ICS312 Set 12

1. ICS312 Set 12 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. Pay close attention to the following slide (and the one so indicated a few slides on). These are the methods used by all commercial compilers You are expected to know these methods off by heart! You’ll be asked to supply them both in a quiz and in the midterm.

7. 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     MOV BP,SP        ;BP points 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

8. Call by Value Using the Stack(Cont.) Stack Representation for NEAR Call by Value in this version of the program: InstructionStack ContentsSPBP (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 reg

9. 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).

10. 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

11. NOTE • C assumes that • 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.

12. Call by Reference Using the Stack Here is another version to demonstrate passing arguments by reference on the stack. TITLE MAIN3 (main3.asm) EXTRN SUB2: NEAR .MODEL SMALL .STACK 100H .DATA X DW 30 Y DW 40

13. .CODE MAIN3 PROC     MOV AX,@DATA     MOV DS,AX PUSH OFFSET Y ;using call by reference PUSH OFFSET X ;using call by reference CALL CALC ; answer should be in AX MOV AX,4C00H     INT 21H MAIN3 ENDP     END MAIN3

14. The following slide (and its continuation) is the other method (call by reference) used by commercial compilers and which you are expected to know off by heart!

15. Call by Reference Using the Stack TITLE SUB2 (sub2.asm - a separate file) PUBLIC SUB2 .MODEL SMALL .CODE SUB2 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

16. MOV BX, [BP+4]   ;BX has address of X (not its value) MOV AX, [BX] ;AX has the value of X     MOV BX, [BP+6]   ;BX has address of Y SUB AX, [BX] ;AX = X - Y SUB AX, [BX] ;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 SUB2 ENDP     END

17. Stack Representation for call by reference example InstructionStack contentsSPBP (at end of this code) PUSH AX          Y address     SP -=2      [BP+6]= Y address PUSH AX          X address     SP -=2      [BP+4]= X address CALL ADDNOS      IP                SP -=2      [BP+2] = return addr. offset PUSH BP          BP                SP -=2      [BP] = orig. contents of BP MOV BP, SP BP = SP PUSH regs        regs         SP -=2/reg 

18. Example on storing a result in an argument Call SUB(X, Y, Z), Result is to set Z = Y – X Main Program . . PUSH OFFSET X PUSH OFFSET Y PUSH OFFSET Z CALL SUB . .

19. Example on storing a result in an argument (Cont.1) Title SUB3 .ModelSmall .586 PUBLIC SUB .CODE SUB PROC NEAR PUSH BP ;Save BP MOV BP, SP PUSH DX ;Save DX PUSH BX ;Save BX MOV BX, [BP+6] ;BX = OFFSET of ADDRESS of Y MOV DX, [BX] ;DX = Y MOV BX, [BP+8] ;BX = OFFSET of ADDRESS of X SUB DX, [BX] ;DX = Y – X

20. Example on storing a result in an argument (Cont.2) ; to store DX in Z MOV BX, [BP+4] ; puts offset of Z into BX MOV [BX], DX POP BX ; restore original value of BX POP DX POP BP RET 6 SUB ENDP END

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

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

23. factorial proc 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

24. imul word ptr [bp+4] endup: pop bp ret 2 factorial endp end

25. 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. 25

26. 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) ) 26

27. If a = b, then obviously the GCD of (a,b) is a, and we have a*1 + b*0 = a Otherwise, proceed as follows:

28. 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 28

29. EXAMPLE. To find the GCD d of 75 and 30, and, further to find x, y such that 75x + 30y = d. E(75, 30) = (x1, y1, d) to be filled in later 75 = 2*30 + 15 (so q1 = 2) E(30, 15) = (x2, y2, d) to be filled in later 30 = 2*15 + 0 (so q2 = 2) E(15, 0) = (x3, y3, d) = (1, 0, 15). So d = 15. Now x2 =y3=0 and y2 = x3 – q2y3 = 1 and x1 =y2=1 and y1 = x2 – q1y2 = -2 So d = 15 and 1*75 + (-2)*30 = 15 29

30. PROOF THAT THE ALGORITHM WORKS (optional) First of all note that since a = qb + r, any number that divides both b and r must also divide a (so it divides both a and b). And since r = a – qb, any number that divides both a and b must also divide r (so it divides both b and r). Thus the largest number that divides both b and r must also be the largest number that divides both a and b i.e. the GCD of a,b = GCD of b,r

31. 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 and hence also of a,b Since r = a - qb, this provides Xb + Y(a-qb) = D Giving Ya + (X-qY)b = D 31

32. Finally note that the algorithm terminates, because the second argument decreases in each successive recursive call. So the sequence of iterations must end up with one in which the second argument is zero 32

33. Textbook Reading (Jones): Chapter 13  Procedures and High-Level Languages