include stdio include math include float double EPS double MAX_IT 1000

#include <stdio.h>
#include <math.h>
#include <float.h>
double EPS;
double MAX_IT=1000;
double K=10000000;

typedef struct inter{
  double a;
  double a_val;
  double b;    
  double b_val;    
  double len;
} interval;

double f_02(double x) {
return (cos(x)-exp(-((x*x)/2))+x-1);
}


double f_02_it(double x) {
return (-cos(x)+exp(-((x*x)/2))+1);
}


double f_09(double x){
  return x*x-log(1+x)-3;
}

double f_09_it(double x){
  return sqrt(log(1+x)+3);   
}


double f_10(double x){
  return 2*x*sin(x)-cos(x);
}

double f_10_it(double x){
  return asin(sqrt(1/(4*x*x+1)));
}



interval divide(interval i,double (*func)(double)){
  double c=(i.a+i.b)/2;
  double c_val=(*func)(c);
  if (c_val==0){
    i.a=i.b=c;
    i.a_val=i.b_val=c_val;
    i.len=0;
    return i;
  }
  
  if(c_val*i.a_val>0){
    i.a=c;
    i.a_val=c_val;
    i.len=fabs(i.b-i.a);
  }
  else if(c_val*i.b_val>0){
    i.b=c;
    i.b_val=c_val;
    i.len=fabs(i.b-i.a);
  }
  
  return i;
}



double dichotomy(double a, double b, double (*func)(double),int &it){ 
  double x;
  it=0;
  interval i,i_old;
  i.a=a;
  i.a_val=(*func)(a);
  i.b=b;
  i.b_val=(*func)(b);
  i.len=fabs(i.b-i.a);
  
  do{
    i_old=i;
    i= divide(i,func);
    it++;
  }while(i.len>EPS && fabs(i.len-i_old.len)>EPS && it<MAX_IT);
  
  if(i.len==0){
   return i.a;
  }
  else{
   x=(i.a+i.b)/2;      
  }
  return x;
}


double iteration(double a, double b, double (*func_it)(double), double (*func)(double), int &it){
  it=0; 
  double x=(a+b)/2;
  double x0=x;
  do{
    x0=x;
    x=(func_it)(x0);
    it++;
  }while(fabs(x-x0)>EPS && (func)(x)!=0 && it<MAX_IT);
  return x;
}

double derivation(double (*func)(double), double x){
  return (func(x+EPS)-func(x))/EPS;
}

double newton(double a, double b, double (*func)(double), int &it){
  double x=(a+b)/2;
  double x0=x;
  it=0;
  do{
    x0=x;
    x=x0 - (func)(x0)/derivation(func,x0);

    it++;
  }while(fabs(x-x0)>EPS && it<MAX_IT && func(x)!=0);
  return x;              
}




void print_methods(double a, double b, double (*func)(double),double (*func_it)(double),
 char *str, char *str_func, char *str_func_it){
  int it=0;    
  double x=0;
  printf ("=====================================================================\n               %s\n",str);
  printf ("   Function 1: %s\n",str_func);
  printf ("   Function 2: %s\n",str_func_it);     
  printf ("     Interval: [%f,%f]\n\n",a,b); 
  printf ("--------------+-----------------+----------------+-------------------\n");  
  printf ("  Method      |      Root       |     Value      |    Iterations\n");  
  printf ("--------------+-----------------+----------------+-------------------\n");  
  x=dichotomy(a,b,func,it);
  printf ("  Dichotomy   | % 1.12f | % e  |      %4i\n",x,(func)(x),it);
  printf ("--------------+-----------------+----------------+-------------------\n");   
  x=iteration(a,b,func_it, func, it);
  printf ("  Iteration   | % 1.12f | % e  |      %4i\n",x,(func)(x),it);
  printf ("--------------+-----------------+----------------+-------------------\n"); 
  x=newton(a,b,func,it);
  printf ("  Newton      | % 1.12f | % e  |      %4i\n",x,(func)(x),it);
  printf ("--------------+-----------------+----------------+-------------------\n"); 
  printf ("=====================================================================\n\n");
   
     
}

int main(){
  
  EPS=DBL_EPSILON*K;

  printf ("  DBL_EPSILON: %e\n",DBL_EPSILON);
  printf ("      Epsilon: %2.3f*DBL_EPSILON\n",K);
  
  
  print_methods(1,2,f_02,f_02_it,"Variant 2","","");
  print_methods(2,3,f_09,f_09_it,"Variant 9","x*x-log(1+x)-3","sqrt(log(1+x)+3)");
  
  print_methods(0.4,1,f_10,f_10_it,"Variant 10","2*x*sin(x)-cos(x)","asin(sqrt(1/(4*x*x+1)))");
scanf(" ");
}