I am trying to perform cumulative multiplication. I am trying two methods to do this
sample data:
DECLARE @TEST TABLE
(
PAR_COLUMN INT,
PERIOD INT,
VALUE NUMERIC(22, 6)
)
INSERT INTO @TEST VALUES
(1,601,10 ),
(1,602,20 ),
(1,603,30 ),
(1,604,40 ),
(1,605,50 ),
(1,606,60 ),
(2,601,100),
(2,602,200),
(2,603,300),
(2,604,400),
(2,605,500),
(2,606,600)
Note: The data in value
column will never be integer and values will have decimal part. To show approximation problem I have kept example values as integers.
Method 1: EXP + LOG + SUM() Over(Order by)
In this method am using EXP + LOG + SUM() Over(Order by)
technique to find cumulative multiplication. In this method values are not accurate; there is some rounding and approximation issue in the result.
SELECT *,
Exp(Sum(Log(Abs(NULLIF(VALUE, 0))))
OVER(
PARTITION BY PAR_COLUMN
ORDER BY PERIOD)) AS CUM_MUL
FROM @TEST;
Result:
PAR_COLUMN PERIOD VALUE CUM_MUL
---------- ------ --------- ----------------
1 601 10.000000 10
1 602 20.000000 200 -- 10 * 20 = 200(correct)
1 603 30.000000 6000.00000000001 -- 200 * 30 = 6000.000000000 (not 6000.00000000001) incorrect
1 604 40.000000 240000
1 605 50.000000 12000000
1 606 60.000000 720000000.000001 -- 12000000 * 60 = 720000000.000000 (not 720000000.000001) incorrect
2 601 100.000000 100
2 602 200.000000 20000
2 603 300.000000 5999999.99999999 -- 20000.000000 *300.000000 = 6000000.000000 (not 5999999.99999999) incorrect
2 604 400.000000 2399999999.99999
2 605 500.000000 1199999999999.99
2 606 600.000000 719999999999998
Method 2: Tradictional Multiplication (Recursive CTE)
This method works perfectly without any rounding or approximation problem.
;WITH CTE
AS (SELECT TOP 1 WITH TIES PAR_COLUMN,
PERIOD,
VALUE,
CUM_MUL = VALUE
FROM @TEST
ORDER BY PERIOD
UNION ALL
SELECT T.PAR_COLUMN,
T.PERIOD,
T.VALUE,
Cast(T.VALUE * C.CUM_MUL AS NUMERIC(22, 6))
FROM CTE C
INNER JOIN @TEST T
ON C.PAR_COLUMN = T.PAR_COLUMN
AND T.PERIOD = C.PERIOD + 1)
SELECT *
FROM CTE
ORDER BY PAR_COLUMN,PERIOD
Result
PAR_COLUMN PERIOD VALUE CUM_MUL
---------- ------ --------- ----------------
1 601 10.000000 10.000000
1 602 20.000000 200.000000
1 603 30.000000 6000.000000
1 604 40.000000 240000.000000
1 605 50.000000 12000000.000000
1 606 60.000000 720000000.000000
2 601 100.000000 100.000000
2 602 200.000000 20000.000000
2 603 300.000000 6000000.000000
2 604 400.000000 2400000000.000000
2 605 500.000000 1200000000000.000000
2 606 600.000000 720000000000000.000000
Can anyone tell me why in method 1 values are not accurate and how to fix it? I tried by changing the data types to Float
and by increasing the scale
in numeric
but no use.
I really want to use method 1 which is much faster than method 2.
Edit: Now I know the reason for approximation. Can anyone find a fix for this problem?
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