How to calculate Running Multiplication

Question

I have two tables

WAC table

ID  wac_inc             item
--  -----------------   ----
1   2.310000000000000   A
2   1.100000000000000   A
3   2.130000000000000   A
4   1.340000000000000   A

Baseline Table

item    baseline
----    ------------------
A       10.000000000000000

Expected Result

ID  wac_inc             item    Running_Mul   
--  -----------------   ----    -----------
1   2.310000000000000   A       10.231     --  10 * (1+(2.310000000000000/100))
2   1.100000000000000   A       10.343541  --  10.231 * (1+(1.100000000000000/100))
3   2.130000000000000   A       10.563858  --  10.343541 * (1+(2.130000000000000/100))
4   1.340000000000000   A       10.705413  --  10.563858 * (1+(1.340000000000000/100))

Formula to find running_mul is

Baseline * (1 + (wac_inc/100))

SQLFIDDLE

here for every row previous row Running_Mul value is the baseline and for the first row baseline will be coming from baseline table.

Hope i made it clear. AFAIK we can do this using CURSOR but i want to avoid RBAR as much as possible. Can anyone suggest me the better way of doing it.

Answer 1

Try:

DECLARE @t TABLE
    (
      ID INT ,
      wac DECIMAL(30, 10) ,
      item CHAR(1)
    )
DECLARE @b TABLE
    (
      item CHAR(1) ,
      baseline DECIMAL(30, 10)
    )

INSERT  INTO @t
VALUES  ( 1, 2.31, 'A' ),
        ( 2, 1.10, 'A' ),
        ( 3, 2.13, 'A' ),
        ( 4, 1.34, 'A' )


INSERT  INTO @b
VALUES  ( 'A', 10 );


WITH    ordercte
          AS ( SELECT   * ,
                        ROW_NUMBER() OVER ( PARTITION BY item ORDER BY ID ) AS rn
               FROM     @t
             ),
        rec
          AS ( SELECT   t.item ,
                        t.ID ,
                        t.wac ,
                        t.rn ,
                        b.baseline * ( 1 + ( t.wac / 100 ) ) AS m
               FROM     ordercte t
                        JOIN @b b ON b.item = t.item
               WHERE    t.rn = 1
               UNION ALL
               SELECT   t.item ,
                        t.ID ,
                        t.wac ,
                        t.rn ,
                        c.m * ( 1 + ( t.wac / 100 ) )
               FROM     ordercte t
                        JOIN rec c ON t.item = c.item
                                      AND t.rn = c.rn + 1
             )
    SELECT  id ,
            wac ,
            item ,
            m
    FROM    rec

Output:

id  wac             item    m
1   2.3100000000    A       10.231000
2   1.1000000000    A       10.343541
3   2.1300000000    A       10.563858
4   1.3400000000    A       10.705414

EDIT1

I was trying to implement LOG EXP trick but could not manage unless @usr lead me to solution. So all credits to user @usr:

WITH    ordercte
          AS ( SELECT   t.ID ,
                        t.wac ,
                        t.item ,
                        b.baseline ,
                        ROW_NUMBER() OVER ( PARTITION BY t.item ORDER BY ID ) AS rn
               FROM     @t t
                        JOIN @b b ON b.item = t.item
             )
    SELECT  baseline
            * EXP(SUM(LOG(( 1 + ( wac / 100 ) ))) OVER ( PARTITION BY item ORDER BY rn )) AS m
    FROM    ordercte

Or just:

SELECT  t.ID, t.wac, t.item, baseline
        * EXP(SUM(LOG(( 1 + ( wac / 100 ) ))) OVER ( PARTITION BY t.item ORDER BY t.ID )) AS m
FROM    @t t
        JOIN @b b ON b.item = t.item  

if ID is the field you order by.

Output:

ID  wac             item    m
1   2.3100000000    A       10.231
2   1.1000000000    A       10.343541
3   2.1300000000    A       10.5638584233
4   1.3400000000    A       10.7054141261722

EDIT2

For SQL 2008 use:

WITH    cte
          AS ( SELECT   t.ID ,
                        t.wac ,
                        t.item ,
                        baseline ,
                        ( SELECT    SUM(LOG(( 1 + ( wac / 100 ) )))
                          FROM      @t it
                          WHERE     it.item = t.item AND it.ID <= t.ID
                        ) AS e
               FROM     @t t
                        JOIN @b b ON b.item = t.item
             )
    SELECT  ID, wac, item, baseline * EXP(e) AS m
    FROM    cte

EDIT3

Here is complete solution for SQL Server 2008 with dialing with NULLs and negative values:

WITH    cte
          AS ( SELECT   t.ID ,
                        t.wac ,
                        t.item ,
                        b.baseline , 
                        ca.e,
                        ca.n,
                        ca.m
               FROM     @t t
               JOIN @b b ON b.item = t.item
               CROSS APPLY(SELECT   SUM(LOG(ABS(NULLIF( 1 +  wac / 100 , 0)))) as e,
                                    SUM(SIGN(CASE WHEN 1 +  wac / 100 < 0 THEN 1 ELSE 0 END)) AS n,
                                    MIN(ABS(1 +  wac / 100)) AS m
                          FROM      @t it
                          WHERE     it.item = t.item AND it.ID <= t.ID
                          ) ca
             )
    SELECT  ID, wac, item, baseline *
                        CASE
                            WHEN m = 0 THEN 0
                            WHEN n % 2 = 1 THEN -1 * EXP(e)
                            ELSE EXP(e) 
                        END as Result
    FROM    cte

Answer 2

You can transform a series of multiplications into a series of additions with the following math trick:

exp(log(a) + log(b)) = a * b

So MUL(a) is EXP(SUM(LOG(a))).

SELECT SUM(val) AS [Sum], EXP(SUM(LOG(val))) AS Product
FROM (VALUES 
    (1), (2), (3), (4)
) x(val)

This emits sum = 10, product = 24.

Potential problems are rounding errors and zero factors.

You can now use one of the usual ways to achieve a running aggregate such as windowing functions. That's a solved problem.