Luhn algorithm (credit card verify / check) implementation - FIX

The Luhn algorithm implemention I posted earlier (upthread) is
internally consistent and will verify checksums it created, but it is
actually not a correct implementation of the Luhn algorithm.

The earlier code added the doubled digits directly to the checksum,
rather than adding each digit of the the doubled digits.

Here's a corrected version that passes tests against other
implementations in other languages.

--
-- 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.
--
-- See: http://en.wikipedia.org/wiki/Luhn_algorithm
--

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,
-- we must add each digit individually rather than adding the
-- 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, ceil(log( $1 ))::integer - 1) 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, ceil(log($1))::integer - 1) 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.';