//  File:  horner.pde
//
//  Demonstrate Horner's rule for evaluating a polynomial

void setup() {
  Serial.begin(9600);
}

// ----------------------------------------------------------------------------
void loop() {
  int   n=5;                                 //  n coefficients for degree n-1
  float a[5] = {1.0, 3.0, 2.1, 4.0, -1.7};   //  Coefficients of made-up polynomial
  float x, y;
  
  x = 5.0;
  y = horner(n,a,x);
  Serial.print(x,2);  Serial.print("  ");   Serial.println(y,2);
  
}

// ----------------------------------------------------------------------------
//  y = horner(n,c,x) evaluates a polynomial y = f(x) at x.  The polynomial has
//                    degree n-1.  The coefficients of the polynomial are stored
//                    in the 1-D array c, which has n elements.
//
//  NOTE:  The polynomial coefficients are multipliers of monomial terms of
//         decreasing order.  In other words, the polynomial is assumed to be
//         written in the form
//
//            y = c_1*x^n + c_2*x^(n-1) + ... + c_(n-2)*x + c_(n-1)
//
//  Also note that if there are n coefficients, the polynomial is of degree n-1
//  and the largest index in c is n-1

float horner(int n, float *c, float x) {
  
  float f;
  
  f = c[0];
  for ( int i=1; i<n; i++ ) {
    f = f*x + c[i];
  }
  return(f);
}