1. Computer Programming 1 More on functions

2. Computer Programming 2 Objectives Function overloading Scope rules and namespace Inline Templates Pass by value and pass by reference Recursion

3. Computer Programming 3 Scope What is wrong with the following piece of code? int n; n++; double n; Although the two function have parameters with same name, they compiler will not complain about re-declaring n twice! int sum (int n) { return n * (n + 1) / 2; } int sum (int m, int n){ assert ( m < n) ; return (n – m + 1) * (n + m) / 2; }

4. Computer Programming 4 Scope, scope rules The scope of an identifier is the portion of the program where it can be accessed. The scope rules are: 1. If an identifier is declared within a block, its scope runs from that point to end of block 2. If an identifier is a function parameter, its scope is the body of the function 3. If an identifier is declared in the initialization of a for loop, its scope is to the end of the loop 4. If an identifier's scope is declared outside all blocks and it is not a parameter, then it scope runs from that point to the end of the file

5. Computer Programming 5 Namespaces To be able to re-use declarations, namespace can be used Declarations can be placed within a namespace block namespace belNS { int value; //other declarations, definitions … } namespace mohNS { int value; } Elements within the namespace can be accessed – By using the fully qualified name belNS::value – mohNS::value – By its unqualified name (if no conflict), value, if using using namespace belNS::value; or sing namespace belNS;

6. Computer Programming 6 Function Overloading Can we have two functions with the same name and at the same time hold to the rule about no redeclaration of identifiers? The function signatures were different – Different numbers of parameters – Different types of parameters When this occurs we say the function name has been "overloaded" int sum (int n); int sum (int m, int n); int sum(double n);

7. Computer Programming 7 Inline Functions When one function calls another void f( int n ){... x = g(n);... } the process takes time for the program to transfer to a different location within the machine code With inline, it is possible to avoid the overhead required by this transfer

8. Computer Programming 8 Inline Functions Use the inline specifier in the prototype and definition inline double fahrToCelsius (double temp);... inline double fahrToCelsius (double temp){ return (temp – 32.0)/1.8; } The compiler now places actual code for the function in each location it is called – There is no jump to one location for the code at run time – This is very useful when a function with small code is called several times Inline functions are a trade-off – Faster execution at run time … but … – Larger.exe file Note that the compiler has the choice to inline a function or not Sometimes, a compiler may inline a function although the inline keyword is used

9. Computer Programming 9 Pass by value and Pass by reference So far, we have dealt with pass by value: only the value of the arguments are passed to the parameters double x = 212.0; change (x); //what’s the value of x? How can we change the value of x after change ? – Changing a value parameter changes the copy not its corresponding argument. Consider the task to divide two integers – We compute both the quotient and the remainder – We desire a function which returns both values, but we can only return value. What can we use to solve this? void change (double t) { t = 10.0; }

10. Computer Programming 10 Pass by reference Reference parameters – Parameters declared with an ampersand (&) – Following the parameter’s type (and before its name). A reference parameter is an alias to its corresponding argument. – Acts like another name for actual parameter Changing the value of a reference parameter changes the value of its corresponding argument.

11. Computer Programming 11 Pass by reference Function stub with reference parameters: void divideInts (int op1, int op2, int &quotient, int &remainder) { … } quotient and remainder are passed by reference. So, the values they have when divideInts returns are the values that the arguments will receive when its called. int i = 10,j=3; int quot=0,rem=0; divideInts(i,j,quot,rem); //the values of q and r becomes 3 and 1

12. Computer Programming 12 Passing values to parameters Value parameter – A distinct variable containing a copy of its argument – In previous example, op1 and op2 are value parameters

13. Computer Programming 13 Pass by reference Reference parameter – An alias of (alternate name for) the corresponding argument in the call – Changes to value of reference parameter will change the value of the corresponding argument in the call 1 2

14. Computer Programming 14 Pass by reference When the parameters are large then it is wise to use references Passing large arguments by valuing can be very expensive – Copying the value of the argument is very expensive when it is large – To avoid changing the value a parameter the use of the keyword const is very important int length(const string& s){ return s.length(); }

15. Computer Programming 15 Function template Consider the following swap function void swap(char& first, char& second){ char temporary = first; first = second; second = temporary; } Suppose we want to swap int s, doubles, strings, etc.. Are we going to write this function for every type? – This is were function templates come in!

16. Computer Programming 16 Function Templates Templates provide a pattern for the compiler to generate functions for whatever type of parameters are used in the call template void swap(Type &a, Type &b){ Type tmp = a; a = b; b = tmp; }

17. Computer Programming 17 Recursion Consider a function to calculate n-factorial – From mathematics – It can be defined recursively as follows

18. Computer Programming 18 Recursion A recursive definition must have two parts 1. A base/default case (s) The value is specified for one or more values of the parameter(s) 2. An inductive/recursive step The value for the parameter is specified in terms of previously defined value(s) and/or parameters

19. Computer Programming 19 Recursion To calculate 5! we go through the following steps:

20. Computer Programming 20 Recursion Then we backtrack

21. Computer Programming 21 Recursive Function The recursive factorial function int factorial (int n){ assert (n >= 0); if (n == 0) return 1; else return n * factorial (n – 1); }

22. Computer Programming 22 Execution of Recursive Function Observe the sequence of recursive calls when int number = factorial(4); Successive recursive calls

23. Computer Programming 23 Execution of Recursive Function When factorial(n - 1) eventually sends a 0 as the value parameter, the base case is executed – No more recursive calls...

24. Computer Programming 24 Execution of Recursive Function Now the calculated values are returned 1 1 2 2 6 6 24

25. Computer Programming 25 Numerical Methods Mathematical models used to solve practical problems Computer programs are used to manipulate such equations – Called "numerical methods" Examples – Curve fitting – Equation solving – Differential equations – Solving linear systems – Integration

26. Computer Programming 26 Numerical Methods Example Approximating the area under a curve Numerical methods approach – Divide region into strips, sum the areas – Trapezoidal method

27. Computer Programming 27 Function pointers Consider the problem described in the previous slide: – Compute the area under a function  – If the function  is known in advance, then it is easy to do. But suppose we want our program to take any function, how should we proceed? Use function pointers

28. Computer Programming 28 Function pointers Function pointers allow us to treat functions as if they are one of the basic types typedef double (*Fx)(double); double integral(double a, double b, Fx f) { double sum = 0.0,x; int n; // Evaluate integral{a,b} f(x) dx for (n = 0; n <= 100; n++) { x = (n/100.0)*(b-a) + a; sum += (*f)(x) * (b-a)/101.0; //you can f instead of (*f) } return sum; } double square(double x){ return x*x; } double third(double x){ return x*x*x; } … integral(0.0,1.0,square); integral(0.0,1.0,third);