1. Microprocessor and Assembly Language
Lecture-15-Recursion
Muhammad Hafeez
Department of Computer Science
GC University Lahore

2. Today’s Agenda Recursion Theory in Assembly
Implementation in 8086 Environment

3. Recursion A process is recursive if its defined in terms of itself
Main Characteristics of a recursive process
The Main Problem is break down to simpler problem, each of these simpler problem are solved exactly the way, main problem is solved
There must be an escape case
One sub problem is solved, proceed to next step of solving main problem

4. Example: Factorial Non-recursive way
Factorial (N) = N x (N-1) x (N-2)x…x3x2x1
Recursive Way:
Factorial (N) = N x Factorial (N-1)

5. Algorithm for Factorial:
PROCEDURE FACTORIAL (INPUT:N, OUTPUT: RESULT)
IF N =1 THEN
RESULT=1
ELSE
CALL FACTORIAL(INPUT:N-1, OUTPUT:RESULT)
RESULT = N X RESULT
END_IF
RETURN

6. Algorithm for Find Max in An Array:
If N = 1 then largest entry is A[1], else largest entry is either A[N] or largest of A[1] …A [N-1]
PROCEDURE FIND_MAX(INPUT:N, OUPUT:MAX)
IF N = 1 THEN
MAX = A[1]
ELSE
CALL FIND_MAX(N-1,MAX)
IF A[N] > MAX THEN
MAX = A[N]
MAX = MAX
END_IF
RETURN

7. Revision-Passing Parameters to Procedure on the Stack
Write a procedure that adds two words and return the result in AX
Pass words to procedure using Stack

8. The Activation Record
Each new call to a recursive procedure require the parameters and local variables to be reinitialized for that particular call
When the call is completed the procedure resumes the previous call, on the point it left off.
Hence, the procedure needs to ‘remember’ the point, the parameters and local values of the previous call, this is called ‘the activation record’

9. Example:
Activation Record First Call
Activation Record 2nd Call

10. Example: Activation Record First Call
Suppose, 3rd call is the escape case, result of this call is computed and stored in a register or memory location to be available to 2nd call and so on..

11. Implementation of Factorial using Recursion:
MODEL SMALL
.STACK 100H
.CODE
MAIN PROC
MOV AX,3 ;N = 3
PUSH AX ;N on stack
CALL FACTORIAL ;AX has 3 factorial
MOV AH,4CH
INT 21H ;dos return
MAIN ENDP

12. Implementation of Factorial using Recursion:
FACTORIAL PROC NEAR ; computes N factorial
; input: stack on entry - ret. addr.(top), N ;
output: AX
PUSH BP ;save BP
MOV BP,SP ;BP pts to stacktop ;if
CMP WORD PTR[BP+4],1 ;N = 1?
JG END_IF ;no , N>1
;then
MOV AX,1 ;result = 1
JMP RETURN ;to to return
END_IF:
MOV CX,[BP+4] ;get N
DEC CX ;N-1
PUSH CX ;save on stack
CALL FACTORIAL ;recursive call
MUL WORD PTR[BP+4] ;RESULT = N*RESULT RETURN:
POP BP ;restore BP
RET 2 ;return and discard N FACTORIAL ENDP END MAIN