4. Functions. March 10, 2010

Transcription

1 March 10, 2010 Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 1 of 40

2 Outline Recapitulation Functions Part 1 What is a Procedure? Call-by-value and Call-by-reference Functions Part 2 The Details Recursion An Example: gcd (greatest common divisor) Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 2 of 40

3 Recapitulation What is the difference between = and ==? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

4 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

5 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

6 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

7 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

8 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Can we modify a parameter within a while-loop? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

9 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Can we modify a parameter within a while-loop? What happens if a single integer is argument/guard of a while-loop? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

10 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Can we modify a parameter within a while-loop? What happens if a single integer is argument/guard of a while-loop? What is dangerous if we declare two integer variables in one row: i n t a, b=10; Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

11 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Can we modify a parameter within a while-loop? What happens if a single integer is argument/guard of a while-loop? What is dangerous if we declare two integer variables in one row: i n t a, b=10; What is the difference of the compiler and the linker? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

12 Recapitulation What is the difference between = and ==? What is a strict boolean expression? Why should an if-statement always be followed by a {? What is a scope? What is the meaning of a while-loop? What does a while-loop look like? Can we modify a parameter within a while-loop? What happens if a single integer is argument/guard of a while-loop? What is dangerous if we declare two integer variables in one row: i n t a, b=10; What is the difference of the compiler and the linker? What is the difference of a declaration and the definition? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 3 of 40

13 4.1. Functions 1 What do these two sayings have in common? Common saying: Good things come in small packages. Common saying: Never reinvent the wheel. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 4 of 40

14 Code Dublication i n t main ( ) { double priceofmoutainbike = ; double exchangeratejanuary = ; / / January double exchangeratefebruary = ; / / February double exchangeratemarch = 1,3569; / / March / We always have to pay 60% of t o t a l cost t h i s month. / double f i r s t P a y m e n t = ; double t o t a l C o s t ; t o t a l C o s t = ( firstpayment priceofmoutainbike ) exchangeratejanuary + ( ( firstpayment ) priceofmoutainbike ) exchangeratefebruary ; std : : cout << p r i c e of January : << t o t a l C o s t << std : : endl ; t o t a l C o s t = ( firstpayment priceofmoutainbike ) exchangeratefebruary + ( ( firstpayment ) priceofmoutainbike ) exchangeratemarch ; std : : cout << p r i c e of February : << t o t a l C o s t << std : : endl ; There is two bugs in this code! Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 5 of 40

15 Code Dublication Duplicated code is difficult to maintain, to fix, and to extend. void main ( ) { code p a r t A code p a r t A Long code is difficult to read and to understand (Spaghetti code). void main ( ) { code doing one t h i n g code doing something d i f f e r e n t Duplicated code is a loss of development time. void main ( ) { code implementing Gauss quadrature void main ( ) { another implementing Gauss quadrature Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 6 of 40

16 Functions void compute ( double price, double firstpayment, double ratea, double rateb ) { double t o t a l C o s t = ( firstpayment price ) ratea + ((1.0 firstpayment ) price ) rateb ; std : : cout << t o t a l C o s t << std : : endl ; i n t main ( ) { double p r i c e = ; double january = ; / / January double f e b r uary = ; / / February double march = 1,3569; / / March double f i r s t P a y m e n t = ; std : : cout << January : ; compute ( price, firstpayment, january, february ) ; std : : cout << February : ; compute ( price, firstpayment, february, march ) ; Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 7 of 40

17 void foo ( i n t a ) { a += 20; std : : cout << a ; foo ( 3 9 ) ; i n t b=20; foo ( b ) ; foo ( b +10); C/C++ mechanism: Function or procedure. A function is a helper/assistant of the whole program. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 8 of 40

18 void foo ( i n t a ) { a += 20; std : : cout << a ; foo ( 3 9 ) ; i n t b=20; foo ( b ) ; foo ( b +10); C/C++ mechanism: Function or procedure. A function is a helper/assistant of the whole program. i n t a0 = 39; / / foo (39) a0 += 20; std : : cout << a0 ; i n t b=20; i n t a1 = b ; / / foo ( b ) a1 += 20; std : : cout << a1 ; i n t a2 = b+10; / / foo ( b+10) Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 8 of 40

19 Functions and Scopes void foo ( i n t a ) { a += 20; std : : cout << a ; b += 1; void bar ( i n t b ) { foo ( b ) ; foo ( b +10); foo ( b +20); What happens here? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 9 of 40

20 Functions and Scopes void foo ( i n t a ) { a += 20; std : : cout << a ; b += 1; void bar ( i n t b ) { foo ( b ) ; foo ( b +10); foo ( b +20); What happens here? Functions define a scope due to the brackets { (basis block). Variables of other scopes are not defined within the function. Code above consequently does not work. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 9 of 40

21 Global Variables i n t b ; void foo ( i n t a ) { a += 20; std : : cout << a ; b += 1; void bar ( i n t b ) { foo ( b ) ; foo ( b +10); foo ( b +20); C/C++ allows programmer to define (global variables). Good practice: avoid them due to side effects. Now, code does work. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 10 of 40

22 Functions and the Program Counter Memory void foo() { foo1; foo2; foo3;... foo(); // call foo foo(); PC 21: 22; foo1 // first operation of foo 23; foo2 24; foo3 25; 26; 27; foo() // call of foo 28: foo() Function call modifies program counter. Computer remembers where to jump back. Function code is only stored once in memory. Not only the program counter is remembered, but all the variables. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 11 of 40

23 The Call-Stack void foo ( ) { i n t a = 20; / / do something with a / / a now equals 50; void bar ( ) { i n t a = 30; foo ( ) ; Function call modifies program counter. Computer remembers where to jump back. Function code is only stored once in memory. Not only the program counter is remembered, but all the variables. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 12 of 40

24 The Return Statements i n t increment ( i n t a ) { a = a+1; r e t u r n a ; void bar ( ) { i n t a = 30; i n t b = increment ( a ) ; std : : cout << b ; Functions can return a value due to the return command. Returned type has to equal the type of the function. If a function doesn t return a value, the function s type is void. Consequently, void is a new primitive datatype. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 13 of 40

25 What is the main Function? i n t main ( ) { / / do something void bar ( ) { / / do something double foo ( ) { / / do something Any program is a collection of functions. They have to have unique signatures (names). At startup, the computer has to know where to set the program counter to. It always sets it to the main function. The main function returns 0 if it has been successful (error code). This is a UNIX convention. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 14 of 40

26 Functions Some Best Practices i n t main ( ) { / / do something void bar ( ) { / / do something double foo ( ) { / / do something One purpose, one function. Any function should concentrate solely on one job. One page, one function. With a less, one should be able to see the complete function. A function without documentation does not exist. Functions should have meaningful names (verbs). Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 15 of 40

27 4.2. Call-by-reference vs. Call-by-value The Call-Stack and Variables void foo ( ) { i n t a = 20; / / do something with a / / a now equals 50; void bar ( ) { i n t a = 30; i n t b = 20; foo ( ) ; Computer encounters function call (foo()). It stores away all variables and remembers where it has been called from. It resets the program counter. As soon as the function terminates, it jumps back to the place of invocation, and it restores all variables. This way, a function cannot modify an outer variable. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 16 of 40

28 Call-by-value void foo ( i n t x ) { / / do something with x / / x now equals 50; void bar ( ) { i n t a = 30; i n t b = 20; foo ( a ) ; Computer encounters function call (foo()) with argument a. It stores away all variables and remembers where it has been called from. Furthermore, it creates a copy of a. It resets the program counter. This way, a function cannot modify an outer variable. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 17 of 40

29 Call-by-value In C/C++, parameters (arguments) are passed call-by-value. Functions work on copies of the original variables. The original variables are saved away on the call stack. As soon as the operation terminates, the old variable values are restored. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 18 of 40

30 The Return Statement and Call-by-value i n t foo ( i n t x ) { x = x 2; r e t u r n x ; void bar ( ) { i n t a = 30; i n t b = foo ( a ) ; a = foo ( a ) ; The return statement takes the value of the function s copy and writes it to the left-hand side of the function invocation. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 19 of 40

31 Call-by-reference i n t foo ( i n t & x ) { x = x 2; r e t u r n x ; void bar ( ) { i n t a = 30; i n t b = foo ( a ) ; The & operator is the reference operator. It tells C/C++ to pass the argument with call-by-reference semantics. Then, C/C++ does not create a copy, but the operation works on the original variable. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 20 of 40

32 i n t foo ( i n t & x ) { x = x 2; r e t u r n x ; void bar ( ) { i n t a = 30; i n t b = foo ( a ) ; a = foo ( a ) ; The & operator is the reference operator. It tells C/C++ to pass the argument with call-by-reference semantics. Then, C/C++ does not create a copy, but the operation works on the original variable. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 21 of 40

33 Exercise: Swap Two Variables void main ( ) { i n t a = 3; i n t b = 4; / / interchange a and b a = b ; b = a ; std : : cout << a << std : : endl ; std : : cout << b << std : : endl ; Fix the code above. Extract the swap functionality in a function of its own. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 22 of 40

34 Efficient Codes Copy-by-value is save as it forbids side-effects. Whenever possible, use copy-by-value (default). Copy-by-reference is faster. Question: Can we write fast and save code? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 23 of 40

35 Const References void foo ( i n t a, i n t b ) { void bar ( i n t & a, i n t & b ) { void e f f i c i e n t F o o ( const i n t & a, const i n t & b ) { Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 24 of 40

36 4.3. const Modifier an Excursus In C++, we can mark any argument to be a const argument, i.e. the function is not allowed to modify it. void foo ( const i n t a ) { const allows compiler to optimise code aggressively. const allows you to write bug-safe code (user cannot modify a variable by accident). const closes the performance gap between C/C++ and Fortran. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 25 of 40

37 Please, Use Const Remember the 80 : 20 rule you never know the performance properties. Remember that it might help others and you to produce less bugs. Remeber the implications. void foo ( i n t & a ) { void bar ( i n t a ) { / / t h i s f u n c t i o n i s very slow and has to be tune foo ( a ) ; / / continue c a l c u l a t i o n s foo ( 1 0 ) ; / / t h i s does not work, instead we have to w r i t e i n t tmp = 10; foo ( tmp ) ; We cannot optimise bar, as foo does not have a const signature. The last example is an aritificial one, but we will encounter similar problems soon. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 26 of 40

38 4. 2 The Signature of a Function i n t foo ( ) i n t bar ( ) i n t foo ( i n t a ) i n t foo ( double x ) i n t foo ( i n t a, const double& b, double x ) A function is unique due to its name, and due to the number of arguments, and due to the type of the arguments, and due to the const modifiers of its arguments, and due to a const modifier (not addressed yet). Everything besides the name defines the signature. The name and the signature make the function unique. The return value however does not come into play. Some definition make the const modifier not part of the signature. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 27 of 40

39 Overloading i n t foo ( ) i n t foo ( i n t a ) { i n t foo ( double a ) { foo ( ) ; foo ( 3. 4 ) ; foo ( 4 ) ; To overload a function means to offer it with different signatures. C/C++ then automatically tries to find the right signature. However, be aware of automatic type conversions. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 28 of 40

40 Automatic Type Conversion i n t foo ( ) i n t foo ( i n t a ) { i n t foo ( double a ) { i n t a = 10; double b = a ; foo ( a ) ; foo ( b ) ; foo ( a / 3. 0 ) ; Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 29 of 40

41 Priority i n t foo ( ) i n t foo ( i n t a ) { i n t foo ( double a ) { i n t bar ( i n t a, i n t b ) { i n t bar ( double a, double b ) { i n t a = 10; double b = a ; foo ( a ) ; foo ( b ) ; foo ( a / 3. 0 ) ; bar ( a, 3 ) ; bar ( b, 3 ) ; bar ( a, 3. 0 ) ; Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 30 of 40

42 Rules for Overloading If the arguments match exactly without type conversion, use this definition. If there is no exact match but a match due to automatic type conversion, C/C++ uses this definition. If there s a const and a non-const argument, C/C++ uses the const variant (not for all compilers). Besides, the automatic type conversion, also take care of return type conversion: double foo ( i n t a ) { r e t u r n a / 3 ; foo ( 4. 0 ) ; / / well, t h i s does not work foo ( 4 ) ; Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 31 of 40

43 Default Arguments void foo ( i n t a = 3 ) ; void bar ( ) ; void bar ( i n t b = 3 ) ; / / not allowed void tee1 ( i n t c, double d = 2. 0 ) ; void tee2 ( i n t c =2, double d ) ; / / not allowed void tee3 ( i n t c =2, double d = 4. 0 ) ; foo ( ) ; foo ( 7 ) ; tee3 ( ) ; tee1 ( 1 ) ; tee1 ( 1, 4. 0 ) ; C/C++ support default arguments. They may not interfere with overloaded functions. They may not be followed by arguments without default arguments. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 32 of 40

44 Return Statements double foo ( double a, double h ) { i f ( h==0) { r e t u r n 0. 0 ; i f ( a==0) r e t u r n ; / / e r r o r / / do something complicated with a and h r e t u r n a ; void foo ( double a, double h ) { r e t u r n 1; / / e r r o r A return statements makes the application leave the current function. A return statement accepts one argument: the return value (if it is not a void function). A return statement may be everywhere in the function. However, multiple return statements often are considered to be bad style. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 33 of 40

45 4.5. Recursion A Simple Game void foo ( i n t l e f t, i n t r i g h t, i n t t ) { / / value of v a r i a b l e s i n t b = l e f t + r i g h t ; / / value of v a r i a b l e s b /= 2; / / value of v a r i a b l e s i f ( b<t ) { foo ( b, r i g h t, t ) ; / / value of v a r i a b l e s i f ( b>t ) { foo ( l e f t, b, t ) ; / / value of v a r i a b l e s foo ( 12,40,7); Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 34 of 40

46 Recursion Principles void foo1 ( i n t a ) { i f ( a==0) { return ; foo1 ( a 1); Functions may call themselves (recursion). Each function call has its own copy of all the variables. This may not terminate, so we have to be careful. So code a proper termination criterion. The underlying pattern often is referred to divide and conquer (which is not a Roman saying!). Recursion is a very powerful tool (matrix block algorithms, multiscale basis systems, adaptive mesh refinement, e.g.) a tool many programmers however do not understand. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 35 of 40

47 Greatest Common Divisor Write a recursive function gcd(int a, int b) which computes the greatest common divisor. Test it for a=50,b=54. Make it plot the trace. Idea: a%b = 0 b is the gcd. Otherwise gcd(a, b) gcd(b, a%b). Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 36 of 40

48 Types of Recursion Linear vs. Non-linear Recursion / / Finonacci implementation 1 void foo ( i n t a ) { i f ( a==0) { return ; foo1 ( a 1); / / Finonacci implementation 2 void bar ( i n t a ) { i f ( a==0) { return ; bar ( a 1); bar ( a 2); Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 37 of 40

49 Types of Recursion (Linear) Tail Recursion / / Finonacci implementation 1 void foo ( i n t a ) { i f ( a==0) { return ; foo1 ( a 1); void bar ( i n t a ) { while ( ) { i f ( a==0) { return ; Theorem: You can rewrite every tail recursion into a loop. Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 38 of 40

50 Tail Recursion in Action i n t foo ( i n t a ) { i f ( a <= 1) { r e t u r n 1; return a foo ( a 1); What is the semantics of foo(int)? Rewrite foo(int) without recursion. Which variant might perform faster? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 39 of 40

51 Indirekt Recursion (Kaskadische Rekursion void foo ( i n t a ) { i f ( ) { foo ( a 4); bar ( a 1); foo ( a 1); void bar ( i n t a ) { foo ( a 1); Is foo a recursive function? Is foo a tail recursion? Is foo linear? Is bar a recursive function? Is bar a tail recursion? Is bar linear? Einführung in die Programmierung Introduction to C/C++, Tobias Weinzierl page 40 of 40