Modulus 10 formula

I've been going back and forth on my Modulus10 routine because, as it turns
are the seems to be a variance in the way IBM does it and the LUHN formula.

The biggest issue is a subtle one but it is as follows,

With IBM, you always start with the left most digit (highest order digit)
and selects every even position digit, moving to the right and multiples it
by two.

This seems to be done regardless of the length of the original number;
ttherefore,  34567 would use 3, 5 and 7, and 4567 would use 4 and 6.

But the LUHN Modulus 10 formula begins with the rightmost digit (lowest
order digit) and selects every other digit moving to the left, and multiples
it by two.

 

So with IBM we would get this (starting on the left):

Start with:  3456

Step 1:  Multiple 3 and 5 by 2 =  6 10 

Step 2: Add them:  6 + 4 + 1 + 0 + 6  = 17

Step 3:  20 - 17 = 3

Check Digit = 3

   3456-3

 

But with the LUHN formula we would get this:

Start with 3456

Step 1: Multiple 4 and 6 by 2 = 12 and 8

Step 2: Add them:  3 + 8 + 5 + 1 + 2 = 19

Step 3:  20 - 19 = 1

Check Digit = 1

  3456-1

 

So is the IBM one screwy or are there two of them?

 

-Bob Cozzi