# Luhn algorithm

Luhn algorithm

Works with PostgreSQL

Any version

Written in

SQL

Depends on

Nothing

Luhn algorithm implementation by Craig Ringer in pure SQL (PostgreSQL function dialect, but should be easily adapted to other DBMSs). Note that this implementation is purely arithmetic; it avoids string manipulation entirely.

```CREATE OR REPLACE FUNCTION luhn_verify(int8) RETURNS boolean AS \$\$
-- Take the sum of the
-- doubled digits and the even-numbered undoubled digits, and see if
-- the sum is evenly divisible by zero.
SELECT
-- Doubled digits might in turn be two digits. In that case,
-- doubled digit value to the sum. Ie if the original digit was
-- `6' the doubled result was `12' and we must add `1+2' to the
-- sum rather than `12'.
MOD(SUM(doubled_digit / INT8 '10' + doubled_digit % INT8 '10'), 10) = 0
FROM
-- Double odd-numbered digits (counting left with
-- least significant as zero). If the doubled digits end up
-- having values
-- > 10 (ie they're two digits), add their digits together.
(SELECT
-- Extract digit `n' counting left from least significant
-- as zero
MOD( ( \$1::int8 / (10^n)::int8 ), 10::int8)
-- Double odd-numbered digits
* (MOD(n,2) + 1)
AS doubled_digit
FROM generate_series(0, floor(log( \$1 ))::integer) AS n
) AS doubled_digits;

\$\$ LANGUAGE 'SQL'
IMMUTABLE
STRICT;

COMMENT ON FUNCTION luhn_verify(int8) IS 'Return true iff the last digit of the
input is a correct check digit for the rest of the input according to Luhn''s
algorithm.';
```
```CREATE OR REPLACE FUNCTION luhn_generate_checkdigit(int8) RETURNS int8 AS \$\$
SELECT
-- Add the digits, doubling even-numbered digits (counting left
-- with least-significant as zero). Subtract the remainder of
-- dividing the sum by 10 from 10, and take the remainder
-- of dividing that by 10 in turn.
((INT8 '10' - SUM(doubled_digit / INT8 '10' + doubled_digit % INT8 '10') %
INT8 '10') % INT8 '10')::INT8
FROM (SELECT
-- Extract digit `n' counting left from least significant\
-- as zero
MOD( (\$1::int8 / (10^n)::int8), 10::int8 )
-- double even-numbered digits
* (2 - MOD(n,2))
AS doubled_digit
FROM generate_series(0, floor(log( \$1 ))::integer) AS n
) AS doubled_digits;

\$\$ LANGUAGE 'SQL'
IMMUTABLE
STRICT;

COMMENT ON FUNCTION luhn_generate_checkdigit(int8) IS 'For the input
value, generate a check digit according to Luhn''s algorithm';
```
```CREATE OR REPLACE FUNCTION luhn_generate(int8) RETURNS int8 AS \$\$
SELECT 10 * \$1 + luhn_generate_checkdigit(\$1);
\$\$ LANGUAGE 'SQL'
IMMUTABLE
STRICT;

COMMENT ON FUNCTION luhn_generate(int8) IS 'Append a check digit generated
according to Luhn''s algorithm to the input value. The input value must be no
greater than (maxbigint/10).';
```
```CREATE OR REPLACE FUNCTION luhn_strip(int8) RETURNS int8 AS \$\$
SELECT \$1 / 10;
\$\$ LANGUAGE 'SQL'
IMMUTABLE
STRICT;

COMMENT ON FUNCTION luhn_strip(int8) IS 'Strip the least significant digit from
the input value. Intended for use when stripping the check digit from a number
including a Luhn''s algorithm check digit.';
```