CREATE OR REPLACE FUNCTION @extschema@.luhn_verify(int8)
RETURNS boolean
AS $$
--
-- >>> SELECT @extschema@.luhn_verify(NULL) IS NULL
-- true
-- >>> SELECT @extschema@.luhn_verify(18)
-- true
-- >>> SELECT @extschema@.luhn_verify(50)
-- false

-- 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, floor(log( $1 ))::integer) AS n
) AS doubled_digits;

$$ LANGUAGE SQL
IMMUTABLE
STRICT;

COMMENT ON FUNCTION @extschema@.luhn_verify(int8)
IS '
  Return true if 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 @extschema@.luhn_generate_checkdigit(int8)
RETURNS int8
AS $$
--
-- >>> SELECT @extschema@.luhn_generate_checkdigit(NULL) IS NULL
-- true
-- >>> SELECT @extschema@.luhn_generate_checkdigit(1)
-- 8
-- >>> SELECT @extschema@.luhn_generate_checkdigit(1354646574456456546)
-- 1
--
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 pg_catalog.generate_series(0, floor(log( $1 ))::integer) AS n
) AS doubled_digits;

$$ LANGUAGE SQL
IMMUTABLE
STRICT;

COMMENT ON FUNCTION @extschema@.luhn_generate_checkdigit(int8)
IS 'For the input
value, generate a check digit according to Luhn''s algorithm';


CREATE OR REPLACE FUNCTION @extschema@.luhn_generate(int8)
RETURNS int8
AS $$
--
-- >>> SELECT @extschema@.luhn_generate(NULL) IS NULL
-- true
-- >>> SELECT @extschema@.luhn_generate(8)
-- 83
-- >>> SELECT @extschema@.luhn_generate(9999999999)
-- 99999999990
--
  SELECT 10 * $1 + @extschema@.luhn_generate_checkdigit($1);
$$ LANGUAGE SQL
IMMUTABLE
STRICT;

COMMENT ON FUNCTION @extschema@.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 @extschema@.luhn_strip(int8)
RETURNS int8
AS $$
--
-- >>> SELECT @extschema@.luhn_strip(NULL) IS NULL
-- true
-- >>> SELECT @extschema@.luhn_strip(0)
-- 0
-- >>> SELECT @extschema@.luhn_strip(12345)
-- 1234
--
  SELECT $1 / 10;
$$ LANGUAGE SQL
IMMUTABLE
STRICT;

COMMENT ON FUNCTION @extschema@.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.';