SQL 服务器：避免舍入错误

Question

I need help with floating-point Maths in SQL Server. Simplified version of the problem is given below

DECLARE @TOTALCOST NUMERIC(18, 4) = 1.125;

WITH CTE AS (
    SELECT item='Item1', volume=3.636
    UNION
    SELECT item='Item2', volume=14.946
    UNION
    SELECT item='Item3', volume=26.05
)
SELECT
    item,
    volume,
    totVol = (SUM(volume) OVER (PARTITION BY NULL)),
    proportion =  (SUM(volume) OVER (PARTITION BY item)) / (SUM(volume) OVER (PARTITION BY NULL)),
    costAllocation = (SUM(volume) OVER (PARTITION BY item)) * @TOTALCOST / (SUM(volume) OVER (PARTITION BY NULL))
FROM CTE

ITEM    Volume  totVol  Proportion  costAllocation
==========================================
Item1   3.636   44.632  0.081466    0.091649
Item2   14.946  44.632  0.334871    0.376730
Item3   26.050  44.632  0.583661    0.656619

Basically proportion is ratio of item1 volume to total volume of three items, and then 1.125 is divided in that ratio. That is for item1 proportion = 3.636 / 44.632 cost allocation = 3.636 * 1.125 / 44.632

What I want is round proportion and costAllocation to only 3 decimal places, but they exactly add upto 1 and 1.125 respectively.

I have tried putting Round() function in various permutations but somehow, I am not able to exactly figure how to divide in proportion so that it exactly adds up to 1, and 1.125. I don't mind if there is an error in the last decimal place of one numbers. For example 1 can be divided equally in 3 parts = 0.333___ each, so even if we use regular round function to 3 places it will still show up as 0.333, and sum it 3 times will only be 0.999

So I am ok with reporting the proportion as 0.333, 0.333, and 0.334 so that it adds up to exactly 1.

Answer 1

What you are dealing with is not floating point mathematics but just lack of decimal precision due to rounding.

A solution I've implemented (mainly in reporting) is to do something like the below, where you calculate the difference due to rounding and add that to one row (usually the largest value to minimise the effect).

declare @TOTALCOST numeric(18, 4) = 1.125;

with CTE as (
    select item='Item1', volume=3.636
    union
    select item='Item2', volume=14.946
    union
    select item='Item3', volume=26.05
), cte2 as (
select
    item,
    volume,
    totVol = (Sum(volume) over ()),
    proportion =  Round((Sum(volume) over (partition by item)) / (Sum(volume) over ()),3),
    costAllocation = Round((Sum(volume) over (partition by item)) * @TOTALCOST / (Sum(volume) over ()),3),
    Row_Number() over(order by volume desc) rn
from CTE
)
select item, volume, totVol, proportion, 
    costAllocation + case when rn=1 then @TOTALCOST-Sum(costAllocation) over() else 0 end costAllocation
from cte2