# verhoeff.py - functions for performing the Verhoeff checksum
#
# Copyright (C) 2010-2021 Arthur de Jong
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 2.1 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with this library; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
# 02110-1301 USA
"""The Verhoeff algorithm.
The Verhoeff algorithm is a checksum algorithm that should catch most common
(typing) errors in numbers. The algorithm uses two tables for permutations
and multiplications and as a result is more complex than the Luhn algorithm.
More information:
* https://en.wikipedia.org/wiki/Verhoeff_algorithm
* https://en.wikibooks.org/wiki/Algorithm_Implementation/Checksums/Verhoeff_Algorithm
The module provides the checksum() function to calculate the Verhoeff
checksum a calc_check_digit() function to generate a check digit that can be
append to an existing number to result in a number with a valid checksum and
validation functions.
>>> validate('1234')
Traceback (most recent call last):
...
InvalidChecksum: ...
>>> checksum('1234')
1
>>> calc_check_digit('1234')
'0'
>>> validate('12340')
'12340'
"""
from stdnum.exceptions import *
# These are the multiplication and permutation tables used in the
# Verhoeff algorithm.
_multiplication_table = (
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
(1, 2, 3, 4, 0, 6, 7, 8, 9, 5),
(2, 3, 4, 0, 1, 7, 8, 9, 5, 6),
(3, 4, 0, 1, 2, 8, 9, 5, 6, 7),
(4, 0, 1, 2, 3, 9, 5, 6, 7, 8),
(5, 9, 8, 7, 6, 0, 4, 3, 2, 1),
(6, 5, 9, 8, 7, 1, 0, 4, 3, 2),
(7, 6, 5, 9, 8, 2, 1, 0, 4, 3),
(8, 7, 6, 5, 9, 3, 2, 1, 0, 4),
(9, 8, 7, 6, 5, 4, 3, 2, 1, 0))
_permutation_table = (
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
(1, 5, 7, 6, 2, 8, 3, 0, 9, 4),
(5, 8, 0, 3, 7, 9, 6, 1, 4, 2),
(8, 9, 1, 6, 0, 4, 3, 5, 2, 7),
(9, 4, 5, 3, 1, 2, 6, 8, 7, 0),
(4, 2, 8, 6, 5, 7, 3, 9, 0, 1),
(2, 7, 9, 3, 8, 0, 6, 4, 1, 5),
(7, 0, 4, 6, 9, 1, 3, 2, 5, 8))
def checksum(number):
"""Calculate the Verhoeff checksum over the provided number. The checksum
is returned as an int. Valid numbers should have a checksum of 0."""
# transform number list
number = tuple(int(n) for n in reversed(str(number)))
# calculate checksum
check = 0
for i, n in enumerate(number):
check = _multiplication_table[check][_permutation_table[i % 8][n]]
return check
def validate(number):
"""Check if the number provided passes the Verhoeff checksum."""
if not bool(number):
raise InvalidFormat()
try:
valid = checksum(number) == 0
except Exception: # noqa: B902
raise InvalidFormat()
if not valid:
raise InvalidChecksum()
return number
def is_valid(number):
"""Check if the number provided passes the Verhoeff checksum."""
try:
return bool(validate(number))
except ValidationError:
return False
def calc_check_digit(number):
"""Calculate the extra digit that should be appended to the number to
make it a valid number."""
return str(_multiplication_table[checksum(str(number) + '0')].index(0))