double bisect2 ( double a, double b, double f ( double x ) )
//
//  BISECT2 is a revised version of BISECT1 which allows us to pass
//  the name of the function as an extra input.
//
//  This means the actual name of the function does not have to be "F".
//
//  Because we call FABS() the program needs the "#include <cmath>" statement.
//
{
  double c;
//
//  Make sure [A,B] is a change of sign interval.
//
  if ( 0 < f ( a ) * f ( b ) )
  {
    cerr << "\n";
    cerr << "BISECT2 - Fatal error!\n";
    cerr << "  F(A) = " << f(a) << "\n";
    cerr << "  F(B) = " << f(b) << "\n";
    cerr << "  [" << a << ", " << b << "] is not a change of sign interval.\n";
  }

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