# Nondeterministic jumps¶

We can now describe a code pattern, called “nondeterministic jumps”,
that combines Conditional jumps
and Hints.
A nondeterministic jump is a jump instruction that may or may not be executed,
according to the **prover’s** decision (rather than according to a condition on values which
were computed before).
To do this, use the Cairo instruction:

```
jmp label if [ap] != 0, ap++;
```

The idea is to use an unused memory cell (`[ap]`

) to decide whether or not to jump.
Do not forget to increase `ap`

to make sure the following instructions will not use this memory
cell.

As with every nondeterministic instruction, a hint must be attached to let the prover know whether to jump or not. For example:

```
%{ memory[ap] = 1 if x > 10 else 0 %}
jmp label if [ap] != 0, ap++;
```

## Exercise¶

The following code tries to compute the expression \(\lfloor x / 2 \rfloor\) using the formula

(recall that since we’re working in a field,
the operation `/ 2`

is division by 2 in the field,
rather than integer division).

Can you explain what’s wrong with the following code?

```
func div2(x) {
%{ memory[ap] = ids.x % 2 %}
jmp odd if [ap] != 0, ap++;
even:
// Case x % 2 == 0.
[ap] = x / 2, ap++;
ret;
odd:
// Case x % 2 == 1.
[ap] = x - 1, ap++;
[ap] = [ap - 1] / 2, ap++;
ret;
}
```

In Integer division you will see how to implement this function using the range-check builtin.

## Hint

Consider the verifier point of view. Can you give an example of what a malicious prover
can do so that `div2`

will return the wrong value?

## Hint2

Try to change the hint to `%{ memory[ap] = 1 - (ids.x % 2) %}`

and see what happens when you
call div2(2). Do you get the expected result (1)?