real_zeros_of_ the_polynomial_function.c

/*

    real_zeros_of_ the_polynomial_function.c

https://www.emathhelp.net/calculators/algebra-2/zeros-calculator/?f=x%5E4%2B0x%5E3-5x%5E2%2B0x%2B4%3D0&var=&sa=0&a=-inf&b=inf&sb=0&real=on
https://www.symbolab.com/solver/roots-calculator/roots%20x%5E%7B4%7D%2B0x%5E%7B3%7D-5x%5E%7B2%7D%2B0x%2B4
https://www.wolframalpha.com/widgets/view.jsp?id=b858339e64fa997454dd12f77cb1ece1


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

// print function
void print_function( int degree, double coefficient[])
{
    int i;

    printf("\n f(x) = ");
    for(i=degree;i>=0; i--)
    {
        if(coefficient[i]>=0)
            printf("+");

        if(i>0)
            printf("%.4f x^%d ", coefficient[i], i );
        else
            printf("%.4f ", coefficient[i]);
    }
    printf("\n\n");
}

// get value of function for x
double function(double x, double coefficient[], int degree)
{
    int i;
    double xd = 1.0, f = coefficient[0];

    for(i=1; i<=degree; i++)
    {
        xd = xd * x;
        f = f + coefficient[i] * xd;
    }
    return f;
}

int main(void)
{
    int i, degree=4, number_of_real_zeros=0;
    unsigned long long int iterations_by_step=0, iterations_by_epsilon=0;
    double f1, f2, x1, x2, low_lim=-1000.0, upp_lim=1000.0, step=1e-3 , epsilon=1e-10;
    double zeros[20];

// x^4-17x^3+91x^2-224x+245=0 , x = 3.42182383859132 , x = 9.76947662492925
//  double coefficient[] = {245.0 , -224.0 , 91.0 , -17.0 , 1.0 };

// x^4-16x^3+90x^2-224x+245=0 , x = 5.0 , x = 7.0
//  double coefficient[] = {245.0 , -224.0 , 90.0 , -16.0 , 1.0 };

// x^4+0x^3-5x^2+0x+4=0 , x = -2.0 , x = -1.0 , x = 1.0 , x = 2.0
    double coefficient[] = {4.0 , 0.0 , -5.0 , 0.0 , 1.0 };

    printf("\n Real zeros of function \n");
    print_function(degree,coefficient);                 // print function
    printf(" in interval [ %.4f , %.4f ] \n\n", low_lim, upp_lim );

    x2 = low_lim - epsilon;                             // initial value
    do                                                  // do while( x1<=upp_lim )
    {
        do                                              // do while( f1*f2>0 && x1<=upp_lim )
        {
            x1 = x2;                                    // next values
            x2 = x2 + step;
            f1 = function(x1, coefficient, degree);     // f(x1)
            f2 = function(x2, coefficient, degree);     // f(x2)
            iterations_by_step++;                       // count number of iterations_by_step by step
        } while( f1*f2>0 && x1<=upp_lim );  // until the function changes sign and until the end of the interval
        if ( f1*f2<=0 )                     // if the function has changed the sign between x1 and x2
        {                                   // then zero is between x1 and x2
            do                                          // do while( f1*f2>0 && x1<=upp_lim )
            {
                x1 = x1 + epsilon;                      // next values
                x2 = x1 + epsilon;
                f1 = function(x1, coefficient, degree); // f(x1)
                f2 = function(x2, coefficient, degree); // f(x2)
                iterations_by_epsilon++;                // count number of iterations_by_epsilon by epsilon
            } while( f1*f2>0 && x1<=upp_lim );  // until the function changes sign and until the end of the interval

            zeros[number_of_real_zeros] = x1;           // it is real zero
            number_of_real_zeros++;                     // count number of real zeros
        }
    } while( x1<=upp_lim );                             // until the end of the interval

    if( number_of_real_zeros > 0 )                      // if there are real zeros, print report
    {
        printf("\n step    = %.10f \n", step );         // print step
        printf("\n epsilon = %.10f \n", epsilon );      // print epsilon
        printf("\n iterations_by_step         = %llu \n", iterations_by_step );    // print number of iterations_by_step
        printf("\n iterations_by_epsilon      = %llu \n", iterations_by_epsilon ); // print number of iterations_by_epsilon
        printf("\n total number of iterations = %llu \n", iterations_by_step + iterations_by_epsilon);
        printf("\n number_of_real_zeros = %d \n\n", number_of_real_zeros );   // print number of zeros

        for(i=0;i<number_of_real_zeros; i++)            // print real zeros and values of function in zeros
            printf("\n x%d = %.9f \t f( %.9f ) = %.9f \n",
                    i+1, zeros[i], zeros[i], function(zeros[i], coefficient, degree) );
    }
    else                                                // if there are no real zeros
        printf("\n The function has no real zeros on the interval [ %.4f , %.4f ] \n\n", low_lim, upp_lim );

    return 0;
}