1. Subroutines: Passing Arguments Using the Stack

2. Passing Arguments via the Stack Arguments to a subroutine are pushed onto the stack. The subroutine accesses the arguments from the stack using the Base Pointer (BP) and indirect addressing. Arguments can be passed by value (their values are pushed onto the stack, or by reference (their offsets are pushed onto the stack).

3. The calling routine used in MAIN3 can be either: To use CALL by Value : PUSH X PUSH Y CALL SUB1 To use CALL by Reference : PUSH OFFSET X PUSH OFFSET Y CALL SUB1

4. Call by Value Using the Stack Suppose that X and Y are defined in the MAIN file: X DW... Y DW... To call a subroutine CALC to evaluate X - 2Y using call by value:

5. TITLE MAIN3 (main3.asm) EXTRN CALC: NEAR.MODEL SMALL.STACK 100H.DATA X DW 30 Y DW 40.CODE MAIN3 PROC MOV AX, @DATA MOV DS, AX PUSH Y ; call by value PUSH X CALL CALC ; the answer should be returned in AX MOV AX,4C00H INT 21H MAIN3 ENDP END MAIN3

6. Call by Value Using the Stack(Cont.) TITLE CALC (CALC.ASM - a separate file) PUBLIC CALC.MODEL SMALL.CODE CALC PROC NEAR ;evaluates X - 2Y with result in AX PUSH BP ;save BP (and DEC SP) MOV BP,SP ;BP pts to stack top ; push any registers to be used in the subroutine and ; restored before returning from the subroutine here MOV AX,[BP+4] ;AX has X SUB AX,[BP+6] ;AX = X - Y SUB AX,[BP+6] ;AX = X - 2Y ; pop any registers that were saved in the subroutine here POP BP ;restore BP RET 4 ;pop IP and add 4 bytes to SP CALC ENDP END

7. Call by Value Using the Stack(Cont.) Stack Representation for NEAR Call by Value in this version of the program: Instruction Stack Contents SP BP (at the end of this code) PUSH Y (Arg1) Y SP -=2 [BP+6] = offset of Y on stack PUSH X (Arg2) X SP -=2 [BP+4] = offset of X on stack CALL CALC Ret Address SP -=2 [BP+2] = RETADDR (IP) PUSH BP BP SP -=2 [BP] = original contents of BP MOV BP, SP BP = SP push regs regs SP -=2/each

8. Call by Value Using the Stack(Cont.) The purpose of using the BP in this way is because it gives a standard way to retrieve arguments from the stack that is not affected by pushing any additional registers or other values within the subroutine. Note: if BP is used for indirect addressing, it is assumed to be referring to an offset in the stack segment (SS). Any other register used for indirect addressing is assumed to be an offset in the data segment (DS).

9. TITLE CALC (CALC.ASM - a separate file) PUBLIC CALC.MODEL SMALL.CODE CALC PROC NEAR ;evaluates X - 2Y with result in AX PUSH BP ;save BP MOV BP,SP ;BP points to stack top ; push any registers to be used in the subroutine MOV AX, [BP+4] ;AX has X SUB AX, [BP+6] ;AX = X - Y SUB AX, [BP+6] ;AX = X - 2Y ; pop any registers that were saved in the subroutine POP BP ;restore BP RET 4 ;pop IP and add 4 bytes to SP CALC ENDP END

10. NOTE C assumes that (1)the calling program will fix the stack after the return from a subroutine (2) arguments will be passed using call by value (3) arguments are pushed in reverse order, as shown above. Different compilers use different calling conventions.

11. FIXING UP THE STACK If the subroutine is to fix up the stack, then it should end up with: RET 2*no. of arguments e.g. if there are 3 arguments, then it should end up with: RET 6 If the calling program is to fix up the stack, then the subroutine should end up with: RET and, assuming that the subroutine is SUB1, the calling program should contain the code: call sub1 add sp, 6 (i.e. 2*no. of arguments)

12. ILLUSTRATION OF A RECURSIVE PROCEDURE A procedure to evaluate factorial(n) if n = 1 return 1 else return n*factorial(n-1)

13. factorialproc near push bp mov bp,sp cmp word ptr [bp+4], 1 jg cont mov ax, 1 jmp endup cont:mov bx, [bp+4] dec bx push bx call factorial

14. imulword ptr [bp+4] endup: pop bp ret 2 factorial endp end

15. An Example of a Recursive Procedure Employed in Cryptography Definition. The GCD (greatest common denominator) of two numbers a, b is the largest number that divides both a and b. 15

16. Euler’s Extended Algorithm. For given a, b to find: (a) the GCD d of a, b (b) numbers x and y (positive, negative or zero) such that xa + yb = d (Euler’s original algorithm is just part (a) ) 16

17. Define E(a,b) as a function whose value is the triple (x, y, d) such that d is the GCD of a, b and xa + yb = d. E(a,b) can then be evaluated using the following recursive algorithm: Function E(a, b) where a > b If b = 0 then return (1, 0, a), else evaluate q, r such that a = qb + r and 0 ≤ r < b. Evaluate E(b, r), let result be (X, Y, D) Return (Y, X – qY, D) End function 17

18. EXAMPLE. To find the GCD d of 75 and 30, and, further to find x, y such that 75x + 30y = d. E(75, 30) = (x 1, y 1, d) to be filled in later 75 = 2*30 + 15 (so q 1 = 2) E(30, 15) = (x 2, y 2, d) to be filled in later 30 = 2*15 + 0 (so q 2 = 2) E(15, 0) = (x 3, y 3, d) = (1, 0, 15). So d = 15. Now x 2 =y 3 =0 and y 2 = x 3 – q 2 y 3 = 1 and x 1 =y 2 =1 and y 1 = x 2 – q 1 y 2 = -2 So d = 15 and 1*75 + (-2)*30 = 15 18

19. Proof that the algorithm works (optional) The case where b = 0 obviously returns the correct result, since 1*a + 0*0 = a, and a is the GCD of a and 0. If b > 0, and q, r, X, Y, D are as defined in the algorithm, then Xb + Yr = D where D is the GCD of b,r Since r = a - qb, this provides Xb + Y(a-qb) = D Giving Ya + (X-qY)b = D 19

20. The previous slide showed showed that if x, y are evaluated as in the algorithm, then xa + yb = D But is D the gcd of a,b ? By defn. D | b and D | r. So since a = qb + r, we get D | a. Let d be any no. that divides both a and b. Then since r = a - qb, it follows that d | r. We now have d | b and d | r. So by defn. d  D. It follows that D is the GCD of a,b. 20

21. Finally note that the algorithm terminates, because each recursive call involves nonnegative arguments whose sum is less than that of the previous iteration. So the sequence of iterations must end up with one in which the smaller second argument is zero 21