/***************************************************
*         Test program for Horner's rule           *
* ------------------------------------------------ *
* Reference: BASIC Scientific Subroutines, Vol. II *
* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
*                                                  *
*           C++ Version By J.-P. Moreau, Paris.    *
*                    (www.jpmoreau.fr)             *
* ------------------------------------------------ *
* SAMPLE RUN:                                      *
*                                                  *
* Input the five coefficients:                     *
*                                                  *
*    A( 0) =  1                                    *
*    A( 1) =  4                                    *
*    A( 2) =  6                                    *
*    A( 3) =  4                                    *
*    A( 4) =  1                                    *
*                                                  *
* What is the expansion point: 1                   *
*                                                  *
* The shifted coefficients are:                    *
*                                                  *
*    B( 0) =  16                                   *
*    B( 1) =  32                                   *
*    B( 2) =  24                                   *
*    B( 3) =   8                                   *
*    B( 4) =   1                                   *
*                                                  *
***************************************************/
#include <stdio.h>
#include <math.h>


double  C[5][6];
double  A[6], B[6];
double  x0;
int     i;


/**************************************************
*       Horner's shifting rule subroutine         *
* ----------------------------------------------- *             
* This routine takes a given quartic polynomial   *
* and converts it to a Taylor expansion.          *
* The input series coefficients are A(i), the     *
* expansion point is x0. The shifted coefficients *
* are returned in B(i).                           *
**************************************************/
void Horner_Shift()  {
  int i, j;
  for (j=0; j < 5; j++)
    C[j][0] = A[4-j];
  i=0;
  while (i<5) {
    C[0][i+1] = C[0][i];
    j = 1;
    while (j <= 4-i) {
      C[j][i+1] = x0*C[j-1][i+1]+C[j][i];
      j++;
    }
    i++;
  }
  for (i=0; i < 5; i++)  
    B[4-i] = C[i][4-i+1];
}


void main()  {

  // Init();
  printf("\n Input the five coefficients:\n\n");
  for (i=0; i < 5; i++) {
    printf("  A(%d) = ",i); scanf("%lf",&A[i]);
  }
  printf("\n What is the expansion point: "); scanf("%lf",&x0);

  Horner_Shift();

  printf("\n\n The shifted coefficients are:\n\n");
  for (i=0; i < 5; i++) 
    printf("  B(%d) = %6.0f\n",i,B[i]); 
  printf("\n");

}

//End of file horner.cpp