSum = sum . map (fromIntegral . digitToInt)

isValid :: Integral a => a -> Bool
isValid n = mod (luhnSum n) 10 == 0

makeValid :: Integral a => a -> a
makeValid n = 10*n + mod (10 - mod (luhnSum \$ 10*n) 10) 10
```
2. […] today’s Programming Praxis exercise our goal is to write to functions related to the Luhn credit card […]

3. Graham said

I came up with two versions of my intermediate Luhn sum function: one that
creates a list and modifies it in-place, and another that uses iterators
instead. My solution is available on github.

4. Jussi Piitulainen said

Just numbers; just one recursive branch / two vectors.
First I missed that (- 10 (modulo 30 10)) is 10, not 0.
Then Ikarus thought that (modulo -30 10) => 10. Sigh.

```(define (luhn-digit digits)
(define (modulo n m) (- n (* m (floor (/ n m))))) ;...
(let loop ((digits digits) (neg-sum 0)
(vig '#(0 2 4 6 8 1 3 5 7 9))
(vug '#(0 1 2 3 4 5 6 7 8 9)))
(if (zero? digits)
(modulo neg-sum 10)
(loop (quotient digits 10)
(- neg-sum (vector-ref vig (modulo digits 10)))
vug vig))))

(define (luhn? digits) (= digits (luhn (quotient digits 10))))

(define (luhn digits) (+ (* digits 10) (luhn-digit digits)))

(write (luhn? 49927398716))
(write (luhn? 3020))
(write (luhn? 3129))
(newline)
```
5. arturasl said

Wanted to see if I still remember Linux assembly so I wrote my answer in it: github. It might be possible to make the answer more readable and shorter, but that would take me an additional hour…

6. Mike said
```dd = ((0,0), (1,2), (2,4), (3,6), (4,8),
(5,1), (6,3), (7,5), (8,7), (9,9))

def luhn(ds):
'''
>>> n = "49927398716"
>>> luhn(n[:-1])
6
'''

return -sum(dd[int(d)][~n&1] for n,d in enumerate(ds[::-1])) % 10

def is_valid(ds):
'''
n = "49927398716"
>>> is_valid(n)
True
'''

return luhn(ds[:-1]) == int(ds[-1])

'''
n = "4992739871"
'49927398716'
'''

return ds + str(luhn(ds))
```
7. David said

Factor Language solution.

```USING: kernel math math.parser math.ranges sequences ;
IN: luhn

: reversed-digits ( n -- list )
{ } swap
[ dup 0 > ]
[ 10 /mod  swapd suffix  swap ]
while drop ;

: luhn-sum  ( n -- n )
reversed-digits dup length iota [
2dup swap nth
swap odd? [ 2 *  10 /mod + ] when
] map sum
nip ;

: luhn? ( n -- ? )
luhn-sum 10 mod 0 = ;

: make-luhn ( n -- n )
10 * dup luhn-sum 10 mod 10 swap - 10 mod + ;
```

( scratchpad ) 2771 luhn? .
f
( scratchpad ) 2771 make-luhn dup . luhn? .
27714
t
( scratchpad ) 49927398716 luhn? .
t
( scratchpad ) 49927398716 make-luhn dup . luhn? .
499273987168
t

8. […] or Canadian Social Insurance Numbers are validated you can take a look at this Programming Praxis article . It’s all about a simple, tiny, patented (now public domain) algorithm invented by […]

9. My python 3.x solution:

```def luhn_check(num):
''' Number - List of reversed digits '''
digits = [int(x) for x in reversed(str(num))]
check_sum = sum(digits[::2]) + sum((dig//10 + dig%10) for dig in [2*el for el in digits[1::2]])
return check_sum%10 == 0

if __name__ == "__main__":
print(luhn_check(543298376
```
10. ```))
```
11. rohit said

nice solution

12. Rainer said

My try in REXX

```
numeric digits 30
debug = 0

number = '49927398716'

say number 'is' check_luhn(number)

number = '4992739871'
say number 'plus check_digit =' add_check_digit(number)

exit

check_luhn: procedure
parse arg test
test = reverse(test)
summe = 0
ind = 0
do i = 1 to length(test)
ind = ind + 1
ziffer = substr(test,i,1)
say 'Ziffer' ziffer
if even(ind) then do
ziffer = ziffer * 2
if length(ziffer) > 1 then summe = summe + left(ziffer,1)
end
summe = summe + right(ziffer,1)
say 'Summe' summe
end
if (summe//10) > 0 then return 'wrong'
else return 'correct'

parse arg urtest
test = reverse(urtest)
summe = 0
ind = 0
do i = 1 to length(test)
ind = ind + 1
ziffer = substr(test,i,1)
if odd(ind) then do
ziffer = ziffer * 2
if length(ziffer) > 1 then summe = summe + left(ziffer,1)
end
summe = summe + right(ziffer,1)
say 'Summe' summe
end
if (summe//10) > 0 then return urtest||(summe%10*10)+10-summe
else return urtest||0

even: procedure
parse arg number
return \ odd(number)

odd: procedure
parse arg number
return (number//2)

```
13. Khanh Nguyen said
```open System

let rec sum_digit inp =
if inp < 10 then inp else sum_digit (inp / 10) + (inp % 10)

let f (inp: string) =
inp.ToCharArray()
|> List.ofArray
|> List.map (fun x -> (int x) - (int '0'))
|> List.rev
|> List.zip [1.. String.length inp]
|> List.map (fun (i, v) -> if i % 2 = 1 then v*2 else v)
|> List.map sum_digit
|> List.sum

let add_check_digit (inp : string) =
inp + string(10 - (f inp) % 10)
let isValid (inp : string) =
inp = add_check_digit (inp.Remove(String.length inp - 1))

isValid "49927398715"
isValid "49927398716"

```
14. Ben Atwell said

My solution in Python 3.2

number = int(str(number)[::-1])
numString = str(number)
check = False
mySum = 0
for ch in numString:
num = int(ch)
if (check):
num = num * 2
strNum = str(num)
for c in strNum:
num2 = int(c)
mySum += num2
else:
mySum += num
check = not check
return mySum

def validate(number):
if (mySum % 10 == 0):
return True
else:
return False