C++ Horner's Rule - Recursive Array Implementation

Question

I've implemented the Horner's Method using arrays as follows.

double hornerRule( const double x, const double a[], const int n ) {
    double ans = *a;
    if ( n > 0 ) { ans += x * hornerFunction( x, ++a, n - 1 ); }
    return ans;
}

I'm a bit new to the pointer arithmetic and have a few questions:

1. Did I commit any sins? Is there a better way to do it?
2. An analogous implementation uses std::vector and avoids passing the array size n . What are the pros/cons of these two implementations?

Answer 1

With a new C++ compiler the modern way would be to have a std::span or gsl::span parameter. It contains the pointer and the length, sub-arrays can be built from it easily.

Depending on n, it could improve the performance, if you change n to a template parameter. Then the recursion could be unrolled without problems and the compiler could do its optimization magic.

You could do the unrolling by manuelly convertig to a loop, too.

It all depends on your aims. Should the function just work correctly. Or is it performance-critical.