extern crate roots;
use roots::Roots;
use roots::find_roots_cubic;
use roots::find_root_brent;
use roots::find_root_secant;

// Find the root of a complex function in the area determined by a simpler polynom
fn find_solution<F>(enormous_function: F, root_area_polynom:(f64,f64,f64,f64)) -> Option<f64>
  where F: Fn(f64) -> f64
{
  // de-structure polynom coefficients
  match root_area_polynom {
    (a3,a2,a1,a0) => {
      // Find root area by solving the polynom
      match find_roots_cubic(a3,a2,a1,a0) {
        // Try to find the root by one of iterative methods
        Roots::Three(roots) => {
          // Three roots found, normal case
          find_root_brent(roots[0],roots[2],enormous_function, &mut 1e-8f64).ok()
        },
        Roots::Two(roots) => {
          // Two roots found, High precision required
          find_root_brent(roots[0],roots[1],enormous_function,&mut 1e-15f64).ok()
        },
        Roots::One(roots) => {
          // One root found, Low precision is enough
          find_root_secant(roots[0]-1f64,roots[0]+1f64,enormous_function,&mut 1e-3f64).ok()
        },
        _ => None,
      }
    },
    _ => None,
  }
}