Benefits of pure function

Today i was reading about pure function, got confused with its use:

A function is said to be pure if it returns same set of values for same set of inputs and does not have any observable side effects.

e.g. strlen() is a pure function while rand() is an impure one.

__attribute__ ((pure)) int fun(int i)
{
    return i*i;
}

int main()
{
    int i=10;
    printf("%d",fun(i));//outputs 100
    return 0;
}

http://ideone.com/33XJU

The above program behaves in the same way as in the absence of pure declaration.

What are the benefits of declaring a function as pure[if there is no change in output]?

pure lets the compiler know that it can make certain optimisations about the function: imagine a bit of code like

for (int i = 0; i < 1000; i++)
{
    printf("%d", fun(10));
}

With a pure function, the compiler can know that it needs to evaluate fun(10) once and once only, rather than 1000 times. For a complex function, that's a big win.

When you say a function is 'pure' you are guaranteeing that it has no externally visible side-effects (and as a comment says, if you lie, bad things can happen). Knowing that a function is 'pure' has benefits for the compiler, which can use this knowledge to do certain optimizations.

Here is what the GCC documentation says about the pure attribute:

pure

Many functions have no effects except the return value and their return value depends only on the parameters and/or global variables. Such a function can be subject to common subexpression elimination and loop optimization just as an arithmetic operator would be. These functions should be declared with the attribute pure. For example,

          int square (int) __attribute__ ((pure));

Philip's answer already shows how knowing a function is 'pure' can help with loop optimizations.

Here is one for common sub-expression elimination (given foo is pure):

a = foo (99) * x + y;
b = foo (99) * x + z;

Can become:

_tmp = foo (99) * x;
a = _tmp + y;
b = _tmp + z;