Chapter 6 Functions

Functions

All programs are a series of functions, one of which must be called main.
Function form.

All functions have the following form:
```
<type> function name(<list of parameters>)
{
 <body of function>
}
```
< > indicate that this is optional. If the type is omitted, then int is assumed.
C/C++ do not support procedures, only functions. The same result as using a procedure can be achieved by ignoring the return value or by not not returning a value.
Functions that do not return a value should be typed as void.
Functions may NOT be nested. All functions are at the same level.
Functions may be coded in any order it is not necessary for a function to be ahead of its invocation. However before using a function it must be prototyped to declare the number and types of arguments.

When a function is invoked, control is passed to the function.

#include <iostream>

void sub1();  //  prototype
void sub2();  //  prototype 
using namespace std;
int main()
{
 cout << "main" << endl;
 sub1();
 cout << "main" << endl;
 system("pause");
 return 0;
}
void sub1()
{
 cout << "Sub 1" << endl;
 sub2();
 cout << "Sub 1" << endl;
 return;
}
void sub2()
{
 cout << "Sub 2" << endl;
 return;
}

main
Sub 1
Sub 2
Sub 1
main

return

Functions may or may not contain a return statement. If there is not a return statement, control is passed back to the calling function after all statements have been executed in order. If a return statement is present control is return as soon as a return is executed. If a function uses return without a value the function type should be void. A function may have multiple return statements.

The return statement has two forms:
```
 return ;
 return (expression);
```
The first form transfers control, the second form returns the value of the expression.

Variable scope

Variables may declared anywhere in a program after the start of a block { }. The following is an example of name overloading, using the same name for different variables. In the following example the if block cannot reference the int i value.

#include <iostream>
using namespace std;
int main()
{
 int i=2;
 
 cout << i << " - ";
 if(i) {
     float i=3.14159;
     cout << i << " - ";
 }
 cout << i << endl;;
 system("pause");
 return 0;
}

2 - 3.14159 - 2

Local vs Global Variables.
Variables inside a block are local to it and may only be used in that block. If there is name overloading as in the example, local variables precede global variables.

Variables defined outside of a function block are global to the whole program.

#include <iostream>
using namespace std;

void sub1(); // prototype

int i=1;  // global

int main()
{ 
  i++;
  cout << i << endl;
  sub1();
  system("pause");
  return 0;
}
void sub1()
{
  i++;
  cout << i << endl;
  return;
}

2
3

Generally the use of global variables is frowned upon as it can lead to side effects.

static variables.
Variables declared inside of a block are deallocated when the code leaves the block. A special type of variable, static is retained so it value can be used. But it is not available outside the block.

#inclue <iostream>
using namespace std;
int main()
{
  int x;
  for(x=0;x<3;x++) {
    int i=10;
    cout << i << endl;
    i--;
  }
  for(x=0;x<3;x++) {
    static int i=10;
    cout << i << endl;
    i--;
  }
  system("pause");
  return 0;
}

Parameters
Values may be passed to functions using the parameter passing mechanism. The actual arguments are specified in the function call, the formal parameters are in the function definition. All scalar arguments are passed by value, while all array references are passed by address. There is a one to one correspondence between actual and formal arguments based on position (not name).

#include <iostream>
using namespace std;

int sub1(int, int);  // prototype 

int main()
{
  int x=1,y=2,z;
  z=sub1(x,y);       /*actual parameters */
  cout << x << " " << y << " " << z << endl;
  system("pause");
  return 0;
}
int sub1(int a,int b)           /* formal parameters */
{
  a++;
  b++;
  return(a+b);
}

 
1 2 5

Note changing a and b in the function sub1 did not affect the values in x and y in function main. Why? Only the value of the variables was passed to the function. This is commonly known as call by value. In order to change the value in a variable, the invoking function will pass the address of the variable the using function will need to use indirection. This is commonly known as call by reference or call by name.

#include <iostream>

using namespace std;

int sub1(int, int*); // prototype 

int main()
{ 
  int x=1,y=2,z;
  z=sub1(x,&y);       /*actual parameters */
  cout << x << " " << y << " " << z << endl;
  system("pause");
  return 0;
}
int sub1(int a,int *b)           /* formal parameters */
{
  a++;
  *b+=1;
  return(a+*b);
}

 
1 3 5

C++ extensions

Reference type

This feature removes the need for passing by address and using pointer notation.

#include <iostream.h>

using namespace std;

void fun(int&);  // protoype

int main()
{ 
  int i=1,j;
  fun(i);
  cout << i <<endl;
  system("pause");
  return 0;
}
void fun(int& x)
{
 x++;
 return;
}

Default Arguments.

#include <iostream>
 
using namespace std;
 
void area(int length=2, int width=2);   // prototype
 
int main()
{
 area(3,4);
 area(7);
 area();
 system("pause");
 return 0;
}
 
void area(int length, int width)
{
 cout << endl;
 cout << "length=" << length << endl;
 cout << "width=" << width << endl;
}


length=3
width=4
 
length=7
width=2
 
length=2
width=2

Overloaded Functions.

#include <iostream>
using namespace std;

float area(float);         // area of a circle pass the radius
float area(float, float); // area of rectange pass length and width

int main()
{
   cout << "The area of a circle with  a diameter of 10 is "
        << area(10.0/2) << endl;
   cout << "The area of a rectangle with sides of 3 and 4 is "
        << area(3,4) << endl;
   system("pause");
   return 0;
}

float area(float radius)
{
   return radius * radius * 3.14159;
}
        
float area(float length, float width)
{
   return length * width;
}

The area of a circle with  a diameter of 10 is 78.5397
The area of a rectangle with sides of 3 and 4 is 12
Press any key to continue . . .

Examples

Simple function.

#include <iostream.h>

using namepsace std;

int prime(int);  // prototype

int main()
{
 int i;
 
 for(i=2;i<10;i++)
    if(prime(i)) cout << i << " is prime" << endl;
    else cout << i << " is not prime" << endl;
 system("pause");
 return 0;
}
int prime(int x)
{
 int i;
 for(i=2;i<=x/2;i++)
    if(!(x%i)) return (0);
 return (1);
}

 
2 is prime
3 is prime
4 is not prime
5 is prime
6 is not prime
7 is prime
8 is not prime
9 is not prime

Float example

#include <iostream>
using namespace std;
 
float hmean(float, float);  // Prototype

int main()
{
 float a,b,c;
 int i;
 
 for(i=1;i<10;i++) {
    a=rand()%100;
    b=rand()%100;
    c=hmean(a,b);
    cout << "harmonic mean of " << a << " and " << b  
             << " is " << c << endl;
 }
 system("pause");
 return 0;
}
float hmean(float x,float y)
{
 float hm;
 hm = (2*x*y)/(x+y);
 return hm;
}

 
harmonic mean of 38 and 58 is 45.9167
harmonic mean of 13 and 15 is 13.9286
harmonic mean of 51 and 27 is 35.3077
harmonic mean of 10 and 19 is 13.1034
harmonic mean of 12 and 86 is 21.0612
harmonic mean of 49 and 67 is 56.6034
harmonic mean of 84 and 60 is 70
harmonic mean of 25 and 43 is 31.6176
harmonic mean of 89 and 83 is 85.8953

Using static variables

#include <iostream>
using namespace std;

int fib(); // prototype

int main()
{
 int i;
 for(i=1;i<11;i++) 
     cout << fib() << endl;
 system("pause");
 return 0;
}
int fib()
{
 static int f1=0,f2=0;
 int nf;
 if(!f2) {
       f2=1;
       return 1;
 }
 nf=f1+f2;
 f1=f2;
 f2=nf;
 return nf;
}

Using global variables

 
#include <iostream>
using namespace std;

int fib();  // prototype

int f1=0,f2=0; //globals

int main()
{ 
 int i;
 for(i=1;i<11;i++) 
   cout << fib() << endl;
 system("pause");
 return 0;
}
int fib()
{
 int nf;
 if(!f2) {
       f2=1;
       return 1;
 }
 nf=f1+f2;
 f1=f2;
 f2=nf;
 return nf;
}

Using pointers to change variables;

#include <iostream>

using namespace std;
 
void swap(int*, int*);  // prototype

int main()
{
 int a,b,c;
 a=rand()%100;
 b=rand()%100;
 c=rand()%100;
 if(a>b) swap(&a,&b);
 if(a>c) swap(&a,&c);
 if(b>c) swap(&b,&c);
 cout << a << " " << b << " " << c << endl;
 system('pause");
 return 0;
}
void swap(int *x,int *y)
{
 int t;
 t=*x;
 *x=*y;
 *y=t;
 return;
}

 
14 27 53

Financial example
Value of an Annuity.
An Annuity, or installment plan, is a series of payments made at equal intervals of time. Examples are pensions, IRAs and premiums on life insurance. More often than not, the interest conversion period is unequal to the payment interval. The Following formula determines the eventual cash cash value, s, of an annuity of r dollars paid per year in p installments for n years at an interest rate of j percent converted m times per year.

x = 1 + j/m

s = r [ (x^mn-1)/ p(x^m/p-1)]

Where s = eventual cash value 
r = payment per year 
p = installments per year 
n = duration of the annuity in years 
j = nominal interest rate 
m = conversions per year

Write a program to determine the eventual cash value after requesting the necessary information. To test use r=2000 p=12 n=20 j=13% m=2, you should get 180,330.40

//
// value of an annuity
//
#include <iostream>
#include <iomanip>
#include <cmath>
 
using namespace std;
using std::string;
 
float prompt(string);   //  prototype
 
int main()
{
    float r;  //  payment per year 
    float p;  //  installments per year 
    float n;  //  duration of the annuity in yea
    float j;  //  nominal interest rate 
    float m;  //  conversions per year
    float x;  //  working variable
    float numerator, denominator;
    float s;  // eventual value
    
    r=prompt("payment per year");
    p=prompt("installments per year");
    n=prompt("duration of the annuity in years");
    j=prompt("nominal interest rate");
    m=prompt("conversions per year");
    
    if(j > 1.0) j/=100.0;
    
    x=1 + j/m;
    
    numerator=pow(x,m*n)-1;
    denominator=p * (pow(x,m/p)-1);
    
    s=r*(numerator/denominator);
    
    cout << setiosflags( ios:: showpoint | ios::fixed);
    cout << "The cash value of this annuity is " 
         << setprecision(2) << s << endl;
         
    system("pause");
    return(0);
 
}

float prompt(string text)
{
      float fValue=0.0;
      while (fValue <= 0) 
      { 
        cout << "Enter the " << text << " : ";
        cin >> fValue;
      }
      return fValue;
}

Enter the payment per year : 2000
Enter the installments per year : 12
Enter the duration of the annuity in years : 20
Enter the nominal interest rate : .13
Enter the conversions per year : 2
The cash value of this annuity is 180330.44
Press any key to continue . . .