Recursion, Runtime Environment and the Control Stack

Reference

• "Runtime Environments", Chapter 7 of "Compilers, Principles, Techniques and Tools" by Aho, Sethi, and Ullman, Addison Wesley.

Recursive Functions

• A recursive function is one which calls itself.
• See Recursion
• Simplifies program structure at a cost of function calls
• 

Recursive power

• double power(double val, unsigned int pow) { if (pow == 0) /* pow(x, 0) returns 1 */ return(1.0); else return(power(val, pow - 1) * val); }

• power_rec.c

Fibonacci value of a number

• int fib(int num) { switch(num) { case 0: return(0); break; case 1: return(1); break; default: /* Including recursive calls */ return(fib(num - 1) + fib(num - 2)); break; } }

• fib_rec.c

Trace Fibonacci

• In this implementation the function calls itself twice

• Input Value	Number of invocations
  0	1
  1	1
  2	3
  3	5
  4	9
  5	15
  6	25
  7	41
  8	67
  9	109
  10	177

Iterative (Non-recursive) Solutions

• Recursive functions are sometimes the simplest answer
• There is always an alternative non-recursive solution available

• #include <stdio.h> int main() { unsigned int num; unsigned int i, fn, fn_1 = 1, fn_2 = 0; printf("Enter a non-negative integer: "); if (scanf("%u", &num) != 1) { printf("ERROR: failed to read input number!\n"); return -1; } if (num == 0) fn = 0; else if (num == 1) fn = 1; else { for (i = 2; i <= num; ++i) { fn = fn_2 + fn_1; fn_2 = fn_1; fn_1 = fn; } } printf("Fibonacci of %d is %d\n", num, fn); return 0; }

• fib_iter.c

Top Down Recursion

• Outputs an integer comma separated

• void int_comma(int num) { if (num < 1000) printf("%3d", num); else { int_comma(num / 1000); printf(",%03d", num % 1000); } }

• int_comma.c
• trace

• int_comma(893427165) int_comma(893427) int_comma(893)

Recursion Underpinnings

• Every instance of a function execution (call) creates an Activation Record, (frame) for the function.
• Acivation records hold required execution information for functions:
  • Temporary values (e.g., arised in the evaluation if expressions).
  • Local data (e.g., variables)
  • The machine status consits of the state of the machine just before the
  • The control link points to the activation record of the caller function is called (e.g., program counter, machine registers)
  • Supplied parameters to the called function (often passed in a registers)
  • Return value of the function (often returned in a register)

Runtime Stack

• Activation records are created and stored in an area of memory termed the runtime stack.
  

Storage Organization

• Typical C program execution memory model
  
• The program stack grows each time a function call is made
• Infinite regression results in a collision between the runtime stack and the heap termed a run-time stack overflow error.
• Illegal pointer de-references (garbage, dangling-references) often result in memory references outside the operating system allocated partition, (segment) for the C program resulting in a segmentation error (GPF - access violation) and core dump.

Mutually Recursive Functions

• Towers of Hanoi

  #include <stdio.h> /*! forward declarations */ void move_right(int id); void move_left(int id); void move_right(int id) { if (0 == id) return; move_left(id - 1); /* move id - 1 discs one peg to left */ printf("Shift disc %d one peg to right.\n", id); move_left(id - 1); /* move id - 1 discs one peg to left */ } void move_left(int id) { if (0 == id) return; move_right(id - 1); /* move id - 1 discs one peg to right */ printf("Shift disc %d one peg to left.\n", id); move_right(id - 1); /* move id - 1 discs one peg to right */ } int main(void) { move_left(4); /* solve 4 disc problem */ return 0; }

• hanoi.c

Riddle - Crystal Balls

• First count the maximum number of floors that can be covered, given an allowed number of experiments e.
  f(e,0) = 0
f(0,b) = 0
f(e,b) = f(e-1,b) + f(e-1,b-1) + 1
• A program that reads the number of floors f and the number of b balls, and prints out the minimum number of experiments required.

  #include <stdio.h> int comp_floors(int exprs, int balls) { if (balls == 0) return 0; if (exprs == 0) return 0; return comp_floors(exprs - 1, balls) + comp_floors(exprs - 1, balls - 1) + 1; } int main() { int floors, exprs, balls; printf("Enter number of floors followed by number of balls: "); if (scanf("%d %d", &floors, &balls) != 2) { printf("ERROR: cannot read input!\n"); return -1; } for (exprs = 0; 1; exprs++) { if (comp_floors(exprs, balls) >= floors) break; } printf("Required %d exprs\n", exprs); return 0; }

• crystal.c