1. More on FunctionsCS-2301 B-term 20081 More on Functions CS-2301, System Programming for Non-majors (Slides include materials from The C Programming Language, 2 nd ed., by Kernighan and Ritchie and from C: How to Program, 5 th ed., by Deitel and Deitel)

2. More on FunctionsCS-2301 B-term 20082 Data Storage in Memory Variables may be automatic or static Automatic variables may only be declared within functions and compound statements Storage allocated when function is entered Storage is released when function returns Arguments and result are (somewhat) like automatic variables Storage is allocated and initialized by caller of function Storage is released after function returns to caller.

3. More on FunctionsCS-2301 B-term 20083 Static variables may be declared within or outside of functions Storage allocated when program is initialized Storage is released when program exits Static variables outside of functions may be visible to linker Compiler sets aside storage for all static variables at compiler or link time Values retained across function calls Initialization must evaluate to compile-time constant Static Data

4. More on FunctionsCS-2301 B-term 20084 Static Variable Examples int j;//static, visible to linker & all functs static float f; // not visible to linker, visible to // to all functions in this program int fcn (float a, int b) { // nothing inside of {} is visible to linker int i = b;//automatic double g;//automatic static double h;//static, not visible to // linker; value retained from call to call body – may access j, f, a, b, i, g, h }//int fcn( … )

5. More on FunctionsCS-2301 B-term 20085 Static Variable Examples (continued) int j;//static, visible to linker & all functs static float f; // not visible to linker, visible to // to all functions in this program int fcn (float a, int b) { // nothing inside of {} is visible to linker int i = b;//automatic double g;//automatic static double h;//static, not visible to // linker; value retained from call to call body – may access j, f, a, b, i, g, h }//int fcn( … ) Declaration outside any function:– always static static storage class:– not visible to linker

6. More on FunctionsCS-2301 B-term 20086 Static Variable Examples (continued) int j;//static, visible to linker & all functs static float f; // not visible to linker, visible to // to all functions in this program int fcn (float a, int b) { // nothing inside of {} is visible to linker int i = b;//automatic double g;//automatic static double h;//static, not visible to // linker; value retained from call to call body – may access j, f, a, b, i, g, h }//int fcn( … ) Inside function:– default is automatic static storage class:– not visible to linker

7. More on FunctionsCS-2301 B-term 20087 Static Variable Examples (continued) int j;//static, visible to linker & all functs static float f; // not visible to linker, visible to // to all functions in this program int fcn (float a, int b) { // nothing inside of {} is visible to linker int i = b;//automatic double g;//automatic static double h;//static, not visible to // linker; value retained from call to call body – may access j, f, a, b, i, g, h }//int fcn( … ) Note: value of h is retained from one call to next

8. More on FunctionsCS-2301 B-term 20088 Extern Variables int j;//static, visible to linker & all functs static float f; // not visible to linker, visible to // to all functions in this program extern float p; // static, defined in another program int fcn (float a, int b) { // nothing inside of {} is visible to linker int i = b;//automatic double g;//automatic static double h;//static, not visible to // linker; value retained from call to call body – may access j, f, a, b, i, g, h, p }//int fcn( … ) extern storage class:– a static variable defined in another C program

9. More on FunctionsCS-2301 B-term 20089 Questions?

10. More on FunctionsCS-2301 B-term 200810 Automatic Variables Arguments & Results Allocated on The Stack Definition – The Stack –A last-in, first-out data structure provided by the operating system for each running program –For temporary storage of automatic variables, arguments, function results, and other stuff Used by all modern programming languages –Even assembly languages for modern processors –… but not Fortran or Cobol!

11. More on FunctionsCS-2301 B-term 200811 Automatic Variables Allocated when function or compound statement is entered Released when function or compound statement is exited Values not retained from execution to next

12. More on FunctionsCS-2301 B-term 200812 Arguments and Results Arguments are values calculated by caller of function Placed on The Stack by caller for use by function Function may assign new value to argument, but … …caller never looks at argument values again! Result is storage allocated by caller On The Stack Assigned by return statement of function For use by caller Arguments & result are removed by caller After function returns, after caller has absorbed return value

13. More on FunctionsCS-2301 B-term 200813 Typical Implementation of The Stack Linear region of memory Stack Pointer “growing” downward Each time some information is pushed onto The Stack, pointer moves downward Each time info is popped off of The Stack, pointer moves back upward

14. More on FunctionsCS-2301 B-term 200814 Typical Memory for Running Program (Windows & Linux) 0x00000000 0xFFFFFFFF address space program code (text) static data heap (dynamically allocated) stack (dynamically allocated) PC SP

15. More on FunctionsCS-2301 B-term 200815 Typical Memory for Running Program (Windows & Linux) 0x00000000 0xFFFFFFFF address space program code (text) static data heap (dynamically allocated) stack (dynamically allocated) PC SP Heap to be discussed later in course

16. More on FunctionsCS-2301 B-term 200816 How it works Imagine the following program:– int factorial(int n){ … /* body of factorial function */ … }// factorial Imagine also the caller:– int x = factorial(100); What does compiled code look like?

17. More on FunctionsCS-2301 B-term 200817 Compiled code: the caller int x = factorial(100); Put the value “100” somewhere that factorial function can find Put the current program counter somewhere so that factorial function can return to the right place in calling function Provide a place to put the result, so that calling function can find it

18. More on FunctionsCS-2301 B-term 200818 Compiled code: factorial function Save the caller’s registers somewhere Get the argument n from the agreed-upon place Set aside some memory for local variables and intermediate results Do whatever factorial was programmed to do Put the result where the caller can find it Restore the caller’s registers Transfer back to the program counter saved by the caller

19. More on FunctionsCS-2301 B-term 200819 Question: Where is “somewhere”? So that caller can provide as many arguments as needed (within reason)? So that called routine can decide at run-time how much temporary space is needed? So that called routine can call any other routine, potentially recursively? We will explain recursion shortly

20. More on FunctionsCS-2301 B-term 200820 Answer: The Stack Calling function Push return address, space for result, and arguments onto stack Jump to called function Called function Push registers and automatic storage space onto stack Do work of the routine, store result in space pushed above Pop registers and automatic storage off stack Jump to return address left by calling routine

21. More on FunctionsCS-2301 B-term 200821 Typical Address Space (Windows & Linux) 0x00000000 0xFFFFFFFF Memory address space program code (text) static data heap (dynamically allocated) stack (dynamically allocated) PC SP

22. More on FunctionsCS-2301 B-term 200822 Note Through the magic of operating systems, each running program has its own memory –Complete with stack & everything else Called a process Windows, Linux, Unix, etc.

23. More on FunctionsCS-2301 B-term 200823 Note (continued) Not necessarily true in small, embedded systems Real-time & control systems Mobile phone & PDA Remote sensors, instrumentation, etc. Multiple running programs share a memory Each in own partition with own stack Barriers to prevent each from corrupting others

24. More on FunctionsCS-2301 B-term 200824 Shared Physical Memory OS Kernel stack Process 1 stack Process 2 0x00000000 0x0000FFFF Physical memory stack Process 3

25. More on FunctionsCS-2301 B-term 200825 Questions?

26. More on FunctionsCS-2301 B-term 200826 Why a Stack? Engineering reason – Computer architectures without stacks are not “rich” enough to support demands of modern computing Multiple running programs at the same time Complex interactions among running programs Modern computer languages Mathematical reason – To support recursive programs Not often by ordinary programmers with ordinary skills Some problems are too hard to solve without it Most notably, the compiler!

27. More on FunctionsCS-2301 B-term 200827 Why a Stack? Engineering reason – Computer architectures without stacks are not “rich” enough to support demands of modern computing Multiple running programs at the same time Complex interactions among running programs Modern computer languages Mathematical reason – To support recursive programs Not often by ordinary programmers with ordinary skills Some problems are too hard to solve without it Most notably, the compiler!

28. More on FunctionsCS-2301 B-term 200828 Why a Stack? Engineering reason – Computer architectures without stacks are not “rich” enough to support demands of modern computing Multiple running programs at the same time Complex interactions among running programs Modern computer languages Mathematical reason – To support recursive programs Not often used by programmers with ordinary skills, but … Some problems are too hard to solve without recursion Most notably, the compiler!

29. More on FunctionsCS-2301 B-term 200829 Why a Stack? Engineering reason – Computer architectures without stacks are not “rich” enough to support demands of modern computing Multiple running programs at the same time Complex interactions among running programs Modern computer languages Mathematical reason – To support recursive programs Not often used by programmers with ordinary skills, but … Some problems are too hard to solve without it Also, advanced games and robotics with “intelligent” objects

30. More on FunctionsCS-2301 B-term 200830 Definition – Recursion When a function calls itself, directly or indirectly When a mathematical or programmatic concept is defined in terms of itself E.g., definition of compound statement in §A9.3, p.223

31. More on FunctionsCS-2301 B-term 200831 Definition – Recursion When a function calls itself, directly or indirectly When a mathematical or programmatic concept is defined in terms of itself E.g., definition of compound statement in §A9.3, p.223 In both cases, something is needed to break the circularity

32. More on FunctionsCS-2301 B-term 200832 Example – Towers of Hanoi Move stack of disks from one peg to another Move one disk at a time Larger disk may never be on top of smaller disk

33. More on FunctionsCS-2301 B-term 200833 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0) { move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move

34. More on FunctionsCS-2301 B-term 200834 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move The function main – gets number of disks and invokes function move

35. More on FunctionsCS-2301 B-term 200835 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move The function move – where the action is

36. More on FunctionsCS-2301 B-term 200836 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move First move all but one of the disks to temporary peg

37. More on FunctionsCS-2301 B-term 200837 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move Next, move the remaining disk to the destination peg

38. More on FunctionsCS-2301 B-term 200838 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move Finally, move disks from temporary to destination peg

39. More on FunctionsCS-2301 B-term 200839 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move Notice that move calls itself twice, but with one fewer disks each time

40. More on FunctionsCS-2301 B-term 200840 Implementation on The Stack n SP Stack entry for main …

41. More on FunctionsCS-2301 B-term 200841 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move

42. More on FunctionsCS-2301 B-term 200842 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move

43. More on FunctionsCS-2301 B-term 200843 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 1 c = 2 b = 3 disks = n-1 Args for 2 nd call to move

44. More on FunctionsCS-2301 B-term 200844 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 1 c = 2 b = 3 disks = n-1 Args for 2 nd call to move Args for subsequent calls to move go here

45. More on FunctionsCS-2301 B-term 200845 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 1 c = 2 b = 3 disks = n-1 Args for 2 nd call to move Eventually, disks = 0, so no more calls to move All existing calls return

46. More on FunctionsCS-2301 B-term 200846 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move Leaving stack like this again

47. More on FunctionsCS-2301 B-term 200847 Tower of Hanoi Program #include void move (int disks, int a, int c, int b); int main() { int n; printf ("How many disks?"); scanf ("%d", &n); printf ("\n"); move (n, 1, 3, 2); return 0; }// main /* PRE: n >= 0; a, b, and c represent some order of the distinct integers 1, 2, 3 POST: the function displays the individual moves necessary to move n disks from needle a to needle c, using needle b as a temporary storage needle */ void move (int disks, int a, int c, int b) { if (disks > 0){ move (disks-1, a, b, c); printf ("Move one disk from %d to %d\n", a, c); move (disks-1, b, c, a); }// if (disks > 0 return; }//move

48. More on FunctionsCS-2301 B-term 200848 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move move now moves one disk from peg1 to peg3, and then calls move again!

49. More on FunctionsCS-2301 B-term 200849 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 3 c = 2 b = 1 disks = n-1 Args for call to move disks back from peg3 to peg2

50. More on FunctionsCS-2301 B-term 200850 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 3 c = 2 b = 1 disks = n-1 Args for call to move back Args for subsequent calls to move back go here

51. More on FunctionsCS-2301 B-term 200851 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move return address a = 3 c = 2 b = 1 disks = n-1 Args for 2 nd call to move Eventually, disks = 0, so no more calls to move All existing calls return

52. More on FunctionsCS-2301 B-term 200852 Implementation on The Stack (continued) n SP Stack entry for main … return address a = 1 c = 3 b = 2 disks = n Args for call to move Leaving stack like this again, but with all disks moved to peg 3

53. More on FunctionsCS-2301 B-term 200853 Implementation on The Stack n SP Stack entry for main … move returns back to main

54. More on FunctionsCS-2301 B-term 200854 Fundamental Principle Stack provides a simple mechanism for implementing recursive functions Arbitrary numbers of intermediate functions Eventually, something must break the circularity of recursion Or stack will grow until it overflows memory!

55. More on FunctionsCS-2301 B-term 200855 Note on Recursive Functions Some simple recursive functions can be “unwound” into loops – e.g., int factorial(int n) { return (n <= 1) ? 1 : (n * factorial(n-1)); }//factorial is equivalent to int factorial(int n) { int product = 1; for (int k=1; k <= n; k++) product *= k; return product } //factorial

56. More on FunctionsCS-2301 B-term 200856 Note on Recursive Functions (continued) Other recursive functions are much too difficult to understand if unwound E.g., Tower of Hanoi Keeping track of which disk is on which peg requires superhuman intellect, very complex code!

57. More on FunctionsCS-2301 B-term 200857 Questions