Download Decision Instructions

CDA 3101
Spring 2016
Introduction to Computer Organization
Instruction Representation
19, 21 January 2016
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)
A[300] = h + A[300];
lw $t0, 1200($t1)
add $t0, $s2, $t0
sw $t0, 1200($t1)
10101101001010000000010010110000
00000010010010000100000000100000
10001101001010000000010010110000
Instruction Formats
6 bits
5 bits
5 bits
5 bits
5 bits
6 bits
R:
op
rs
rt
rd
shamt
funct
I:
op
rs
rt
J:
op
address / immediate
target address
op: basic operation of the instruction (opcode)
rs: first source operand register
rt: second source operand register
rd: destination operand register
shamt: shift amount
funct: selects the specific variant of the opcode (function code)
address: offset for load/store instructions (+/-215)
immediate: constants for immediate instructions
R Format
add $t0, $s1, $s2 (add $8, $17, $18 # $8 = $17 + $18)
6 bits
5 bits
5 bits
5 bits
5 bits
6 bits
0
17
18
8
0
32
000000
10001
10010
01000
00000
100000
sub $t1, $s1, $s2 (sub $9, $17, $18
# $9 = $17 - $18)
6 bits
5 bits
5 bits
5 bits
5 bits
6 bits
0
17
18
9
0
34
000000
10001
10010
01001
00000
100010
I Format
lw $t0, 52($s3)
lw $8, 52($19)
6 bits
5 bits
5 bits
35
19
8
16 bits
52
100011
10011
01000
0000 0000 0011 0100
sw $t0, 52($s3)
sw $8, 52($19)
6 bits
5 bits
5 bits
43
19
8
16 bits
52
101011
10011
01000
0000 0000 0011 0100
Example
A[300] = h + A[300];
/* $t1 <= base of array A; $s2 <= h */
Compiler
lw $t0, 1200($t1)
add $t0, $s2, $t0
sw $t0, 1200($t1)
# temporary register $t0 gets A[300]
# temporary register $t0 gets h +A[300]
# stores h + A[300] back into A[300]
Assembler
35
0
43
9
18
9
8
8
8
100011
000000
101011
01001
10010
01001
01000
01000
01000
8
1200
0
1200
32
0000 0100 1011 0000
01000
00000
100000
0000 0100 1011 0000
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
8
001000
23
10111
# $t0 = $s7 + 4
8
01000
4
0000 0000 0000 0100
Arithmetic Overflow
• Computers have limited precision (32 bits)
15
+3
18
1111
0011
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)
shamt
000000
00000
10001
01000
01000
0001 0010 0011 0100 0101 0110 0111 0100
Zero Fill
0000 0000 0001 0010 0011 0100 0101 0110
000010
Multiplication and Division
• Use special purpose registers (hi, lo)
– 32-bit value x 32-bit value = 64-bit value
• Mult $s0, $s1
000000 10000 10001 00000 00000 011000
– hi: upper half of product
– lo: lower half of product
• Div $s0, $s1
000000 10000 10001 00000 00000 011010
– hi: remainder ($s0 / $s1)
– lo: quotient ($s0 % $s1)
• Move results into general purpose registers:
– mfhi $s0
– mflo $s1
000000 00000 00000 10000 00000 010000
000000 00000 00000 10001 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
$zero
$at
$v0-$v1
$a0-$a3
$t0-$t7
$s0-$s7
$t8-$t9
$k0-$k1
$gp
$sp
$fp
$ra
Register Number
0
1
2-3
4-7
8-15
16-23
24-25
26-27
28
29
30
31
Usage
the constant value 0
reserved for the assembler
value for results and expressions
arguments (procedures/functions)
temporaries
saved
more temporaries
reserved for the operating system
global pointer
stack pointer
frame pointer
return address
Preserved on call
n.a.
n.a.
no
yes
no
yes
no
n.a.
yes
yes
yes
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
6 bits
5 bits
5 bits
4
19
20
16 bits
5
000100
10011
10100
0000 0000 0000 0101
Labels
• No need to calculate addresses for branches
f
g
h
i
j
if (i = = j) go to L1;
f = g + h;
L1:
f = f – i;
(4000) beq $s3, $s4, L1
=>
=>
=>
=>
=>
$s0
$s1
$s2
$s3
$s4
# 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, True
sub $0, $s1, $s2
j False
True: add $s0, $s1, $s2
False:
Loops
Loop: g = g + A[i];
i = i + j;
if (i != h) goto Loop;
g: $s1
h: $s2
i: $s3
j: $s4
Base of A: $s5
Clever method of
multiplying by 4 to
get byte offset for
one word
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
While Loop
while (save[i] = = k)
i = i +j;
# i: $s3; j: $s4; k: $s5; base of save: $s6
Loop: add $t1, $s3, $s3
add $t1, $t1, $t1
add $t1, $t1, $s6
lw $t0, 0($t1)
bne $t0, $s5, Exit
add $s3, $s3, $s4
j Loop
Exit:
# $t1 = 2 * i
# $t1 = 4 * i
# $t1 = address of save[i]
# $t0 = save[i]
# go to Exit if save[i] != k
# i = i +j
# go to Loop
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
Loop
Partially
Unrolled
6
Instr’s
add $t1, $s3, $s3
add $t1, $t1, $t1
add $t1, $t1, $s6
lw $t0, 0($t1)
bne $t0, $s5, Exit
Loop: add $s3, $s3, $s4
add $t1, $s3, $s3
add $t1, $t1, $t1
add $t1, $t1, $s6
lw $t0, 0($t1)
beq $t0, $s5, Loop
Exit:
# Temp reg $t1 = 2 * i
# Temp reg $t1 = 4 * i
# $t1 = address of save[i]
# Temp reg $t0 = save[i]
# go to Exit if save[i] k
#i=i+j
# Temp reg $t1 = 2 * i
# Temp reg $t1 = 4 * i
# $t1 = address of save[i]
# Temp reg $t0 = save[i]
# go to Loop if save[i] = k
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.
Do-While Loop
do {
g = g + A[i];
i = i + j;
} while (i != h);
g: $s1
h: $s2
i: $s3
j: $s4
Base of A: $s5
Rewrite
L1: g = g + A[i];
i = i + j;
if (i != h) goto L1
L1: sll $t1, $s3, 2
add $t1, $t1, $s5
lw $t1, 0($t1)
add $s1, $s1, $t1
add $s3, $s3, $s4
bne $s3, $s2, L1
# $t1 = 4*i
# $t1 = addr of A
# $t1 = A[i]
# g = g + A[i]
# i =i+j
# go to L1 if i != h
• The conditional branch is the key to decision making
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;
g: $s0
h: $s1
slt $t0, $s0, $s1
bne $t0, $0, Less
• slti: useful in for loops if (g >= 1) goto Loop
slti $t0, $s0, 1
beq $t0, $0, Loop
# $t0 = 1 if g < 1
# 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
slt $at, $t1, $t2
bne $at, $zero,
L
slt $at, $t2,
$t1
beq $at, $zero,
L
slt $at, $t2,
$t1 bne $at,
$zero, L
slt $at, $t1, $t2
# if ($t1 >= $t2) gobeq
to L
$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
add $s0, $s3, $s4
j
Exit
L1: addi $t0, $s5, -1
bne $t0, $0, L2
add $s0, $s1, $s2
j
Exit
L2: addi $t0, $s5, -2
bne $t0, $0, L3
sub $s0, $s1, $s2
j
Exit
L3: addi $t0, $s5, -3
bne $t0, $0, Exit
sub $s0, $s3, $s4
Exit:
# branch k != 0
#f=i+j
# end of case
# $t0 = k - 1
# branch k != 1
#f=g+h
# end of case
# $t0 = k - 2
# branch k != 2
#f=g-h
# end of case
# $t0 = k - 3
# branch k != 3
#f=i-j
Jump Tables
• Jump register instruction
- jr <register>
- unconditional branch to
address contained in register
Jump
Table
L0
L1
L2
L3
# 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 register
L0: add $s0, $s3, $s4
# k == 0
j
Exit
# break
L1: add $s0, $1, $s2
# k == 1
j
Exit
# break
L2: sub $s0, $s1, $s2
# k == 2
j
Exit
# break
L3:sub $s0, $s3, $s4
# k == 3
Exit:
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)
• Improve Performance: loop unrolling
Anticipate the Weekend