Editing Luhn algorithm (section)

==Description==
The check digit is computed as follows:
# Drop the check digit from the number (if it's already present). This leaves the payload.
# Start with the payload digits. Moving from right to left, double every second digit, starting from the last digit. If doubling a digit results in a value > 9, subtract 9 from it (or sum its digits). 
# Sum all the resulting digits (including the ones that were not doubled).
# The check digit is calculated by <math>(10 - (s \bmod 10)) \bmod 10</math>, where s is the sum from step 3.  This is the smallest number (possibly zero) that must be added to <math>s</math> to make a multiple of 10. Other valid formulas giving the same value are <math>9 - ((s + 9)\bmod 10)</math>, <math>(10 - s)\bmod    10</math>, and <math>10\lceil s/10\rceil - s</math>. Note that the formula <math>(10 - s)\bmod 10</math> will not work in all environments due to differences in how negative numbers are handled by the [[modulo]] operation.

=== Example for computing check digit ===

Assume an example of an account number 1789372997 (just the "payload", check digit not yet included):

{| class="wikitable" style="text-align:center;border:none;" 
! style="width:1.5em" | Digits reversed
| style="width:1.5em" | 7
| style="width:1.5em" | 9
| style="width:1.5em" | 9
| style="width:1.5em" | 2
| style="width:1.5em" | 7
| style="width:1.5em" | 3
| style="width:1.5em" | 9
| style="width:1.5em" | 8
| style="width:1.5em" | 7
| style="width:1.5em" | 1
|-
! Multipliers
| 2
| 1
| 2
| 1
| 2
| 1
| 2
| 1
| 2
| 1
|-
! 
| =
| =
| =
| =
| =
| =
| =
| =
| =
| =
|-
! 
| style="background: #FFA; color: #000;" | '''14'''
| 9
| style="background: #FFA; color: #000;" | '''18'''
| 2
| style="background: #FFA; color: #000;" | '''14'''
| 3
| style="background: #FFA; color: #000;" | '''18'''
| 8
| style="background: #FFA; color: #000;" | '''14'''
| 1
|-
! Sum digits
|'''5''' <br> (1+4)
|9 <br> &nbsp;
|'''9''' <br> (1+8)
|2 <br> &nbsp;
|'''5''' <br> (1+4)
|3 <br> &nbsp;
|'''9''' <br> (1+8)
|8 <br> &nbsp;
|'''5''' <br> (1+4)
|1 <br> &nbsp;
|}

The sum of the resulting digits is 56.

The check digit is equal to <math>(10 - (56 \bmod 10))\bmod 10 = 4</math>.

This makes the full account number read 17893729974.

=== Example for validating check digit ===

# Drop the check digit (last digit) of the number to validate. (e.g. 17893729974 &rarr; 1789372997)
# Calculate the check digit (see above)
# Compare your result with the original check digit. If both numbers match, the result is valid. {{nowrap|1=(e.g. (givenCheckDigit = calculatedCheckDigit) &hArr; (isValidCheckDigit)).}}