CDA 3101 Fall 2013

Introduction to Computer Organization

Instruction Representation

06 September 2013

Review• ISA: hardware / software interface

– Design principles, tradeoffs

• MIPS instructions– Arithmetic: add/sub $t0, $s0, $s1– Data transfer: lw/sw $t1, 8($s1)

• Operands must be registers– 32 32-bit registers– $t0 - $t7 => $8 - $15– $s0 - $s7 => $16 - $23

• Memory: large, single dimension array of bytes M[232]– Memory address is an index into that array of bytes– Aligned words: M[0], M[4], M[8], ….M[4,294,967,292]– Big/little endian byte order

Machine Language -- MIPS• All instructions have the same length (32 bits)• DP3: Good design demands good compromises

– Same instruction length or same format

• Three different formats– R: arithmetic instruction format– I: transfer, branch, immediate format– J: jump instruction format

• add $t0, $s1, $s2 – 32 bits in machine language– Fields for:– Operation (add)

• Operands ($s1, $s2, $t0)

10101110101101001010000000010010110000

00000010010010000100000000100000

10001101001010000000010010110000

lw $t0, 1200($t1)add $t0, $s2, $t0sw $t0, 1200($t1)

A[300] = h + A[300];

Instruction Formats

op functrs rt rd shamt

6 bits 6 bits5 bits 5 bits 5 bits 5 bits

op address / immediaters rt

op target address

R:

I:

J:

op: basic operation of the instruction (opcode)rs: first source operand registerrt: second source operand registerrd: destination operand registershamt: shift amountfunct: selects the specific variant of the opcode (function code)address: offset for load/store instructions (+/-215)immediate: constants for immediate instructions

R Format

0 3217 18 8 0

000000 10000010001 10010 01000 00000

6 bits 6 bits5 bits 5 bits 5 bits 5 bits

add $t0, $s1, $s2 (add $8, $17, $18 # $8 = $17 + $18)

sub $t1, $s1, $s2 (sub $9, $17, $18 # $9 = $17 - $18)

0 3417 18 9 0

000000 10001010001 10010 01001 00000

6 bits 6 bits5 bits 5 bits 5 bits 5 bits

I Format

35 5219 8

100011 0000 0000 0011 010010011 01000

6 bits 16 bits5 bits 5 bits

lw $t0, 52($s3) lw $8, 52($19)

43 5219 8

101011 0000 0000 0011 010010011 01000

6 bits 16 bits5 bits 5 bits

sw $t0, 52($s3) sw $8, 52($19)

Example

A[300] = h + A[300]; /* $t1 <= base of array A; $s2 <= h */

lw $t0, 1200($t1) # temporary register $t0 gets A[300]

add $t0, $s2, $t0 # temporary register $t0 gets h +A[300]

sw $t0, 1200($t1) # stores h + A[300] back into A[300]

0 3218 8 8 0

000000 10000010010 01000 01000 00000

35 12009 8

43 12009 8

100011 0000 0100 1011 000001001 01000

101011 0000 0100 1011 000001001 01000

Compiler

Assembler

Immediates (Numerical Constants)• Small constants are used frequently (50% of operands)

– A = A + 5;– C = C – 1;

• Solutions– Put typical constants in memory and load them– Create hardwired registers (e.g. $0 or $zero)

• DP4: make the common case fast• MIPS instructions for constants (I format)

– addi $t0, $s7, 4 # $t0 = $s7 + 4

8 423 8

001000 0000 0000 0000 010010111 01000

Arithmetic Overflow• Computers have limited precision (32 bits)

15 1111

+ 3 0011

18 10010

• Some languages detect overflow (Ada), some don’t (C)• MIPS provides 2 types of arithmetic instructions:

– Add, sub, and addi: cause overflow

– Addu, subu, and addiu: do not cause overflow

• MIPS C compilers produce addu, subu, addiu by default

Logical Instructions• Bitwise operations

– View contents of registers as 32 bits rather than as a single 32-bit number

• Instructions– and, or: the 3 operands are registers (R format)– andi, ori: the 3rd argument is an immediate (I format)

• Example: masks (andi $t0, $t0, 0xFFF) 1011 0110 1010 0100 0011 1101 1001 1010 0000 0000 0000 0000 0000 1111 1111 1111 0000 0000 0000 0000 0000 1101 1001 1010

Shift Instructions• Move all the bits in a register to the left/right

– sll (shift left logical): fills emptied bits with 0s– srl (shift right logical): fills emptied bits with 0s– sra (shift right arithmetic): sign extends emptied bits

• Example: srl $t0, $s1, 8 (R format)

000000 00001000000 10001 01000 01000

0001 0010 0011 0100 0101 0110 0111 0100

0000 0000 0001 0010 0011 0100 0101 0110

shamt

Zero Fill

Multiplication and Division• Use special purpose registers (hi, lo)

– 32-bit value x 32-bit value = 64-bit value

• Mult $s0, $s1 – hi: upper half of product– lo: lower half of product

• Div $s0, $s1– hi: remainder ($s0 / $s1)– lo: quotient ($s0 % $s1)

• Move results into general purpose registers:– mfhi $s0– mflo $s1

000000 10000 0000010001 00000 011000

000000 10000 0000010001 00000 011010

000000 00000 1000000000 00000 010000

000000 00000 1000100000 00000 010010

Assembly vs. Machine Language• Assembly provides convenient symbolic representation

– Much easier than writing numbers

– Destination operand first

– Pseudo instructions

– Labels to identify and name words that hold instructions/data

• Machine language is the underlying reality– Destination operand is no longer first

– Efficient format

• Assembly can provide pseudo instructions– Move $t0, $t1 (add $t0, $t1, $zero)

• When considering performance (IC) you should count real instructions

Register Conventions

Name Register Number Usage Preserved on call

$zero 0 the constant value 0 n.a.$at 1 reserved for the assembler n.a.

$v0-$v1 2-3 value for results and expressions no$a0-$a3 4-7 arguments (procedures/functions) yes$t0-$t7 8-15 temporaries no$s0-$s7 16-23 saved yes$t8-$t9 24-25 more temporaries no$k0-$k1 26-27 reserved for the operating system n.a.

$gp 28 global pointer yes$sp 29 stack pointer yes$fp 30 frame pointer yes$ra 31 return address yes

New Topic – Decision Instructions

• Conditional branches– If-then– If-then-else

• Loops– While– Do while– For

• Inequalities

• Switch statement

Conditional Branches

• Decision-Making Instructions• Branch if equal

– beq register1, register2, destination_address

• Branch if not equal– bne register1, register2, destination_address

• Example: beq $s3, $s4, 20

4 519 20

000100 0000 0000 0000 010110011 10100

6 bits 16 bits5 bits 5 bits

Labels

• No need to calculate addresses for branches

if (i = = j) go to L1;

f = g + h;

L1: f = f – i;

f => $s0g => $s1h => $s2i => $s3j => $s4

(4000) beq $s3, $s4, L1 # if i equals j go to L1

(4004) add $s0, $s1, $s2 # f = g + h

L1: (4008) sub $s0, $s0, $s3 # f = f - i

L1 corresponds to the address of the subtract instruction

If Statements

if (condition) clause1;else clause2;

if (condition) goto L1; clause2; goto L2;L1: clause1;L2:

if (i = = j) f = g + h;else f = g - h;

beq $3, $4, Truesub $0, $s1, $s2j False

True: add $s0, $s1, $s2False:

Loops

Loop: g = g + A[i]; i = i + j; if (i != h) goto Loop;

g: $s1h: $s2i: $s3j: $s4Base of A: $s5

Loop: add $t1, $s3 $s3 # $t1 = 2 * i add $t1, $t1, $t1 # $t1 = 4 * I add $t1, $t1, $5 # $t1=address of A[i] lw $t0, 0($t1) # $t0 = A[i] add $s1, $s1, $t0 # g = g + A[i] add $s3, $s3, $s4 # i = i + j bne $s3, $s2, Loop # go to Loop if i != h

Basic Block

Clever method of multiplying by 4 to get byte offset for one word

While Loop

while (save[i] = = k) i = i +j;

# i: $s3; j: $s4; k: $s5; base of save: $s6

Loop: add $t1, $s3, $s3 # $t1 = 2 * i add $t1, $t1, $t1 # $t1 = 4 * i add $t1, $t1, $s6 # $t1 = address of save[i] lw $t0, 0($t1) # $t0 = save[i] bne $t0, $s5, Exit # go to Exit if save[i] != k add $s3, $s3, $s4 # i = i +j j Loop # go to LoopExit:

Number of instructions executed if save[i + m * j] does not equal k for m = 10 and does equal k for 0 m 9 is 10 7 + 5 = 75

Optimization

add $t1, $s3, $s3 # Temp reg $t1 = 2 * i add $t1, $t1, $t1 # Temp reg $t1 = 4 * i add $t1, $t1, $s6 # $t1 = address of save[i] lw $t0, 0($t1) # Temp reg $t0 = save[i] bne $t0, $s5, Exit # go to Exit if save[i] kLoop: add $s3, $s3, $s4 # i = i + j add $t1, $s3, $s3 # Temp reg $t1 = 2 * i add $t1, $t1, $t1 # Temp reg $t1 = 4 * i add $t1, $t1, $s6 # $t1 = address of save[i] lw $t0, 0($t1) # Temp reg $t0 = save[i] beq $t0, $s5, Loop # go to Loop if save[i] = kExit:

The number of instructions executed by this new form of the loop is 5 + 10 6 = 65 Efficiency = 1.15 = 75/65. If 4 i is computed

before the loop, then further efficiency in the loop body is possible.

6

Instr’s

Loop PartiallyUnrolled

Do-While Loop

do { g = g + A[i]; i = i + j;} while (i != h);

L1: g = g + A[i]; i = i + j; if (i != h) goto L1

L1: sll $t1, $s3, 2 # $t1 = 4*i add $t1, $t1, $s5 # $t1 = addr of A lw $t1, 0($t1) # $t1 = A[i] add $s1, $s1, $t1 # g = g + A[i] add $s3, $s3, $s4 # i = i + j bne $s3, $s2, L1 # go to L1 if i != h

g: $s1h: $s2i: $s3j: $s4Base of A: $s5

• The conditional branch is the key to decision making

Rewrite

Inequalities• Programs need to test < and >• Set on less than instruction• slt register1, register2, register3

– register1 = (register2 < register3)? 1 : 0;

• Example: if (g < h) goto Less;

• slti: useful in for loops if (g >= 1) goto Loop

slt $t0, $s0, $s1bne $t0, $0, Less

g: $s0h: $s1

slti $t0, $s0, 1 # $t0 = 1 if g < 1beq $t0, $0, Loop # goto Loop if g >= 1

• Unsigned versions: sltu and sltiu

Relative Conditions

• == != < <= > >=• MIPS does not support directly the last four• Compilers use slt, beq, bne, $zero,

and $at

• Pseudoinstructions• blt $t1, $t2, L # if ($t1 < $t2) go to L

• ble $t1, $t2, L # if ($t1 <= $t2) go to L

• bgt $t1, $t2, L # if ($t1 > $t2) go to L

• bge $t1, $t2, L # if ($t1 >= $t2) go to L

slt $at, $t1, $t2bne $at, $zero, Lslt $at, $t2, $t1 beq $at, $zero, Lslt $at, $t2, $t1 bne $at, $zero, L

slt $at, $t1, $t2beq $at, $zero, L

The C Switch Statement

switch (k) { case 0: f = i + j; break; case 1: f = g + h; break; case 2: f = g - h; break; case 3: f = i - j; break;}

if (k==0) f = i + j; else if (k==1) f = g + h; else if (k==2) f = g - h; else if (k==3) f = i - j;

# f: $s0; g: $s1; h: $s2; i: $s3; j: $s4; k:$s5

bne $s5, $0, L1 # branch k != 0 add $s0, $s3, $s4 # f = i + j j Exit # end of caseL1: addi $t0, $s5, -1 # $t0 = k - 1 bne $t0, $0, L2 # branch k != 1 add $s0, $s1, $s2 # f = g + h j Exit # end of caseL2: addi $t0, $s5, -2 # $t0 = k - 2 bne $t0, $0, L3 # branch k != 2 sub $s0, $s1, $s2 # f = g - h j Exit # end of caseL3: addi $t0, $s5, -3 # $t0 = k - 3 bne $t0, $0, Exit # branch k != 3 sub $s0, $s3, $s4 # f = i - jExit:

Jump Tables# f: $s0; g: $s1; h: $s2; i: $s3; j: $s4; k:$s5# $t2 = 4; $t4 = base address of JT slt $t3, $s5, $zero # test k < 0 bne $t3, $zero, Exit # if so, exit slt $t3, $s5, $t2 # test k < 4 beq $t3, $zero, Exit # if so, exit add $t1, $s5, $5 # $t1 = 2*k add $t1, $t1, $t1 # $t1 = 4*k add $t1, $t1, $t4 # $t1 = &JT[k] lw $t0, 0($t1) # $t0 = JT[k] jr $t0 # jump registerL0: add $s0, $s3, $s4 # k == 0 j Exit # breakL1: add $s0, $1, $s2 # k == 1 j Exit # breakL2: sub $s0, $s1, $s2 # k == 2 j Exit # breakL3:sub $s0, $s3, $s4 # k == 3Exit:

L0

L3

L2

L1Jump Table

• Jump register instruction - jr <register> - unconditional branch to address contained in register

Conclusions

• MIPS instruction format – 32 bits• Assembly: Destination = first operand• Machine Language: Dest = last operand• Three MIPS formats: R (arithmetic)

I (immediate)J (jump)

• Decision instructions – use jump (goto)• Performance improvement - loop unrolling