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Lecture 5 . Multiplication, Division and Branches Dr. Dimitrios S. Nikolopoulos CSL/UIUC. Outline. Where are we Multiplication Division Comparison Jump instructions. By now you should be able to…. Move data between registers and memory Address memory in 17 ways

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## Lecture 5

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**Lecture 5**Multiplication, Division and Branches Dr. Dimitrios S. Nikolopoulos CSL/UIUC**Outline**• Where are we • Multiplication • Division • Comparison • Jump instructions**By now you should be able to…**• Move data between registers and memory • Address memory in 17 ways • Use logic and shifting operations to • Apply bit masks • Multiple with sums of powers of two • Divide by powers of two • Use addition and subtraction with both signed and unsigned numbers • Organize simple programs**Unsigned Multiplication**• MUL X, where X can be register or memory location • Poor choice of the architects because they ran out of opcodes… • Second argument is implicit, it is stored in • AL if X is 8-bit number • AX if X is 16-bit number • EAX if X is 32-bit number • Result stored in • AX if arguments are 8-bit • DX:AX if arguments are 16-bit • EDX:EAX if arguments are 32-bit**The mess with flags**• The values of A,S,Z,P are undefined after multiplication • This means that you cannot check the Z flag to see if the result is 0! • You have to compare the result with the value 0 using a CMP instruction • The C and O flags are cleared if the result fits in a half-size register**Signed Multiplication**• The architects tried to apologize for the inconvenience in 80286 and later processors • 2’s complement signed integers • IMUL reg/mem • IMUL reg, reg/mem • IMUL reg, immediate • IMUL reg, reg/mem, immediate data**Signed Multiplication**• IMUL X behaves like MUL • IMUL A, B computes A=A*B • IMUL A,B,C computes A=B*C • There is no 8-bit by 8-bit multiplication, last operand may be 8-bit • The instruction does not produce a 2n bit result so 16-bit by 16-bit produces as 16-bit number • When the result does not fit in half-sized register the instruction sets the C and O flags • What a mess…**Simple Examples**• IMUL BL ; AX=AL*BL, single operand like MUL • IMUL BX ; DX:AX=BX*AX, single operand like MUL • IMUL CX,DX,12h ; CX=DX*12h, result in 16-bit CX**Use of MUL/IMUL**• Accessing multidimensional arrays • Let A a NxM array of words with row-major ordering • A[I,J] is accessed as A+(I*M+J)*2 • Let a NxMxO array of words with row-major ordering • A[I,J,K] is accessed as A+((I*M+J)*O+K)*2 • It is convenient but it is slow**Unsigned division**• DIV X, X register or memory • Nominator is implicit, stored in AX if X 8-bit, DX:AX if X is 16-bit, EDX:EAX is X is 32-bit • If X 8-bit quotient is stored in AL and remainder in AH • If X 16-bit quotient is stored in AX and remainder in DX • If X 32-bit quotient in stored in EAX and remainder in EDX**Dividing equally sized words**• Use sign-extension of the nominator • Special instructions for sign extensions • CBW (Convert Byte to Word) • Before: AX=xxxx xxxx snnn nnnn • After: AX=ssss ssss snnn nnnn • CWD (Convert Word to Double Word) • Before AX=snnn nnnn nnnn nnnn • After DX=ssss ssss ssss ssss AX=snnn nnnn nnnn nnnn • CWDE • Similar to CWD but sign extends in EAX instead of DX**Flags**• Division just scrambles the flags • Division by 0 though produces an interrupt by the microprocessor (more on interrupts next week) • If the quotient does not fit in the register, this also produces an interrupt • E.g. 1000/2=500, argument (2) is 8-bit but quotient (500) does not fit in AL, there is a divide overflow and an interrupt is produced**Rounding**• We get rid of the remainder when we want to truncate the result • We can double the remainder, compare it to the denominator and then adjust the quotient • If (remainder*2) > denominator, increment quotient**Unconditional Jumps**• Transfer the control flow of the program to a specified instruction, other than the next instruction in sequential execution • Jumps are performed with labels pointing to the address of the target instruction • It is the equivalent of a goto statement • Goto is good in assembly!**Unconditional jumps**• Short jump • JMP SHORT label, where label is within –128/+127 bytes off the current instruction • Near jump • JMP label, where label is within –32,768/+32,767 bytes off the current instruction • Far jump • JMP label, where label is any memory address, in segment:offset format • In protected mode near and far jumps are the same**Conditional Jumps**• Jumps performed if a condition evaluates to true • Conditions are evaluated based on the values of the bits in the FLAGS register • Test S, Z, P, C, O • If condition is true the jump is performed to the location specified • If condition is false the code proceeds with the next instruction in sequence • Short or near jumps in 80386**Comparisons**• CMP A, B • Executes A-B without modifying A (non-destructive) • CMP is most of the time followed by a conditional jump based on the outcome of the comparison CMP AL, 10h ; If AL >= 10 jump JAE target • CMP is a non-destructive SUB, it sets the flags exactly like the SUB instruction**Comparisons**• Unsigned A,B • If (A<B), C=1 • If (A>B), C=0 • Z tested for equality/inequality • Signed A,B • If (S XOR O = = 1) A<B else A>B • Z tested for equality/inequality**Signed comparisons**• Case 1, Sign=1, Overflow=0 • A-B looks negative • There is no overflow, so A<B • Case 2, Sign=0, Overflow=1 • A-B looks positive • But there is overflow so the sign bit is wrong and A<B • Case 3, Sign=0, Overflow=0 • A-B looks positive • No overflow, so A>B • Case 4, Sign=1, Overflow=1 • A-B looks negative • But overflow bit is set so the sign flag is wrong therefore A>B**Conditional Jumps**• Syntax: JX, where X denotes the condition • J -> Jump • N -> Not • E -> Equal • A/B -> Above/Below for unsigned arithmetic • G/L -> Greater/Less for signed arithmetic**Conditional jump instructions**• JL, jump if less • Jumps if A<B, that is if S XOR O = 1 • JA, JNBE (above == not (below or equal)) • Jumps if C=0&Z=0 • JBE, JNA (below or equal == not above) • Jumps if Z=1 | C=1 • JAE, JNB, JNC (above or equal == not below==no carry) • C=0**Conditional jump instructions**• JB, JNA, JC (below == not above == carry set) • C=1 • JE, JZ (equal == result is 0) • Z=1 • JNE, JNZ (not equal == result is not 0) • Z=0 • JNS (sign, no sign) • S=0 • JO • O=1 • JS • S=1**Conditional jump instructions**• JNO • O=0 • JG, JNLE (greater==not (less or equal)) • S=0, Z=0 • JGE, JNL (greater or equal == not less) • S=0 • JL, JNGE (less == not (greater or equal)) • S XOR O = 1 • JLE, JNG (less or equal == not greater) • (S XOR O = 1) | Z=1 • JCXZ (counter register is 0), useful for loops**Loops**• LOOP label • Combination of CMP and JNZ • Decrement the CX register and if register has not become 0 jump to the specified label • If CX becomes 0 the instruction following the LOOP instruction is executed**Example**ADDS mov cx, 100 ;load count mov si, BLOCK1 mov di, BLOCK2 .Again lodsw ;get Block1 data ; AX = [SI]; SI = SI + 2 add AX, [ES:DI] ;add Block2 data stosw ;store in Block2 ; [DI] = AX; DI = DI + 2 loop .Again ;repeat 100 times ret**mov ax, [a]**mov bx, [b] cmp ax,bx ja .true ; false instructions jmp .done .true ; true instructions If (a>b) { /* true instructions */ } else { /* false instructions */ } If then else in assembly**cmp al, ‘a’**jne .b ; these are the ‘a’ instructions jmp .done .b cmp al, ‘b’ jne .default ; these are the ‘b’ instructions .default ;default instructions .done switch (var) { case ‘a’: /* a instructions */ break; case ‘b’: /* b instructions */ break; default /* default instructions */ } Switch in assembly**.begin**; instructions… mov ax, [a] mov bx, [b] cmp a,b je .begin do { /* instructions */ } while (a==b); Do while in assembly**While do in assembly**.begin mov ax, [a] mov bx, [b] cmp ax,bx jne .done ; instructions jmp begin .done while (a==b) { /* instructions */ };**mov cx, 10**.begin ; instructions loop .begin for (i=10;i>0;i--) { /* instructions */ } For loop**Examples**; if (J <= K) then ; L := L + 1 ; else L := L - 1 ; J, K, L are signed words mov ax, [J] cmp ax, [K] jnel .DoElse inc word [L] jmp .ifDone .DoElse: dec word [L] .ifDone: ; while (J >= K) do begin ; J := J - 1; ; K := K + 1; ; L := J * K; ; end; .WhlLoop: mov ax, [J] cmp ax, [K] jnge .QuitLoop dec word [J] inc word [K] mov ax, [J] imul [K] mov [L], ax jmp .WhlLoop .QuitLoop:**Now you’re able to…**• Finish HW1 • Do all the math and logic needed for MP1 • Only thing missing for MP1 is stacks, they will be covered in Lecture 6

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