### 2.4.1 Numerical Operators

The basic numerical operators in Perl are like others that you might see
in other high level languages. In fact, Perl's numeric operators were
designed to mimic those in the C programming language.

First, consider this example:

use strict;
my $x = 5 * 2 + 3; # $x is 13
my $y = 2 * $x / 4; # $y is 6.5
my $z = (2 ** 6) ** 2; # $z is 4096
my $a = ($z - 96) * 2; # $a is 8000
my $b = $x % 5; # 3, 13 modulo 5

As you can see from this code, the operators work similar to rules of
algebra. When using the operators there are two rules that you have to
keep in mind--the rules of *precedence* and the rules of
*associativity*.

Precedence involves which operators will get evaluated first when the
expression is ambiguous. For example, consider the first line in our
example, which includes the expression, `5 * 2 + 3`

. Since the
multiplication operator (`*`

) has precedence over the addition
operator (`+`

), the multiplication operation occurs first. Thus,
the expression evaluates to `10 + 3`

temporarily, and finally
evaluates to `13`

. In other words, precedence dictates which
operation occurs first.

What happens when two operations have the same precedence? That is when
associativity comes into play. Associativity is either left or right
(7). For example, in the expression `2 * $x / 4`

we have two operators with equal precedence, `*`

and `/`

.
Perl needs to make a choice about the order in which they get carried
out. To do this, it uses the associativity. Since multiplication and
division are left associative, it works the expression from left to
right, first evaluating to `26 / 4`

(since `$x`

was
`13`

), and then finally evaluating to `6.5`

.

Briefly, for the sake of example, we will take a look at an operator
that is left associative, so we can contrast the difference with right
associativity. Notice when we used the exponentiation (`**`

)
operator in the example above, we had to write `(2 ** 6) ** 2`

, and
not `2 ** 6 ** 2`

.

What does `2 ** 6 ** 2`

evaluate to? Since `**`

(exponentiation) is **right associative**, first the `6 ** 2`

gets evaluated, yielding the expression `2 ** 36`

, which yields
`68719476736`

, which is definitely not `4096`

!

Here is a table of the operators we have talked about so far. They are
listed in order of precedence. Each line in the table is one order of
precedence. Naturally, operators on the same line have the same
precedence. The higher an operator is in the table, the higher its
precedence.

**Operator** | **Associativity** | **Description** |

** | right | exponentiation |

*, /, % | left | multiplication, division, modulus |

+, - | left | addition, subtraction |