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CS152
Computer Architecture and Engineering
Lecture 3
Performance, Technology & Delay Modeling
©UCB Fall 2001
CS152
Lec3.1
Review: Salient features of MIPS I
• 32-bit fixed format inst (3 formats)
• 32 32-bit GPR (R0 contains zero) and 32 FP registers (+ HI LO)
– partitioned by software convention
• 3-address, reg-reg arithmetic instr.
• Single address mode for load/store: base+displacement
– no indirection, scaled
• 16-bit immediate plus LUI
• Simple branch conditions
– compare against zero or two registers for =,
– no integer condition codes
• Support for 8bit, 16bit, and 32bit integers
• Support for 32bit and 64bit floating point.
Lec3.2
Review: MIPS Addressing Modes/Instruction Formats
• All instructions 32 bits wide
Register (direct)
op
rs
rt
rd
register
Immediate
Base+index
op
rs
rt
immed
op
rs
rt
immed
register
PC-relative
op
rs
PC
rt
Memory
+
immed
Memory
+
Lec3.3
Review: When does MIPS sign extend?
• When value is sign extended, copy upper bit to full value:
Examples of sign extending 8 bits to 16 bits:
00001010  00000000 00001010
10001100  11111111 10001100
• When is an immediate value sign extended?
– Arithmetic instructions (add, sub, etc.) sign extend immediates
even for the unsigned versions of the instructions!
– Logical instructions do not sign extend
addi $r2, $r3, -1
has 0xFFFF in immediate field
and will extend to 0xFFFFFFFF before adding
andi $r2, $r3, -1
has 0xFFFF in immediate field
and will extend to 0x0000FFFF before anding
– Kinda weird to put negative numbers in logical instructions
Lec3.4
Review: Details of the MIPS instruction set
• Register zero always has the value zero (even if you try to write it)
• Branch/jump and link put the return addr.
PC+4 into the link register (R31), also called “ra”
• All instructions change all 32 bits of the destination register
(including lui, lb, lh) and all read all 32 bits of sources (add, and, …)
• The difference between signed and unsigned versions:
– For add and subtract: signed causes exception on overflow
» No difference in sign-extension behavior!
– For multiply and divide, distinguishes type of operation
• Thus, overflow can occur in these arithmetic and logical instructions:
– add, sub, addi
– it cannot occur in addu, subu, addiu, and, or, xor, nor, shifts, mult, multu,
div, divu
• Immediate arithmetic and logical instructions are extended as follows:
– logical immediates ops are zero extended to 32 bits
– arithmetic immediates ops are sign extended to 32 bits (including addu)
• The data loaded by the instructions lb and lh are extended as follows:
– lbu, lhu are zero extended
– lb, lh are sign extended
Lec3.5
Performance
• Purchasing perspective
– given a collection of machines, which has the
» best performance ?
» least cost ?
» best performance / cost ?
• Design perspective
– faced with design options, which has the
» best performance improvement ?
» least cost ?
» best performance / cost ?
• Both require
– basis for comparison
– metric for evaluation
• Our goal is to understand cost & performance implications of
architectural choices
Lec3.6
Two notions of “performance”
Plane
DC to Paris
Speed
Passengers
Throughput
(pmph)
Boeing 747
6.5 hours
610 mph
470
286,700
BAD/Sud
Concorde
3 hours
1350 mph
132
178,200
Which has higher performance?
° Time to do the task (Execution Time)
– execution time, response time, latency
° Tasks per day, hour, week, sec, ns. .. (Performance)
– throughput, bandwidth
Response time and throughput often are in opposition
Lec3.7
Definitions
• Performance is in units of things-per-second
– bigger is better
• If we are primarily concerned with response time
– performance(x) =
1
execution_time(x)
" X is n times faster than Y" means
Performance(X)
n
=
---------------------Performance(Y)
Lec3.8
Example
• Time of Concorde vs. Boeing 747?
• Concord is 1350 mph / 610 mph = 2.2 times faster
= 6.5 hours / 3 hours
• Throughput of Concorde vs. Boeing 747 ?
• Concord is 178,200 pmph / 286,700 pmph = 0.62 “times faster”
• Boeing is 286,700 pmph / 178,200 pmph = 1.60 “times faster”
• Boeing is 1.6 times (“60%”) faster in terms of throughput
• Concord is 2.2 times (“120%”) faster in terms of flying time
We will focus primarily on execution time for a single job
Lots of instructions in a program => Instruction throughput important!
Lec3.9
Basis of Evaluation
Cons
Pros
• representative
Actual Target Workload
• portable
• widely used
• improvements
useful in reality
• easy to run, early in
design cycle
• identify peak
capability and
potential bottlenecks
• very specific
• non-portable
• difficult to run, or
measure
• hard to identify cause
•less representative
Full Application Benchmarks
Small “Kernel”
Benchmarks
Microbenchmarks
• easy to “fool”
• “peak” may be a long
way from application
performance
Lec3.10
SPEC95
• Eighteen application benchmarks (with inputs) reflecting a
technical computing workload
• Eight integer
– go, m88ksim, gcc, compress, li, ijpeg, perl, vortex
• Ten floating-point intensive
– tomcatv, swim, su2cor, hydro2d, mgrid, applu, turb3d,
apsi, fppp, wave5
• Must run with standard compiler flags
– eliminate special undocumented incantations that may
not even generate working code for real programs
Lec3.11
Metrics of performance
Seconds per program
Application
Useful Operations per second
Programming
Language
Compiler
ISA
(millions) of Instructions per second – MIPS
(millions) of (F.P.) operations per second – MFLOP/s
Datapath
Control
Megabytes per second
Function Units
Transistors Wires Pins
Cycles per second (clock rate)
Each metric has a place and a purpose, and each can be misused
Lec3.12
CPI
“Average cycles per instruction”
CPIave = (CPU Time * Clock Rate) / Instruction Count
= Clock Cycles / Instruction Count
n
CPU time = ClockCycleTime *
CPI i * I i
i =1
n
CPI =
 CPI i *
i =1
F
i
where F
i
=
I
i
Instruction Count
"instruction frequency"
Invest Resources where time is Spent!
Lec3.13
Aspects of CPU Performance
CPU time
= Seconds
Program
= Instructions x Cycles
Program
instr count
CPI
Instruction
x Seconds
Cycle
clock rate
Program
Compiler
Instr. Set
Organization
Technology
Lec3.14
Amdahl's Law
Speedup due to enhancement E:
ExTime w/o E
Speedup(E) = -------------------- =
ExTime w/ E
Performance w/ E
--------------------Performance w/o E
Suppose that enhancement E accelerates a fraction F of the
task
by a factor S and the remainder of the task is unaffected
then,
ExTime(with E) = ((1-F) + F/S) X ExTime(without E)
Speedup(with E) =
1
(1-F) + F/S
Lec3.15
Example (RISC processor)
Base Machine (Reg / Reg)
Op
Freq Cycles CPI(i)
ALU
50%
1
.5
Load
20%
5
1.0
Store
10%
3
.3
Branch
20%
2
.4
2.2
% Time
23%
45%
14%
18%
Typical Mix
How much faster would the machine be if a better data cache
reduced the average load time to 2 cycles?
How does this compare with using branch prediction to shave a
cycle off the branch time?
What if two ALU instructions could be executed at once?
Lec3.16
Summary: Evaluating Instruction Sets and Implementation
Design-time metrics:
° Can it be implemented, in how long, at what cost?
° Can it be programmed? Ease of compilation?
Static Metrics:
° How many bytes does the program occupy in memory?
Dynamic Metrics:
° How many instructions are executed?
° How many bytes does the processor fetch to execute the
program?
CPI
° How many clocks are required per instruction?
° How "lean" a clock is practical?
Best Metric: Time to execute the program!
Inst. Count
Cycle Time
NOTE: this depends on instructions set, processor organization, and
compilation techniques.
Lec3.17
Administrative Matters
Lec3.18
Finite State Machines:
• System state is explicit in representation
• Transitions between states represented as arrows with inputs on arcs.
• Output may be either part of state or on arcs
1
“Mod 3 Machine”
Input (MSB first)
Mod 3
106
1
Alpha/
0
0
1
Beta/
1
0
1 1 0101 0
Delta/
100122 1
1
0
2
Lec3.19
Implementation as Combinational logic + Latch
1/0
“Moore Machine”
“Mealey Machine”
Latch
Combinational
Logic
Alpha/
0
0/0
1/1
Beta/
0/1
Delta/
1/1
00
01
10
00
01
10
0/0
2
Input State old State new
0
0
0
1
1
1
1
00
10
01
01
00
10
Div
0
0
1
0
1
1
Lec3.20
Performance and Technology Trends
1000
Supercomputers
Performance
100
Mainframes
10
Minicomputers
Microprocessors
1
0.1
1965
1970
1975
1980
1985
1990
1995
2000
Year
• Technology Power: 1.2 x 1.2 x 1.2 = 1.7 x / year
– Feature Size: shrinks 10% / yr. => Switching speed improves 1.2 / yr.
– Density: improves 1.2x / yr.
– Die Area: 1.2x / yr.
• The lesson of RISC is to keep the ISA as simple as possible:
– Shorter design cycle => fully exploit the advancing technology (~3yr)
– Advanced branch prediction and pipeline techniques
– Bigger and more sophisticated on-chip caches
Lec3.21
Range of Design Styles
Custom Control Logic
Custom Design
Standard Cell
Gates
Custom
ALU
Gates
Routing Channel
Standard
ALU
Custom
Register File
Gate Array/FPGA/CPLD
Standard Registers
Gates
Routing Channel
Gates
Performance
Design Complexity (Design Time)
Compact
Longer wires
Lec3.22
Basic Technology: CMOS
• CMOS: Complementary Metal Oxide Semiconductor
– NMOS (N-Type Metal Oxide Semiconductor) transistors
– PMOS (P-Type Metal Oxide Semiconductor) transistors
• NMOS Transistor
– Apply a HIGH (Vdd) to its gate
turns the transistor into a “conductor”
– Apply a LOW (GND) to its gate
shuts off the conduction path
• PMOS Transistor
– Apply a HIGH (Vdd) to its gate
shuts off the conduction path
– Apply a LOW (GND) to its gate
turns the transistor into a “conductor”
Vdd = 5V
GND = 0v
Vdd = 5V
GND = 0v
Lec3.23
Basic Components: CMOS Inverter
Vdd
Symbol
In
Circuit
PMOS
In
Out
Out
NMOS
• Inverter Operation
Vdd
Vout
Vdd
Vdd
Vdd
Open
Charge
Out
Open
Vdd
Vin
Discharge
Lec3.24
Basic Components: CMOS Logic Gates
NOR Gate
NAND Gate
A
A
Out
B Out
0
0
1
1
B
0
1
0
1
1
1
1
0
A
A
Out
B
Vdd
0
0
1
1
B Out
0
1
0
1
1
0
0
0
Vdd
A
Out
B
B
Out
A
Lec3.25
Voltage waveforms versus time
Voltage
1 => Vdd
Vout
Vin
Vout
Vin
0 => GND
Time
Lec3.26
Series Connection
Vin
V1
G1
Vdd
Vout
Vin
G2
G1
Vdd
V1
G2
C1
Vout
Cout
Voltage
Vdd
V1
Vout
Vin
Vdd/2
d1
d2
GND
Time
• Total Propagation Delay = Sum of individual delays = d1 + d2
• Capacitance C1 has two components:
– Capacitance of the wire connecting the two gates
– Input capacitance of the second inverter
Lec3.27
Gate Comparison
Vdd
Vdd
A
Out
B
B
Out
A
NAND Gate
NOR Gate
• PMOS are 3 times slower than NMOS (3 times higher resistance) so if all
devices are the same size then a NAND Low to High will be
• Better to put NMOS transistors in series
Lec3.28
Calculating Delays
Vin
V1
Vdd
V2
Vin
G1
V3
Vdd
V1
G2
V2
C1
Vdd
• Sum delays along serial paths
G3
V3
• Delay (Vin -> V2) ! = Delay (Vin -> V3)
– Delay (Vin -> V2) = Delay (Vin -> V1) + Delay (V1 -> V2)
– Delay (Vin -> V3) = Delay (Vin -> V1) + Delay (V1 -> V2) + Delay (V1 > V3)
• Critical Path = The longest delay path (Vin->V3)
• C1 = Wire Capacitance + Cin of Gate 2 + Cin of Gate 3
Lec3.29
General C/L Cell Delay Model
Vout
A
B
.
.
.
Combinational
Logic Cell
Delay
Va -> Vout
Cout
X
X
X
Internal Delay
X
delay per load (Cload)
X
Nanoseconds/femtoFarad
= ns/fF
Ccritical
Cout
• Combinational Cell (symbol) is fully specified by:
– functional (input -> output) behavior
» truth-table, logic equation, VHDL
– load at each input
– critical propagation delay from each input to each output for each
transition
» THL(A, o) = Fixed Internal Delay + Load-dependent-delay x load
capacitance
– Linear model is good enough up to Ccritical
Lec3.30
Characterize a Gate
• Input capacitance for each input
• For each input-to-output path:
– For each output transition (H->L, L->H)
» Internal delay (ns) - e.g. for low to high from A to O: TPAOlh
» Load dependent delay (ns / fF) - e.g. TPAOlhf
• Example: 2-input NAND Gate
A
Delay A -> O
O: Low -> High
O
B
Slope =
0.0021ns / fF
For A and B: Input Load = 61 fF
0.5ns
For A -> O :
TPAOlh = 0.5ns TPAOlhf = 0.0021ns / fF
TPAOhl = 0.1ns TPAOhlf = 0.0020ns / fF
CO
Lec3.31
A Specific Example: 2 to 1 MUX
A
Gate 3
B
Gate 2
B
Y = (A and !S)
or (A and S)
Wire 2
2 x 1 Mux
Gate 1
Wire 0
A
Wire 1
S
S
Inv: I.L. = 50 fF; T I.D.= .01 ns; T L.D.D. = .01 ns/fF
• Input Load (I.L.)
– A, B: I.L. (NAND) = 61 fF
– S: I.L. (INV) + I.L. (NAND) = 50 fF + 61 fF = 111 fF
• Load Dependent Delay (L.D.D.): Set by Gate 3
– TAYlhf = 0.021 ns / fF
TAYhlf = 0.020 ns / fF
– TBYlhf = 0.021 ns / fF
– TSYlhf = 0.021 ns / fF
TBYhlf = 0.020 ns / fF
TSYlhf = 0.020 ns / fF
Lec3.32
Y
2 to 1 MUX: Internal Delay Calculation
A
Gate 1
Wire 0
Wire 1
Y = (A and !S) or (A and S)
Gate 3
B
Gate 2
S
Wire 2
L.D.D. = Load Dependent Delay
I.D. = Internal Delay
• Internal Delay (I.D.):
– A to Y: I.D. G1 + (Wire_1_C + G3_Input_C) * L.D.D G1 + I.D. G3
– B to Y: I.D. G2 + (Wire_2_C + G3_Input_C) * L.D.D. G2 + I.D. G3
– S to Y (Worst Case) : I.D. Inv + (Wire_0_C + G1_Input_C) * L.D.D. Inv
+ Internal Delay A to Y
• We can approximate the size of “Wire_1_C” by:
– Assume Wire 1 has the same C as the input capacitance off all the
gates attached to it (G3 in this case).
Therefore the total C that Gate1 needs to drive = 2.0 x G3_Input_C
Lec3.33
2 to 1 MUX: Internal Delay Calculation (continue)
A
Gate 1
Wire 0
Wire 1
Y = (A and !S) or (A and S)
Gate 3
B
Gate 2
Wire 2
S
• Internal Delay (I.D.):
– A to Y: I.D. G1 + (Wire 1 C + G3 Input C) * L.D.D G1 + I.D. G3
– B to Y: I.D. G2 + (Wire 2 C + G3 Input C) * L.D.D. G2 + I.D. G3
– S to Y (Worst Case): I.D. Inv + (Wire 0 C + G1 Input C) * L.D.D. Inv +
Internal Delay A to Y
• Specific Example:
– TAYlh = TPhl G1 + (2.0 * 61 fF) * TPhlf G1 + TPlh G3
= 0.1ns + 122 fF * 0.0020 ns/fF + 0.5ns = 0.844 ns
Lec3.34
Abstraction: 2 to 1 MUX
A
Gate 3
B
Y
B
2 x 1 Mux
A
Gate 1
Y
Gate 2
S
S
• Input Load: A = 61 fF, B = 61 fF, S = 111 fF
• Load Dependent Delay:
– TAYlhf = 0.021 ns / fF
– TBYlhf = 0.021 ns / fF
– TSYlhf = 0.021 ns / fF
TAYhlf = 0.020 ns / fF
TBYhlf = 0.020 ns / fF
TSYlhf = 0.020 ns / f F
• Internal Delay:
– TAYlh = TPhl G1 + (2.0 * 61 fF) * TPhlf G1 + TPlh G3
= 0.1ns + 122 fF * 0.0020ns/fF + 0.5ns = 0.844ns
– Fun Exercises!: TAYhl, TBYlh, TSYlh, TSYlh
Lec3.35
Storage Element’s Timing Model
Clk
D
Q
Setup
D
Don’t Care
Hold
Don’t Care
Clock-to-Q
Q
Unknown
• Setup Time: Input must be stable BEFORE the trigger clock edge
• Hold Time: Input must REMAIN stable after the trigger clock edge
• Clock-to-Q time:
– Output cannot change instantaneously at the trigger clock edge
– Similar to delay in logic gates, two components:
» Internal Clock-to-Q
» Load dependent Clock-to-Q
Lec3.36
CS152 Building blocks (maybe more….)
• Logic elements
– NAND2, NAND3, NAND 4
– NOR2, NOR3, NOR4
– INV1x (normal inverter)
– INV4x (inverter with large output drive)
– XOR2
– XNOR2
– PWR: Source of 1’s
– GND: Source of 0’s
– fast MUXes
• Storage Element
– D flip flop - negative edge triggered
Lec3.37
Clocking Methodology
Clk
.
.
.
.
.
.
Combination Logic
.
.
.
.
.
.
• All storage elements are clocked by the same clock edge (but there may
be clock skews)
• The combination logic block’s:
– Inputs are updated at each clock tick
– All outputs MUST be stable before the next clock tick
Lec3.38
Hold Time Violations
Clk-to-Q+Delay
Clk1
Hold Time
Clk2
.
.
.
.
.
.
Combination Logic
Clk1
.
.
.
.
.
.
Clk2
• The worst case scenario for hold time consideration:
– The input register sees CLK1
– The output register sees CLK2
– fast FF1 output must not change input to FF2 for same clock edge
• (CLK-to-Q + Shortest Delay Path - Clock Skew) > Hold Time
Lec3.39
Clock Skew’s Effect on Hold Time Violation
Clk-to-Q+Delay
Clk1
Hold Time
Clk2
Clock Skew
.
.
.
.
.
.
Combination Logic
Clk1
.
.
.
.
.
.
Clk2
• The worst case scenario for hold time consideration:
– The input register sees CLK1
– The output register sees CLK2
– fast FF1 output must not change input to FF2 for same clock edge
• (CLK-to-Q + Shortest Delay Path) > Hold Time + Clock Skew or (CLK-to-Q +
Shortest Delay Path - Clock Skew) > Hold Time
Lec3.40
Critical Path & Cycle Time
Clk
.
.
.
.
.
.
.
.
.
.
.
.
• Critical path: the slowest path between any two storage devices
• Cycle time is a function of the critical path
• must be greater than:
– Clock-to-Q + Longest Path through the Combination Logic + Setup
Lec3.41
Clock Skew’s Effect on Cycle Time
Clk1
Clock Skew
Clk2
Clock Skw
Setup
FF1
FF2
.
.
.
.
.
.
Clk1
.
.
.
.
.
.
Clk2
• The worst case scenario for cycle time consideration:
– The input register sees CLK1
– The output register sees CLK2
• Cycle Time = CLK-to-Q(FF1) + Longest Delay(C/L) + Setup(FF2) +
Clock Skew
Lec3.42
Tricks to Reduce Cycle Time
• Reduce the number of gate levels
A
A
B
B
C
C
D
D
° Pay attention to loading
° One gate driving many gates is a bad idea
° Avoid using a small gate to drive a long wire
° Use multiple stages to drive large load
INV4x
Clarge
INV4x
Lec3.43
How to Avoid Hold Time Violations?
Clk
.
.
.
.
.
.
Combination Logic
.
.
.
.
.
.
• Hold time requirement:
– Input to register must NOT change immediately after the clock tick
• This is usually easy to meet in the “edge trigger” clocking scheme
•
Hold time of most FFs is <= 0 ns
• CLK-to-Q + Shortest Delay Path must be greater than Hold Time
Lec3.44
Hold Time Violation
Clk1
Clk-to-Q+Delay
Clk2
Hold Time
.
.
.
.
.
.
Combination Logic
Clk1
.
.
.
.
.
.
Clk2
• The worst case scenario for hold time consideration:
– The input register sees CLK1
– The output register sees CLK2
– fast FF1 output must not change input to FF2 for same clock edge
• For no violation (CLK-to-Q + Shortest Delay Path) > Hold Time
• A violation is shown above
Lec3.45
A hold time violation because of clock skew
Clk-to-Q+Delay
Clk1
Hold Time
Clk2
Clock Skew
.
.
.
.
.
.
Clk1
Combination Logic
.
.
.
.
.
.
Clk2
• For no violation
(CLK-to-Q + Shortest Delay Path) > Hold Time + Clock Skew
or (CLK-to-Q + Shortest Delay Path - Clock Skew) > Hold Time
Lec3.46
Summary
• Total execution time is the most reliable measure of performance
• Amdall’s law: Law of Diminishing Returns
• Performance and Technology Trends
– Keep the design simple (KISS rule) to take advantage of the latest
technology
– CMOS inverter and CMOS logic gates
• Delay Modeling and Gate Characterization
– Delay = Internal Delay + (Load Dependent Delay x Output Load)
• Clocking Methodology and Timing Considerations
– Simplest clocking methodology
» All storage elements use the SAME clock edge
– Cycle Time  CLK-to-Q + Longest Delay Path + Setup + Clock Skew
– (CLK-to-Q + Shortest Delay Path - Clock Skew) > Hold Time
Lec3.47
To Get More Information
• EECS 141 - Digital Integrated Circuit Design - 105 no
longer a prerequisite - only EECS 40 required!
• Book: Digital Integrated Circuits - A design
perspective - by Jan Rabaey
• Web page (slides from book)
– http://bwrc.eecs.berkeley.edu/icdesign/instructors.html
Lec3.48