#include<math.h>
#include<stdio.h>


long double f(long double x) {
  long double sum=1-x, term=-x;
  int n=2;
  while(1+term != 1) {
    term *= -x/(n*n); sum += term;
    if( ((n%2==0)?sum:-sum) < 0 ) break;
    n++;
  }
  printf("nf(% .8Lf,[%2d])=% .8Lf (f(...,[%2d])=% .8Lf)", x,n,sum,n-1,sum-term);
  return sum;
}

int main(void) {
    const int dp = 5;
    long double eps=0.5*powl(10,-dp);
    int i=0;
    long double a=0, fa = f(a);
    long double b=2, fb = f(b);

    if(signbit(fb)==signbit(fa)) {
        printf("Warning, initial values do not have opposite sign!n");
    }

    do {
        long double c=(a*fb-b*fa)/(fb-fa), fc = f(c);

        if( signbit(fc)!=signbit(fa) ) {
            b=a; fb=fa;
            a=c; fa=fc;
        } else {
            a=c; fa=fc;
            fb *= 0.5;
        }
        i++;
    } while(fabsl(b-a)>eps);

    printf("ngoal reached after %d iterationsn",i);

    return 0;
}

f( 0.00000000,[ 2])= 1.00000000 (f(...,[ 1])= 1.00000000)
f( 2.00000000,[ 4])=-0.19444444 (f(...,[ 3])=-0.22222222)
f( 1.67441860,[ 4])=-0.09025591 (f(...,[ 3])=-0.10390280)
f( 1.53580328,[ 4])=-0.03709625 (f(...,[ 3])=-0.04675498)
f( 1.42972818,[ 3])= 0.00012083 (f(...,[ 2])= 0.08130249)
f( 1.43007256,[ 5])= 0.00680985 (f(...,[ 4])= 0.00722521)
f( 1.45846639,[ 4])=-0.00500612 (f(...,[ 3])=-0.01286142)
f( 1.44643666,[ 6])=-0.00027582 (f(...,[ 5])=-0.00029349)
f( 1.44521038,[ 5])= 0.00023604 (f(...,[ 4])= 0.00067386)
f( 1.44577586,[ 7])= 0.00000890 (f(...,[ 6])= 0.00000942)
f( 1.44581590,[ 6])=-0.00000787 (f(...,[ 5])=-0.00002549)
f( 1.44579710,[ 8])=-0.00000026 (f(...,[ 7])=-0.00000028)
f( 1.44579591,[ 7])= 0.00000024 (f(...,[ 6])= 0.00000076)
goal reached after 11 iterations