#include <iostream>

// The 'Vector_3d.hpp' file contains all the class and
// function declarations, as well as the class definition.
//
// The 'Vector_3d.cpp' file contains all the function
// definitions. You can treat all of these functions as if
// they were defined in this file.
//
// Together, these two files provide the Vector_3d class and
// the functions that operate on Vector_3d objects.
#include "Vector_3d.hpp"

// Function declaration (for this file only)
int main();

// Function definition (for this file only)

int main() {
  Vector_3d u{ 3.2, -4.5,  2.1 };
  Vector_3d v{ 2.5,  7.2, -9.1 };

  std::cout << "The original vectors:" << std::endl;
  std::cout << "  u = " << to_string( u ) << std::endl;
  std::cout << "  v = " << to_string( v ) << std::endl;

  // Test inner( u, v ).
  std::cout << std::endl
            << "The inner product of u and v:" << std::endl;
  std::cout << "  inner( u, v ) = "
            << inner( u, v ) << std::endl;

  // Test norm( u ).
  std::cout << std::endl
            << "The norm of u:" << std::endl;
  std::cout << "  norm( u ) = "
            << norm( u ) << std::endl;

  // Test add( u, v ).
  std::cout << std::endl
            << "Adding u and v:" << std::endl;
  std::cout << "  u + v = "
            << to_string( add( u, v ) ) << std::endl;

  // Test both versions of mul(...).
  std::cout << std::endl
            << "Multiplying u by 3:" << std::endl;
  std::cout << "  3u = "
            << to_string( mul( 3.0, u ) ) << std::endl;
  std::cout << "  u3 = "
            << to_string( mul( u, 3.0 ) ) << std::endl;

  // Test negate( u ).
  std::cout << std::endl
            << "The additive inverse of u:" << std::endl;
  std::cout << "  -u = "
            << to_string( negate( u ) ) << std::endl;

  // Test sub( u, v ).
  std::cout << std::endl
            << "Subtracting v from u:" << std::endl;
  std::cout << "  u - v = "
            << to_string( sub( u, v ) ) << std::endl;

  // Test div( u, 2.0 ).
  std::cout << std::endl
            << "Dividing u by 2:" << std::endl;
  std::cout << "  u/2 = "
            << to_string( div( u, 2.0 ) ) << std::endl;

  // Test proj( u, v ).
  std::cout << std::endl
            << "Projecting u onto v:" << std::endl;
  std::cout << "  proj_v(u) = "
            << to_string( proj( u, v ) ) << std::endl;

  // Test cross( u, v ).
  std::cout << std::endl
            << "The cross product of u and v:" << std::endl;
  std::cout << "  u x v = "
            << to_string( cross( u, v ) ) << std::endl;

  // Display Boolean values as 'true' and 'false' rather
  // than as the integers 1 and 0.
  std::cout << std::boolalpha;

  // Test equal( u, v ).
  std::cout << std::endl
            << "Testing vectors for equality:" << std::endl;
  std::cout << "  equal( u, v ) = "
            << equal( u, v ) << std::endl;
  std::cout << "  equal( u, u ) = "
            << equal( u, u ) << std::endl;

  // The calls to to_string( u ) and to_string( v ) above
  // have already demonstrated the to_string(...) function.

  //////////////////////////////////////////////////////////
  // The remaining functions modify their first argument. //
  //////////////////////////////////////////////////////////

  // Test normalize( w ).
  Vector_3d w{ u };

  std::cout << std::endl
            << "Normalizing a copy of u:" << std::endl;
  std::cout << "  before: w = "
            << to_string( w ) << std::endl;

  normalize( w );

  std::cout << "  after:  w = "
            << to_string( w ) << std::endl;
  std::cout << "  norm( w ) = "
            << norm( w ) << std::endl;

  // Test add_to( w, v ).
  w = u;

  std::cout << std::endl
            << "Adding v to a copy of u:" << std::endl;
  std::cout << "  before: w = "
            << to_string( w ) << std::endl;

  add_to( w, v );

  std::cout << "  after:  w = "
            << to_string( w ) << std::endl;

  // Test sub_from( w, v ).
  w = u;

  std::cout << std::endl
            << "Subtracting v from a copy of u:" << std::endl;
  std::cout << "  before: w = "
            << to_string( w ) << std::endl;

  sub_from( w, v );

  std::cout << "  after:  w = "
            << to_string( w ) << std::endl;

  // Test mul_by( w, 3.0 ).
  w = u;

  std::cout << std::endl
            << "Multiplying a copy of u by 3:" << std::endl;
  std::cout << "  before: w = "
            << to_string( w ) << std::endl;

  mul_by( w, 3.0 );

  std::cout << "  after:  w = "
            << to_string( w ) << std::endl;

  // Test div_by( w, 2.0 ).
  w = u;

  std::cout << std::endl
            << "Dividing a copy of u by 2:" << std::endl;
  std::cout << "  before: w = "
            << to_string( w ) << std::endl;

  div_by( w, 2.0 );

  std::cout << "  after:  w = "
            << to_string( w ) << std::endl;

  return 0;
}