Is there a bug in the Rosetta code for Luhn numbers for 19 digit numbers?
Wikipedia says about Payment_card_number:
The leading six or eight digits of the card number comprise the
issuer identification number (IIN) sometimes referred to as the
"bank identification number (BIN)". The remaining numbers on the
card, except the last digit, are the individual account
identification number. The last digit is the Luhn check digit.
IINs and PANs have a certain level of internal structure and
share a common numbering scheme set by ISO/IEC 7812. Payment
card numbers are composed of 8 to 19 digits, as follows:
Wikipedia also gives the Luhn algorithm:
From the rightmost digit (excluding the
check digit) and moving left, double the value of every second
digit. The check digit is neither doubled nor included in this
calculation; the first digit doubled is the digit located
immediately left of the check digit. If the result of this
doubling operation is greater than 9 (e.g., 8 × 2 = 16), then
add the digits of the result (e.g., 16: 1 + 6 = 7, 18: 1 + 8 =
9) or, alternatively, the same final result can be found by
subtracting 9 from that result (e.g., 16: 16 − 9 = 7, 18: 18 − 9
Take the sum of all the digits.
If the total modulo 10 is equal to 0 (if the total
ends in zero) then the number is valid according to the Luhn
formula; otherwise it is not valid.
The Rosetta code "Luhn test of credit card numbers" validation:
used by some credit card companies to distinguish valid credit
card numbers from what could be a random selection of digits.
Those companies using credit card numbers that can be
validated by the Luhn test have numbers that pass the following
Reverse the order of the
digits in the number.
Take the first, third, ...
and every other odd digit in the reversed digits and sum
them to form the partial sum s1
Taking the second, fourth
... and every other even digit in the reversed digits:
Multiply each digit by
two and sum the digits if the answer is greater than
nine to form partial sums for the even digits
Sum the partial sums
of the even digits to form s2
If s1 + s2 ends in zero
then the original number is in the form of a valid credit
card number as verified by the Luhn test.
The Luhn algorithm doubles every second digit read from the right.
Take '372' which is valid according to Wikipedia. It is invalid
according to Rosetta where s1 is 3+2=5. s2 is 4. The sum is 9 which
does not end in 0.
It seems to me that the Rosetta code only works for even-numbered
codes. This seems unbelievable. What have I missed?