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

On Tue, May 12, 2009 at 02:54:29PM +0800, Craig Ringer wrote:
> 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.

This looks like a great candidate for inclusion in the Snippets page
<http://wiki.postgresql.org/wiki/Snippets> page, or possibly even the
docs for SQL functions :)

Cheers,
David.
>
> 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.';
>
>
>
> --
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--
David Fetter <david(at)fetter(dot)org> http://fetter.org/
Phone: +1 415 235 3778 AIM: dfetter666 Yahoo!: dfetter
Skype: davidfetter XMPP: david(dot)fetter(at)gmail(dot)com

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