## Chapter 5. Number Crunching

A little arithmetic can go a long way in SQL. The language includes the math functions that you would expect to find in any computer language, plus a few that are peculiar to databases. It includes functions such as `ISNULL`, `COALESCE`, and `NULLIF`, which help to deal with `NULL`s. It also includes the aggregating functions such as `COUNT`, `SUM`, `MAX`, `MIN`, and `AVG` that are used in `GROUP` `BY` queries.

## Multiply Across a Result Set

With certain calculations, such as compound interest, you need to multiply a set of values. How come there’s no PRODUCT aggregate function that is to multiplication as SUM is to addition?

SQL has no aggregate function for multiplication, but you can use logarithms to achieve the desired result. When you add the logarithms of a list of numbers you get the same result you would get if you had taken the logarithm of their product:

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

The inverse of the logarithm is the exponent function:

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

So, to multiply the values `3`, `4`, and `5` without using multiplication, you could do the following:

```mysql> `select exp( ln(3)+ln(4)+ln(5) );`
+------------------------+
| exp(ln(3)+ln(4)+ln(5)) |
+------------------------+
|                     60 |
+------------------------+```

You can also use this technique to achieve the same effect as a `PRODUCT()` aggregate function. Suppose you have invested \$100 in a savings account that has produced the interest rates shown in Table 5-1.

Table 5-1. Interest rates by year
 yr rate 2002 ...

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