# include <cstdlib>
# include <iostream>
# include <cmath>

using namespace std;
//
//  We can declare BISECT1 and F1 here, and they will be usable by
//  any function within this file.
//
double bisect1 ( double a, double b );
double f1 ( double x );

int main ( )
//
//  BISECT1_F1 is a program which uses BISECT1 to solve for a solution
//  of F1(X) = 0.  
//
//  Note that we had to rename "F()" to "F1()" in BISECT1 in order for
//  this to work.
//
{
//
//  A and B are the "bracket" values we've chosen for our function.
//
  double a = -10.0, b = +10.0, c;

  c = bisect1 ( a, b );

  cout << "\n";
  cout << "BISECT1 returned solution estimate C = " << c << "\n";
  cout << "F1(C) = " << f1 ( c ) << "\n";

  return 0;
}
double bisect1 ( double a, double b )
//
//  BISECT1 is our simple bisection solver.
//
{
  double c;

  while ( true )
  {
//
//  C = midpoint.
//
    c = ( a + b ) / 2.0;
//
//  Is F(C) extremely close to 0?
//
    if ( fabs ( f1 ( c ) ) <= 0.000001 )
    {
      break;
    }
//
//  If F(C) is opposite in sign to F(A), C replaces B.
//
    if ( f1 ( c ) * f1 ( a ) < 0.0 )
    {
      b = c;
    }
    else
    {
      a = c;
    }
  }
  return c;
}
double f1 ( double x )
//
//  F1 is our "cosine" function.
//
{
  double value;

  value = cos ( x ) - x;

  return value;
}