Re: Random-looking primary keys in the range 100000..999999

[Kynn Jones <kynnjo@xxxxxxxxx>]

Thanks to Gavin and Martijn for their suggestions.  They're both simple good-ol' LCGs, and both avoid the need to check for collisions.

I ultimately went with a multiplicative LCG, like Martijn's, mostly because I understand better how it avoids collisions, so it was easier for me to tweak it in various ways.

In particular, I changed the prime number from 899981 to the very lucky prime 900001.  This happens to work *perfectly*, because the range of such a generator is p-1, not p.  (BTW, Martijn's choice of the "random" 2345 for the multiplier was a somewhat lucky one, since such generators are not full for arbitrary multipliers; for example, the one with modulus 899981 is not full for a multiplier of 3456, say.)

I also followed Martijn's pointer regarding the 3-argument form of python's pow function, and implemented a 3-argument pow for PL/PgSQL.  I include all the code below, including a snippet borrowed from Gavin's post, and modified here and there.  (I'm not very experienced with PL/PgSQL, so please feel free to point out ways in which my PL/PgSQL code can be improved.)

First the functions:

    CREATE OR REPLACE FUNCTION pow_mod(bigx bigint, n bigint, m bigint) returns bigint AS $$

    DECLARE

    x  bigint;

    xx bigint;

    BEGIN

      IF n = 0 THEN RETURN 1; END IF;

      x := bigx % m;

      xx := (x * x) % m;

      IF n % 2 = 0 THEN

        RETURN pow_mod(xx, n/2, m);

      ELSE

        RETURN (x * pow_mod(xx, (n-1)/2, m)) % m;

      END IF;

    END;

    $$ LANGUAGE plpgsql strict immutable;

    -- "mcg" = "multiplicative congruential generator"

    CREATE OR REPLACE FUNCTION mcg_900001(i bigint) returns int AS $$

    BEGIN

      -- CHECK (0 < i AND i < 900001)                                                                                                                                                                             

      RETURN 99999 + pow_mod(<INSERT YOUR MULTIPLIER HERE>, i, 900001);

    END;

    $$ LANGUAGE plpgsql strict immutable;

And here's a small demo:

    DROP TABLE IF EXISTS rtab;

    DROP SEQUENCE IF EXISTS rseq;

    CREATE SEQUENCE rseq;

    CREATE TABLE rtab

    (

        id       int PRIMARY KEY DEFAULT mcg_900001(nextval('rseq')),

        payload  int NOT NULL

    );

    \timing on \\ INSERT INTO rtab (payload) VALUES (generate_series(1, 900000)); \timing off

    -- Timing is on.

    -- INSERT 0 900000

    -- Time: 201450.781 ms

    -- Timing is off.

    SELECT * FROM rtab WHERE 449990 < payload AND payload < 450011;

    --    id   | payload

    -- --------+---------

    --  539815 |  449991

    --  901731 |  449992

    --  878336 |  449993

    --  564275 |  449994

    --  863664 |  449995

    --  720159 |  449996

    --  987833 |  449997

    --  999471 |  449998

    --  999977 |  449999

    --  999999 |  450000

    --  921739 |  450001

    --  722684 |  450002

    --  596638 |  450003

    --  121592 |  450004

    --  687895 |  450005

    --  477734 |  450006

    --  585988 |  450007

    --  942869 |  450008

    --  175776 |  450009

    --  377207 |  450010

    -- (20 rows)

kj

On Sat, Jul 5, 2014 at 4:35 AM, Martijn van Oosterhout <kleptog@xxxxxxxxx> wrote:

On Fri, Jul 04, 2014 at 09:24:31AM -0400, Kynn Jones wrote:
> I'm looking for a way to implement pseudorandom primary keys in the range
> 100000..999999.
>
> The randomization scheme does not need to be cryptographically strong.  As
> long as it is not easy to figure out in a few minutes it's good enough.

Well, a trick that produces a not too easy to guess sequence is:

X(n) = p^n mod q

where q is prime. Pick the largest prime that will fit, in this case
899981 (I beleive) and some random p, say 2345.

Then 100000 + (2345^n) mod 899981

should be a sequence fitting your purpose. Unfortunatly, the pow()
function in Postgres can't be used here (too slow and it overflows),
but python has a helpful function:

In [113]: len( set( pow(2345, n, 899981) for n in range(899981)  ) )
Out[113]: 899980

You could probably write an equivalent function in Postgres if
necessary.

Hope this helps,
--
Martijn van Oosterhout   <kleptog@xxxxxxxxx>   http://svana.org/kleptog/
> He who writes carelessly confesses thereby at the very outset that he does
> not attach much importance to his own thoughts.
   -- Arthur Schopenhauer

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