/***************************************************
*        Program to demonstrate the series         *
*                inversion function                *
* ------------------------------------------------ *
* 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:                                      *
*                                                  *
* What is the degree of the input polynomial: 2    *
*                                                  *
* What is the degree of the inverted polynomial: 6 *
*                                                  *
* Input the polynomial coefficients:               *
*                                                  *
*    A( 0) = ? 1                                   *
*    A( 1) = ? .1                                  *
*    A( 2) = ? .01                                 *
*                                                  *
* The inverted polynomial coefficients are:        *
*                                                  *
*    B( 0) =  1.000000                             *
*    B( 1) = -0.100000                             *
*    B( 2) =  0.000000                             *
*    B( 3) =  0.001000                             *
*    B( 4) = -0.000100                             *
*    B( 5) =  0.000000                             *
*    B( 6) =  0.000001                             *
*                                                  *
***************************************************/
#include <stdio.h>
#include <math.h>

double A[10], B[10];
int    i, m, n;


/*****************************************************
*       Reciprocal power series procedure            *
* Reference: Computational analysis by Henrici       *
* -------------------------------------------------- *
* The input series coefficients are A(i). The output *
* series coefficients are B(i). The degree of the    *
* input polynomial is n. The degree of the inverted  *
* polynomial is m. The routine takes care of norma-  *
* lization using l = A(0).                           *
*****************************************************/
void Reciprocal()  {
// Label used: e100
  double l;
  int i,j;
  l = A[0];
  for (i = 0; i < n+1; i++) {
    A[i] = A[i] / l; B[i] = 0.0;
  }
  // Clear arrays
  for (i = n + 1; i < m+1; i++) {
    A[i] = 0; B[i] = 0;
  }
  // Calculate the B(i) coefficients
  B[0] = 1;
  for (i = 1; i < m+1; i++)  {
    j = 1;
e100: B[i] = B[i] - A[j] * B[i - j];
    j++;
    if (j <= i) goto e100;
  }
  // Un-normalize the A(i) and B(i)
  for (i = 0; i < m+1; i++) {
    A[i] = A[i] * l;
    B[i] = B[i] / l;
  }
}


void main()  {
  printf("\n What is the degree of the input polynomial; "); scanf("%d",&n);
  printf("\n What is the degree of the inverted polynomial; "); scanf("%d",&m);
  printf("\n\n Input the polynomial coefficients;\n\n");

  for(i = 0; i < n+1; i++)  {
    printf("  A(%d) = ",i); scanf("%lf",&A[i]);
  }

  Reciprocal();

  printf("\n The inverted polynomial coefficients are;\n\n");
  
  for (i = 0; i < m+1; i++)
    printf("  B(%d) = %f\n",i,B[i]);
  printf("\n");
}

// End of file recipro.cpp