Question

what is this syntax for double x[]?

Is it a C way to declare an array?

If I have a function like

void evaluate(double x[], double *f)
{
   // evaluate
}

Can I pass a parameter x with any length?

Answer 1

A parameter of array type behaves exactly like it is a pointer. You can not truly pass an array as a function argument. However, this syntax gives the illusion that you can for the sake of readability. So your function is equivalent to:

void evaluate(double *x, double *f)
{
  // evaluate
}

From §8.3.5/5 of ISO/IEC 14882:2011:

After determining the type of each parameter, any parameter of type “array of T” or “function returning T” is adjusted to be “pointer to T” or “pointer to function returning T,” respectively.

An expression that denotes an array will decay to a pointer to its first element, so you can still do this:

void evaluate(double x[]);
int array[] = {1, 2, 3, 4, 5};
evaluate(array); // The array decays to a pointer to its first element

From §4.2:

An lvalue or rvalue of type “array of N T” or “array of unknown bound of T” can be converted to a prvalue of type “pointer to T”. The result is a pointer to the first element of the array.

So yes, you can indeed pass an array of any length. In reality, you are just passing a pointer to the first element. You will, however, need to pass the length of the array as well, if you need it.