Chapter 5: Functions I

Chapter Goals

• To be able to program functions and procedures
• To become familiar with the concept of parameter passing
• To recognize when to use value and reference passing
• To appreciate the importance of function comments

Functions as Black Boxes

• A function is a piece of code assigned to a name. We have used a number of functions that were provided by the C++ system library.
• sqrt(x) - computes the square root of a floating point number x
• getline(cin, s) - reads a line from the cin stream
• Functions can be thought of as black boxes - you don't need to know the internals of the code.
• Example:

  int main()
  { cout << "Enter a positive number: ";
    double x;
    cin >> x;
    x = sqrt(x); // sqrt is running
    cout << "The result is " << x << "\n";
    return 0;
  }

• The execution of main() is temporarily suspended while the function sqrt is running.
• The sqrt function becomes active and computes the output or return value - using some method that will yield the concrete result.
• The return value is transferred back to main, which resume the computation using the return value.
• Many functions have input values or parameters that are transferred or passed into the function.
• The x in y = sqrt(x);
• Both the x and the y in z = pow(x,y);
• Could be an expression as in sqrt(b * b - 4 * a * c);

• Many functions have output or return values. Each function returns a value of a particular type.

• Each function takes values of particular types.
• You cannot compute sqrt("Harry");
• You cannot assign string s = sqrt(5.5);

Writing Functions (Function Definition)

• Let us compute the value of a saving account with an initial balance of $1000 after 10 years with the interest rate of p percent (compound interest).
• To create a function, we must supply its return type, name, and a list of parameters (types and  names).

  double future_value(double p)

• For the duration of the function, the parameter is stored in a parameter variable (in this example, p).
• The body of the function is delimited by braces (just like main()):

  double future_value(double p)
  {
     . . . 
  }

• Code is included to perform the computation. The result is returned to the caller function.

  double future_value(double p)
  {  double b = 1000 * pow(1 + p / 100, 10);
     return b;
  }

Writing Functions

return_type function_name(parameter1, ..., parametern)
{
   statements
}

double abs(double x)
{  if (x >= 0) return x;
   else return -x;
}

Writing Functions (Hard Wired Values)

• The future_value function is flawed because the starting amount of the investment and the number of years are hard-wired.
• Hard-wiring prevents reuse of functions:
  • Computing the balance after 20 years.
  • Computing the balance with a different initial balance.
• We avoid hard-wiring values into functions by passing them in as additional parameters.
• Functions are more valuable when they are reusable.

double future_value(double initial_balance, double p, int n)
{  double b = initial_balance * pow(1 + p / 100, n);
   return b;
}

double balance = future_value(1000, rate, 10);

• futval.cpp
  

Function Comments

• We must comment every function, even if it seems silly.
• Comments are for human readers, not compilers.
• There is no universal standard for comment layout, but our textbook uses the javadoc style.
  • An @param entry explaining each parameter
  • An @return entry describing the return value
• Comments do not explain the implementation, but the idea.
• Writing comments first, before writing the function code, to test your understanding of what you need to program.

 /**
   Computes the value of an investment with compound interest.
   @param initial_balance - the initial value of the investment
   @param p the interest rate per period in percent
   @param n the number of periods the investment is held
   @return the balance after n periods
*/
double future_value(double initial_balance, double p, int n)
{  double b = initial_balance * pow(1 + p / 100, n);
   return b;
}

Return Values

• When the return statement is processed, the function exits immediately. We put the exceptional cases at the beginning.

  double future_value(double initial_balance, double p, int n)
  {  if (n < 0) return 0;
     if (p < 0) return 0;
     double b = initial_balance * pow(1 + p / 100, n);
     return b;
  }

• It is important that every branch of a function return a value.

  double future_value(double initial_balance, double p, int n)
  {  if (p >= 0) 
        return initial_balance * pow(1 + p / 100, n);
     /* Error */
  }

• The last statement of every function ought to be a return statement.
• Functions that returns a truth value is called a predicate.
  
• The function approx_equal (x, y) tests whether two floating point numbers x and y are approximately equal (approximation relative error).

  bool approx_equal(double x, double y)
  {  const double EPSILON = 1E-14;
     if (x == 0) return fabs(y) <= EPSILON;
     if (y == 0) return fabs(x) <= EPSILON;
     return fabs(x - y) / max(fabs(x), fabs(y)) <= EPSILON;
  }

 return expression;

 return pow(1 + p / 100, n);

Return Values (approx.cpp)

Parameters

• When a function starts, its parameter variables are initialized with the expressions in the function call.

  b = future_value(total / 2, rate, year2 - year1);

• [Picture]
  
• It is entirely legal to modify the values of the parameter variables later.

  double future_value(double initial_balance, double p, int n)
  {  p = 1 + p / 100;
     double b = initial_balance * pow(p, n);
     return b;
  }

• Many programmers consider this practice bad style.

Side Effects

• An externally observable effect of a function is called a side effect.
  • Displaying characters on the screen (including error messages).
  • Updating variables outside the functions.
  • Terminating the program.
• A function should leave no trace of its existence except for returning a value.
• Functions that print values become worthless in certain situations.
  • Graphics programs that have no output streams.
  • Programs where the user's language is not English.
  • Programs that don't want to print the value!
• Ideally, a function computes a single value and has no other side effect.

Procedures

• A function without a return value is called a procedure.

  print_time(now);

• The missing return value is indicated by the keyword void.

  void print_time(Time t)
  {  cout << t.get_hours() << ":";
     if (t.get_minutes() < 10) cout << "0";
     cout << t.get_minutes() << ":";
     if (t.get_seconds() < 10) cout << "0";
     cout << t.get_seconds();
  }

• Since a procedure does not have a return value, it must have a side effect.
• Ideally, a procedure has only one side effect. Commonly, procedures return a status value.
  

Procedures (printime.cpp)

Reference Parameters

• The parameter variables we have looked at so far are called value parameters.
• Value parameters are separate variables from the ones in main() (or another calling function).
• Modification of value parameters does not affect the original value.
• A reference parameter does not create a new variable, but refer to an existing variable.
• Any change in a reference parameter is actually a change in the variable to which it refers.
• Reference parameters are indicated using an & between the parameter's type and name.

  void raise_salary(Employee& e, double by)
  {  double new_salary = e.get_salary() * ( 1 + by / 100);
     e.set_salary(new_salary);
  }

 type_name& parameter_name

 Employee& e
 int& result

Reference Parameters (raisesal.cpp)

 const type_name& parameter_name

 const Employee& e

• Reference parameters are more efficient than value parameters because they do not make copies of the parameters.
• Passing variables by constant reference improves performance, but prevents the function from changing the value of the parameter.
• Objects make good constant reference parameters because they tend to have several attributes that need to be copied. Passing numbers by constant reference is generally not worth the effort.