## Archive for September 21st, 2009

## Rounding numbers preserving their sum

Comments enabled. I *really* need your comment

From **Stack Overflow**:

I'm looking for a way to round every value contained in a column without changing the total sum (which is known to be an integer, or very close to an integer because of float number precision).

Rounding every value to the nearest integer won't work (ex :

(1.5, 1.5)will be rounded to either(1, 1)or(2, 2))It's quite easy to do this using several requests (e. g. storing the original sum, rounding, computing the new sum, and updating as many rows as needed to go back to the original sum), but this is not a very elegant solution.

Is there a way to do this using a single

SQLrequest?I'm using

SQL Server 2008, so solutions taking advantage of this specific vendor are welcome.I'm looking for a request minimizing the differences between the old values and the new ones. In other words, a value should never be rounded up if a greater value has been rounded down, and vice-versa

We have two restrictions here:

- The sum of the rounded numbers should be equal to that of the unrounded ones.
- When rounding, no number with a greater fractional part can be rounded down if there is a number with a smaller fractional part that had been rounded up.

We cannot round **(1.4, 1.4, 1.2)** to **(1, 1, 2)**, since **1.4** would be rounded down while **1.2** (with smaller fractional part) is rounded up. However, we can round them to **(1, 2, 1)** or **(1, 2, 1)**, since nothing prevents us from rounding numbers with *equal* fractional part differently.

Given this, we should build a query that would take a set of numbers and round them taking these two restrictions into account.

It is easily seen than to satisfy the second restriction a certain rounding threshold should exist: all numbers with the fractional part greater than this threshold are rounded up, those with the fractional part smaller than then threshold are rounded down, those with the fractional part equal to the threshold can be rounded both ways.

However, calculating this threshold is, first, quite a difficult task and, second, we still don't know what to do with the numbers having the fractional part equal to the threshold.

Instead, we use another approach.

Let's create a sample tables and show this approach: