/************************************************************************
*           EVALUATE A COMPLEX POLYNOMIAL BY HORNER'S METHOD            *
* --------------------------------------------------------------------- *
* SAMPLE RUN:                                                           *
*                                                                       *
*  EVALUATE A CPMPLEX POLYNOMIAL BY HORNER'S METHOD                     *
*                                                                       *
*  Example: P(Z) = (1+i) Z^4 + (2-i) Z^3 +(3+0.5i) Z^2 + (4-2i) Z       *
*                + (5-0.75i)                                            *
*                                                                       *
*  For Z = (1.500000, 2.000000)                                         *
*                                                                       *
*  P(Z) = (-28.937500, -6.937500)                                       *
*                                                                       *
*                                                                       *
*                                C++ Release 1.0 By J-P Moreau, Paris   *
*                                         (www.jpmoreau.fr)             *
************************************************************************/  
#include <stdio.h>
#include <math.h>

#define  NMAX  25


  //complex number
  typedef  struct {
    double x,y;  //algebraic form
  } COMPLEX; 

  double AR[NMAX], AI[NMAX], RR[NMAX], RI[NMAX];
  COMPLEX Z;
  double Y0R, Y0I;
  int N;

// multiply two complex numbers}
  void ZMult(COMPLEX z1,COMPLEX z2, COMPLEX *z) {
    z->x=(z1.x*z2.x)-(z1.y*z2.y);
    z->y=(z1.x*z2.y)+(z1.y*z2.x);
  }

  void CHorner(double *AR, double *AI, int N, COMPLEX X0, double *YR, double *YI) {
    int i; COMPLEX tmp,tmp0; 
    *YR = AR[N]; *YI = AI[N];
    for (i=N-1; i>=0; i--) {
      tmp0.x=*YR; tmp0.y=*YI; 
      ZMult(tmp0,X0,&tmp);
      *YR = tmp.x + AR[i];
      *YI = tmp.y + AI[i];
    }
  }


void main() {

  N = 4;      // ORDER OF POLYNOMIAL

// define complex coefficients
  AR[4] = 1.0; AI[4] =  1.0;    // power 4
  AR[3] = 2.0; AI[3] = -1.0;    // power 3
  AR[2] = 3.0; AI[2] =  0.5;    // power 2
  AR[1] = 4.0; AI[1] = -2.0;    // power 1
  AR[0] = 5.0; AI[0] = -0.75;   // power 0

  Z.x = 1.5;   // complex argument
  Z.y = 2.0;

  printf("\n  EVALUATE A COMPLEX POLYNOMIAL BY HORNER'S METHOD\n\n");
  
  CHorner(AR, AI, N, Z, &Y0R, &Y0I);

  printf("  For Z = (%f, %f)\n\n", Z.x, Z.y);
  printf("  P(Z) = (%f, %f)\n\n", Y0R, Y0I);

}

// end of file chorner.cpp