Lectures for 3rd Edition
Note: these lectures are often supplemented with other
materials and also problems from the text worked out
on the blackboard. You’ll want to customize these
lectures for your class. The student audience for
these lectures have had exposure to logic design and
attend a hands-on assembly language programming
lab that does not follow a typical lecture format.
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Chapter 1
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Introduction
•
This course is all about how computers work
•
But what do we mean by a computer?
– Different types: desktop, servers, embedded devices
– Different uses: automobiles, graphics, finance, genomics…
– Different manufacturers: Intel, Apple, IBM, Microsoft, Sun…
– Different underlying technologies and different costs!
•
Analogy: Consider a course on “automotive vehicles”
– Many similarities from vehicle to vehicle (e.g., wheels)
– Huge differences from vehicle to vehicle (e.g., gas vs. electric)
•
Best way to learn:
– Focus on a specific instance and learn how it works
– While learning general principles and historical perspectives
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Why learn this stuff?
•
You want to call yourself a “computer scientist”
•
You want to build software people use (need performance)
•
You need to make a purchasing decision or offer “expert” advice
•
Both Hardware and Software affect performance:
– Algorithm determines number of source-level statements
– Language/Compiler/Architecture determine machine instructions
(Chapter 2 and 3)
– Processor/Memory determine how fast instructions are executed
(Chapter 5, 6, and 7)
•
Assessing and Understanding Performance in Chapter 4
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What is a computer?
•
•
Components:
– input (mouse, keyboard)
– output (display, printer)
– memory (disk drives, DRAM, SRAM, CD)
– network
Our primary focus: the processor (datapath and control)
– implemented using millions of transistors
– Impossible to understand by looking at each transistor
– We need...
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Abstraction
•
Delving into the depths
reveals more information
•
An abstraction omits unneeded detail,
helps us cope with complexity
What are some of the details that
appear in these familiar abstractions?
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How do computers work?
•
Need to understand abstractions such as:
– Applications software
– Systems software
– Assembly Language
– Machine Language
– Architectural Issues: i.e., Caches, Virtual Memory, Pipelining
– Sequential logic, finite state machines
– Combinational logic, arithmetic circuits
– Boolean logic, 1s and 0s
– Transistors used to build logic gates (CMOS)
– Semiconductors/Silicon used to build transistors
– Properties of atoms, electrons, and quantum dynamics
•
So much to learn!
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Instruction Set Architecture
•
A very important abstraction
– interface between hardware and low-level software
– standardizes instructions, machine language bit patterns, etc.
– advantage: different implementations of the same architecture
– disadvantage: sometimes prevents using new innovations
True or False: Binary compatibility is extraordinarily important?
•
Modern instruction set architectures:
– IA-32, PowerPC, MIPS, SPARC, ARM, and others
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Historical Perspective
•
ENIAC built in World War II was the first general purpose computer
– Used for computing artillery firing tables
– 80 feet long by 8.5 feet high and several feet wide
– Each of the twenty 10 digit registers was 2 feet long
– Used 18,000 vacuum tubes
– Performed 1900 additions per second
–Since then:
Moore’s Law:
transistor capacity doubles
every 18-24 months
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Chapter 2
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Instructions:
•
•
Language of the Machine
We’ll be working with the MIPS instruction set architecture
– similar to other architectures developed since the 1980's
– Almost 100 million MIPS processors manufactured in 2002
– used by NEC, Nintendo, Cisco, Silicon Graphics, Sony, …
1400
1300
1200
1100
1000
900
800
Other
SPARC
Hitachi SH
PowerPC
Motorola 68K
MIPS
IA-32
ARM
700
600
500
400
300
200
100
0
1998
1999
2000
2001
2002
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MIPS arithmetic
•
•
All instructions have 3 operands
Operand order is fixed (destination first)
Example:
C code:
a = b + c
MIPS ‘code’:
add a, b, c
(we’ll talk about registers in a bit)
“The natural number of operands for an operation like addition is
three…requiring every instruction to have exactly three operands, no
more and no less, conforms to the philosophy of keeping the
hardware simple”
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MIPS arithmetic
•
•
Design Principle: simplicity favors regularity.
Of course this complicates some things...
C code:
a = b + c + d;
MIPS code:
add a, b, c
add a, a, d
•
•
Operands must be registers, only 32 registers provided
Each register contains 32 bits
•
Design Principle: smaller is faster.
Why?
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Registers vs. Memory
•
•
•
Arithmetic instructions operands must be registers,
— only 32 registers provided
Compiler associates variables with registers
What about programs with lots of variables
Control
Input
Memory
Datapath
Processor
Output
I/O
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Memory Organization
•
•
•
Viewed as a large, single-dimension array, with an address.
A memory address is an index into the array
"Byte addressing" means that the index points to a byte of memory.
0
1
2
3
4
5
6
...
8 bits of data
8 bits of data
8 bits of data
8 bits of data
8 bits of data
8 bits of data
8 bits of data
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Memory Organization
•
•
•
•
•
Bytes are nice, but most data items use larger "words"
For MIPS, a word is 32 bits or 4 bytes.
0 32 bits of data
4 32 bits of data
Registers hold 32 bits of data
32
bits
of
data
8
12 32 bits of data
...
232 bytes with byte addresses from 0 to 232-1
230 words with byte addresses 0, 4, 8, ... 232-4
Words are aligned
i.e., what are the least 2 significant bits of a word address?
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Instructions
•
•
•
•
•
Load and store instructions
Example:
C code:
A[12] = h + A[8];
MIPS code:
lw $t0, 32($s3)
add $t0, $s2, $t0
sw $t0, 48($s3)
Can refer to registers by name (e.g., $s2, $t2) instead of number
Store word has destination last
Remember arithmetic operands are registers, not memory!
Can’t write:
add 48($s3), $s2, 32($s3)
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Our First Example
•
Can we figure out the code?
swap(int v[], int k);
{ int temp;
temp = v[k]
v[k] = v[k+1];
v[k+1] = temp;
swap:
}
muli $2, $5, 4
add $2, $4, $2
lw $15, 0($2)
lw $16, 4($2)
sw $16, 0($2)
sw $15, 4($2)
jr $31
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So far we’ve learned:
•
MIPS
— loading words but addressing bytes
— arithmetic on registers only
•
Instruction
Meaning
add $s1, $s2, $s3
sub $s1, $s2, $s3
lw $s1, 100($s2)
sw $s1, 100($s2)
$s1 = $s2 + $s3
$s1 = $s2 – $s3
$s1 = Memory[$s2+100]
Memory[$s2+100] = $s1
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Machine Language
•
Instructions, like registers and words of data, are also 32 bits long
– Example: add $t1, $s1, $s2
– registers have numbers, $t1=9, $s1=17, $s2=18
•
Instruction Format:
000000 10001
op
•
rs
10010
rt
01000
rd
00000
100000
shamt
funct
Can you guess what the field names stand for?
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Machine Language
•
•
•
•
Consider the load-word and store-word instructions,
– What would the regularity principle have us do?
– New principle: Good design demands a compromise
Introduce a new type of instruction format
– I-type for data transfer instructions
– other format was R-type for register
Example: lw $t0, 32($s2)
35
18
9
op
rs
rt
32
16 bit number
Where's the compromise?
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Stored Program Concept
•
•
Instructions are bits
Programs are stored in memory
— to be read or written just like data
Processor
•
Memory
memory for data, programs,
compilers, editors, etc.
Fetch & Execute Cycle
– Instructions are fetched and put into a special register
– Bits in the register "control" the subsequent actions
– Fetch the “next” instruction and continue
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Control
•
Decision making instructions
– alter the control flow,
– i.e., change the "next" instruction to be executed
•
MIPS conditional branch instructions:
bne $t0, $t1, Label
beq $t0, $t1, Label
•
Example:
if (i==j) h = i + j;
bne $s0, $s1, Label
add $s3, $s0, $s1
Label: ....
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Control
•
MIPS unconditional branch instructions:
j label
•
Example:
if (i!=j)
h=i+j;
else
h=i-j;
•
beq $s4, $s5, Lab1
add $s3, $s4, $s5
j Lab2
Lab1: sub $s3, $s4, $s5
Lab2: ...
Can you build a simple for loop?
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So far:
•
•
Instruction
Meaning
add $s1,$s2,$s3
sub $s1,$s2,$s3
lw $s1,100($s2)
sw $s1,100($s2)
bne $s4,$s5,L
beq $s4,$s5,L
j Label
$s1 = $s2 + $s3
$s1 = $s2 – $s3
$s1 = Memory[$s2+100]
Memory[$s2+100] = $s1
Next instr. is at Label if $s4 ≠ $s5
Next instr. is at Label if $s4 = $s5
Next instr. is at Label
Formats:
R
op
rs
rt
rd
I
op
rs
rt
16 bit address
J
op
shamt
funct
26 bit address
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Control Flow
•
•
We have: beq, bne, what about Branch-if-less-than?
New instruction:
if $s1 < $s2 then
$t0 = 1
slt $t0, $s1, $s2
else
$t0 = 0
•
Can use this instruction to build "blt $s1, $s2, Label"
— can now build general control structures
Note that the assembler needs a register to do this,
— there are policy of use conventions for registers
•
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Policy of Use Conventions
Name Register number
$zero
0
$v0-$v1
2-3
$a0-$a3
4-7
$t0-$t7
8-15
$s0-$s7
16-23
$t8-$t9
24-25
$gp
28
$sp
29
$fp
30
$ra
31
Usage
the constant value 0
values for results and expression evaluation
arguments
temporaries
saved
more temporaries
global pointer
stack pointer
frame pointer
return address
Register 1 ($at) reserved for assembler, 26-27 for operating system
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Constants
•
•
•
Small constants are used quite frequently (50% of operands)
e.g.,
A = A + 5;
B = B + 1;
C = C - 18;
Solutions? Why not?
– put 'typical constants' in memory and load them.
– create hard-wired registers (like $zero) for constants like one.
MIPS Instructions:
addi $29, $29, 4
slti $8, $18, 10
andi $29, $29, 6
ori $29, $29, 4
•
Design Principle: Make the common case fast.
Which format?
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How about larger constants?
•
•
We'd like to be able to load a 32 bit constant into a register
Must use two instructions, new "load upper immediate" instruction
lui $t0, 1010101010101010
1010101010101010
•
filled with zeros
0000000000000000
Then must get the lower order bits right, i.e.,
ori $t0, $t0, 1010101010101010
1010101010101010
0000000000000000
0000000000000000
1010101010101010
1010101010101010
1010101010101010
ori
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Assembly Language vs. Machine Language
•
•
•
•
Assembly provides convenient symbolic representation
– much easier than writing down numbers
– e.g., destination first
Machine language is the underlying reality
– e.g., destination is no longer first
Assembly can provide 'pseudoinstructions'
– e.g., “move $t0, $t1” exists only in Assembly
– would be implemented using “add $t0,$t1,$zero”
When considering performance you should count real instructions
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Other Issues
•
Discussed in your assembly language programming lab:
support for procedures
linkers, loaders, memory layout
stacks, frames, recursion
manipulating strings and pointers
interrupts and exceptions
system calls and conventions
•
Some of these we'll talk more about later
•
We’ll talk about compiler optimizations when we hit chapter 4.
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Overview of MIPS
•
•
•
•
•
simple instructions all 32 bits wide
very structured, no unnecessary baggage
only three instruction formats
R
op
rs
rt
rd
I
op
rs
rt
16 bit address
J
op
shamt
funct
26 bit address
rely on compiler to achieve performance
— what are the compiler's goals?
help compiler where we can
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Addresses in Branches and Jumps
•
•
•
Instructions:
bne $t4,$t5,Label
$t5
beq $t4,$t5,Label
$t5
j Label
op
I
Formats:
op
J
rs
Next instruction is at Label if $t4 °
Next instruction is at Label if $t4 =
Next instruction is at Label
rt
16 bit address
26 bit address
Addresses are not 32 bits
— How do we handle this with load and store instructions?
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Addresses in Branches
•
•
Instructions:
bne $t4,$t5,Label
beq $t4,$t5,Label
Formats:
I
•
•
Next instruction is at Label if $t4≠$t5
Next instruction is at Label if $t4=$t5
op
rs
rt
16 bit address
Could specify a register (like lw and sw) and add it to address
– use Instruction Address Register (PC = program counter)
– most branches are local (principle of locality)
Jump instructions just use high order bits of PC
– address boundaries of 256 MB
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To summarize:
MIPS operands
Name
32 registers
Example
Comments
$s0-$s7, $t0-$t9, $zero, Fast locations for data. In MIPS, data must be in registers to perform
$a0-$a3, $v0-$v1, $gp,
arithmetic. MIPS register $zero always equals 0. Register $at is
$fp, $sp, $ra, $at
reserved for the assembler to handle large constants.
Memory[0],
2
30
Accessed only by data transfer instructions. MIPS uses byte addresses, so
memory Memory[4], ...,
words
and spilled registers, such as those saved on procedure calls.
add
MIPS assembly language
Example
Meaning
add $s1, $s2, $s3
$s1 = $s2 + $s3
Three operands; data in registers
subtract
sub $s1, $s2, $s3
$s1 = $s2 - $s3
Three operands; data in registers
$s1 = $s2 + 100
$s1 = Memory[$s2 + 100]
Memory[$s2 + 100] = $s1
$s1 = Memory[$s2 + 100]
Memory[$s2 + 100] = $s1
Used to add constants
Category
Arithmetic
sequential words differ by 4. Memory holds data structures, such as arrays,
Memory[4294967292]
Instruction
addi $s1, $s2, 100
lw $s1, 100($s2)
sw $s1, 100($s2)
store word
lb $s1, 100($s2)
load byte
sb $s1, 100($s2)
store byte
load upper immediate lui $s1, 100
add immediate
load word
Data transfer
Conditional
branch
Unconditional jump
$s1 = 100 * 2
16
Comments
Word from memory to register
Word from register to memory
Byte from memory to register
Byte from register to memory
Loads constant in upper 16 bits
branch on equal
beq
$s1, $s2, 25
if ($s1 == $s2) go to
PC + 4 + 100
Equal test; PC-relative branch
branch on not equal
bne
$s1, $s2, 25
if ($s1 != $s2) go to
PC + 4 + 100
Not equal test; PC-relative
set on less than
slt
$s1, $s2, $s3
if ($s2 < $s3) $s1 = 1;
else $s1 = 0
Compare less than; for beq, bne
set less than
immediate
slti
jump
j
jr
jal
jump register
jump and link
$s1, $s2, 100 if ($s2 < 100) $s1 = 1;
Compare less than constant
else $s1 = 0
2500
$ra
2500
Jump to target address
go to 10000
For switch, procedure return
go to $ra
$ra = PC + 4; go to 10000 For procedure call
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1. Immediate addressing
op
rs
rt
Immediate
2. Register addressing
op
rs
rt
rd
...
funct
Registers
Register
3. Base addressing
op
rs
rt
Memory
Address
+
Register
Byte
Halfword
Word
4. PC-relative addressing
op
rs
rt
Memory
Address
PC
+
Word
5. Pseudodirect addressing
op
Address
PC
Memory
Word
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Alternative Architectures
•
Design alternative:
– provide more powerful operations
– goal is to reduce number of instructions executed
– danger is a slower cycle time and/or a higher CPI
–“The path toward operation complexity is thus fraught with peril.
To avoid these problems, designers have moved toward simpler
instructions”
•
Let’s look (briefly) at IA-32
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IA - 32
•
•
•
•
•
•
•
•
•
•
•
1978: The Intel 8086 is announced (16 bit architecture)
1980: The 8087 floating point coprocessor is added
1982: The 80286 increases address space to 24 bits, +instructions
1985: The 80386 extends to 32 bits, new addressing modes
1989-1995: The 80486, Pentium, Pentium Pro add a few instructions
(mostly designed for higher performance)
1997: 57 new “MMX” instructions are added, Pentium II
1999: The Pentium III added another 70 instructions (SSE)
2001: Another 144 instructions (SSE2)
2003: AMD extends the architecture to increase address space to 64 bits,
widens all registers to 64 bits and other changes (AMD64)
2004: Intel capitulates and embraces AMD64 (calls it EM64T) and adds
more media extensions
“This history illustrates the impact of the “golden handcuffs” of compatibility
“adding new features as someone might add clothing to a packed bag”
“an architecture that is difficult to explain and impossible to love”
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IA-32 Overview
•
•
Complexity:
– Instructions from 1 to 17 bytes long
– one operand must act as both a source and destination
– one operand can come from memory
– complex addressing modes
e.g., “base or scaled index with 8 or 32 bit displacement”
Saving grace:
– the most frequently used instructions are not too difficult to
build
– compilers avoid the portions of the architecture that are slow
“what the 80x86 lacks in style is made up in quantity,
making it beautiful from the right perspective”
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IA-32 Registers and Data Addressing
•
Registers in the 32-bit subset that originated with 80386
Name
Use
31
0
EAX
GPR 0
ECX
GPR 1
EDX
GPR 2
EBX
GPR 3
ESP
GPR 4
EBP
GPR 5
ESI
GPR 6
EDI
GPR 7
EIP
EFLAGS
CS
Code segment pointer
SS
Stack segment pointer (top of stack)
DS
Data segment pointer 0
ES
Data segment pointer 1
FS
Data segment pointer 2
GS
Data segment pointer 3
Instruction pointer (PC)
Condition codes
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IA-32 Register Restrictions
•
Registers are not “general purpose” – note the restrictions below
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IA-32 Typical Instructions
•
Four major types of integer instructions:
– Data movement including move, push, pop
– Arithmetic and logical (destination register or memory)
– Control flow (use of condition codes / flags )
– String instructions, including string move and string compare
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IA-32 instruction Formats
•
Typical formats: (notice the different lengths)
a. JE EIP + displacement
4
4
8
CondiDisplacement
tion
JE
b. CALL
8
32
CALL
Offset
c. MOV
6
MOV
EBX, [EDI + 45]
1 1
8
d w
r/m
Postbyte
8
Displacement
d. PUSH ESI
5
3
PUSH
Reg
e. ADD EAX, #6765
4
3 1
32
ADD Reg w
f. TEST EDX, #42
7
1
TEST
w
Immediate
8
32
Postbyte
Immediate
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Summary
•
•
•
Instruction complexity is only one variable
– lower instruction count vs. higher CPI / lower clock rate
Design Principles:
– simplicity favors regularity
– smaller is faster
– good design demands compromise
– make the common case fast
Instruction set architecture
– a very important abstraction indeed!
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Chapter Three
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Numbers
•
•
•
•
Bits are just bits (no inherent meaning)
— conventions define relationship between bits and numbers
Binary numbers (base 2)
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001...
decimal: 0...2n-1
Of course it gets more complicated:
numbers are finite (overflow)
fractions and real numbers
negative numbers
e.g., no MIPS subi instruction; addi can add a negative number
How do we represent negative numbers?
i.e., which bit patterns will represent which numbers?
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Possible Representations
•
Sign Magnitude:
000 = +0
001 = +1
010 = +2
011 = +3
100 = -0
101 = -1
110 = -2
111 = -3
•
•
One's Complement
Two's Complement
000 = +0
001 = +1
010 = +2
011 = +3
100 = -3
101 = -2
110 = -1
111 = -0
000 = +0
001 = +1
010 = +2
011 = +3
100 = -4
101 = -3
110 = -2
111 = -1
Issues: balance, number of zeros, ease of operations
Which one is best? Why?
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MIPS
•
32 bit signed numbers:
0000
0000
0000
...
0111
0111
1000
1000
1000
...
1111
1111
1111
0000 0000 0000 0000 0000 0000 0000two = 0ten
0000 0000 0000 0000 0000 0000 0001two = + 1ten
0000 0000 0000 0000 0000 0000 0010two = + 2ten
1111
1111
0000
0000
0000
1111
1111
0000
0000
0000
1111
1111
0000
0000
0000
1111
1111
0000
0000
0000
1111
1111
0000
0000
0000
1111
1111
0000
0000
0000
1110two
1111two
0000two
0001two
0010two
=
=
=
=
=
+
+
–
–
–
2,147,483,646ten
2,147,483,647ten
2,147,483,648ten
2,147,483,647ten
2,147,483,646ten
maxint
minint
1111 1111 1111 1111 1111 1111 1101two = – 3ten
1111 1111 1111 1111 1111 1111 1110two = – 2ten
1111 1111 1111 1111 1111 1111 1111two = – 1ten
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Two's Complement Operations
•
Negating a two's complement number: invert all bits and add 1
– remember: “negate” and “invert” are quite different!
•
Converting n bit numbers into numbers with more than n bits:
– MIPS 16 bit immediate gets converted to 32 bits for arithmetic
– copy the most significant bit (the sign bit) into the other bits
0010
-> 0000 0010
1010
-> 1111 1010
– "sign extension" (lbu vs. lb)
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Addition & Subtraction
•
Just like in grade school (carry/borrow 1s)
0111
0111
0110
+ 0110
- 0110
- 0101
•
Two's complement operations easy
– subtraction using addition of negative numbers
0111
+ 1010
•
Overflow (result too large for finite computer word):
– e.g., adding two n-bit numbers does not yield an n-bit number
0111
+ 0001
note that overflow term is somewhat misleading,
1000
it does not mean a carry “overflowed”
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Detecting Overflow
•
•
•
•
No overflow when adding a positive and a negative number
No overflow when signs are the same for subtraction
Overflow occurs when the value affects the sign:
– overflow when adding two positives yields a negative
– or, adding two negatives gives a positive
– or, subtract a negative from a positive and get a negative
– or, subtract a positive from a negative and get a positive
Consider the operations A + B, and A – B
– Can overflow occur if B is 0 ?
– Can overflow occur if A is 0 ?
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Effects of Overflow
•
•
•
An exception (interrupt) occurs
– Control jumps to predefined address for exception
– Interrupted address is saved for possible resumption
Details based on software system / language
– example: flight control vs. homework assignment
Don't always want to detect overflow
— new MIPS instructions: addu, addiu, subu
note: addiu still sign-extends!
note: sltu, sltiu for unsigned comparisons
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52
Multiplication
•
•
•
More complicated than addition
– accomplished via shifting and addition
More time and more area
Let's look at 3 versions based on a gradeschool algorithm
0010
__x_1011
•
(multiplicand)
(multiplier)
Negative numbers: convert and multiply
– there are better techniques, we won’t look at them
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Multiplication: Implementation
Start
Multiplier0 = 1
1. Test
Multiplier0 = 0
Multiplier0
1a. Add multiplicand to product and
Multiplicand
place the result in Product register
Shift left
64 bits
Multiplier
Shift right
64-bit ALU
2. Shift the Multiplicand register left 1 bit
32 bits
Product
Write
3. Shift the Multiplier register right 1 bit
Control test
64 bits
No: < 32 repetitions
32nd repetition?
Datapath
Yes: 32 repetitions
Control
Done
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Final Version
Start
•Multiplier starts in right half of product
Product0 = 1
1. Test
Product0 = 0
Product0
Multiplicand
32 bits
32-bit ALU
Product
Shift right
Write
Control
test
3. Shift the Product register right 1 bit
64 bits
No: < 32 repetitions
32nd repetition?
What goes here?
Yes: 32 repetitions
Done
2004 Morgan Kaufmann Publishers
55
Floating Point (a brief look)
•
We need a way to represent
– numbers with fractions, e.g., 3.1416
– very small numbers, e.g., .000000001
– very large numbers, e.g., 3.15576  109
•
Representation:
– sign, exponent, significand:
(–1)sign  significand  2exponent
– more bits for significand gives more accuracy
– more bits for exponent increases range
•
IEEE 754 floating point standard:
– single precision: 8 bit exponent, 23 bit significand
– double precision: 11 bit exponent, 52 bit significand
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IEEE 754 floating-point standard
•
Leading “1” bit of significand is implicit
•
Exponent is “biased” to make sorting easier
– all 0s is smallest exponent all 1s is largest
– bias of 127 for single precision and 1023 for double precision
– summary: (–1)sign  (1+significand)  2exponent – bias
•
Example:
– decimal: -.75 = - ( ½ + ¼ )
– binary: -.11 = -1.1 x 2-1
– floating point: exponent = 126 = 01111110
– IEEE single precision: 10111111010000000000000000000000
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Floating point addition
•
Sign
Exponent
Fraction
Sign
Exponent
1. Compare the exponents of the two numbers.
Shift the smaller number to the right until its
exponent would match the larger exponent
Small ALU
Exponent
difference
0
Start
Fraction
2. Add the significands
1
0
1
0
1
3. Normalize the sum, either shifting right and
incrementing the exponent or shifting left
and decrementing the exponent
Shift right
Control
Overflow or
underflow?
Big ALU
Yes
No
0
0
1
Increment or
decrement
Exception
1
4. Round the significand to the appropriate
number of bits
Shift left or right
No
Rounding hardware
Still normalized?
Yes
Sign
Exponent
Fraction
Done
2004 Morgan Kaufmann Publishers
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Floating Point Complexities
•
Operations are somewhat more complicated (see text)
•
In addition to overflow we can have “underflow”
•
Accuracy can be a big problem
– IEEE 754 keeps two extra bits, guard and round
– four rounding modes
– positive divided by zero yields “infinity”
– zero divide by zero yields “not a number”
– other complexities
•
•
Implementing the standard can be tricky
Not using the standard can be even worse
– see text for description of 80x86 and Pentium bug!
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Chapter Three Summary
•
Computer arithmetic is constrained by limited precision
•
Bit patterns have no inherent meaning but standards do exist
– two’s complement
– IEEE 754 floating point
•
Computer instructions determine “meaning” of the bit patterns
•
Performance and accuracy are important so there are many
complexities in real machines
•
Algorithm choice is important and may lead to hardware
optimizations for both space and time (e.g., multiplication)
•
You may want to look back (Section 3.10 is great reading!)
2004 Morgan Kaufmann Publishers
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Chapter 4
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Performance
•
•
•
•
Measure, Report, and Summarize
Make intelligent choices
See through the marketing hype
Key to understanding underlying organizational motivation
Why is some hardware better than others for different programs?
What factors of system performance are hardware related?
(e.g., Do we need a new machine, or a new operating system?)
How does the machine's instruction set affect performance?
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Which of these airplanes has the best performance?
Airplane
Passengers
Boeing 737-100
Boeing 747
BAC/Sud Concorde
Douglas DC-8-50
101
470
132
146
Range (mi) Speed (mph)
630
4150
4000
8720
598
610
1350
544
•How much faster is the Concorde compared to the 747?
•How much bigger is the 747 than the Douglas DC-8?
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Computer Performance: TIME, TIME, TIME
•
Response Time (latency)
— How long does it take for my job to run?
— How long does it take to execute a job?
— How long must I wait for the database query?
•
Throughput
— How many jobs can the machine run at once?
— What is the average execution rate?
— How much work is getting done?
•
If we upgrade a machine with a new processor what do we increase?
•
If we add a new machine to the lab what do we increase?
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Execution Time
•
•
•
Elapsed Time
– counts everything (disk and memory accesses, I/O , etc.)
– a useful number, but often not good for comparison purposes
CPU time
– doesn't count I/O or time spent running other programs
– can be broken up into system time, and user time
Our focus: user CPU time
– time spent executing the lines of code that are "in" our program
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Book's Definition of Performance
•
For some program running on machine X,
PerformanceX = 1 / Execution timeX
•
"X is n times faster than Y"
PerformanceX / PerformanceY = n
•
Problem:
– machine A runs a program in 20 seconds
– machine B runs the same program in 25 seconds
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Clock Cycles
•
Instead of reporting execution time in seconds, we often use cycles
seconds
cycles
seconds


program program
cycle
•
Clock “ticks” indicate when to start activities (one abstraction):
time
•
•
cycle time = time between ticks = seconds per cycle
clock rate (frequency) = cycles per second (1 Hz. = 1 cycle/sec)
A 4 Ghz. clock has a
1
4 109
1012  250 picosecond s (ps) cycle time
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How to Improve Performance
seconds
cycles
seconds


program program
cycle
So, to improve performance (everything else being equal) you can
either (increase or decrease?)
________ the # of required cycles for a program, or
________ the clock cycle time or, said another way,
________ the clock rate.
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How many cycles are required for a program?
...
6th
5th
4th
3rd instruction
2nd instruction
Could assume that number of cycles equals number of instructions
1st instruction
•
time
This assumption is incorrect,
different instructions take different amounts of time on different machines.
Why? hint: remember that these are machine instructions, not lines of C code
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Different numbers of cycles for different instructions
time
•
Multiplication takes more time than addition
•
Floating point operations take longer than integer ones
•
Accessing memory takes more time than accessing registers
•
Important point: changing the cycle time often changes the number of
cycles required for various instructions (more later)
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Example
•
Our favorite program runs in 10 seconds on computer A, which has a
4 GHz. clock. We are trying to help a computer designer build a new
machine B, that will run this program in 6 seconds. The designer can use
new (or perhaps more expensive) technology to substantially increase the
clock rate, but has informed us that this increase will affect the rest of the
CPU design, causing machine B to require 1.2 times as many clock cycles as
machine A for the same program. What clock rate should we tell the
designer to target?"
•
Don't Panic, can easily work this out from basic principles
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Now that we understand cycles
•
A given program will require
– some number of instructions (machine instructions)
– some number of cycles
– some number of seconds
•
We have a vocabulary that relates these quantities:
– cycle time (seconds per cycle)
– clock rate (cycles per second)
– CPI (cycles per instruction)
a floating point intensive application might have a higher CPI
– MIPS (millions of instructions per second)
this would be higher for a program using simple instructions
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Performance
•
•
Performance is determined by execution time
Do any of the other variables equal performance?
– # of cycles to execute program?
– # of instructions in program?
– # of cycles per second?
– average # of cycles per instruction?
– average # of instructions per second?
•
Common pitfall: thinking one of the variables is indicative of
performance when it really isn’t.
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CPI Example
•
Suppose we have two implementations of the same instruction set
architecture (ISA).
For some program,
Machine A has a clock cycle time of 250 ps and a CPI of 2.0
Machine B has a clock cycle time of 500 ps and a CPI of 1.2
What machine is faster for this program, and by how much?
•
If two machines have the same ISA which of our quantities (e.g., clock rate,
CPI, execution time, # of instructions, MIPS) will always be identical?
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# of Instructions Example
•
A compiler designer is trying to decide between two code sequences
for a particular machine. Based on the hardware implementation,
there are three different classes of instructions: Class A, Class B, and
Class C, and they require one, two, and three cycles (respectively).
The first code sequence has 5 instructions: 2 of A, 1 of B, and 2 of C
The second sequence has 6 instructions: 4 of A, 1 of B, and 1 of C.
Which sequence will be faster? How much?
What is the CPI for each sequence?
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MIPS example
•
Two different compilers are being tested for a 4 GHz. machine with
three different classes of instructions: Class A, Class B, and Class
C, which require one, two, and three cycles (respectively). Both
compilers are used to produce code for a large piece of software.
The first compiler's code uses 5 million Class A instructions, 1
million Class B instructions, and 1 million Class C instructions.
The second compiler's code uses 10 million Class A instructions, 1
million Class B instructions, and 1 million Class C instructions.
•
•
Which sequence will be faster according to MIPS?
Which sequence will be faster according to execution time?
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Benchmarks
•
•
•
Performance best determined by running a real application
– Use programs typical of expected workload
– Or, typical of expected class of applications
e.g., compilers/editors, scientific applications, graphics, etc.
Small benchmarks
– nice for architects and designers
– easy to standardize
– can be abused
SPEC (System Performance Evaluation Cooperative)
– companies have agreed on a set of real program and inputs
– valuable indicator of performance (and compiler technology)
– can still be abused
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Benchmark Games
•
An embarrassed Intel Corp. acknowledged Friday that a bug in a
software program known as a compiler had led the company to
overstate the speed of its microprocessor chips on an industry
benchmark by 10 percent. However, industry analysts said the
coding error…was a sad commentary on a common industry
practice of “cheating” on standardized performance tests…The error
was pointed out to Intel two days ago by a competitor, Motorola
…came in a test known as SPECint92…Intel acknowledged that it
had “optimized” its compiler to improve its test scores. The
company had also said that it did not like the practice but felt to
compelled to make the optimizations because its competitors were
doing the same thing…At the heart of Intel’s problem is the practice
of “tuning” compiler programs to recognize certain computing
problems in the test and then substituting special handwritten
pieces of code…
Saturday, January 6, 1996 New York Times
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SPEC ‘89
Compiler “enhancements” and performance
800
700
600
SPEC performance ratio
•
500
400
300
200
100
0
gcc
espresso
spice
doduc
nasa7
li
eqntott
matrix300
fpppp
tomcatv
Benchmark
Compiler
Enhanced compiler
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SPEC CPU2000
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SPEC 2000
Does doubling the clock rate double the performance?
Can a machine with a slower clock rate have better performance?
1.6
Pentium M @ 1.6/0.6 GHz
Pentium 4-M @ 2.4/1.2 GHz
Pentium III-M @ 1.2/0.8 GHz
1400
1.4
1200
1.2
Pentium 4 CFP2000
1000
Pentium 4 CINT2000
1.0
800
0.8
600
0.6
Pentium III CINT2000
400
0.4
Pentium III CFP2000
200
0.2
0
0.0
500
1000
1500
2000
Clock rate in MHz
2500
3000
3500
SPECINT2000 SPECFP2000 SPECINT2000 SPECFP2000 SPECINT2000 SPECFP2000
Always on/maximum clock
Laptop mode/adaptive
clock
Minimum power/minimum
clock
Benchmark and power mode
2004 Morgan Kaufmann Publishers
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Experiment
•
Phone a major computer retailer and tell them you are having trouble
deciding between two different computers, specifically you are
confused about the processors strengths and weaknesses
(e.g., Pentium 4 at 2Ghz vs. Celeron M at 1.4 Ghz )
•
What kind of response are you likely to get?
•
What kind of response could you give a friend with the same
question?
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Amdahl's Law
Execution Time After Improvement =
Execution Time Unaffected +( Execution Time Affected / Amount of Improvement )
•
Example:
"Suppose a program runs in 100 seconds on a machine, with
multiply responsible for 80 seconds of this time. How much do we have to
improve the speed of multiplication if we want the program to run 4 times
faster?"
How about making it 5 times faster?
•
Principle: Make the common case fast
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Example
•
Suppose we enhance a machine making all floating-point instructions run
five times faster. If the execution time of some benchmark before the
floating-point enhancement is 10 seconds, what will the speedup be if half of
the 10 seconds is spent executing floating-point instructions?
•
We are looking for a benchmark to show off the new floating-point unit
described above, and want the overall benchmark to show a speedup of 3.
One benchmark we are considering runs for 100 seconds with the old
floating-point hardware. How much of the execution time would floatingpoint instructions have to account for in this program in order to yield our
desired speedup on this benchmark?
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Remember
•
Performance is specific to a particular program/s
– Total execution time is a consistent summary of performance
•
For a given architecture performance increases come from:
–
–
–
–
•
increases in clock rate (without adverse CPI affects)
improvements in processor organization that lower CPI
compiler enhancements that lower CPI and/or instruction count
Algorithm/Language choices that affect instruction count
Pitfall: expecting improvement in one aspect of a machine’s
performance to affect the total performance
2004 Morgan Kaufmann Publishers
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Lets Build a Processor
•
•
Almost ready to move into chapter 5 and start building a processor
First, let’s review Boolean Logic and build the ALU we’ll need
(Material from Appendix B)
operation
a
32
ALU
result
32
b
32
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Review: Boolean Algebra & Gates
•
Problem: Consider a logic function with three inputs: A, B, and C.
Output D is true if at least one input is true
Output E is true if exactly two inputs are true
Output F is true only if all three inputs are true
•
Show the truth table for these three functions.
•
Show the Boolean equations for these three functions.
•
Show an implementation consisting of inverters, AND, and OR gates.
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An ALU (arithmetic logic unit)
•
Let's build an ALU to support the andi and ori instructions
– we'll just build a 1 bit ALU, and use 32 of them
operation
a
op a
b
res
result
b
•
Possible Implementation (sum-of-products):
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Review: The Multiplexor
•
Selects one of the inputs to be the output, based on a control input
S
•
A
0
B
1
C
note: we call this a 2-input mux
even though it has 3 inputs!
Lets build our ALU using a MUX:
2004 Morgan Kaufmann Publishers
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Different Implementations
•
Not easy to decide the “best” way to build something
•
– Don't want too many inputs to a single gate
– Don’t want to have to go through too many gates
– for our purposes, ease of comprehension is important
Let's look at a 1-bit ALU for addition:
CarryIn
a
Sum
b
cout = a b + a cin + b cin
sum = a xor b xor cin
CarryOut
•
How could we build a 1-bit ALU for add, and, and or?
•
How could we build a 32-bit ALU?
2004 Morgan Kaufmann Publishers
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Building a 32 bit ALU
CarryIn
a0
b0
Operation
CarryIn
ALU0
Result0
CarryOut
Operation
CarryIn
a1
a
0
b1
CarryIn
ALU1
Result1
CarryOut
1
Result
a2
2
b
b2
CarryIn
ALU2
Result2
CarryOut
CarryOut
a31
b31
CarryIn
ALU31
Result31
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What about subtraction (a – b) ?
•
•
Two's complement approach: just negate b and add.
How do we negate?
•
A very clever solution:
Binvert
Operation
CarryIn
a
0
1
b
0
Result
2
1
CarryOut
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Adding a NOR function
•
Can also choose to invert a. How do we get “a NOR b” ?
Ainvert
Operation
Binvert
a
CarryIn
0
0
1
1
b
0
+
Result
2
1
CarryOut
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Tailoring the ALU to the MIPS
•
Need to support the set-on-less-than instruction (slt)
– remember: slt is an arithmetic instruction
– produces a 1 if rs < rt and 0 otherwise
– use subtraction: (a-b) < 0 implies a < b
•
Need to support test for equality (beq $t5, $t6, $t7)
– use subtraction: (a-b) = 0 implies a = b
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Supporting slt
•
Can we figure out the idea?
Binvert
a
Binvert
CarryIn
a
0
Operation
Ainvert
Operation
Ainvert
CarryIn
0
0
0
1
1
1
1
Result
b
0
+
Result
b
0
2
+
2
1
1
Less
Less
3
3
Set
CarryOut
Overflow
detection
Overflow
Use this ALU for most significant bit
all other bits
Supporting slt
Operation
Binvert
Ainvert
CarryIn
a0
b0
CarryIn
ALU0
Less
CarryOut
Result0
a1
b1
0
CarryIn
ALU1
Less
CarryOut
Result1
a2
b2
0
CarryIn
ALU2
Less
CarryOut
Result2
..
.
a31
b31
0
..
. CarryIn
CarryIn
ALU31
Less
..
.
Result31
Set
Overflow
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Test for equality
•
Notice control lines:
Operation
Bnegate
Ainvert
0000
0001
0010
0110
0111
1100
=
=
=
=
=
=
and
or
add
subtract
slt
NOR
•Note: zero is a 1 when the result is zero!
a0
b0
CarryIn
ALU0
Less
CarryOut
a1
b1
0
CarryIn
ALU1
Less
CarryOut
a2
b2
0
CarryIn
ALU2
Less
CarryOut
..
.
a31
b31
0
Result0
Result1
..
.
Result2
..
. CarryIn
CarryIn
ALU31
Less
Zero
..
.
..
.
Result31
Set
Overflow
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Conclusion
•
We can build an ALU to support the MIPS instruction set
– key idea: use multiplexor to select the output we want
– we can efficiently perform subtraction using two’s complement
– we can replicate a 1-bit ALU to produce a 32-bit ALU
•
Important points about hardware
– all of the gates are always working
– the speed of a gate is affected by the number of inputs to the
gate
– the speed of a circuit is affected by the number of gates in series
(on the “critical path” or the “deepest level of logic”)
•
Our primary focus: comprehension, however,
– Clever changes to organization can improve performance
(similar to using better algorithms in software)
– We saw this in multiplication, let’s look at addition now
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Problem: ripple carry adder is slow
•
•
Is a 32-bit ALU as fast as a 1-bit ALU?
Is there more than one way to do addition?
– two extremes: ripple carry and sum-of-products
Can you see the ripple? How could you get rid of it?
c1
c2
c3
c4
=
=
=
=
b0c0
b1c1
b2c2
b3c3
+
+
+
+
a0c0
a1c1
a2c2
a3c3
+
+
+
+
a0b0
a1b1c2 =
a2b2
a3b3
c3 =
c4 =
Not feasible! Why?
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Carry-lookahead adder
•
•
An approach in-between our two extremes
Motivation:
– If we didn't know the value of carry-in, what could we do?
– When would we always generate a carry?
gi = ai bi
– When would we propagate the carry?
pi = ai + bi
•
Did we get rid of the ripple?
c1
c2
c3
c4
=
=
=
=
g0
g1
g2
g3
+
+
+
+
p0c0
p1c1 c2 =
p2c2 c3 =
p3c3 c4 =
Feasible! Why?
2004 Morgan Kaufmann Publishers
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Use principle to build bigger adders
CarryIn
a0
b0
a1
b1
a2
b2
a3
b3
a4
b4
a5
b5
a6
b6
a7
b7
a8
b8
a9
b9
a10
b10
a11
b11
a12
b12
a13
b13
a14
b14
a15
b15
CarryIn
Result0–3
ALU0
P0
G0
pi
gi
C1
ci + 1
CarryIn
Carry-lookahead unit
Result4–7
ALU1
P1
G1
•
•
•
pi + 1
gi + 1
C2
ci + 2
CarryIn
Can’t build a 16 bit adder this way... (too big)
Could use ripple carry of 4-bit CLA adders
Better: use the CLA principle again!
Result8–11
ALU2
P2
G2
pi + 2
gi + 2
C3
ci + 3
CarryIn
Result12–15
ALU3
P3
G3
pi + 3
gi + 3
C4
ci + 4
CarryOut
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ALU Summary
•
•
•
•
We can build an ALU to support MIPS addition
Our focus is on comprehension, not performance
Real processors use more sophisticated techniques for arithmetic
Where performance is not critical, hardware description languages
allow designers to completely automate the creation of hardware!
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Chapter Five
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103
The Processor: Datapath & Control
•
•
We're ready to look at an implementation of the MIPS
Simplified to contain only:
– memory-reference instructions: lw, sw
– arithmetic-logical instructions: add, sub, and, or, slt
– control flow instructions: beq, j
•
Generic Implementation:
–
–
–
–
•
use the program counter (PC) to supply instruction address
get the instruction from memory
read registers
use the instruction to decide exactly what to do
All instructions use the ALU after reading the registers
Why? memory-reference? arithmetic? control flow?
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More Implementation Details
•
Abstract / Simplified View:
4
Add
Add
Data
PC
Address Instruction
Instruction
memory
Register #
Registers
Register #
ALU
Address
Data
memory
Register #
Data
Two types of functional units:
– elements that operate on data values (combinational)
– elements that contain state (sequential)
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State Elements
•
•
Unclocked vs. Clocked
Clocks used in synchronous logic
– when should an element that contains state be updated?
Falling edge
Clock period
Rising edge
cycle time
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An unclocked state element
•
The set-reset latch
– output depends on present inputs and also on past inputs
R
Q
Q
S
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Latches and Flip-flops
•
•
•
•
Output is equal to the stored value inside the element
(don't need to ask for permission to look at the value)
Change of state (value) is based on the clock
Latches: whenever the inputs change, and the clock is asserted
Flip-flop: state changes only on a clock edge
(edge-triggered methodology)
"logically true",
— could mean electrically low
A clocking methodology defines when signals can be read and written
— wouldn't want to read a signal at the same time it was being written
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D-latch
•
•
Two inputs:
– the data value to be stored (D)
– the clock signal (C) indicating when to read & store D
Two outputs:
– the value of the internal state (Q) and it's complement
C
Q
D
C
_
Q
Q
D
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D flip-flop
•
Output changes only on the clock edge
D
D
C
Q
D
latch
D
C
Q
D
latch
Q
Q
Q
C
D
C
Q
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Our Implementation
•
•
An edge triggered methodology
Typical execution:
– read contents of some state elements,
– send values through some combinational logic
– write results to one or more state elements
State
element
1
Combinational logic
State
element
2
Clock cycle
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Register File
•
Built using D flip-flops
Read register
number 1
Register 0
Register 1
Read register
number 1
Read
data 1
Read register
number 2
Write
register
Write
data
Register file
Read
data 2
M
...
u
Register n – 2
x
Read data 1
Register n – 1
Read register
number 2
Write
M
u
Read data 2
x
Do you understand? What is the “Mux” above?
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Abstraction
•
•
Make sure you understand the abstractions!
Sometimes it is easy to think you do, when you don’t
Select
A31
Select
B31
A
B
M
u
x
C31
32
32
M
u
x
32
C
A30
B30
M
u
x
C30
..
.
..
.
A0
B0
M
u
x
C0
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Register File
•
Note: we still use the real clock to determine when to write
Write
C
0
1
Register number
n-to-2n
decoder
Register 0
.
..
D
C
Register 1
n–1
n
D
..
.
C
Register n – 2
D
C
Register n – 1
Register data
D
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Simple Implementation
•
Include the functional units we need for each instruction
Instruction
address
MemWrite
Instruction
Add Sum
PC
Address
Read
data
16
Instruction
memory
a. Instruction memory
b. Program counter
c. Adder
Write
data
Data
memory
Sign
extend
32
MemRead
a. Data memory unit
Register
numbers
5
Read
register 1
5
Read
register 2
5
Data
Write
register
4
b. Sign-extension unit
ALU operation
Read
data 1
Data
Registers
Zero
ALU ALU
result
Read
data 2
Write
Data
Why do we need this stuff?
RegWrite
a. Registers
b. ALU
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Building the Datapath
•
Use multiplexors to stitch them together
PCSrc
M
u
x
Add
Add
4
ALU
result
Shift
left 2
PC
Read
address
Instruction
Instruction
memory
Read
register 1
ALUSrc
Read
data 1
ALU operation
MemWrite
Read
register 2
Registers Read
Write
data 2
register
MemtoReg
Zero
M
u
x
Write
data
ALU ALU
result
Address
Write
data
RegWrite
16
4
Sign
extend
32
Read
data
M
u
x
Data
memory
MemRead
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Control
•
Selecting the operations to perform (ALU, read/write, etc.)
•
Controlling the flow of data (multiplexor inputs)
•
Information comes from the 32 bits of the instruction
•
Example:
add $8, $17, $18
•
Instruction Format:
000000
10001
10010
01000
op
rs
rt
rd
00000 100000
shamt
funct
ALU's operation based on instruction type and function code
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Control
•
•
•
e.g., what should the ALU do with this instruction
Example: lw $1, 100($2)
35
2
1
op
rs
rt
16 bit offset
ALU control input
0000
0001
0010
0110
0111
1100
•
100
AND
OR
add
subtract
set-on-less-than
NOR
Why is the code for subtract 0110 and not 0011?
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Control
•
Must describe hardware to compute 4-bit ALU control input
– given instruction type
00 = lw, sw
ALUOp
01 = beq,
computed from instruction type
10 = arithmetic
– function code for arithmetic
•
Describe it using a truth table (can turn into gates):
2004 Morgan Kaufmann Publishers
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0
M
u
x
Add
Add
4
Control
PC
Instruction [25–21]
Read
register 1
Instruction [20–16]
Read
register 2
Read
address
Instruction
[31–0]
Instruction
memory
0
M
u
Instruction [15–11] x
1
Write
register
Write
data
Instruction [15–0]
16
1
Shift
left 2
RegDst
Branch
MemRead
MemtoReg
ALUOp
MemWrite
ALUSrc
RegWrite
Instruction [31–26]
ALU
result
Read
data 1
Zero
Read
data 2
Registers
Sign
extend
0
M
u
x
1
ALU ALU
result
Address
Read
data
1
M
u
x
0
Data
Write memory
data
32
ALU
control
Instruction [5–0]
Memto- Reg Mem Mem
Instruction RegDst ALUSrc
Reg
Write Read Write Branch ALUOp1 ALUp0
R-format
1
0
0
1
0
0
0
1
0
lw
0
1
1
1
1
0
0
0
0
sw
X
1
X
0
0
1
0
0
0
beq
X
0
X
0
0
0
1
0
1
Control
•
Simple combinational logic (truth tables)
Inputs
Op5
Op4
Op3
Op2
ALUOp
Op1
ALU control block
Op0
ALUOp0
ALUOp1
Outputs
F3
F2
F (5– 0)
Operation2
Operation1
Operation
Iw
sw
beq
RegDst
ALUSrc
MemtoReg
F1
Operation0
F0
R-format
RegWrite
MemRead
MemWrite
Branch
ALUOp1
ALUOpO
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Our Simple Control Structure
•
All of the logic is combinational
•
We wait for everything to settle down, and the right thing to be done
– ALU might not produce “right answer” right away
– we use write signals along with clock to determine when to write
•
Cycle time determined by length of the longest path
State
element
1
Combinational logic
State
element
2
Clock cycle
We are ignoring some details like setup and hold times
2004 Morgan Kaufmann Publishers
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Single Cycle Implementation
•
Calculate cycle time assuming negligible delays except:
– memory (200ps),
ALU and adders (100ps),
register file access (50ps)
PCSrc
M
u
x
Add
Add
4
ALU
result
Shift
left 2
PC
Read
address
Instruction
Instruction
memory
Read
register 1
ALUSrc
Read
data 1
ALU operation
MemWrite
Read
register 2
Registers Read
Write
data 2
register
MemtoReg
Zero
M
u
x
Write
data
ALU ALU
result
Address
Write
data
RegWrite
16
4
Sign
extend
32
Read
data
M
u
x
Data
memory
MemRead
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Where we are headed
•
•
Single Cycle Problems:
– what if we had a more complicated instruction like floating
point?
– wasteful of area
One Solution:
– use a “smaller” cycle time
– have different instructions take different numbers of cycles
– a “multicycle” datapath:
PC
Address
Instruction
register
A
Register #
Registers
Register #
Instruction
or data
Memory
Data
Data
Memory
data
register
ALU
ALUOut
B
Register #
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Multicycle Approach
•
•
•
We will be reusing functional units
– ALU used to compute address and to increment PC
– Memory used for instruction and data
Our control signals will not be determined directly by instruction
– e.g., what should the ALU do for a “subtract” instruction?
We’ll use a finite state machine for control
2004 Morgan Kaufmann Publishers
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Multicycle Approach
•
•
Break up the instructions into steps, each step takes a cycle
– balance the amount of work to be done
– restrict each cycle to use only one major functional unit
At the end of a cycle
– store values for use in later cycles (easiest thing to do)
– introduce additional “internal” registers
PC
0
M
u
x
1
Address
Memory
MemData
Write
data
Instruction
[20–16]
Instruction
[15–0]
Instruction
register
Instruction
[15–0]
Memory
data
register
0
M
u
x
1
Read
register 1
Instruction
[25–21]
0
M
Instruction u
x
[15–11]
1
Read
data 1
Read
register 2
Registers
Write
Read
register
data 2
A
B
4
Write
data
0
M
u
x
1
16
Sign
extend
32
Zero
ALU ALU
result
ALUOut
0
1M
u
2 x
3
Shift
left 2
2004 Morgan Kaufmann Publishers
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Instructions from ISA perspective
•
•
Consider each instruction from perspective of ISA.
Example:
– The add instruction changes a register.
– Register specified by bits 15:11 of instruction.
– Instruction specified by the PC.
– New value is the sum (“op”) of two registers.
– Registers specified by bits 25:21 and 20:16 of the instruction
Reg[Memory[PC][15:11]] <=
Reg[Memory[PC][25:21]] op
Reg[Memory[PC][20:16]]
– In order to accomplish this we must break up the instruction.
(kind of like introducing variables when programming)
2004 Morgan Kaufmann Publishers
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Breaking down an instruction
•
ISA definition of arithmetic:
Reg[Memory[PC][15:11]] <= Reg[Memory[PC][25:21]] op
Reg[Memory[PC][20:16]]
•
Could break down to:
– IR <= Memory[PC]
– A <= Reg[IR[25:21]]
– B <= Reg[IR[20:16]]
– ALUOut <= A op B
– Reg[IR[20:16]] <= ALUOut
•
We forgot an important part of the definition of arithmetic!
– PC <= PC + 4
2004 Morgan Kaufmann Publishers
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Idea behind multicycle approach
•
We define each instruction from the ISA perspective (do this!)
•
Break it down into steps following our rule that data flows through at
most one major functional unit (e.g., balance work across steps)
•
Introduce new registers as needed (e.g, A, B, ALUOut, MDR, etc.)
•
Finally try and pack as much work into each step
(avoid unnecessary cycles)
while also trying to share steps where possible
(minimizes control, helps to simplify solution)
•
Result: Our book’s multicycle Implementation!
2004 Morgan Kaufmann Publishers
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Five Execution Steps
•
Instruction Fetch
•
Instruction Decode and Register Fetch
•
Execution, Memory Address Computation, or Branch Completion
•
Memory Access or R-type instruction completion
•
Write-back step
INSTRUCTIONS TAKE FROM 3 - 5 CYCLES!
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Step 1: Instruction Fetch
•
•
•
Use PC to get instruction and put it in the Instruction Register.
Increment the PC by 4 and put the result back in the PC.
Can be described succinctly using RTL "Register-Transfer Language"
IR <= Memory[PC];
PC <= PC + 4;
Can we figure out the values of the control signals?
What is the advantage of updating the PC now?
2004 Morgan Kaufmann Publishers
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Step 2: Instruction Decode and Register Fetch
•
•
•
Read registers rs and rt in case we need them
Compute the branch address in case the instruction is a branch
RTL:
A <= Reg[IR[25:21]];
B <= Reg[IR[20:16]];
ALUOut <= PC + (sign-extend(IR[15:0]) << 2);
•
We aren't setting any control lines based on the instruction type
(we are busy "decoding" it in our control logic)
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Step 3 (instruction dependent)
•
ALU is performing one of three functions, based on instruction type
•
Memory Reference:
ALUOut <= A + sign-extend(IR[15:0]);
•
R-type:
ALUOut <= A op B;
•
Branch:
if (A==B) PC <= ALUOut;
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Step 4 (R-type or memory-access)
•
Loads and stores access memory
MDR <= Memory[ALUOut];
or
Memory[ALUOut] <= B;
•
R-type instructions finish
Reg[IR[15:11]] <= ALUOut;
The write actually takes place at the end of the cycle on the edge
2004 Morgan Kaufmann Publishers
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Write-back step
• Reg[IR[20:16]] <= MDR;
Which instruction needs this?
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Summary:
2004 Morgan Kaufmann Publishers
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Simple Questions
•
How many cycles will it take to execute this code?
Label:
•
•
lw $t2, 0($t3)
lw $t3, 4($t3)
beq $t2, $t3, Label
add $t5, $t2, $t3
sw $t5, 8($t3)
...
#assume not
What is going on during the 8th cycle of execution?
In what cycle does the actual addition of $t2 and $t3 takes place?
2004 Morgan Kaufmann Publishers
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PCSource
PCWriteCond
PCWrite
ALUOp
Outputs
IorD
MemRead
ALUSrcB
Control
ALUSrcA
MemWrite
MemtoReg
Op
[5–0]
RegWrite
IRWrite
0
RegDst
26
Instruction [25-0]
PC
0
M
u
x
1
Instruction
[31–26]
Address
Memory
MemData
Write
data
Instruction
[20–16]
Instruction
[15–0]
Instruction
register
Instruction
[15–0]
Memory
data
register
0
M
u
x
1
Read
register 1
Instruction
[25–21]
Read
data 1
Read
register 2
Registers
Write
Read
register
data 2
0
M
Instruction u
x
[15–11]
1
A
16
Sign
extend
B
4
32
Instruction [5–0]
28
PC [31–28]
Zero
ALU ALU
result
Write
data
0
M
u
x
1
Shift
left 2
Shift
left 2
Jump
address
[31–0]
0
1M
u
2 x
3
ALU
control
ALUOut
M
1 u
x
2
Review: finite state machines
•
Finite state machines:
– a set of states and
– next state function (determined by current state and the input)
– output function (determined by current state and possibly input)
Next
state
Current state
Next-state
function
Clock
Inputs
Output
function
Outputs
– We’ll use a Moore machine (output based only on current state)
2004 Morgan Kaufmann Publishers
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Review: finite state machines
•
Example:
B. 37 A friend would like you to build an “electronic eye” for use as a fake security
device. The device consists of three lights lined up in a row, controlled by the outputs
Left, Middle, and Right, which, if asserted, indicate that a light should be on. Only one
light is on at a time, and the light “moves” from left to right and then from right to left,
thus scaring away thieves who believe that the device is monitoring their activity. Draw
the graphical representation for the finite state machine used to specify the electronic
eye. Note that the rate of the eye’s movement will be controlled by the clock speed (which
should not be too great) and that there are essentially no inputs.
2004 Morgan Kaufmann Publishers
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Implementing the Control
•
Value of control signals is dependent upon:
– what instruction is being executed
– which step is being performed
•
Use the information we’ve accumulated to specify a finite state machine
– specify the finite state machine graphically, or
– use microprogramming
•
Implementation can be derived from specification
2004 Morgan Kaufmann Publishers
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Graphical Specification of FSM
Instruction fetch
MemRead
ALUSrcA = 0
IorD = 0
IRWrite
ALUSrcB = 01
ALUOp = 00
PCWrite
PCSource = 00
0
Start
•
Note:
Instruction decode/
register fetch
1
ALUSrcA = 0
ALUSrcB = 11
ALUOp = 00
– don’t care if not mentioned
– asserted if name only
– otherwise exact value
Memory address
computation
•
2
How many state
bits will we need?
6
ALUSrcA = 1
ALUSrcB = 10
ALUOp = 00
8
ALUSrcA = 1
ALUSrcB = 00
ALUOp = 10
Memory
access
3
Memory
access
5
MemRead
IorD = 1
Branch
completion
Execution
Jump
completion
9
ALUSrcA = 1
ALUSrcB = 00
ALUOp = 01
PCWriteCond
PCSource = 01
PCWrite
PCSource = 10
R-type completion
7
MemWrite
IorD = 1
RegDst = 1
RegWrite
MemtoReg = 0
Memory read
completon step
4
RegDst = 1
RegWrite
MemtoReg = 0
2004 Morgan Kaufmann Publishers
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Finite State Machine for Control
Implementation:
PCWrite
PCWriteCond
IorD
MemRead
MemWrite
IRWrite
Control logic
MemtoReg
PCSource
ALUOp
Outputs
ALUSrcB
ALUSrcA
RegWrite
RegDst
NS3
NS2
NS1
NS0
Instruction register
opcode field
S0
S1
S2
S3
Op0
Op1
Op2
Op3
Op4
Inputs
Op5
•
State register
2004 Morgan Kaufmann Publishers
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PLA Implementation
•
If I picked a horizontal or vertical line could you explain it?
Op5
Op4
Op3
Op2
Op1
Op0
S3
S2
S1
S0
PCWrite
PCWriteCond
IorD
MemRead
MemWrite
IRWrite
MemtoReg
PCSource1
PCSource0
ALUOp1
ALUOp0
ALUSrcB1
ALUSrcB0
ALUSrcA
RegWrite
RegDst
NS3
NS2
NS1
NS0
2004 Morgan Kaufmann Publishers
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ROM Implementation
•
•
ROM = "Read Only Memory"
– values of memory locations are fixed ahead of time
A ROM can be used to implement a truth table
– if the address is m-bits, we can address 2m entries in the ROM.
– our outputs are the bits of data that the address points to.
m
n
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
m is the "height", and n is the "width"
2004 Morgan Kaufmann Publishers
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ROM Implementation
•
•
How many inputs are there?
6 bits for opcode, 4 bits for state = 10 address lines
(i.e., 210 = 1024 different addresses)
How many outputs are there?
16 datapath-control outputs, 4 state bits = 20 outputs
•
ROM is 210 x 20 = 20K bits
•
Rather wasteful, since for lots of the entries, the outputs are the
same
— i.e., opcode is often ignored
(and a rather unusual size)
2004 Morgan Kaufmann Publishers
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ROM vs PLA
•
Break up the table into two parts
— 4 state bits tell you the 16 outputs, 24 x 16 bits of ROM
— 10 bits tell you the 4 next state bits, 210 x 4 bits of ROM
— Total: 4.3K bits of ROM
•
PLA is much smaller
— can share product terms
— only need entries that produce an active output
— can take into account don't cares
•
Size is (#inputs  #product-terms) + (#outputs  #product-terms)
For this example = (10x17)+(20x17) = 510 PLA cells
•
PLA cells usually about the size of a ROM cell (slightly bigger)
2004 Morgan Kaufmann Publishers
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Another Implementation Style
Complex instructions: the "next state" is often current state + 1
Control unit
PLA or ROM
Outputs
Input
PCWrite
PCWriteCond
IorD
MemRead
MemWrite
IRWrite
BWrite
MemtoReg
PCSource
ALUOp
ALUSrcB
ALUSrcA
RegWrite
RegDst
AddrCtl
1
State
Adder
Address select logic
Op[5– 0]
•
Instruction register
opcode field
2004 Morgan Kaufmann Publishers
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Details
Op
000000
000010
000100
100011
101011
Dispatch ROM 1
Opcode name
R-format
jmp
beq
lw
sw
Value
0110
1001
1000
0010
0010
Op
100011
101011
Dispatch ROM 2
Opcode name
lw
sw
Value
0011
0101
PLA or ROM
1
State
Adder
3
Mux
2 1
AddrCtl
0
0
Dispatch ROM 2
Dispatch ROM 1
Address select logic
Instruction register
opcode field
State number
0
1
2
3
4
5
6
7
8
9
Address-control action
Use incremented state
Use dispatch ROM 1
Use dispatch ROM 2
Use incremented state
Replace state number by 0
Replace state number by 0
Use incremented state
Replace state number by 0
Replace state number by 0
Replace state number by 0
Value of AddrCtl
3
1
2
3
0
0
3
0
0
0
2004 Morgan Kaufmann Publishers
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Microprogramming
Control unit
Microcode memory
Outputs
Input
PCWrite
PCWriteCond
IorD
MemRead
MemWrite
IRWrite
BWrite
MemtoReg
PCSource
ALUOp
ALUSrcB
ALUSrcA
RegWrite
RegDst
AddrCtl
Datapath
1
Microprogram counter
Adder
Address select logic
Instruction register
opcode field
•
What are the “microinstructions” ?
2004 Morgan Kaufmann Publishers
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Microprogramming
•
A specification methodology
– appropriate if hundreds of opcodes, modes, cycles, etc.
– signals specified symbolically using microinstructions
Label
Fetch
Mem1
LW2
ALU
control
Add
Add
Add
SRC1
PC
PC
A
Register
control
SRC2
4
Extshft Read
Extend
PCWrite
Memory
control
Read PC ALU
Read ALU
Write MDR
SW2
Rformat1 Func code A
Write ALU
B
Write ALU
BEQ1
JUMP1
•
•
Subt
A
B
ALUOut-cond
Jump address
Sequencing
Seq
Dispatch 1
Dispatch 2
Seq
Fetch
Fetch
Seq
Fetch
Fetch
Fetch
Will two implementations of the same architecture have the same microcode?
What would a microassembler do?
2004 Morgan Kaufmann Publishers
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Microinstruction format
Field name
ALU control
SRC1
SRC2
Value
Add
Subt
Func code
PC
A
B
4
Extend
Extshft
Read
ALUOp = 10
ALUSrcA = 0
ALUSrcA = 1
ALUSrcB = 00
ALUSrcB = 01
ALUSrcB = 10
ALUSrcB = 11
Write ALU
RegWrite,
RegDst = 1,
MemtoReg = 0
RegWrite,
RegDst = 0,
MemtoReg = 1
MemRead,
lorD = 0
MemRead,
lorD = 1
MemWrite,
lorD = 1
PCSource = 00
PCWrite
PCSource = 01,
PCWriteCond
PCSource = 10,
PCWrite
AddrCtl = 11
AddrCtl = 00
AddrCtl = 01
AddrCtl = 10
Register
control
Write MDR
Read PC
Memory
Read ALU
Write ALU
ALU
PC write control
ALUOut-cond
jump address
Sequencing
Signals active
ALUOp = 00
ALUOp = 01
Seq
Fetch
Dispatch 1
Dispatch 2
Comment
Cause the ALU to add.
Cause the ALU to subtract; this implements the compare for
branches.
Use the instruction's function code to determine ALU control.
Use the PC as the first ALU input.
Register A is the first ALU input.
Register B is the second ALU input.
Use 4 as the second ALU input.
Use output of the sign extension unit as the second ALU input.
Use the output of the shift-by-two unit as the second ALU input.
Read two registers using the rs and rt fields of the IR as the register
numbers and putting the data into registers A and B.
Write a register using the rd field of the IR as the register number and
the contents of the ALUOut as the data.
Write a register using the rt field of the IR as the register number and
the contents of the MDR as the data.
Read memory using the PC as address; write result into IR (and
the MDR).
Read memory using the ALUOut as address; write result into MDR.
Write memory using the ALUOut as address, contents of B as the
data.
Write the output of the ALU into the PC.
If the Zero output of the ALU is active, write the PC with the contents
of the register ALUOut.
Write the PC with the jump address from the instruction.
Choose the next microinstruction sequentially.
Go to the first microinstruction to begin a new instruction.
Dispatch using the ROM 1.
Dispatch using the ROM 2.
2004 Morgan Kaufmann Publishers
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Maximally vs. Minimally Encoded
•
No encoding:
– 1 bit for each datapath operation
– faster, requires more memory (logic)
– used for Vax 780 — an astonishing 400K of memory!
•
Lots of encoding:
– send the microinstructions through logic to get control signals
– uses less memory, slower
•
Historical context of CISC:
– Too much logic to put on a single chip with everything else
– Use a ROM (or even RAM) to hold the microcode
– It’s easy to add new instructions
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Microcode: Trade-offs
•
Distinction between specification and implementation is sometimes blurred
•
Specification Advantages:
– Easy to design and write
– Design architecture and microcode in parallel
•
Implementation (off-chip ROM) Advantages
– Easy to change since values are in memory
– Can emulate other architectures
– Can make use of internal registers
•
Implementation Disadvantages, SLOWER now that:
– Control is implemented on same chip as processor
– ROM is no longer faster than RAM
– No need to go back and make changes
2004 Morgan Kaufmann Publishers
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Historical Perspective
•
•
•
•
•
In the ‘60s and ‘70s microprogramming was very important for
implementing machines
This led to more sophisticated ISAs and the VAX
In the ‘80s RISC processors based on pipelining became popular
Pipelining the microinstructions is also possible!
Implementations of IA-32 architecture processors since 486 use:
– “hardwired control” for simpler instructions
(few cycles, FSM control implemented using PLA or random logic)
– “microcoded control” for more complex instructions
(large numbers of cycles, central control store)
•
The IA-64 architecture uses a RISC-style ISA and can be
implemented without a large central control store
2004 Morgan Kaufmann Publishers
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Pentium 4
•
Pipelining is important (last IA-32 without it was 80386 in 1985)
Control
Control
I/O
interface
Chapter 7
Instruction cache
Data
cache
Enhanced
floating point
and multimedia
Integer
datapath
Control
Advanced pipelining
hyperthreading support
•
Secondary
cache
and
memory
interface
Chapter 6
Control
Pipelining is used for the simple instructions favored by compilers
“Simply put, a high performance implementation needs to ensure that the simple
instructions execute quickly, and that the burden of the complexities of the
instruction set penalize the complex, less frequently used, instructions”
2004 Morgan Kaufmann Publishers
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Pentium 4
•
Somewhere in all that “control we must handle complex instructions
Control
Control
I/O
interface
Instruction cache
Data
cache
Enhanced
floating point
and multimedia
Integer
datapath
Control
Advanced pipelining
hyperthreading support
•
•
•
•
Secondary
cache
and
memory
interface
Control
Processor executes simple microinstructions, 70 bits wide (hardwired)
120 control lines for integer datapath (400 for floating point)
If an instruction requires more than 4 microinstructions to implement,
control from microcode ROM (8000 microinstructions)
Its complicated!
2004 Morgan Kaufmann Publishers
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Chapter 5 Summary
•
If we understand the instructions…
We can build a simple processor!
•
If instructions take different amounts of time, multi-cycle is better
•
Datapath implemented using:
– Combinational logic for arithmetic
– State holding elements to remember bits
•
Control implemented using:
– Combinational logic for single-cycle implementation
– Finite state machine for multi-cycle implementation
2004 Morgan Kaufmann Publishers
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Chapter Six
2004 Morgan Kaufmann Publishers
159
Pipelining
•
Improve performance by increasing instruction throughput
Program
execution
Time
order
(in instructions)
200
lw $1, 100($0) Instruction
fetch Reg
lw $2, 200($0)
400
600
Data
access
ALU
800
1000
1200
1400
ALU
Data
access
1600
1800
Reg
Instruction Reg
fetch
800 ps
lw $3, 300($0)
Reg
Instruction
fetch
800 ps
Note:
timing assumptions changed
for this example
800 ps
Program
execution
Time
order
(in instructions)
200
400
600
Instruction
fetch
Reg
lw $2, 200($0) 200 ps
Instruction
fetch
Reg
200 ps
Instruction
fetch
lw $1, 100($0)
lw $3, 300($0)
ALU
800
Data
access
ALU
Reg
1000
1200
1400
Reg
Data
access
ALU
Reg
Data
access
Reg
200 ps 200 ps 200 ps 200 ps 200 ps
Ideal speedup is number of stages in the pipeline. Do we achieve this?
2004 Morgan Kaufmann Publishers
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Pipelining
•
What makes it easy
– all instructions are the same length
– just a few instruction formats
– memory operands appear only in loads and stores
•
What makes it hard?
– structural hazards: suppose we had only one memory
– control hazards: need to worry about branch instructions
– data hazards: an instruction depends on a previous instruction
•
We’ll build a simple pipeline and look at these issues
•
We’ll talk about modern processors and what really makes it hard:
– exception handling
– trying to improve performance with out-of-order execution, etc.
2004 Morgan Kaufmann Publishers
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Basic Idea
IF: Instruction fetch
ID: Instruction decode/
register file read
EX: Execute/
address calculation
MEM: Memory access
WB: Write back
Add
4
Shift
left 2
P
C
Address
Instruction
Instruction
memory
Read Read
register 1 data1
Read
register 2
Registers
Write
Read
register
data2
Write
data
16
•
ADD Add
result
Zero
ALU ALU
result
Address
Read
data
Data
Memory
Write
data
Sign 32
extend
What do we need to add to actually split the datapath into stages?
2004 Morgan Kaufmann Publishers
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Pipelined Datapath
IF/ID
ID/EX
EX/MEM
MEM/WB
Add
4
Shift
left 2
PC
Address
Instruction
memory
Add Add
result
Read
register 1
Read
data 1
Read
register 2
Registers
Read
Write
data 2
register
Zero
ALU ALU
result
Read
data
Address
Data
memory
Write
data
Write
data
16
Sign
extend
32
Can you find a problem even if there are no dependencies?
What instructions can we execute to manifest the problem?
2004 Morgan Kaufmann Publishers
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Corrected Datapath
IF/ID
ID/EX
EX/MEM
MEM/WB
Add
4
Shift
left 2
PC
Address
Instruction
memory
Add Add
result
Read
register 1
Read
data 1
Read
register 2
Registers
Read
Write
data 2
register
Zero
ALU ALU
result
Read
data
Address
Data
memory
Write
data
Write
data
16
Sign
extend
32
2004 Morgan Kaufmann Publishers
164
Graphically Representing Pipelines
Time (in clock cycles)
Program
execution
order
(in instructions)
lw $1, 100($0)
lw $2, 200($0)
lw $3, 300($0)
•
CC 1
CC 2
IM
Reg
IM
CC 3
ALU
Reg
IM
CC 4
CC 5
DM
Reg
ALU
DM
Reg
ALU
DM
Reg
CC 6
CC7
Reg
Can help with answering questions like:
– how many cycles does it take to execute this code?
– what is the ALU doing during cycle 4?
– use this representation to help understand datapaths
2004 Morgan Kaufmann Publishers
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Pipeline Control
PCSrc
IF/ID
ID/EX
EX/MEM
MEM/WB
Add
Add Add
result
4
Shift
left 2
Branch
RegWrite
PC
Address
Instruction
memory
Read
register 1
Read
data 1
Read
register 2
Registers
Read
Write
data 2
register
MemWrite
ALUSrc
Zero
Add ALU
result
MemtoReg
Read
data
Address
Data
memory
Write
data
Write
data
Instruction
(15Ð0)
Instruction
(20Ð16)
16
Sign
extend
32
6
ALU
control
MemRead
ALUOp
Instruction
(15Ð11)
RegDst
2004 Morgan Kaufmann Publishers
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Pipeline control
•
We have 5 stages. What needs to be controlled in each stage?
– Instruction Fetch and PC Increment
– Instruction Decode / Register Fetch
– Execution
– Memory Stage
– Write Back
•
How would control be handled in an automobile plant?
– a fancy control center telling everyone what to do?
– should we use a finite state machine?
2004 Morgan Kaufmann Publishers
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Pipeline Control
•
Pass control signals along just like the data
Instruction
R-format
lw
sw
beq
Execution/Address Calculation Memory access stage
stage control lines
control lines
Reg
ALU
ALU
ALU
Mem
Mem
Dst
Op1
Op0
Src Branch Read Write
1
1
0
0
0
0
0
0
0
0
1
0
1
0
X
0
0
1
0
0
1
X
0
1
0
1
0
0
Write-back
stage control
lines
Reg Mem to
write
Reg
1
0
1
1
0
X
0
X
WB
Instruction
IF/ID
Control
M
WB
EX
M
WB
ID/EX
EX/MEM
MEM/WB
2004 Morgan Kaufmann Publishers
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Datapath with Control
PCSrc
ID/EX
WB
Control
IF/ID
EX/MEM
M
WB
EX
M
MEM/WB
WB
Add
4
Shift
left 2
PC
Address
Instruction
memory
Add Add
result
Branch
ALUSrc
Read
register 1
Read
data 1
Read
register 2
Registers
Read
Write
data 2
register
Zero
ALU ALU
result
Read
data
Address
Data
memory
Write
data
Write
data
Instruction
[15–0]
Instruction
[20–16]
16
Sign
extend
32
6
ALU
control
MemRead
ALUOp
Instruction
[15–11]
RegDst
2004 Morgan Kaufmann Publishers
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Dependencies
•
Problem with starting next instruction before first is finished
– dependencies that “go backward in time” are data hazards
Time (in clock cycles)
CC 1
CC 2
CC 3
CC 4
CC 5
CC 6
CC 7
CC 8
CC 9
10
10
10
10
10/–20
–20
–20
–20
–20
IM
Reg
DM
Reg
Value of
register $2:
Program
execution
order
(in instructions)
sub $2, $1, $3
and $12, $2, $5
or $13, $6, $2
add $14, $2, $2
sw $15, 100($2)
IM
Reg
IM
DM
Reg
IM
Reg
DM
Reg
IM
Reg
DM
Reg
Reg
DM
Reg
2004 Morgan Kaufmann Publishers
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Software Solution
•
•
Have compiler guarantee no hazards
Where do we insert the “nops” ?
sub
and
or
add
sw
•
$2, $1, $3
$12, $2, $5
$13, $6, $2
$14, $2, $2
$15, 100($2)
Problem: this really slows us down!
2004 Morgan Kaufmann Publishers
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Forwarding
•
Use temporary results, don’t wait for them to be written
– register file forwarding to handle read/write to same register
– ALU forwarding
Time (in clock cycles)
CC 1
CC 2
Value of register $2:
10
10
Value of EX/MEM:
X
X
Value of MEM/WB:
X
X
CC 3
CC 4
CC 5
CC 6
CC 7
CC 8
CC 9
10
X
X
10
–20
X
10/–20
X
–20
–20
X
X
–20
X
X
–20
X
X
–20
X
X
DM
Reg
Program
execution
order
(in instructions)
sub $2, $1, $3
and $12, $2, $5
or $13, $6, $2
add $14,$2 , $2
sw $15, 100($2)
what if this $2 was $13?
IM
Reg
IM
Reg
IM
DM
Reg
IM
Reg
DM
Reg
IM
Reg
DM
Reg
Reg
DM
Reg
2004 Morgan Kaufmann Publishers
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Forwarding
•
The main idea (some details not shown)
ID/EX
EX/MEM
MEM/WB
M
u
x
ForwardA
Registers
ALU
M
u
x
Data
memory
M
u
x
ForwardB
Rs
Rt
Rt
Rd
EX/MEM.RegisterRd
M
u
x
Forwarding
unit
MEM/WB.RegisterRd
2004 Morgan Kaufmann Publishers
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Can't always forward
•
Load word can still cause a hazard:
– an instruction tries to read a register following a load instruction
that writes to the same register.
Time (in clock cycles)
CC 1
CC 2
CC 3
CC 4
CC 5
DM
Reg
CC 6
CC 7
CC 8
CC 9
Program
execution
order
(in instructions)
lw $2, 20($1)
and $4, $2, $5
or $8, $2, $6
add $9, $4, $2
slt $1, $6, $7
•
IM
Reg
IM
Reg
IM
DM
Reg
IM
Reg
DM
Reg
IM
Reg
DM
Reg
Reg
DM
Reg
Thus, we need a hazard detection unit to “stall” the load instruction
2004 Morgan Kaufmann Publishers
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Stalling
•
We can stall the pipeline by keeping an instruction in the same stage
Time (in clock cycles)
CC 1
CC 2
CC 3
CC 4
CC 5
Reg
DM
Reg
CC 6
CC 7
CC 8
CC 9
CC 10
Program
execution
order
(in instructions)
lw $2, 20($1)
IM
bubble
and becomes nop
add $4, $2, $5
or $8, $2, $6
add $9, $4, $2
IM
Reg
IM
DM
Reg
IM
Reg
DM
DM
Reg
IM
Reg
Reg
Reg
DM
Reg
2004 Morgan Kaufmann Publishers
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Hazard Detection Unit
•
Stall by letting an instruction that won’t write anything go forward
Hazard
detection
unit
ID/EX.MemRead
ID/EX
WB
M
u
x
Control
0
IF/ID
EX/MEM
M
WB
EX
M
MEM/WB
WB
M
u
x
Registers
M
u
x
ALU
PC
Instruction
memory
M
u
x
Data
memory
IF/ID.RegisterRs
IF/ID.RegisterRt
IF/ID.RegisterRt
Rt
IF/ID.RegisterRd
Rd
M
u
x
ID/EX.RegisterRt
Rs
Rt
Forwarding
unit
2004 Morgan Kaufmann Publishers
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Branch Hazards
•
When we decide to branch, other instructions are in the pipeline!
Time (in clock cycles)
CC 1
CC 2
CC 3
CC 4
CC 5
DM
Reg
CC 6
CC 7
CC 8
CC 9
Program
execution
order
(in instructions)
40 beq $1, $3, 28
44 and $12, $2, $5
48 or $13, $6, $2
52 add $14, $2, $2
72 lw $4, 50($7)
•
IM
Reg
IM
Reg
IM
DM
Reg
IM
Reg
DM
Reg
IM
Reg
DM
Reg
Reg
DM
Reg
We are predicting “branch not taken”
– need to add hardware for flushing instructions if we are wrong
2004 Morgan Kaufmann Publishers
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Flushing Instructions
IF.Flush
Hazard
detection
unit
ID/EX
WB
Control
0
IF/ID
M
u
x
+
EX/MEM
M
WB
EX/MEM
EX
M
WB
+
4
M
u
x
Shift
left 2
Registers
PC
=
M
u
x
Instruction
memory
ALU
M
u
x
Data
memory
M
u
x
Sign
extend
M
u
x
Fowarding
unit
Note: we’ve also moved branch decision to ID stage
2004 Morgan Kaufmann Publishers
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Branches
•
•
•
•
If the branch is taken, we have a penalty of one cycle
For our simple design, this is reasonable
With deeper pipelines, penalty increases and static branch prediction
drastically hurts performance
Solution: dynamic branch prediction
Taken
Not taken
Predict taken
Predict taken
Taken
Not taken
Taken
Not taken
Predict not taken
Predict not taken
Taken
Not taken
A 2-bit prediction scheme
2004 Morgan Kaufmann Publishers
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Branch Prediction
•
Sophisticated Techniques:
– A “branch target buffer” to help us look up the destination
– Correlating predictors that base prediction on global behavior
and recently executed branches (e.g., prediction for a specific
branch instruction based on what happened in previous branches)
– Tournament predictors that use different types of prediction
strategies and keep track of which one is performing best.
– A “branch delay slot” which the compiler tries to fill with a useful
instruction (make the one cycle delay part of the ISA)
•
Branch prediction is especially important because it enables other
more advanced pipelining techniques to be effective!
•
Modern processors predict correctly 95% of the time!
2004 Morgan Kaufmann Publishers
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Improving Performance
•
Try and avoid stalls! E.g., reorder these instructions:
lw
lw
sw
sw
$t0,
$t2,
$t2,
$t0,
0($t1)
4($t1)
0($t1)
4($t1)
•
Dynamic Pipeline Scheduling
– Hardware chooses which instructions to execute next
– Will execute instructions out of order (e.g., doesn’t wait for a
dependency to be resolved, but rather keeps going!)
– Speculates on branches and keeps the pipeline full
(may need to rollback if prediction incorrect)
•
Trying to exploit instruction-level parallelism
2004 Morgan Kaufmann Publishers
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Advanced Pipelining
•
•
•
•
Increase the depth of the pipeline
Start more than one instruction each cycle (multiple issue)
Loop unrolling to expose more ILP (better scheduling)
“Superscalar” processors
– DEC Alpha 21264: 9 stage pipeline, 6 instruction issue
•
All modern processors are superscalar and issue multiple
instructions usually with some limitations (e.g., different “pipes”)
•
VLIW: very long instruction word, static multiple issue
(relies more on compiler technology)
•
This class has given you the background you need to learn more!
2004 Morgan Kaufmann Publishers
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Chapter 6 Summary
•
Pipelining does not improve latency, but does improve throughput
Deeply
pipelined
Multicycle
(Section 5.5)
Pipelined
Multiple issue
with deep pipeline
(Section 6.10)
Multiple issue
with deep pipeline
(Section 6.10)
Multiple-issue
pipelined
(Section 6.9)
Multiple-issue
pipelined
(Section 6.9)
Single-cycle
(Section 5.4)
Deeply
pipelined
Multicycle
(Section 5.5)
Single-cycle
(Section 5.4)
Slower
Pipelined
Faster
Instructions per clock (IPC = 1/CPI)
1
Several
Use latency in instructions
2004 Morgan Kaufmann Publishers
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Chapter Seven
2004 Morgan Kaufmann Publishers
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Memories: Review
•
SRAM:
– value is stored on a pair of inverting gates
– very fast but takes up more space than DRAM (4 to 6 transistors)
•
DRAM:
– value is stored as a charge on capacitor (must be refreshed)
– very small but slower than SRAM (factor of 5 to 10)
Word line
A
A
B
B
Pass transistor
Capacitor
Bit line
2004 Morgan Kaufmann Publishers
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Exploiting Memory Hierarchy
•
Users want large and fast memories!
SRAM access times are .5 – 5ns at cost of $4000 to $10,000 per GB.
DRAM access times are 50-70ns at cost of $100 to $200 per GB.
Disk access times are 5 to 20 million ns at cost of $.50 to $2 per GB.
•
2004
Try and give it to them anyway
– build a memory hierarchy
CPU
Level 1
Increasing distance
from the CPU in
access time
Levels in the
Level 2
memory hierarchy
Level n
Size of the memory at each level
2004 Morgan Kaufmann Publishers
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Locality
•
A principle that makes having a memory hierarchy a good idea
•
If an item is referenced,
temporal locality: it will tend to be referenced again soon
spatial locality: nearby items will tend to be referenced soon.
Why does code have locality?
•
Our initial focus: two levels (upper, lower)
– block: minimum unit of data
– hit: data requested is in the upper level
– miss: data requested is not in the upper level
2004 Morgan Kaufmann Publishers
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Cache
•
•
Two issues:
– How do we know if a data item is in the cache?
– If it is, how do we find it?
Our first example:
– block size is one word of data
– "direct mapped"
For each item of data at the lower level,
there is exactly one location in the cache where it might be.
e.g., lots of items at the lower level share locations in the upper level
2004 Morgan Kaufmann Publishers
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Direct Mapped Cache
Mapping: address is modulo the number of blocks in the cache
Cache
000
001
010
011
100
101
110
111
•
00001
00101
01001
01101
10001
10101
11001
11101
Memory
2004 Morgan Kaufmann Publishers
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Direct Mapped Cache
•
For MIPS:
Address (showing bit positions)
31 30
Hit
13 12 11
20
2 10
Byte
offset
10
Tag
Data
Index
Index
0
1
2
Valid Tag
Data
1021
1022
1023
20
32
=
What kind of locality are we taking advantage of?
2004 Morgan Kaufmann Publishers
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Direct Mapped Cache
•
Taking advantage of spatial locality:
Address (showing bit positions)
31
14 13
18
Hit
65
8
210
4
Tag
Byte
offset
Data
Block offset
Index
18 bits
V
512 bits
Tag
Data
256
entries
16
32
32
32
=
Mux
32
2004 Morgan Kaufmann Publishers
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Hits vs. Misses
•
Read hits
– this is what we want!
•
Read misses
– stall the CPU, fetch block from memory, deliver to cache, restart
•
Write hits:
– can replace data in cache and memory (write-through)
– write the data only into the cache (write-back the cache later)
•
Write misses:
– read the entire block into the cache, then write the word
2004 Morgan Kaufmann Publishers
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Hardware Issues
•
Make reading multiple words easier by using banks of memory
CPU
CPU
CPU
Multiplexor
Cache
Cache
Cache
Bus
Bus
Memory
b. Wide memory organization
Bus
Memory
Memory
Memory
Memory
bank 0
bank 1
bank 2
bank 3
c. Interleaved memory organization
Memory
a. One-word-wide
memory organization
•
It can get a lot more complicated...
2004 Morgan Kaufmann Publishers
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Performance
•
Increasing the block size tends to decrease miss rate:
40%
35%
Miss rate
30%
25%
20%
15%
10%
5%
0%
4
16
64
Block size (bytes)
256
1 KB
8 KB
16 KB
64 KB
256 KB
•
Use split caches because there is more spatial locality in code:
Program
gcc
spice
Block size in
words
1
4
1
4
Instruction
miss rate
6.1%
2.0%
1.2%
0.3%
Data miss
rate
2.1%
1.7%
1.3%
0.6%
Effective combined
miss rate
5.4%
1.9%
1.2%
0.4%
2004 Morgan Kaufmann Publishers
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Performance
•
Simplified model:
execution time = (execution cycles + stall cycles)  cycle time
stall cycles = # of instructions  miss ratio  miss penalty
•
Two ways of improving performance:
– decreasing the miss ratio
– decreasing the miss penalty
What happens if we increase block size?
2004 Morgan Kaufmann Publishers
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Decreasing miss ratio with associativity
One-way set associative
(direct mapped)
Block
Tag Data
0
Two-way set associative
1
2
3
4
5
6
Set
Tag Data Tag Data
0
1
2
3
7
Four-way set associative
Set
Tag Data Tag Data Tag Data Tag Data
0
1
Eight-way set associative (fully associative)
Tag Data Tag Data Tag Data Tag Data Tag Data Tag Data Tag Data Tag Data
Compared to direct mapped, give a series of references that:
– results in a lower miss ratio using a 2-way set associative cache
– results in a higher miss ratio using a 2-way set associative cache
assuming we use the “least recently used” replacement strategy
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An implementation
Address
31 30
12 11 10 9 8
8
22
Index
0
1
2
V
Tag
Data
V
3210
Tag
Data
V
Tag
Data
V
Tag
Data
253
254
255
22
32
4-to-1 multiplexor
Hit
Data
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Performance
15%
1 KB
12%
2 KB
9%
4 KB
6%
8 KB
16 KB
32 KB
3%
64 KB
128 KB
0
One-way
Two-way
Four-way
Eight-way
Associativity
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Decreasing miss penalty with multilevel caches
•
Add a second level cache:
– often primary cache is on the same chip as the processor
– use SRAMs to add another cache above primary memory (DRAM)
– miss penalty goes down if data is in 2nd level cache
•
Example:
– CPI of 1.0 on a 5 Ghz machine with a 5% miss rate, 100ns DRAM access
– Adding 2nd level cache with 5ns access time decreases miss rate to .5%
•
Using multilevel caches:
– try and optimize the hit time on the 1st level cache
– try and optimize the miss rate on the 2nd level cache
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Cache Complexities
•
Not always easy to understand implications of caches:
1200
2000
Radix sort
1000
Radix sort
1600
800
1200
600
800
400
200
Quicksort
400
0
Quicksort
0
4
8
16
32
64
128
256
512 1024 2048 4096
Size (K items to sort)
Theoretical behavior of
Radix sort vs. Quicksort
4
8
16
32
64
128
256
512 1024 2048 4096
Size (K items to sort)
Observed behavior of
Radix sort vs. Quicksort
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Cache Complexities
•
Here is why:
5
Radix sort
4
3
2
1
Quicksort
0
4
8
16
32
64
128
256
512 1024 2048 4096
Size (K items to sort)
•
Memory system performance is often critical factor
– multilevel caches, pipelined processors, make it harder to predict outcomes
– Compiler optimizations to increase locality sometimes hurt ILP
•
Difficult to predict best algorithm: need experimental data
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Virtual Memory
•
Main memory can act as a cache for the secondary storage (disk)
Virtual addresses
Physical addresses
Address translation
Disk addresses
•
Advantages:
– illusion of having more physical memory
– program relocation
– protection
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Pages: virtual memory blocks
•
Page faults: the data is not in memory, retrieve it from disk
– huge miss penalty, thus pages should be fairly large (e.g., 4KB)
– reducing page faults is important (LRU is worth the price)
– can handle the faults in software instead of hardware
– using write-through is too expensive so we use writeback
Virtual address
31 30 29 28 27
15 14 13 12 11 10 9 8
3210
Page offset
Virtual page number
Translation
29 28 27
15 14 13 12 11 10 9 8
Physical page number
3210
Page offset
Physical address
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Page Tables
Virtual page
number
Page table
Physical page or
Valid disk address
1
1
1
1
0
1
1
0
1
1
0
1
Physical memory
Disk storage
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Page Tables
Page table register
Virtual address
31 30 29 28 27
1 5 1 4 1 3 1 2 11 1 0 9 8
Virtual page number
Page offset
12
20
Valid
3 2 1 0
Physical page number
Page table
18
If 0 then page is not
present in memory
29 28 27
1 5 1 4 1 3 1 2 11 1 0 9 8
Physical page number
3 2 1 0
Page offset
Physical address
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Making Address Translation Fast
•
A cache for address translations: translation lookaside buffer
TLB
Virtual page
number Valid Dirty Ref
1
1
1
1
0
1
0
1
1
0
0
0
Tag
Physical page
address
1
1
1
1
0
1
Physical memory
Page table
Physical page
Valid Dirty Ref or disk address
1
1
1
1
0
1
1
0
1
1
0
1
Typical values:
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
Disk storage
16-512 entries,
miss-rate: .01% - 1%
miss-penalty: 10 – 100 cycles
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TLBs and caches
Virtual address
TLB access
TLB miss
exception
No
Yes
TLB hit?
Physical address
No
Try to read data
from cache
Cache miss stall
while read block
No
Cache hit?
Yes
Write?
No
Yes
Write access
bit on?
Write protection
exception
Yes
Try to write data
to cache
Deliver data
to the CPU
Cache miss stall
while read block
No
Cache hit?
Yes
Write data into cache,
update the dirty bit, and
put the data and the
address into the write buffer
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TLBs and Caches
Virtual address
31 30 29
14 13 12 11 10 9
Virtual page number
3 2 1 0
Page offset
12
20
Valid Dirty
Tag
Physical page number
=
=
=
=
=
=
TLB
TLB hit
20
Page offset
Physical page number
Physical address
Block
Cache index
Physical address tag
offset
18
8
4
Byte
offset
2
8
12
Valid
Data
Tag
Cache
=
Cache hit
32
Data
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Modern Systems
•
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Modern Systems
•
Things are getting complicated!
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Some Issues
•
Processor speeds continue to increase very fast
— much faster than either DRAM or disk access times
100,000
10,000
1,000
Performance
CPU
100
10
Memory
1
Year
•
Design challenge: dealing with this growing disparity
– Prefetching? 3rd level caches and more? Memory design?
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Chapters 8 & 9
(partial coverage)
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Interfacing Processors and Peripherals
•
•
•
I/O Design affected by many factors (expandability, resilience)
Performance:
— access latency
— throughput
— connection between devices and the system
— the memory hierarchy
— the operating system
A variety of different users (e.g., banks, supercomputers, engineers)
Interrupts
Processor
Cache
Memory- I/O bus
Main
memory
I/O
controller
Disk
Disk
I/O
controller
I/O
controller
Graphics
output
Network
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I/O
•
Important but neglected
“The difficulties in assessing and designing I/O systems have
often relegated I/O to second class status”
“courses in every aspect of computing, from programming to
computer architecture often ignore I/O or give it scanty coverage”
“textbooks leave the subject to near the end, making it easier
for students and instructors to skip it!”
•
GUILTY!
— we won’t be looking at I/O in much detail
— be sure and read Chapter 8 in its entirety.
— you should probably take a networking class!
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I/O Devices
•
Very diverse devices
— behavior (i.e., input vs. output)
— partner (who is at the other end?)
— data rate
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I/O Example: Disk Drives
Platters
Tracks
Platter
Sectors
Track
•
To access data:
— seek: position head over the proper track (3 to 14 ms. avg.)
— rotational latency: wait for desired sector (.5 / RPM)
— transfer: grab the data (one or more sectors) 30 to 80 MB/sec
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I/O Example: Buses
•
•
•
•
Shared communication link (one or more wires)
Difficult design:
— may be bottleneck
— length of the bus
— number of devices
— tradeoffs (buffers for higher bandwidth increases latency)
— support for many different devices
— cost
Types of buses:
— processor-memory (short high speed, custom design)
— backplane (high speed, often standardized, e.g., PCI)
— I/O (lengthy, different devices, e.g., USB, Firewire)
Synchronous vs. Asynchronous
— use a clock and a synchronous protocol, fast and small
but every device must operate at same rate and
clock skew requires the bus to be short
— don’t use a clock and instead use handshaking
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I/O Bus Standards
•
Today we have two dominant bus standards:
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Other important issues
•
Bus Arbitration:
— daisy chain arbitration (not very fair)
— centralized arbitration (requires an arbiter), e.g., PCI
— collision detection, e.g., Ethernet
•
Operating system:
— polling
— interrupts
— direct memory access (DMA)
•
Performance Analysis techniques:
— queuing theory
— simulation
— analysis, i.e., find the weakest link (see “I/O System
Design”)
•
Many new developments
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Pentium 4
•
I/O Options
Pentium 4
processor
DDR 400
(3.2 GB/sec)
Main
memory
DIMMs
DDR 400
(3.2 GB/sec)
System bus (800 MHz, 604 GB/sec)
AGP 8X
Memory
(2.1 GB/sec)
Graphics
controller
output
hub
CSA
(north bridge)
(0.266 GB/sec)
1 Gbit Ethernet
82875P
Serial ATA
(150 MB/sec)
(266 MB/sec) Parallel ATA
(100 MB/sec)
Serial ATA
(150 MB/sec)
Parallel ATA
(100 MB/sec)
Disk
Disk
Stereo
(surroundsound)
AC/97
(1 MB/sec)
USB 2.0
(60 MB/sec)
...
I/O
controller
hub
(south bridge)
82801EB
CD/DVD
Tape
(20 MB/sec)
10/100 Mbit Ethernet
PCI bus
(132 MB/sec)
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Fallacies and Pitfalls
•
Fallacy: the rated mean time to failure of disks is 1,200,000 hours,
so disks practically never fail.
•
Fallacy: magnetic disk storage is on its last legs, will be replaced.
•
Fallacy: A 100 MB/sec bus can transfer 100 MB/sec.
•
Pitfall: Moving functions from the CPU to the I/O processor,
expecting to improve performance without analysis.
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Multiprocessors
•
Idea: create powerful computers by connecting many smaller ones
good news: works for timesharing (better than supercomputer)
bad news: its really hard to write good concurrent programs
many commercial failures
Processor
Processor
Processor
Cache
Cache
Cache
Processor
Processor
Processor
Cache
Cache
Cache
Memory
Memory
Memory
Single bus
Memory
I/O
Network
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Questions
•
How do parallel processors share data?
— single address space (SMP vs. NUMA)
— message passing
•
How do parallel processors coordinate?
— synchronization (locks, semaphores)
— built into send / receive primitives
— operating system protocols
•
How are they implemented?
— connected by a single bus
— connected by a network
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Supercomputers
Plot of top 500 supercomputer sites over a decade:
Single Instruction multiple data (SIMD)
500
Cluster
(network of
workstations)
400
Cluster
(network of
SMPs)
300
Massively
parallel
processors
(MPPs)
200
100
Sharedmemory
multiprocessors
(SMPs)
0
93 93 94 94 95 95 96 96 97 97 98 98 99 99 00
Uniprocessors
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Using multiple processors an old idea
•
Some SIMD designs:
•
Costs for the the Illiac IV escalated from $8 million in 1966 to $32 million in
1972 despite completion of only ¼ of the machine. It took three more years
before it was operational!
“For better or worse, computer architects are not easily discouraged”
Lots of interesting designs and ideas, lots of failures, few successes
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Topologies
P0
P1
P2
P3
P0
a. 2-D grid or mesh of 16 nodes
P4
P1
P5
P2
P6
P3
P7
P4
P5
P6
P7
b. Omega network
a. Crossbar
b. n-cube tree of 8 nodes (8 = 23 so n = 3)
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Clusters
•
•
•
•
•
•
Constructed from whole computers
Independent, scalable networks
Strengths:
– Many applications amenable to loosely coupled machines
– Exploit local area networks
– Cost effective / Easy to expand
Weaknesses:
– Administration costs not necessarily lower
– Connected using I/O bus
Highly available due to separation of memories
In theory, we should be able to do better
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Google
•
•
•
•
•
Serve an average of 1000 queries per second
Google uses 6,000 processors and 12,000 disks
Two sites in silicon valley, two in Virginia
Each site connected to internet using OC48 (2488 Mbit/sec)
Reliability:
– On an average day, 20 machines need rebooted (software error)
– 2% of the machines replaced each year
In some sense, simple ideas well executed. Better (and cheaper)
than other approaches involving increased complexity
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Concluding Remarks
•
Evolution vs. Revolution
“More often the expense of innovation comes from being too disruptive
to computer users”
“Acceptance of hardware ideas requires acceptance by software
people; therefore hardware people should learn about software. And if
software people want good machines, they must learn more about hardware
to be able to communicate with and thereby influence hardware engineers.”
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